Daily Papers

Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation" algorithm capable of harnessing this exponential advantage, that can apply polynomial transformations to the singular values of a block of a unitary, generalizing the optimal Hamiltonian simulation results of Low and Chuang. The proposed quantum circuits have a very simple structure, often give rise to optimal algorithms and have appealing constant factors, while usually only use a constant number of ancilla qubits. We show that singular value transformation leads to novel algorithms. We give an efficient solution to a certain "non-commutative" measurement problem and propose a new method for singular value estimation. We also show how to exponentially improve the complexity of implementing fractional queries to unitaries with a gapped spectrum. Finally, as a quantum machine learning application we show how to efficiently implement principal component regression. "Singular value transformation" is conceptually simple and efficient, and leads to a unified framework of quantum algorithms incorporating a variety of quantum speed-ups. We illustrate this by showing how it generalizes a number of prominent quantum algorithms, including: optimal Hamiltonian simulation, implementing the Moore-Penrose pseudoinverse with exponential precision, fixed-point amplitude amplification, robust oblivious amplitude amplification, fast QMA amplification, fast quantum OR lemma, certain quantum walk results and several quantum machine learning algorithms. In order to exploit the strengths of the presented method it is useful to know its limitations too, therefore we also prove a lower bound on the efficiency of singular value transformation, which often gives optimal bounds.

Large language models often struggle with length generalization and solving complex problem instances beyond their training distribution. We present a self-improvement approach where models iteratively generate and learn from their own solutions, progressively tackling harder problems while maintaining a standard transformer architecture. Across diverse tasks including arithmetic, string manipulation, and maze solving, self-improving enables models to solve problems far beyond their initial training distribution-for instance, generalizing from 10-digit to 100-digit addition without apparent saturation. We observe that in some cases filtering for correct self-generated examples leads to exponential improvements in out-of-distribution performance across training rounds. Additionally, starting from pretrained models significantly accelerates this self-improvement process for several tasks. Our results demonstrate how controlled weak-to-strong curricula can systematically teach a model logical extrapolation without any changes to the positional embeddings, or the model architecture.

Does continued scaling of large language models (LLMs) yield diminishing returns? Real-world value often stems from the length of task an agent can complete. We start this work by observing the simple but counterintuitive fact that marginal gains in single-step accuracy can compound into exponential improvements in the length of a task a model can successfully complete. Then, we argue that failures of LLMs when simple tasks are made longer arise from mistakes in execution, rather than an inability to reason. We propose isolating execution capability, by explicitly providing the knowledge and plan needed to solve a long-horizon task. We find that larger models can correctly execute significantly more turns even when small models have 100\% single-turn accuracy. We observe that the per-step accuracy of models degrades as the number of steps increases. This is not just due to long-context limitations -- curiously, we observe a self-conditioning effect -- models become more likely to make mistakes when the context contains their errors from prior turns. Self-conditioning does not reduce by just scaling the model size. In contrast, recent thinking models do not self-condition, and can also execute much longer tasks in a single turn. We conclude by benchmarking frontier thinking models on the length of task they can execute in a single turn. Overall, by focusing on the ability to execute, we hope to reconcile debates on how LLMs can solve complex reasoning problems yet fail at simple tasks when made longer, and highlight the massive benefits of scaling model size and sequential test-time compute for long-horizon tasks.

Graph neural networks (GNNs) have been shown to be highly sensitive to the choice of aggregation function. While summing over a node's neighbours can approximate any permutation-invariant function over discrete inputs, Cohen-Karlik et al. [2020] proved there are set-aggregation problems for which summing cannot generalise to unbounded inputs, proposing recurrent neural networks regularised towards permutation-invariance as a more expressive aggregator. We show that these results carry over to the graph domain: GNNs equipped with recurrent aggregators are competitive with state-of-the-art permutation-invariant aggregators, on both synthetic benchmarks and real-world problems. However, despite the benefits of recurrent aggregators, their O(V) depth makes them both difficult to parallelise and harder to train on large graphs. Inspired by the observation that a well-behaved aggregator for a GNN is a commutative monoid over its latent space, we propose a framework for constructing learnable, commutative, associative binary operators. And with this, we construct an aggregator of O(log V) depth, yielding exponential improvements for both parallelism and dependency length while achieving performance competitive with recurrent aggregators. Based on our empirical observations, our proposed learnable commutative monoid (LCM) aggregator represents a favourable tradeoff between efficient and expressive aggregators.

Pretraining scaling laws reveal that model capability improves predictably with data and compute. But learning from real world environments after deployment remains far less understood. Analyzing roughly 38,000 hours of agent interaction with the environment across 134 real world tasks, we find, to the best of our knowledge, the first evidence that overall performance during environment learning follows a log-sigmoid scaling law with remarkably high precision, reaching R^2 = 0.998. Across model generations, we also find that agent learning speed roughly doubles every three months. This discovery stems from EdgeBench, a suite of 134 real world tasks with ultra-long horizons, spanning scientific discovery, software engineering, combinatorial optimization, professional knowledge work, formal mathematics, and interactive games. Each task sustains at least 12 hours of continuous agent operation under rich, multilevel feedback, and is built through substantial expert effort. We publicly release 51 tasks and our full evaluation framework to accelerate the study of how agents learn from real world experience.

Web-crawled pretraining datasets underlie the impressive "zero-shot" evaluation performance of multimodal models, such as CLIP for classification/retrieval and Stable-Diffusion for image generation. However, it is unclear how meaningful the notion of "zero-shot" generalization is for such multimodal models, as it is not known to what extent their pretraining datasets encompass the downstream concepts targeted for during "zero-shot" evaluation. In this work, we ask: How is the performance of multimodal models on downstream concepts influenced by the frequency of these concepts in their pretraining datasets? We comprehensively investigate this question across 34 models and five standard pretraining datasets (CC-3M, CC-12M, YFCC-15M, LAION-400M, LAION-Aesthetics), generating over 300GB of data artifacts. We consistently find that, far from exhibiting "zero-shot" generalization, multimodal models require exponentially more data to achieve linear improvements in downstream "zero-shot" performance, following a sample inefficient log-linear scaling trend. This trend persists even when controlling for sample-level similarity between pretraining and downstream datasets, and testing on purely synthetic data distributions. Furthermore, upon benchmarking models on long-tailed data sampled based on our analysis, we demonstrate that multimodal models across the board perform poorly. We contribute this long-tail test set as the "Let it Wag!" benchmark to further research in this direction. Taken together, our study reveals an exponential need for training data which implies that the key to "zero-shot" generalization capabilities under large-scale training paradigms remains to be found.

Multi-agent systems (MAS) offer a scalable path forward for agentic AI, comprising multiple LLM-based agents, each assigned a system prompt and a position within a workflow that governs inter-agent coordination and output aggregation. System prompts thus form a critical and accessible optimization surface: they specify agents' roles and behaviors, enabling system-level improvements without model finetuning. Although prompt optimization has shown substantial potential for single LLMs, extending it to MAS poses distinct challenges, notably an exponentially growing search space. It remains unclear whether, when, and by how much prompt optimization improves MAS performance, and how sensitive such gains are to system configuration. In this work, we systematically study system-prompt optimization across a broad range of MAS setups varying in task, workflow, communication protocol, and team size, benchmarking two prompt optimizers that naturally extend state-of-the-art single-agent methods. The results reveal its potential to unlock significant gains while exposing open challenges, characterizing when and how much prompt optimization helps across diverse MAS settings.

Inverse Reinforcement Learning (IRL) is a powerful set of techniques for imitation learning that aims to learn a reward function that rationalizes expert demonstrations. Unfortunately, traditional IRL methods suffer from a computational weakness: they require repeatedly solving a hard reinforcement learning (RL) problem as a subroutine. This is counter-intuitive from the viewpoint of reductions: we have reduced the easier problem of imitation learning to repeatedly solving the harder problem of RL. Another thread of work has proved that access to the side-information of the distribution of states where a strong policy spends time can dramatically reduce the sample and computational complexities of solving an RL problem. In this work, we demonstrate for the first time a more informed imitation learning reduction where we utilize the state distribution of the expert to alleviate the global exploration component of the RL subroutine, providing an exponential speedup in theory. In practice, we find that we are able to significantly speed up the prior art on continuous control tasks.

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

We present algorithms for diffusion model sampling which obtain δ-error in polylog(1/δ) steps, given access to widetilde O(δ)-accurate score estimates in L^2. This is an exponential improvement over all previous results. Specifically, under minimal data assumptions, the complexity is widetilde O(d_star polylog(1/δ)) where d_star is the intrinsic dimension of the data. Further, under a non-uniform L-Lipschitz condition, the complexity reduces to widetilde O(L polylog(1/δ)). Our approach also yields the first polylog(1/δ) complexity sampler for general log-concave distributions using only gradient evaluations.

We consider the question of learning Q-function in a sample efficient manner for reinforcement learning with continuous state and action spaces under a generative model. If Q-function is Lipschitz continuous, then the minimal sample complexity for estimating ε-optimal Q-function is known to scale as Ω(1{ε^{d_1+d_2 +2}}) per classical non-parametric learning theory, where d_1 and d_2 denote the dimensions of the state and action spaces respectively. The Q-function, when viewed as a kernel, induces a Hilbert-Schmidt operator and hence possesses square-summable spectrum. This motivates us to consider a parametric class of Q-functions parameterized by its "rank" r, which contains all Lipschitz Q-functions as r to infty. As our key contribution, we develop a simple, iterative learning algorithm that finds ε-optimal Q-function with sample complexity of O(1{ε^{max(d_1, d_2)+2}}) when the optimal Q-function has low rank r and the discounting factor γ is below a certain threshold. Thus, this provides an exponential improvement in sample complexity. To enable our result, we develop a novel Matrix Estimation algorithm that faithfully estimates an unknown low-rank matrix in the ell_infty sense even in the presence of arbitrary bounded noise, which might be of interest in its own right. Empirical results on several stochastic control tasks confirm the efficacy of our "low-rank" algorithms.

Large language models excel at short-horizon reasoning tasks, but performance drops as reasoning horizon lengths increase. Existing approaches to combat this rely on inference-time scaffolding or costly step-level supervision, neither of which scales easily. In this work, we introduce a scalable method to bootstrap long-horizon reasoning capabilities using only existing, abundant short-horizon data. Our approach synthetically composes simple problems into complex, multi-step dependency chains of arbitrary length. We train models on this data using outcome-only rewards under a curriculum that automatically increases in complexity, allowing RL training to be scaled much further without saturating. Empirically, our method generalizes remarkably well: curriculum training on composed 6th-grade level math problems (GSM8K) boosts accuracy on longer, competition-level benchmarks (GSM-Symbolic, MATH-500, AIME) by up to 2.06x. It also transfers significantly to diverse out-of-distribution ReasoningGym domains and long-context benchmarks, indicating broader generalization. Importantly, our long-horizon improvements are significantly higher than baselines even at high pass@k, showing that models can learn new reasoning paths under RL. Theoretically, we show that curriculum RL with outcome rewards achieves an exponential improvement in sample complexity over full-horizon training, providing training signal comparable to dense supervision. h1 therefore introduces an efficient path towards scaling RL for long-horizon problems using only existing data.

In this work, we study the performance of sub-gradient method (SubGM) on a natural nonconvex and nonsmooth formulation of low-rank matrix recovery with ell_1-loss, where the goal is to recover a low-rank matrix from a limited number of measurements, a subset of which may be grossly corrupted with noise. We study a scenario where the rank of the true solution is unknown and over-estimated instead. The over-estimation of the rank gives rise to an over-parameterized model in which there are more degrees of freedom than needed. Such over-parameterization may lead to overfitting, or adversely affect the performance of the algorithm. We prove that a simple SubGM with small initialization is agnostic to both over-parameterization and noise in the measurements. In particular, we show that small initialization nullifies the effect of over-parameterization on the performance of SubGM, leading to an exponential improvement in its convergence rate. Moreover, we provide the first unifying framework for analyzing the behavior of SubGM under both outlier and Gaussian noise models, showing that SubGM converges to the true solution, even under arbitrarily large and arbitrarily dense noise values, and--perhaps surprisingly--even if the globally optimal solutions do not correspond to the ground truth. At the core of our results is a robust variant of restricted isometry property, called Sign-RIP, which controls the deviation of the sub-differential of the ell_1-loss from that of an ideal, expected loss. As a byproduct of our results, we consider a subclass of robust low-rank matrix recovery with Gaussian measurements, and show that the number of required samples to guarantee the global convergence of SubGM is independent of the over-parameterized rank.

We consider online learning in multi-player smooth monotone games. Existing algorithms have limitations such as (1) being only applicable to strongly monotone games; (2) lacking the no-regret guarantee; (3) having only asymptotic or slow O(1{T}) last-iterate convergence rate to a Nash equilibrium. While the O(1{T}) rate is tight for a large class of algorithms including the well-studied extragradient algorithm and optimistic gradient algorithm, it is not optimal for all gradient-based algorithms. We propose the accelerated optimistic gradient (AOG) algorithm, the first doubly optimal no-regret learning algorithm for smooth monotone games. Namely, our algorithm achieves both (i) the optimal O(T) regret in the adversarial setting under smooth and convex loss functions and (ii) the optimal O(1{T}) last-iterate convergence rate to a Nash equilibrium in multi-player smooth monotone games. As a byproduct of the accelerated last-iterate convergence rate, we further show that each player suffers only an O(log T) individual worst-case dynamic regret, providing an exponential improvement over the previous state-of-the-art O(T) bound.

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need to know the solution x itself, but rather an approximation of the expectation value of some operator associated with x, e.g., x'Mx for some matrix M. In this case, when A is sparse, N by N and has condition number kappa, classical algorithms can find x and estimate x'Mx in O(N sqrt(kappa)) time. Here, we exhibit a quantum algorithm for this task that runs in poly(log N, kappa) time, an exponential improvement over the best classical algorithm.

Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were developed over the centuries by mathematicians, who emphasized the attainability of arbitrary precision. Computers, however, operate on few limited precision types, such as the popular float32. In this study, we show that when aiming for limited precision, existing approximation methods can be outperformed by programs automatically discovered from scratch by a simple evolutionary algorithm. In particular, over real numbers, our method can approximate the exponential function reaching orders of magnitude more precision for a given number of operations when compared to previous approaches. More practically, over float32 numbers and constrained to less than 1 ULP of error, the same method attains a speedup over baselines by generating code that triggers better XLA/LLVM compilation paths. In other words, in both cases, evolution searched a vast space of possible programs, without knowledge of mathematics, to discover previously unknown optimized approximations to high precision, for the first time. We also give evidence that these results extend beyond the exponential. The ubiquity of transcendental functions suggests that our method has the potential to reduce the cost of scientific computing applications.

We study the problem of optimizing a function under a budgeted number of evaluations. We only assume that the function is locally smooth around one of its global optima. The difficulty of optimization is measured in terms of 1) the amount of noise b of the function evaluation and 2) the local smoothness, d, of the function. A smaller d results in smaller optimization error. We come with a new, simple, and parameter-free approach. First, for all values of b and d, this approach recovers at least the state-of-the-art regret guarantees. Second, our approach additionally obtains these results while being agnostic to the values of both b and d. This leads to the first algorithm that naturally adapts to an unknown range of noise b and leads to significant improvements in a moderate and low-noise regime. Third, our approach also obtains a remarkable improvement over the state-of-the-art SOO algorithm when the noise is very low which includes the case of optimization under deterministic feedback (b=0). There, under our minimal local smoothness assumption, this improvement is of exponential magnitude and holds for a class of functions that covers the vast majority of functions that practitioners optimize (d=0). We show that our algorithmic improvement is borne out in experiments as we empirically show faster convergence on common benchmarks.

We expand the exponential kernel of attention into a truncated Taylor series of n terms and factorize each term into a tensor-power inner product, which collapses the causal history into exactly n recurrent states, each updated by one rank-one outer product per token and independent of context length N. The recursion is lossless with respect to the truncated kernel (2.2 times 10^{-16} in float64), and the states are additive across chunks (5.7 times 10^{-14}), so prefill admits a parallel scan. Measured exponents are t propto N^{2.28} for softmax against N^{0.91} for states, with a crossover at N approx 728 and 20.8times at N = 8192; per-token decoding latency is constant at 7.3,μs against N^{1.04} for softmax, giving 76.0times at N = 65536. Accuracy improves exponentially in n while cost grows combinatorially, since the m-th state is d+m-1{m} wide---a bound confirmed by SVD---so the optimum is second order, n = 3, at 6.5 times 10^{-4} error and 9{,}945 elements per head. Query and key normalization is a prerequisite: without it the argument exceeds the convergence radius and adding terms stops helping.

Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and processes that data using a quantum computer, could have significant advantages over conventional experiments in which the physical system is measured and the outcomes are processed using a classical computer. We prove that, in various tasks, quantum machines can learn from exponentially fewer experiments than those required in conventional experiments. The exponential advantage holds in predicting properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. In some tasks, the quantum processing needed to achieve the exponential advantage can be modest; for example, one can simultaneously learn about many noncommuting observables by processing only two copies of the system. Conducting experiments with up to 40 superconducting qubits and 1300 quantum gates, we demonstrate that a substantial quantum advantage can be realized using today's relatively noisy quantum processors. Our results highlight how quantum technology can enable powerful new strategies to learn about nature.

Given the exponential growth of the volume of the ball w.r.t. its radius, the hyperbolic space is capable of embedding trees with arbitrarily small distortion and hence has received wide attention for representing hierarchical datasets. However, this exponential growth property comes at a price of numerical instability such that training hyperbolic learning models will sometimes lead to catastrophic NaN problems, encountering unrepresentable values in floating point arithmetic. In this work, we carefully analyze the limitation of two popular models for the hyperbolic space, namely, the Poincar\'e ball and the Lorentz model. We first show that, under the 64 bit arithmetic system, the Poincar\'e ball has a relatively larger capacity than the Lorentz model for correctly representing points. Then, we theoretically validate the superiority of the Lorentz model over the Poincar\'e ball from the perspective of optimization. Given the numerical limitations of both models, we identify one Euclidean parametrization of the hyperbolic space which can alleviate these limitations. We further extend this Euclidean parametrization to hyperbolic hyperplanes and exhibits its ability in improving the performance of hyperbolic SVM.

State-of-the-art AI systems can be significantly improved without expensive retraining via "post-training enhancements"-techniques applied after initial training like fine-tuning the system to use a web browser. We review recent post-training enhancements, categorizing them into five types: tool-use, prompting methods, scaffolding, solution selection, and data generation. Different enhancements improve performance on different tasks, making it hard to compare their significance. So we translate improvements from different enhancements into a common currency, the compute-equivalent gain: how much additional training compute would be needed to improve performance by the same amount as the enhancement. Our non-experimental work shows that post-training enhancements have significant benefits: most surveyed enhancements improve benchmark performance by more than a 5x increase in training compute, some by more than 20x. Post-training enhancements are relatively cheap to develop: fine-tuning costs are typically <1% of the original training cost. Governing the development of capable post-training enhancements may be challenging because frontier models could be enhanced by a wide range of actors.

Adapting general-purpose large language models to specific tasks requires substantial human effort in designing data and training strategies. Sustaining improvement is especially challenging because model updates change the error distribution, requiring strategies to be continually refined. We introduce ImproveAnyTask, an autonomous post-training harness that improves task performance under a limited compute budget. Drawing inspiration from gradient-based parameter optimization, the harness organizes adaptation into error attribution, update-direction selection, and executable model updates. It combines metric-level and case-level analysis to identify a focal problem, then investigates research-backed strategies and compares their reported gains and reproduction difficulty. The selected strategy is translated into training data and a training configuration, with small-scale execution checks preceding full post-training. Subsequent evaluation guides model selection and further adaptation, while validated strategies and scripts are retained for reuse. Across 11 tasks, ImproveAnyTask achieves mean gains of 18.29 and 11.97 percentage points on the Base and Instruct models, respectively, with a maximum gain of 41.96 points, under a 24-hour budget with resources equivalent to eight H20 GPUs.

Current LLM agent benchmarks, which predominantly focus on binary pass/fail tasks such as code generation or search-based question answering, often neglect the value of real-world engineering that is often captured through the iterative optimization of feasible designs. To this end, we introduce Frontier-Eng, a human-verified benchmark for generative optimization -- an iterative propose-execute-evaluate loop in which an agent generates candidate artifacts, receives executable verifier feedback, and revises them under a fixed interaction budget -- spanning 47 tasks across five broad engineering categories. Unlike previous suites, Frontier-Eng tasks are grounded in industrial-grade simulators and verifiers that provide continuous reward signals and enforce hard feasibility constraints under constrained budgets. We evaluate eight frontier language models using representative search frameworks, finding that while Claude 4.6 Opus achieves the most robust performance, the benchmark remains challenging for all models. Our analysis suggests a dual power-law decay in improvement frequency (sim 1/iteration) and magnitude (sim 1/improvement count). We further show that although width improves parallelism and diversity, depth remains crucial for hard-won improvements under a fixed budget. Frontier-Eng establishes a new standard for assessing the capacity of AI agents to integrate domain knowledge with executable feedback to solve complex, open-ended engineering problems.

We give a classical analogue to Kerenidis and Prakash's quantum recommendation system, previously believed to be one of the strongest candidates for provably exponential speedups in quantum machine learning. Our main result is an algorithm that, given an m times n matrix in a data structure supporting certain ell^2-norm sampling operations, outputs an ell^2-norm sample from a rank-k approximation of that matrix in time O(poly(k)log(mn)), only polynomially slower than the quantum algorithm. As a consequence, Kerenidis and Prakash's algorithm does not in fact give an exponential speedup over classical algorithms. Further, under strong input assumptions, the classical recommendation system resulting from our algorithm produces recommendations exponentially faster than previous classical systems, which run in time linear in m and n. The main insight of this work is the use of simple routines to manipulate ell^2-norm sampling distributions, which play the role of quantum superpositions in the classical setting. This correspondence indicates a potentially fruitful framework for formally comparing quantum machine learning algorithms to classical machine learning algorithms.

AI agents are beginning to automate research and development across the AI stack, from improving training efficiency to optimizing inference. A natural next step is to improve the research efficiency of the agents themselves. When an AI research agent's own code is the object of optimization, each accepted rewrite becomes the agent that the next round edits. We refer to this loop as recursive self-improvement. Its significance lies in a long-standing trend, in which increased cumulative spending on R&D yields diminishing returns. Sustained self-improvement offers a way to counter this trend. We present AIDE^2, a system that implements this loop for a frontier AI research agent. It proposes changes to its own code, benchmarks modified versions of itself on a suite of AI R&D tasks, and keeps the changes that perform best on hidden evaluations. In an autonomous 8-day run, AIDE^2 discovered seven successive improvements, ranging from a new search policy to memory mechanisms that compress and manage the agent's growing context. These gains generalize to four held-out benchmarks spanning machine learning engineering, heuristic algorithm engineering, and physics-based weather forecasting, the last of which is out of distribution from the selection tasks. On all four, the strongest discovered agent matches or exceeds a human-engineered production research agent that ranks among the strongest on FML-Bench. On a separate held-out task family, the discovered agents also exhibit reduced reward hacking, a property the loop never explicitly optimized for: the rate falls from 55% to 32% during the run, 7 percentage points below the human-engineered agent. Together, these results show that an AI research agent can improve its own research efficiency through recursive self-improvement, and that these gains transfer to tasks and domains the loop never encountered.

In continual learning (CL), model growth enhances adaptability to new data. However, when model growth is applied improperly, especially in task-agnostic CL, where the entire grown model is used for inference, it can lead to severe degradation of learned knowledge, a problem we term growth-induced forgetting. Most existing methods that adopt model growth to improve adaptability often overlook the forgetting issue, resulting in compromised knowledge retention, making them unsuitable for task-agnostic settings. To promote both adaptability and knowledge retention with model growth, we identify the key: gradient and parameter sparsity. Introducing SparseGrow, which increases gradient sparsity through layer expansion and gradient gating to enable focused updates on parameters while preserving critical parameters, thus inhibiting forgetting. Moreover, it promotes parameter sparsity with sparse initialization and training, aiming at better control of model plasticity, improving adaptability over new data. Extensive experiments across diverse datasets, task-agnostic settings, and a large number of tasks demonstrate the necessity of controlled layer expansion and validate the effectiveness of SparseGrow in achieving high adaptability while minimizing forgetting in continual learning. By enabling model growth with sparsified gradients and parameters, SparseGrow paves the way for building scalable lifelong learning systems capable of continual adaptation with better knowledge retention.

Recent work in language modeling has raised the possibility of self-improvement, where a language models evaluates and refines its own generations to achieve higher performance without external feedback. It is impossible for this self-improvement to create information that is not already in the model, so why should we expect that this will lead to improved capabilities? We offer a new perspective on the capabilities of self-improvement through a lens we refer to as sharpening. Motivated by the observation that language models are often better at verifying response quality than they are at generating correct responses, we formalize self-improvement as using the model itself as a verifier during post-training in order to ``sharpen'' the model to one placing large mass on high-quality sequences, thereby amortizing the expensive inference-time computation of generating good sequences. We begin by introducing a new statistical framework for sharpening in which the learner aims to sharpen a pre-trained base policy via sample access, and establish fundamental limits. Then we analyze two natural families of self-improvement algorithms based on SFT and RLHF. We find that (i) the SFT-based approach is minimax optimal whenever the initial model has sufficient coverage, but (ii) the RLHF-based approach can improve over SFT-based self-improvement by leveraging online exploration, bypassing the need for coverage. Finally, we empirically validate the sharpening mechanism via inference-time and amortization experiments. We view these findings as a starting point toward a foundational understanding that can guide the design and evaluation of self-improvement algorithms.

We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an Ntimes N matrix M, an N-dimensional vector emph{b}, and an initial vector emph{x}(0), obtain a target vector emph{x}(t) as a function of time t according to the constraint demph{x}(t)/dt=Memph{x}(t)+emph{b}. We show that our algorithm exhibits an exponential speedup over its classical counterpart in certain circumstances. In addition, we demonstrate our quantum algorithm for a 4times4 linear differential equation using a 4-qubit nuclear magnetic resonance quantum information processor. Our algorithm provides a key technique for solving many important problems which rely on the solutions to linear differential equations.

Algorithmic efficiency techniques such as distillation (hinton2015distillation) are useful in improving model quality without increasing serving costs, provided a larger teacher model is available for a smaller student model to learn from during training. Standard distillation methods are limited to only forcing the student to match the teacher's outputs. Given the costs associated with training a large model, we believe we should be extracting more useful information from a teacher model than by just making the student match the teacher's outputs. In this paper, we introduce \guide (Guided Initialization and Distillation of Embeddings). \guide can be considered a distillation technique that forces the student to match the teacher in the parameter space. Using \guide we show 25-26\% reduction in the teacher-student quality gap when using large student models (400M - 1B parameters) trained on approx 20B tokens. We also present a thorough analysis demonstrating that \guide can be combined with knowledge distillation with near additive improvements. Furthermore, we show that applying \guide alone leads to substantially better model quality than applying knowledge distillation by itself. Most importantly, \guide introduces no training or inference overhead and hence any model quality gains from our method are virtually free.

Several recent advances in AI systems (e.g., Tree-of-Thoughts and Program-Aided Language Models) solve problems by providing a "scaffolding" program that structures multiple calls to language models to generate better outputs. A scaffolding program is written in a programming language such as Python. In this work, we use a language-model-infused scaffolding program to improve itself. We start with a seed "improver" that improves an input program according to a given utility function by querying a language model several times and returning the best solution. We then run this seed improver to improve itself. Across a small set of downstream tasks, the resulting improved improver generates programs with significantly better performance than its seed improver. Afterward, we analyze the variety of self-improvement strategies proposed by the language model, including beam search, genetic algorithms, and simulated annealing. Since the language models themselves are not altered, this is not full recursive self-improvement. Nonetheless, it demonstrates that a modern language model, GPT-4 in our proof-of-concept experiments, is capable of writing code that can call itself to improve itself. We critically consider concerns around the development of self-improving technologies and evaluate the frequency with which the generated code bypasses a sandbox.

The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement (EI) and the Upper Confidence Bound (UCB) always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights. We introduce two novel epsilon-greedy acquisition functions. Extensive empirical evaluation of these together with random search, purely exploratory, and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that epsilon-greedy algorithms are generally at least as effective as conventional acquisition functions (e.g., EI and UCB), particularly with a limited budget. In higher dimensions epsilon-greedy approaches are shown to have improved performance over conventional approaches. These results are borne out on a real world computational fluid dynamics optimisation problem and a robotics active learning problem. Our analysis and experiments suggest that the most effective strategy, particularly in higher dimensions, is to be mostly greedy, occasionally selecting a random exploratory solution.

We introduce a boosting algorithm to pre-process data for fairness. Starting from an initial fair but inaccurate distribution, our approach shifts towards better data fitting while still ensuring a minimal fairness guarantee. To do so, it learns the sufficient statistics of an exponential family with boosting-compliant convergence. Importantly, we are able to theoretically prove that the learned distribution will have a representation rate and statistical rate data fairness guarantee. Unlike recent optimization based pre-processing methods, our approach can be easily adapted for continuous domain features. Furthermore, when the weak learners are specified to be decision trees, the sufficient statistics of the learned distribution can be examined to provide clues on sources of (un)fairness. Empirical results are present to display the quality of result on real-world data.

Self-improving AI systems aim to reduce reliance on human engineering by learning to improve their own learning and problem-solving processes. Existing approaches to self-improvement rely on fixed, handcrafted meta-level mechanisms, fundamentally limiting how fast such systems can improve. The Darwin Gödel Machine (DGM) demonstrates open-ended self-improvement in coding by repeatedly generating and evaluating self-modified variants. Because both evaluation and self-modification are coding tasks, gains in coding ability can translate into gains in self-improvement ability. However, this alignment does not generally hold beyond coding domains. We introduce hyperagents, self-referential agents that integrate a task agent (which solves the target task) and a meta agent (which modifies itself and the task agent) into a single editable program. Crucially, the meta-level modification procedure is itself editable, enabling metacognitive self-modification, improving not only the task-solving behavior, but also the mechanism that generates future improvements. We instantiate this framework by extending DGM to create DGM-Hyperagents (DGM-H), eliminating the assumption of domain-specific alignment between task performance and self-modification skill to potentially support self-accelerating progress on any computable task. Across diverse domains, the DGM-H improves performance over time and outperforms baselines without self-improvement or open-ended exploration, as well as prior self-improving systems. Furthermore, the DGM-H improves the process by which it generates new agents (e.g., persistent memory, performance tracking), and these meta-level improvements transfer across domains and accumulate across runs. DGM-Hyperagents offer a glimpse of open-ended AI systems that do not merely search for better solutions, but continually improve their search for how to improve.

We address the problem of optimizing a Brownian motion. We consider a (random) realization W of a Brownian motion with input space in [0,1]. Given W, our goal is to return an ε-approximation of its maximum using the smallest possible number of function evaluations, the sample complexity of the algorithm. We provide an algorithm with sample complexity of order log^2(1/ε). This improves over previous results of Al-Mharmah and Calvin (1996) and Calvin et al. (2017) which provided only polynomial rates. Our algorithm is adaptive---each query depends on previous values---and is an instance of the optimism-in-the-face-of-uncertainty principle.

We present the main improvements and new features in version 2.0 of the open-source C++ library FireFly for the interpolation of rational functions. This includes algorithmic improvements, e.g. a hybrid algorithm for dense and sparse rational functions and an algorithm to identify and remove univariate factors. The new version is applied to a Feynman-integral reduction to showcase the runtime improvements achieved. Moreover, FireFly now supports parallelization with MPI and offers new tools like a parser for expressions or an executable for the insertion of replacement tables.

Stochasticity in language model fine-tuning, often caused by the small batch sizes typically used in this regime, can destabilize training by introducing large oscillations in generation quality. A popular approach to mitigating this instability is to take an Exponential moving average (EMA) of weights throughout training. While EMA reduces stochasticity, thereby smoothing training, the introduction of bias from old iterates often creates a lag in optimization relative to vanilla training. In this work, we propose the Bias-Corrected Exponential Moving Average (BEMA), a simple and practical augmentation of EMA that retains variance-reduction benefits while eliminating bias. BEMA is motivated by a simple theoretical model wherein we demonstrate provable acceleration of BEMA over both a standard EMA and vanilla training. Through an extensive suite of experiments on Language Models, we show that BEMA leads to significantly improved convergence rates and final performance over both EMA and vanilla training in a variety of standard LM benchmarks, making BEMA a practical and theoretically motivated intervention for more stable and efficient fine-tuning.

Recursive self-improvement (RSI) describes a system that improves not only its behavior but also the process by which it improves. Recent digital agents test this idea by rewriting their own code and checking each version with executable tests. Bringing these mechanisms into the physical world requires learning from partial observations through costly trials, while accounting for changing operating conditions and potentially irreversible consequences. We position RSI within robot learning and trace pathways from improving robot capabilities to improving the processes that generate them. We examine how physical experience can strengthen these improvement mechanisms and when the resulting gains can support further self-improvement of the mechanisms themselves. Gains carry forward only when feedback addresses remaining learning needs, the receiving component can use the change, its value survives changes in tasks or hardware, and continued practice remains safe and affordable. Existing studies, concentrated in manipulation, support behavioral improvement, benefits to later learning, and procedure improvement. Some systems also change the improver's knowledge or tools, but the physical studies reviewed here have yet to isolate gains attributable to recursion. We synthesize these findings into evaluation principles and research directions for machines that, trial by trial, safely improve the way they improve.

Large language model (LLM) agents have demonstrated strong capabilities in complex tasks, including code generation, tool use, and multi-hop question answering. Existing self-improvement methods enhance agent performance through model optimization, harness evolution, and executable artifact refinement, while recursive self-improvement (RSI) further extends optimization to the improvement mechanisms themselves. However, adapting self-improvement workflows to evolving performance bottlenecks while improving workflow orchestration through execution feedback remains a key challenge. We propose RSIFlow, a Recursive Self-Improvement framework that integrates adaptive workflow orchestration with meta-agent capability evolution. RSIFlow diagnoses performance bottlenecks from task-agent trajectories and environmental feedback to dynamically select component-specific improvement workflows. The meta-agent then distills workflow outcomes into component-specific skills and cross-component principles, evolving its own harness to improve subsequent workflow orchestration. Experiments across six benchmarks and two backbone models show that RSIFlow achieves the SOTA average performance on all benchmarks. Ablation studies further demonstrate the contributions of adaptive workflow orchestration and meta-harness evolution. Code is available at https://github.com/1HUAN1/RSI-Flow.

Error Feedback (EF) is a highly popular and immensely effective mechanism for fixing convergence issues which arise in distributed training methods (such as distributed GD or SGD) when these are enhanced with greedy communication compression techniques such as TopK. While EF was proposed almost a decade ago (Seide et al., 2014), and despite concentrated effort by the community to advance the theoretical understanding of this mechanism, there is still a lot to explore. In this work we study a modern form of error feedback called EF21 (Richtarik et al., 2021) which offers the currently best-known theoretical guarantees, under the weakest assumptions, and also works well in practice. In particular, while the theoretical communication complexity of EF21 depends on the quadratic mean of certain smoothness parameters, we improve this dependence to their arithmetic mean, which is always smaller, and can be substantially smaller, especially in heterogeneous data regimes. We take the reader on a journey of our discovery process. Starting with the idea of applying EF21 to an equivalent reformulation of the underlying problem which (unfortunately) requires (often impractical) machine cloning, we continue to the discovery of a new weighted version of EF21 which can (fortunately) be executed without any cloning, and finally circle back to an improved analysis of the original EF21 method. While this development applies to the simplest form of EF21, our approach naturally extends to more elaborate variants involving stochastic gradients and partial participation. Further, our technique improves the best-known theory of EF21 in the rare features regime (Richtarik et al., 2023). Finally, we validate our theoretical findings with suitable experiments.

AI agents increasingly operate in environments where they can diagnose failures and improve through experience, yet existing evaluations largely measure what an agent can do at a fixed point in time rather than how effectively it learns. Evaluating self-improvement requires answering three questions: does future performance improve and generalize beyond the interactions that enabled learning; how efficiently are new capabilities acquired; and where does the self-improvement process break down? To answer these questions, we study self-improvement in a controlled setting where agents amortize past experience into reusable artifacts that are inherited by future instances. At each checkpoint, we measure performance on training and held-out environment interactions while accounting for learning cost. We introduce agent plasticity, the efficiency with which an agent converts experience into gains in future held-out performance. Across multiple environments, frontier models exhibit sharply different improvement trajectories despite comparable opportunities to learn. Some achieve substantial and persistent gains, while others remain near or below their initial performance, and gains within the training regime often transfer only partially to out-of-distribution conditions. Endpoint capability and acquisition efficiency also diverge: the agent that ultimately performs best need not be the one that improves most efficiently. Tracing failures through the improvement loop further reveals different candidate bottlenecks. Agents with low plasticity often fail to reuse relevant artifacts, whereas more plastic agents may still fail despite reusing relevant artifacts, pointing to limitations in artifact quality, generalization, or application. Evaluating self-improving agents requires measuring not only what they can do, but how effectively they become better through experience.

Self-improvement is a mechanism in Large Language Model (LLM) pre-training, post-training and test-time inference. We explore a framework where the model verifies its own outputs, filters or reweights data based on this verification, and distills the filtered data. Despite several empirical successes, a fundamental understanding is still lacking. In this work, we initiate a comprehensive, modular and controlled study on LLM self-improvement. We provide a mathematical formulation for self-improvement, which is largely governed by a quantity which we formalize as the generation-verification gap. Through experiments with various model families and tasks, we discover a scaling phenomenon of self-improvement -- a variant of the generation-verification gap scales monotonically with the model pre-training flops. We also examine when self-improvement is possible, an iterative self-improvement procedure, and ways to improve its performance. Our findings not only advance understanding of LLM self-improvement with practical implications, but also open numerous avenues for future research into its capabilities and boundaries.

The current best bounds on the matrix multiplication exponent ω are obtained through a refinement of the laser method called combination loss analysis (Duan et al., 2022; Williams et al., 2024; Alman et al., 2025). In this note, we address the optimization problem at the core of this approach and propose several improvements. First, we reformulate the optimization problem allowing us to solve it in a larger setting than was previously possible. Second, we leverage recent advances in machine learning to design a new optimization algorithm for this problem. Finally, we refine the resulting optimization algorithm with AlphaEvolve. Our combined approach yields an upper bound of ω < 2.371177, improving the previous best bound of 2.371339.

When fitting the learning data of an individual to algorithm-like learning models, the observations are so dependent and non-stationary that one may wonder what the classical Maximum Likelihood Estimator (MLE) could do, even if it is the usual tool applied to experimental cognition. Our objective in this work is to show that the estimation of the learning rate cannot be efficient if the learning rate is constant in the classical Exp3 (Exponential weights for Exploration and Exploitation) algorithm. Secondly, we show that if the learning rate decreases polynomially with the sample size, then the prediction error and in some cases the estimation error of the MLE satisfy bounds in probability that decrease at a polynomial rate.

Today's AI systems have human-designed, fixed architectures and cannot autonomously and continuously improve themselves. The advance of AI could itself be automated. If done safely, that would accelerate AI development and allow us to reap its benefits much sooner. Meta-learning can automate the discovery of novel algorithms, but is limited by first-order improvements and the human design of a suitable search space. The G\"odel machine proposed a theoretical alternative: a self-improving AI that repeatedly modifies itself in a provably beneficial manner. Unfortunately, proving that most changes are net beneficial is impossible in practice. We introduce the Darwin G\"odel Machine (DGM), a self-improving system that iteratively modifies its own code (thereby also improving its ability to modify its own codebase) and empirically validates each change using coding benchmarks. Inspired by Darwinian evolution and open-endedness research, the DGM maintains an archive of generated coding agents. It grows the archive by sampling an agent from it and using a foundation model to create a new, interesting, version of the sampled agent. This open-ended exploration forms a growing tree of diverse, high-quality agents and allows the parallel exploration of many different paths through the search space. Empirically, the DGM automatically improves its coding capabilities (e.g., better code editing tools, long-context window management, peer-review mechanisms), increasing performance on SWE-bench from 20.0% to 50.0%, and on Polyglot from 14.2% to 30.7%. Furthermore, the DGM significantly outperforms baselines without self-improvement or open-ended exploration. All experiments were done with safety precautions (e.g., sandboxing, human oversight). The DGM is a significant step toward self-improving AI, capable of gathering its own stepping stones along paths that unfold into endless innovation.

Follow the regularized leader FTRL is the premier algorithm for online optimization. However, despite decades of research on its convergence in constrained optimization -- and potential games in particular -- its behavior remained hitherto poorly understood. In this paper, we establish that FTRL can take exponential time to converge to a Nash equilibrium in two-player potential games for any (permutation-invariant) regularizer and potentially vanishing learning rate. By known equivalences, this translates to an exponential lower bound for certain mirror descent counterparts, most notably multiplicative weights update. On the positive side, we establish the potential property for FTRL and obtain an exponential upper bound exp(O_ε(1/ε^2)) for any no-regret dynamics executed in a lazy, alternating fashion, matching our lower bound up to factors in the exponent. Finally, in multi-player potential games, we show that fictitious play -- the extreme version of FTRL -- can take doubly exponential time to reach a Nash equilibrium. This constitutes an exponentially stronger lower bound for the foundational learning algorithm in games.

Neural networks are very effective when trained on large datasets for a large number of iterations. However, when they are trained on non-stationary streams of data and in an online fashion, their performance is reduced (1) by the online setup, which limits the availability of data, (2) due to catastrophic forgetting because of the non-stationary nature of the data. Furthermore, several recent works (Caccia et al., 2022; Lange et al., 2023) arXiv:2205.13452 showed that replay methods used in continual learning suffer from the stability gap, encountered when evaluating the model continually (rather than only on task boundaries). In this article, we study the effect of model ensembling as a way to improve performance and stability in online continual learning. We notice that naively ensembling models coming from a variety of training tasks increases the performance in online continual learning considerably. Starting from this observation, and drawing inspirations from semi-supervised learning ensembling methods, we use a lightweight temporal ensemble that computes the exponential moving average of the weights (EMA) at test time, and show that it can drastically increase the performance and stability when used in combination with several methods from the literature.

Self-improving autonomous agents are moving from research prototypes to deployed systems. The primary goal is controllable evolution, or adaptation, from experience with minimal or even no human input. This survey frames modern self-improving agents as adaptive systems that convert experience into accumulated capability gains. We offer a system-level framework that represents a modern agent as a configuration coupling a foundation model with an operational scaffold of prompts, memory, tools, and control logic. Within this framework, self-improvement is formalized as a self-induced update operator that obtains and commits updates to model parameters or scaffold components. We organize prior work by update target and by the signals that drive change, then review applications and discuss evaluation, before closing with open problems and future directions. For convenience, we track technical updates on https://github.com/selfimproving-agent/awesome-Self-Improving-Agents.

Most reported gains from agent-optimization methods are one-shot: an agent is optimized against a fixed benchmark and the resulting improvement is reported as if it were a stable property of the method. This does not test the setting that matters for deployed agents, where optimization is applied recursively as new failures and new tasks appear over time. The central question this raises is whether optimizer-driven gains compound: after an agent has been optimized once, can it be optimized again on newly arrived tasks without eroding the gains the first round produced? We study this question with a two-phase continual-learning evaluation built from hard tasks in Terminal-Bench 2.0, comparing three approaches to agent-harness optimization (GEPA, Meta Harness, and RELAI's Verifiable Continual Learning, RELAI-VCL) under identical optimization budgets. All three methods improve over the baseline agent in the conventional, static, single-phase setting. However, once new tasks are introduced, the methods diverge sharply: GEPA's optimized agent transfers below the unoptimized baseline, Meta Harness transfers well but fails to improve further once given a second optimization budget, and RELAI-VCL is the only method that both transfers positively to unseen tasks and continues improving after those tasks are folded into the optimization objective, reaching the highest pass rate at every evaluated stage and the highest lifelong average pass rate overall (76.4% vs. 66.0% for GEPA, 64.6% for Meta Harness, and 58.7% for the baseline). Our key observation was that optimization gains compounded only when regression control was built into the optimization loop, providing an inductive bias against shortcut solutions that fail to generalize.

The research community has proposed copious modifications to the Transformer architecture since it was introduced over three years ago, relatively few of which have seen widespread adoption. In this paper, we comprehensively evaluate many of these modifications in a shared experimental setting that covers most of the common uses of the Transformer in natural language processing. Surprisingly, we find that most modifications do not meaningfully improve performance. Furthermore, most of the Transformer variants we found beneficial were either developed in the same codebase that we used or are relatively minor changes. We conjecture that performance improvements may strongly depend on implementation details and correspondingly make some recommendations for improving the generality of experimental results.

Since compute grows much faster than web text available for language model pre-training, we ask how one should approach pre-training under fixed data and no compute constraints. We first show that existing data-constrained approaches of increasing epoch count and parameter count eventually overfit, and we significantly improve upon such recipes by properly tuning regularization, finding that the optimal weight decay is 30times larger than standard practice. Since our regularized recipe monotonically decreases loss following a simple power law in parameter count, we estimate its best possible performance via the asymptote of its scaling law rather than the performance at a fixed compute budget. We then identify that ensembling independently trained models achieves a significantly lower loss asymptote than the regularized recipe. Our best intervention combining epoching, regularization, parameter scaling, and ensemble scaling achieves an asymptote at 200M tokens using 5.17times less data than our baseline, and our data scaling laws predict that this improvement persists at higher token budgets. We find that our data efficiency gains can be realized at much smaller parameter counts as we can distill an ensemble into a student model that is 8times smaller and retains 83% of the ensembling benefit. Finally, our interventions designed for validation loss generalize to downstream benchmarks, achieving a 9% improvement for pre-training evals and a 17.5times data efficiency improvement over continued pre-training on math mid-training data. Our results show that simple algorithmic improvements can enable significantly more data-efficient pre-training in a compute-rich future.

Adaptive gradient methods, e.g. Adam, have achieved tremendous success in machine learning. Scaling the learning rate element-wisely by a certain form of second moment estimate of gradients, such methods are able to attain rapid training of modern deep neural networks. Nevertheless, they are observed to suffer from compromised generalization ability compared with stochastic gradient descent (SGD) and tend to be trapped in local minima at an early stage during training. Intriguingly, we discover that substituting the gradient in the second raw moment estimate term with its momentumized version in Adam can resolve the issue. The intuition is that gradient with momentum contains more accurate directional information and therefore its second moment estimation is a more favorable option for learning rate scaling than that of the raw gradient. Thereby we propose AdaMomentum as a new optimizer reaching the goal of training fast while generalizing much better. We further develop a theory to back up the improvement in generalization and provide convergence guarantees under both convex and nonconvex settings. Extensive experiments on a wide range of tasks and models demonstrate that AdaMomentum exhibits state-of-the-art performance and superior training stability consistently.

Risk-averse reinforcement learning finds application in various high-stakes fields. Unlike classical reinforcement learning, which aims to maximize expected returns, risk-averse agents choose policies that minimize risk, occasionally sacrificing expected value. These preferences can be framed through utility theory. We focus on the specific case of the exponential utility function, where we can derive the Bellman equations and employ various reinforcement learning algorithms with few modifications. However, these methods suffer from numerical instability due to the need for exponent computation throughout the process. To address this, we introduce a numerically stable and mathematically sound loss function based on the Itakura-Saito divergence for learning state-value and action-value functions. We evaluate our proposed loss function against established alternatives, both theoretically and empirically. In the experimental section, we explore multiple financial scenarios, some with known analytical solutions, and show that our loss function outperforms the alternatives.

Scaling laws predict how loss decreases with increases in computation. We show, contrary to conventional wisdom, that architectural interventions can modify scaling exponents in pre-training, leading to power-law improvements in performance as computation increases. As an anchoring point, we consider the architectural formulation of looped transformers. Although not typically used in this way, looping, also known as recursive depth, provides a mechanism for model growth, by increasing the number of loops during training. Model growth, with and without shared weights, provides the biggest changes to the scaling exponents. In particular, a 7.4B model growth architecture matches GPT-3 13B on CORE with roughly 20times less compute, and has compute efficiency gains that increase with scale. Moreover, simply using a boundary operator in a vanilla transformer, which normalizes and injects an earlier block, also provides an exponent increase, although to a lesser extent. In the data-constrained, multi-epoch setting, standard looping has a useful regularizing effect, where we find it is compute-optimal to increase the number of loops with scale. These results can be understood through the lens of computational depth: for a given computational budget, we wish to increase the usable depth of the transformer, which can lead to efficiency gains that increase with scale.

Deep learning (DL) creates impactful advances following a virtuous recipe: model architecture search, creating large training data sets, and scaling computation. It is widely believed that growing training sets and models should improve accuracy and result in better products. As DL application domains grow, we would like a deeper understanding of the relationships between training set size, computational scale, and model accuracy improvements to advance the state-of-the-art. This paper presents a large scale empirical characterization of generalization error and model size growth as training sets grow. We introduce a methodology for this measurement and test four machine learning domains: machine translation, language modeling, image processing, and speech recognition. Our empirical results show power-law generalization error scaling across a breadth of factors, resulting in power-law exponents---the "steepness" of the learning curve---yet to be explained by theoretical work. Further, model improvements only shift the error but do not appear to affect the power-law exponent. We also show that model size scales sublinearly with data size. These scaling relationships have significant implications on deep learning research, practice, and systems. They can assist model debugging, setting accuracy targets, and decisions about data set growth. They can also guide computing system design and underscore the importance of continued computational scaling.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

Self-improving agents are state-of-the-art (SOTA) on agentic coding benchmarks and have recently been extended to general domains. However, their search methods generally assume a stationary evaluation criterion: a fixed verifier, benchmark, or labeled dataset that remains valid as the agent improves. This ignores a central feature of evolution: species adapt as their environments change with them. We aim to bring the same principle to recursive self-improvement, making evaluation part of the improvement loop and opening search to evolving evaluators, adversarial objectives, and dynamic utilities that may surpass static benchmarks. We introduce the Red Queen Godel Machine (RQGM), an evolutionary framework for recursive self-improvement under non-stationary utilities. The RQGM makes this possible through controlled utility evolution: search is organized into epochs with a fixed within-epoch evaluation criterion, while the utility can be updated at epoch boundaries, so self-improvement guarantees hold per epoch as the objective evolves across them. We begin by showing that even on verifiable coding tasks, the RQGM improves test pass rate over the prior SOTA by adding a complementary agent-as-a-judge code-review signal. This signal is cheaper and the RQGM uses 1.35x-1.72x fewer tokens. We then turn to scientific paper writing and reviewing, and Olympiad-level proof writing and grading, where the RQGM improves performance over prior self-improving agents: co-evolved writers reach 1.78x-1.86x higher acceptance rates under a diverse agent-as-a-judge panel, while co-evolved graders reach 9% higher ground-truth accuracy. In paper reviewing, the strongest baseline reviewer over-accepts AI-generated papers at up to 1.91x the human rate. The RQGM corrects this by introducing an adversarial objective that discovers reviewers equally stringent on AI and human work.

Recursive self-improvement requires agents to turn accumulated experience into better future behavior. Personal AI agents offer a concrete setting for studying this capability because they retain preferences, task histories, tool routines, and learned skills across sessions. Yet whether retained experience actually improves them over time has not been systematically tested. We introduce PAST-Bench, a benchmark designed to isolate this question. Each agent runs through ordered sequences of fresh-session tasks under matched conditions that turn retained experience on and off. It spans 26 scenarios and 204 episodes across memory, procedural reuse, information gathering, and update. We report both later-task gains and whether those gains follow the intended save, retrieve, and update pathway. Across seven base models and four agent frameworks, improvement is real but uneven across capabilities. Agents with the same headline gain can differ markedly in whether that gain is supported by evidence of the intended pathway. Guided by these findings, we develop Hermes+, which extends Hermes with five targeted interventions across stages of the agent loop. Hermes+ raises the average gain from retained experience and provides clearer pathway evidence, with its strongest improvement on tasks requiring outdated state to be replaced, although the effect remains capability- and model-dependent. Together, PAST-Bench and Hermes+ provide an evaluation and diagnostic foundation for studying how persistent agents can progress from retaining experience to systematically improving through it. Code: https://github.com/Gen-Verse/PAST-Bench

Building agentic systems that can autonomously self-improve from experience is a longstanding goal of AI. Large language models (LLMs) today primarily self-improve via two mechanisms: self-reflection for context updates, and reinforcement learning (RL) for weight updates. In this work, we propose Evolutionary System Prompt Learning (E-SPL), a method for jointly improving model contexts and model weights. In each RL iteration, E-SPL samples trajectories under multiple system prompts in parallel, then jointly applies RL updates to LLM weights and evolutionary updates to system prompts. System prompts evolve via mutation and crossover, two genetic operators driven by LLM self-reflection; selection is based on relative performance ratings updated across RL iterations. E-SPL encourages a natural division between declarative knowledge encoded in prompts and procedural knowledge encoded in weights, resulting in improved performance across reasoning and agentic tasks. For instance, in an easy-to-hard (AIME rightarrow BeyondAIME) generalization setting, E-SPL improves RL success rate from 38.8% rightarrow 45.1% while also outperforming reflective prompt evolution (40.0%). Overall, our results demonstrate that RL and system prompt evolution are deeply synergistic, and combining the two yields consistent gains in sample efficiency and generalization. Code: https://github.com/LunjunZhang/E-SPL

Efficient differential equation solvers have significantly reduced the sampling time of diffusion models (DMs) while retaining high sampling quality. Among these solvers, exponential integrators (EI) have gained prominence by demonstrating state-of-the-art performance. However, existing high-order EI-based sampling algorithms rely on degenerate EI solvers, resulting in inferior error bounds and reduced accuracy in contrast to the theoretically anticipated results under optimal settings. This situation makes the sampling quality extremely vulnerable to seemingly innocuous design choices such as timestep schedules. For example, an inefficient timestep scheduler might necessitate twice the number of steps to achieve a quality comparable to that obtained through carefully optimized timesteps. To address this issue, we reevaluate the design of high-order differential solvers for DMs. Through a thorough order analysis, we reveal that the degeneration of existing high-order EI solvers can be attributed to the absence of essential order conditions. By reformulating the differential equations in DMs and capitalizing on the theory of exponential integrators, we propose refined EI solvers that fulfill all the order conditions, which we designate as Refined Exponential Solver (RES). Utilizing these improved solvers, RES exhibits more favorable error bounds theoretically and achieves superior sampling efficiency and stability in practical applications. For instance, a simple switch from the single-step DPM-Solver++ to our order-satisfied RES solver when Number of Function Evaluations (NFE) =9, results in a reduction of numerical defects by 25.2% and FID improvement of 25.4% (16.77 vs 12.51) on a pre-trained ImageNet diffusion model.

AI systems built around large models increasingly use experience and feedback to make persistent changes to models, prompts, memories, tools, and workflows. Recursive self-improvement (RSI) extends this process to inductive biases and to the mechanisms that govern future updates, which can themselves be revised and reused across improvement cycles. Yet self-modification alone does not guarantee trustworthy improvement. Reported gains may reflect flawed evaluations, previously acquired capabilities may deteriorate, and compliance with behavioral constraints may weaken. Compromised artifacts or sensitive information may also persist in successor systems. Changes to improvement mechanisms may invalidate earlier verification results and make human oversight less effective. This survey presents an operational definition and process framework for RSI and organizes the requirements for trustworthy RSI into four interconnected themes: genuine and sustained improvement; behavioral constraints, alignment, and fairness; system security and privacy; and transparency and controllability. We examine these themes from three perspectives: Improvement Validity, Constraint Preservation, and Effective Oversight. This analysis covers improvement diagnosis, proposal generation, proposal evaluation, and update implementation (S1--S4), including the recursive application of these stages to improvement mechanisms (RI). We review risks, safeguards, and evaluation evidence for individual updates, effects inherited by successor systems, and revisions to improvement mechanisms, while distinguishing direct RSI findings from evidence in related systems. Finally, we examine evaluation settings, identify requirements for independent and longitudinal assessment, and discuss applications and open research problems.

Optimizing multiple competing black-box objectives is a challenging problem in many fields, including science, engineering, and machine learning. Multi-objective Bayesian optimization (MOBO) is a sample-efficient approach for identifying the optimal trade-offs between the objectives. However, many existing methods perform poorly when the observations are corrupted by noise. We propose a novel acquisition function, NEHVI, that overcomes this important practical limitation by applying a Bayesian treatment to the popular expected hypervolume improvement (EHVI) criterion and integrating over this uncertainty in the Pareto frontier. We argue that, even in the noiseless setting, generating multiple candidates in parallel is an incarnation of EHVI with uncertainty in the Pareto frontier and therefore can be addressed using the same underlying technique. Through this lens, we derive a natural parallel variant, qNEHVI, that reduces computational complexity of parallel EHVI from exponential to polynomial with respect to the batch size. qNEHVI is one-step Bayes-optimal for hypervolume maximization in both noisy and noiseless environments, and we show that it can be optimized effectively with gradient-based methods via sample average approximation. Empirically, we demonstrate not only that qNEHVI is substantially more robust to observation noise than existing MOBO approaches, but also that it achieves state-of-the-art optimization performance and competitive wall-times in large-batch environments.

Prior work in parameter-modifying knowledge editing has shown that large-scale sequential editing leads to significant model degradation. In this paper, we study the reasons behind this and scale sequential knowledge editing to 10,000 sequential edits, while maintaining the downstream performance of the original model. We first show that locate-then-edit knowledge editing methods lead to overfitting on the edited facts. We also show that continuous knowledge editing using these methods leads to disproportionate growth in the norm of the edited matrix. We then provide a crucial insight into the inner workings of locate-then-edit methods. We show that norm-growth is a hidden trick employed by these methods that gives larger importance to the output activations produced from the edited layers. With this "importance hacking", the edited layers provide a much larger contributions to the model's output. To mitigate these issues, we present ENCORE - Early stopping and Norm-Constrained Robust knowledge Editing. ENCORE controls for overfitting and the disproportionate norm-growth to enable long-term sequential editing, where we are able to perform up to 10,000 sequential edits without loss of downstream performance. ENCORE is also 61% faster than MEMIT and 64% faster than AlphaEdit on Llama3-8B.

In [7] Krotov and Hopfield suggest a generalized version of the well-known Hopfield model of associative memory. In their version they consider a polynomial interaction function and claim that this increases the storage capacity of the model. We prove this claim and take the "limit" as the degree of the polynomial becomes infinite, i.e. an exponential interaction function. With this interaction we prove that model has an exponential storage capacity in the number of neurons, yet the basins of attraction are almost as large as in the standard Hopfield model.

We prove new convergence rates for a generalized version of stochastic Nesterov acceleration under interpolation conditions. Unlike previous analyses, our approach accelerates any stochastic gradient method which makes sufficient progress in expectation. The proof, which proceeds using the estimating sequences framework, applies to both convex and strongly convex functions and is easily specialized to accelerated SGD under the strong growth condition. In this special case, our analysis reduces the dependence on the strong growth constant from rho to rho as compared to prior work. This improvement is comparable to a square-root of the condition number in the worst case and address criticism that guarantees for stochastic acceleration could be worse than those for SGD.

This paper considers the problem of combinatorial multi-armed bandits with semi-bandit feedback and a cardinality constraint on the super-arm size. Existing algorithms for solving this problem typically involve two key sub-routines: (1) a parameter estimation routine that sequentially estimates a set of base-arm parameters, and (2) a super-arm selection policy for selecting a subset of base arms deemed optimal based on these parameters. State-of-the-art algorithms assume access to an exact oracle for super-arm selection with unbounded computational power. At each instance, this oracle evaluates a list of score functions, the number of which grows as low as linearly and as high as exponentially with the number of arms. This can be prohibitive in the regime of a large number of arms. This paper introduces a novel realistic alternative to the perfect oracle. This algorithm uses a combination of group-testing for selecting the super arms and quantized Thompson sampling for parameter estimation. Under a general separability assumption on the reward function, the proposed algorithm reduces the complexity of the super-arm-selection oracle to be logarithmic in the number of base arms while achieving the same regret order as the state-of-the-art algorithms that use exact oracles. This translates to at least an exponential reduction in complexity compared to the oracle-based approaches.

Long-horizon agents have drawn growing attention for their ability to work autonomously -- from hours to days -- on economically valuable tasks, a capability essential to automated discovery and recursive self-improvement (RSI). Yet open-source models still struggle on long-horizon tasks, largely for lack of both training data and a working recipe, and scaling both is hard: long, complex tasks are difficult to curate and verify, and their rewards are sparse. We address both. First, we introduce Tev-Gym, the first long-horizon agent training dataset with verifiable, dense, progressive rewards -- 1,170 verified task environments across 7 domains. It is built on a latent-world-first approach that first constructs a latent world: a complete and correct hidden specification of the task domain, workflow, and expected state after each step. Each task is then progressively rendered from this specification into an agent-facing environment, enabling controllable complexity and a natural progress metric. Second, we turn this metric into a training recipe: via progress-potential reward shaping (PPRS), we convert progress into a dense per-step reward that improves training efficiency and makes otherwise-intractable tasks trainable. Training with this recipe yields Tev-27B, which achieves substantial gains on the Agents' Last Exam computing and math sciences domains (ALE-CM), matching GPT-6 Astra and Claude Opus 5 at Pass@5. Despite training only on ALE-related data, it generalizes to the Terminal-Bench (TB) 3.0 and 4.0 subsets, surpassing GLM 5.2 and Gemini 3.7 Flash, and reaches Claude Opus 4.8-level performance on middle-horizon tasks such as TB 2.1.

Large pre-trained, zero-shot capable models have shown considerable success both for standard transfer and adaptation tasks, with particular robustness towards distribution shifts. In addition, subsequent fine-tuning can considerably improve performance on a selected downstream task. However, through naive fine-tuning, these zero-shot models lose their generalizability and robustness towards distribution shifts. This is a particular problem for tasks such as Continual Learning (CL), where continuous adaptation has to be performed as new task distributions are introduced sequentially. In this work, we showcase that where fine-tuning falls short to adapt such zero-shot capable models, simple momentum-based weight interpolation can provide consistent improvements for CL tasks in both memory-free and memory-based settings. In particular, we find improvements of over +4% on standard CL benchmarks, while reducing the error to the upper limit of jointly training on all tasks at once in parts by more than half, allowing the continual learner to inch closer to the joint training limits.

Recent work pairs LLMs with evolutionary search to iteratively generate, modify, and select code using task-specific feedback. These systems have produced strong results in mathematical discovery and algorithm design, yet a fundamental question remains: what do they actually evolve? Progress is typically summarized by the best score a run reaches under a task-specific evaluator, but that score can reflect several different mechanisms: new algorithmic structure, re-tuning an existing strategy, recombining ideas already in the model's internal knowledge, or overfitting to the evaluator. Distinguishing these mechanisms requires inspecting the search process itself, not only its final outcome. We introduce EvoTrace, a dataset of evolutionary coding traces spanning four evolutionary frameworks, reasoning and non-reasoning models, and 16 tasks across mathematics and algorithm design. To analyze these traces, we develop EvoReplay, a replay-based methodology that reconstructs the local search states behind high-scoring solutions and tests controlled interventions, including adjusting constants, removing program components and substituting models or prompting contexts. We annotate every code edit in EvoTrace with one of nine recurring edit types using an LLM-as-judge pipeline validated against blind human re-annotation. Across EvoTrace, most score gains come from a small subset of these edit types. We further find a deterministic cycling pattern: about 30% of code lines added during search are byte-identical re-introductions of previously-deleted lines, present throughout nearly every run. These results show that benchmark gains in evolutionary coding agents can arise from qualitatively different mechanisms, only some of which correspond to new algorithmic structure. EvoTrace enables more diagnostic evaluation of evolutionary coding agents beyond final benchmark scores.

Large language models (LLMs) are increasingly deployed as part of compound AI systems that coordinate multiple modules (e.g., retrievers, tools, verifiers) over long-horizon workflows. Recent approaches that propagate textual feedback globally (e.g., TextGrad) make it feasible to optimize such pipelines, but we find that performance degrades as system depth grows. In particular, long-horizon agentic workflows exhibit two depth-scaling failure modes: 1) exploding textual gradient, where textual feedback grows exponentially with depth, leading to prohibitively long message and amplifies evaluation biases; and 2) vanishing textual gradient, where limited long-context ability causes models overemphasize partial feedback and compression of lengthy feedback causes downstream messages to lose specificity gradually as they propagate many hops upstream. To mitigate these issues, we introduce Textual Equilibrium Propagation (TEP), a local learning principle inspired by Equilibrium Propagation in energy-based models. TEP includes two phases: 1) a free phase where a local LLM critics iteratively refine prompts until reaching equilibrium (no further improvements are suggested); and 2) a nudged phase which applies proximal prompt edits with bounded modification intensity, using task-level objectives that propagate via forward signaling rather than backward feedback chains. This design supports local prompt optimization followed by controlled adaptation toward global goals without the computational burden and signal degradation of global textual backpropagation. Across long-horizon QA benchmarks and multi-agent tool-use dataset, TEP consistently improves accuracy and efficiency over global propagation methods such as TextGrad. The gains grows with depth, while preserving the practicality of black-box LLM components in deep compound AI system.

Continual Instruction Tuning (CIT) is adopted to continually instruct Large Models to follow human intent data by data. It is observed that existing gradient update would heavily destroy the performance on previous datasets during CIT process. Instead, Exponential Moving Average (EMA), owns the ability to trace previous parameters, which can aid in decreasing forgetting. Nonetheless, its stable balance weight fails to deal with the ever-changing datasets, leading to the out-of-balance between plasticity and stability. In this paper, we propose a general continual instruction tuning framework to address the challenge. Starting from the trade-off prerequisite and EMA update, we propose the plasticity and stability ideal condition. Based on Taylor expansion in the loss function, we find the optimal balance weight can be automatically determined by the gradients and learned parameters. Therefore, we propose a stable-plasticity balanced coefficient to avoid knowledge interference. Based on the semantic similarity of the instructions, we can determine whether to retrain or expand the training parameters and allocate the most suitable parameters for the testing instances. Extensive experiments across multiple continual instruction tuning benchmarks demonstrate that our approach not only enhances anti-forgetting capabilities but also significantly improves overall continual tuning performance. Our code is available at https://github.com/JingyangQiao/CoIN.

Scientific and engineering progress is fundamentally a long-horizon iterative process: proposing changes, running experiments, measuring outcomes, and continuously refining artifacts. Yet existing benchmarks for frontier models primarily evaluate either single-turn responses or short-horizon agent trajectories, failing to capture the challenges of sustained iterative improvement over extended time horizons. To address this gap, we introduce AutoLab, a new benchmark for ultra long-horizon closed-loop optimization. AutoLab consists of 36 realistic, expert-curated tasks spanning four diverse domains: system optimization, puzzle & challenge, model development, and CUDA kernel optimization. Each task begins with a correct but deliberately suboptimal baseline and challenges agents to improve it within a strict wall-clock budget. Evaluating 17 state-of-the-art models reveals the dominant predictor of success is not the quality of an agent's initial attempt, but its persistence in repeatedly benchmarking, editing, and incorporating empirical feedback. While claude-opus-4.6 exhibits strong long-horizon optimization capabilities, most frontier models, including several proprietary ones, either terminate prematurely or exhaust their budgets with minimal progress. These results underscore the importance of time awareness and persistent iteration in autonomous agents. We open-source the full benchmark, evaluation harness, and task artifacts, to accelerate research toward truly capable long-horizon agents.

Model editing has emerged as a practical approach for mitigating factual errors and outdated knowledge in large language models (LLMs). Among existing methods, the Locate-and-Edit (L&E) paradigm is the dominant framework: it locates MLP parameters implicated in expressing a target fact, and then performs a localized update to rewrite that fact. However, long sequences of edits often trigger abrupt model collapse in L&E beyond a critical point. We empirically identify a strong correlation between collapse and explosive growth of edited MLP weight norms, and formally prove that commonly used L&E update rules can induce exponential norm growth across sequential edits in the absence of explicit norm control. To address this issue, we propose Norm-Anchor Scaling NAS, a plug-and-play norm-constrained strategy. Across extensive experiments, NAS delays the collapse point of representative L&E algorithms by more than 4 times and yields a 72.2% average relative gain in editing performance, requiring only a single additional line of code and incurring negligible computational overhead.

We study first-order methods for convex optimization problems with functions f satisfying the recently proposed ell-smoothness condition ||nabla^{2}f(x)|| le ellleft(||nabla f(x)||right), which generalizes the L-smoothness and (L_{0},L_{1})-smoothness. While accelerated gradient descent AGD is known to reach the optimal complexity O(L R / varepsilon) under L-smoothness, where varepsilon is an error tolerance and R is the distance between a starting and an optimal point, existing extensions to ell-smoothness either incur extra dependence on the initial gradient, suffer exponential factors in L_{1} R, or require costly auxiliary sub-routines, leaving open whether an AGD-type O(ell(0) R / varepsilon) rate is possible for small-varepsilon, even in the (L_{0},L_{1})-smoothness case. We resolve this open question. Leveraging a new Lyapunov function and designing new algorithms, we achieve O(ell(0) R / varepsilon) oracle complexity for small-varepsilon and virtually any ell. For instance, for (L_{0},L_{1})-smoothness, our bound O(L_0 R / varepsilon) is provably optimal in the small-varepsilon regime and removes all non-constant multiplicative factors present in prior accelerated algorithms.

Language model fine-tuning is essential for modern natural language processing, but is computationally expensive and time-consuming. Further, the effectiveness of fine-tuning is limited by the inclusion of training examples that negatively affect performance. Here we present a general fine-tuning method that we call information gain filtration for improving the overall training efficiency and final performance of language model fine-tuning. We define the information gain of an example as the improvement on a test metric after training on that example. A secondary learner is then trained to approximate this quantity. During fine-tuning, this learner selects informative examples and skips uninformative ones. We show that our method has consistent improvement across datasets, fine-tuning tasks, and language model architectures. For example, we achieve a median perplexity of 54.0 on a books dataset compared to 57.3 for standard fine-tuning. We present statistical evidence that offers insight into the improvements of our method over standard fine-tuning. The generality of our method leads us to propose a new paradigm for language model fine-tuning -- we encourage researchers to release pretrained secondary learners on common corpora to promote efficient and effective fine-tuning, thereby improving the performance and reducing the overall energy footprint of language model fine-tuning.

Self-improving AI systems typically treat the agent as the object that improves, by optimizing prompts, workflows, harnesses, or even the agent's own code. This agent-centric view can make improvements expensive to maintain and difficult to transfer, because gains become tied to a particular agent design, task distribution, or adaptation run. We study a complementary paradigm: knowledge-centric self-improvement, in which agents remain generic and disposable while the persistent object is a curated knowledge base that agents can leverage for future tasks. We conduct controlled case studies to operationalize this idea via a simple protocol. Agents attempt one task, then contribute evidence-grounded insights to a shared knowledge base via task-level and cross-task forums, followed by knowledge distillation. Because self-improvement is contained in the knowledge rather than the agent, improvement can be more inspectable, transferable, and portable. Across abstract reasoning, coding, and terminal benchmarks, this protocol improves solve rates while reducing dollar cost relative to agent-centric baselines. The resulting distilled knowledge also transfers to held-out tasks and across LLM families, indicating that the improvement is not merely an LLM- or run-specific behavior. These results support a new view of self-improving agentic systems: progress can be driven primarily by the curated persistent knowledge. Code is available at https://github.com/recursive-knowledge/KSI.

Knowledge Distillation (KD) has proven effective for compressing large teacher models into smaller student models. While it is well known that student models can achieve similar accuracies as the teachers, it has also been shown that they nonetheless often do not learn the same function. It is, however, often highly desirable that the student's and teacher's functions share similar properties such as basing the prediction on the same input features, as this ensures that students learn the 'right features' from the teachers. In this work, we explore whether this can be achieved by not only optimizing the classic KD loss but also the similarity of the explanations generated by the teacher and the student. Despite the idea being simple and intuitive, we find that our proposed 'explanation-enhanced' KD (e^2KD) (1) consistently provides large gains in terms of accuracy and student-teacher agreement, (2) ensures that the student learns from the teacher to be right for the right reasons and to give similar explanations, and (3) is robust with respect to the model architectures, the amount of training data, and even works with 'approximate', pre-computed explanations.

We introduce a simple modification to the embedding layer. The key change is to infuse token embeddings with information about their spelling. Models trained with these embeddings improve not only on spelling, but also across standard benchmarks. We conduct scaling studies for models with 40M to 800M parameters, which suggest that the improvements are equivalent to needing about 8% less compute and data to achieve the same test loss.

Advances in the coding capabilities of LLM agents allow them to inspect and modify their own instructions, tools, and execution procedures. Existing approaches use this ability to search for improved agents through repeated downstream evaluation, which incurs substantial costs and ties the search to the evaluated tasks. We introduce SelfSearch, a reward-free search procedure in which agents modify themselves using records of previous self-improvement episodes. These records capture the reasoning, tool actions, and outcomes of earlier modification attempts, providing concrete experience for improving both task solving and self-modification. Without downstream reward signals during search, SelfSearch improves population-mean success over the initial agent in all six model--benchmark settings, with individual agents gaining up to 11.2 percentage points on Terminal-Bench 2.1. On SWE-bench Multilingual, an agent improves success by 5.0 percentage points while reducing execution cost by 38.5\% on tasks solved by both the initial and evolved agents. SelfSearch achieves competitive task success with evaluation-guided search baselines at lower search cost. With only \$4.03 in search cost, it produces a harness that solves 82.0\% of Terminal-Bench 2.1 tasks with DeepSeek V4 Flash under the settings of a public nine-harness comparison, matching the top-scoring harness, Codex. These results suggest that experience gained through self-modification can improve agents' downstream capabilities and efficiency.

Interest in neural machine translation has grown rapidly as its effectiveness has been demonstrated across language and data scenarios. New research regularly introduces architectural and algorithmic improvements that lead to significant gains over "vanilla" NMT implementations. However, these new techniques are rarely evaluated in the context of previously published techniques, specifically those that are widely used in state-of-theart production and shared-task systems. As a result, it is often difficult to determine whether improvements from research will carry over to systems deployed for real-world use. In this work, we recommend three specific methods that are relatively easy to implement and result in much stronger experimental systems. Beyond reporting significantly higher BLEU scores, we conduct an in-depth analysis of where improvements originate and what inherent weaknesses of basic NMT models are being addressed. We then compare the relative gains afforded by several other techniques proposed in the literature when starting with vanilla systems versus our stronger baselines, showing that experimental conclusions may change depending on the baseline chosen. This indicates that choosing a strong baseline is crucial for reporting reliable experimental results.

In this work, we investigate the application of Taylor expansions in reinforcement learning. In particular, we propose Taylor expansion policy optimization, a policy optimization formalism that generalizes prior work (e.g., TRPO) as a first-order special case. We also show that Taylor expansions intimately relate to off-policy evaluation. Finally, we show that this new formulation entails modifications which improve the performance of several state-of-the-art distributed algorithms.

Machine learning is increasingly used to guide branch-and-cut (B&C) for mixed-integer linear programming by learning score-based policies for selecting branching variables and cutting planes. Many approaches train on local signals from lookahead heuristics such as strong branching, and linear programming (LP) bound improvement for cut selection. Training and evaluation of the learned models often focus on local score accuracy. We show that such local score-based methods can lead to search trees exponentially larger than optimal tree sizes, by identifying two sources of this gap. The first is that these widely used expert signals can be misaligned with overall tree size. LP bound improvement can select a root cut set that yields an exponentially larger strong branching tree than selecting cuts by a simple proxy score, and strong branching itself can be exponentially suboptimal (Dey et al., 2024). The second is that small discrepancies can be amplified by the branch-and-bound recursion. An arbitrarily small perturbation of the right-hand sides in a root cut set can change the minimum tree size from a single node to exponentially many. For branching, arbitrarily small score discrepancies, and differences only in tie-breaking, can produce trees of exponentially different sizes, and even a small number of decision differences along a trajectory can incur exponential growth. These results show that branch-and-cut policies trained and learned using local expert scores do not guarantee small trees, thus motivating the study of data-driven methods that produce policies better aligned with tree size rather than only accuracy on expert scores.

We study reinforcement learning for global decision-making in the presence of many local agents, where the global decision-maker makes decisions affecting all local agents, and the objective is to learn a policy that maximizes the rewards of both the global and the local agents. Such problems find many applications, e.g. demand response, EV charging, queueing, etc. In this setting, scalability has been a long-standing challenge due to the size of the state/action space which can be exponential in the number of agents. This work proposes the SUB-SAMPLE-Q algorithm where the global agent subsamples kleq n local agents to compute an optimal policy in time that is only exponential in k, providing an exponential speedup from standard methods that are exponential in n. We show that the learned policy converges to the optimal policy in the order of O(1/k+epsilon_{k,m}) as the number of sub-sampled agents k increases, where epsilon_{k,m} is the Bellman noise. We also conduct numerical simulations in a demand-response setting and a queueing setting.

Black box optimisation of an unknown function from expensive and noisy evaluations is a ubiquitous problem in machine learning, academic research and industrial production. An abstraction of the problem can be formulated as a kernel based bandit problem (also known as Bayesian optimisation), where a learner aims at optimising a kernelized function through sequential noisy observations. The existing work predominantly assumes feedback is immediately available; an assumption which fails in many real world situations, including recommendation systems, clinical trials and hyperparameter tuning. We consider a kernel bandit problem under stochastically delayed feedback, and propose an algorithm with mathcal{O}(Gamma_k(T)T+E[tau]) regret, where T is the number of time steps, Gamma_k(T) is the maximum information gain of the kernel with T observations, and tau is the delay random variable. This represents a significant improvement over the state of the art regret bound of mathcal{O}(Gamma_k(T)T+E[tau]Gamma_k(T)) reported in Verma et al. (2022). In particular, for very non-smooth kernels, the information gain grows almost linearly in time, trivializing the existing results. We also validate our theoretical results with simulations.

Recent studies operationalize self-improvement through coding agents that edit their own codebases. They grow a tree of self-modifications through expansion strategies that favor higher software engineering benchmark performance, assuming that this implies more promising subsequent self-modifications. However, we identify a mismatch between the agent's self-improvement potential (metaproductivity) and its coding benchmark performance, namely the Metaproductivity-Performance Mismatch. Inspired by Huxley's concept of clade, we propose a metric (CMP) that aggregates the benchmark performances of the descendants of an agent as an indicator of its potential for self-improvement. We show that, in our self-improving coding agent development setting, access to the true CMP is sufficient to simulate how the G\"odel Machine would behave under certain assumptions. We introduce the Huxley-G\"odel Machine (HGM), which, by estimating CMP and using it as guidance, searches the tree of self-modifications. On SWE-bench Verified and Polyglot, HGM outperforms prior self-improving coding agent development methods while using less wall-clock time. Last but not least, HGM demonstrates strong transfer to other coding datasets and large language models. The agent optimized by HGM on SWE-bench Verified with GPT-5-mini and evaluated on SWE-bench Lite with GPT-5 achieves human-level performance, matching the best officially checked results of human-engineered coding agents. Our code is available at https://github.com/metauto-ai/HGM.

This article deals with the following fractional (p,q)-Choquard equation with exponential growth of the form: $varepsilon^{ps}(-Delta)_{p}^{s}u+varepsilon^{qs}(-Delta)_q^su+ Z(x)(|u|^{p-2}u+|u|^{q-2}u)=varepsilon^{mu-N}[|x|^{-mu}*F(u)]f(u) in R^N, where s\in (0,1), \varepsilon>0 is a parameter, 2\leq p=N{s}<q, and 0<\mu<N. The nonlinear function f has an exponential growth at infinity and the continuous potential function Z satisfies suitable natural conditions. With the help of the Ljusternik-Schnirelmann category theory and variational methods, the multiplicity and concentration of positive solutions are obtained for \varepsilon>0$ small enough. In a certain sense, we generalize some previously known results.

A language-model agent is jointly defined by its model and its harness, the executable program that organizes model calls, tool use, and information flow. Because different tasks call for different ways of organizing these operations, the harness needs to be adapted using feedback from the task at hand. We introduce harness learning, which trains a proposer model to revise a solver's harness using execution feedback. We formulate this process as meta-learning over executable programs, with harness revisions playing the role of weight updates in gradient-based adaptation. We train the proposer with reinforcement learning, using the task performance of revised harnesses as the reward. At test time, the proposer uses feedback from successive executions on a new task to refine the harness, without performing any parameter-space update. Experiments on reasoning and multi-hop question answering show that harness learning improves revision quality and that the ability to adapt at test time transfers to unseen tasks. Policies trained on individual revisions can continue improving harnesses over multiple rounds, while the benefits of training on revision sequences vary across settings. These findings suggest a path towards continually learning agents that turn accumulated experience into generalizable improvements.

Code efficiency is a fundamental aspect of software quality, yet how to harness large language models (LLMs) to optimize programs remains challenging. Prior approaches have sought for one-shot rewriting, retrieved exemplars, or prompt-based search, but they do not explicitly distill reusable optimization knowledge, which limits generalization beyond individual instances. In this paper, we present EffiSkill, a framework for code-efficiency optimization that builds a portable optimization toolbox for LLM-based agents. The key idea is to model recurring slow-to-fast transformations as reusable agent skills that capture both concrete transformation mechanisms and higher-level optimization strategies. EffiSkill adopts a two-stage design: Stage I mines Operator and Meta Skills from large-scale slow/fast program pairs to build a skill library; Stage II applies this library to unseen programs through execution-free diagnosis, skill retrieval, plan composition, and candidate generation, without runtime feedback. Results on EffiBench-X show that EffiSkill achieves higher optimization success rates, improving over the strongest baseline by 3.69 to 12.52 percentage points across model and language settings. These findings suggest that mechanism-level skill reuse provides a useful foundation for execution-free code optimization, and that the resulting skill library can serve as a reusable resource for broader agent workflows.

Self-improvement methods enable large language models (LLMs) to generate solutions themselves and iteratively train on filtered, high-quality rationales. This process proves effective and reduces the reliance on human supervision in LLMs' reasoning, but the performance soon plateaus. We delve into the process and find that models tend to over-sample on easy queries and under-sample on queries they have yet to master. As iterations proceed, this imbalance in sampling is exacerbated, leading to a long-tail distribution where solutions to difficult queries almost diminish. This phenomenon limits the performance gain of self-improving models. A straightforward solution is brute-force sampling to balance the distribution, which significantly raises computational costs. In this paper, we introduce Guided Self-Improvement (GSI), a strategy aimed at improving the efficiency of sampling challenging heavy-tailed data. It leverages Socratic-style guidance signals to help LLM reasoning with complex queries, reducing the exploration effort and minimizing computational overhead. Experiments on four models across diverse mathematical tasks show that GSI strikes a balance between performance and efficiency, while also being effective on held-out tasks.

We investigate the extent to which offline demonstration data can improve online learning. It is natural to expect some improvement, but the question is how, and by how much? We show that the degree of improvement must depend on the quality of the demonstration data. To generate portable insights, we focus on Thompson sampling (TS) applied to a multi-armed bandit as a prototypical online learning algorithm and model. The demonstration data is generated by an expert with a given competence level, a notion we introduce. We propose an informed TS algorithm that utilizes the demonstration data in a coherent way through Bayes' rule and derive a prior-dependent Bayesian regret bound. This offers insight into how pretraining can greatly improve online performance and how the degree of improvement increases with the expert's competence level. We also develop a practical, approximate informed TS algorithm through Bayesian bootstrapping and show substantial empirical regret reduction through experiments.

Recent advances in large language models (LLMs) have improved their performance on coding benchmarks. However, improvement is plateauing due to the exhaustion of readily available high-quality data. Prior work has shown the potential of synthetic self-instruct data, but naively training on a model's own outputs can cause error accumulation, especially in coding tasks, where generalization may collapse due to overly simple or erroneous training data, highlighting the need for rigorous quality checks on synthetic data. In this work, we explore an effective approach whereby the model itself verifies the correctness of its own data. We thus propose Sol-Ver, a self-play solver-verifier framework that jointly improves a single model's code and test generation capacity. By iteratively refining code (LLM-as-a-solver) and tests (LLM-as-a-verifier) together, we boost both capabilities without relying on human annotations or larger teacher models. Experiments with the Llama 3.1 8B model demonstrate substantial performance enhancements, achieving average relative improvements of 19.63% in code generation and 17.49% in test generation on MBPP and LiveCodeBench.

Convolutional Neural Networks (CNN) have gained great success in many artificial intelligence tasks. However, finding a good set of hyperparameters for a CNN remains a challenging task. It usually takes an expert with deep knowledge, and trials and errors. Genetic algorithms have been used in hyperparameter optimizations. However, traditional genetic algorithms with fixed-length chromosomes may not be a good fit for optimizing deep learning hyperparameters, because deep learning models have variable number of hyperparameters depending on the model depth. As the depth increases, the number of hyperparameters grows exponentially, and searching becomes exponentially harder. It is important to have an efficient algorithm that can find a good model in reasonable time. In this article, we propose to use a variable length genetic algorithm (GA) to systematically and automatically tune the hyperparameters of a CNN to improve its performance. Experimental results show that our algorithm can find good CNN hyperparameters efficiently. It is clear from our experiments that if more time is spent on optimizing the hyperparameters, better results could be achieved. Theoretically, if we had unlimited time and CPU power, we could find the optimized hyperparameters and achieve the best results in the future.

Harness optimization provides a practical setting for recursive self-improvement (RSI), where agent-generated modifications inform subsequent changes through execution feedback. Recent work such as Meta-Harness implements this process through iterative code generation and evaluation, but retains a fixed development set and proposal policy. These constraints channel evolution along a single search trajectory, increasing the risk of converging to a local optimum. We make the improvement process itself adaptive by organizing search into branches with evolving development subsets and proposal policies. Each branch retains development cases solved by more of its leading harnesses than by those of other branches, drops cases solved by every leading harness across all branches, and revises its proposal policy using its own search history. To deploy the resulting complementary harnesses, we propose a router to select one development-selected branch head for each new input before execution. Across mathematical reasoning and agentic coding benchmarks, our system achieves relative improvements over Meta-Harness of 34.8% on Olympiad-level mathematical reasoning, 11.6% on Terminal-Bench 2.0, and 3.8% on SWE-bench Lite, with harness selection and router configuration based solely on development data. These results show that evolving branch objectives and proposal policies can yield complementary harnesses whose strengths a router combines without access to test outcomes.

In many real-world applications, deep neural networks are retrained from scratch as a dataset grows in size. Given the computational expense for retraining networks, it has been argued that continual learning could make updating networks more efficient. An obstacle to achieving this goal is the stability gap, which refers to an observation that when updating on new data, performance on previously learned data degrades before recovering. Addressing this problem would enable learning new data with fewer network updates, resulting in increased computational efficiency. We study how to mitigate the stability gap. We test a variety of hypotheses to understand why the stability gap occurs. This leads us to discover a method that vastly reduces this gap. In large-scale class incremental learning experiments, we are able to significantly reduce the number of network updates needed for continual learning. Our work has the potential to advance the state-of-the-art in continual learning for real-world applications along with reducing the carbon footprint required to maintain updated neural networks.

We study the problem of black-box optimization of a function f of any dimension, given function evaluations perturbed by noise. The function is assumed to be locally smooth around one of its global optima, but this smoothness is unknown. Our contribution is an adaptive optimization algorithm, POO or parallel optimistic optimization, that is able to deal with this setting. POO performs almost as well as the best known algorithms requiring the knowledge of the smoothness. Furthermore, POO works for a larger class of functions than what was previously considered, especially for functions that are difficult to optimize, in a very precise sense. We provide a finite-time analysis of POO's performance, which shows that its error after n evaluations is at most a factor of sqrt(ln n) away from the error of the best known optimization algorithms using the knowledge of the smoothness.

Large Language Models (LLMs) can self-improve through reinforcement learning, where they generate trajectories to explore and discover better solutions. However, this exploration process is computationally expensive, often forcing current methods to assign limited exploration budgets to each task. This uniform allocation creates problematic edge cases: easy tasks consistently succeed while difficult tasks consistently fail, both producing zero gradients during training updates for the widely used Group Relative Policy Optimization (GRPO). We address this problem from the lens of exploration budget allocation. Viewing each task's exploration as an "item" with a distinct "value" and "cost", we establish a connection to the classical knapsack problem. This formulation allows us to derive an optimal assignment rule that adaptively distributes resources based on the model's current learning status. When applied to GRPO, our method increases the effective ratio of non-zero policy gradients by 20-40% during training. Acting as a computational "free lunch", our approach could reallocate exploration budgets from tasks where learning is saturated to those where it is most impactful. This enables significantly larger budgets (e.g., 93 rollouts) for especially challenging problems, which would be computationally prohibitive under a uniform allocation. These improvements translate to meaningful gains on mathematical reasoning benchmarks, with average improvements of 2-4 points and peak gains of 9 points on specific tasks. Notably, achieving comparable performance with traditional homogeneous allocation would require about 2x the computational resources.

You are a robot and you live in a Markov decision process (MDP) with a finite or an infinite number of transitions from state-action to next states. You got brains and so you plan before you act. Luckily, your roboparents equipped you with a generative model to do some Monte-Carlo planning. The world is waiting for you and you have no time to waste. You want your planning to be efficient. Sample-efficient. Indeed, you want to exploit the possible structure of the MDP by exploring only a subset of states reachable by following near-optimal policies. You want guarantees on sample complexity that depend on a measure of the quantity of near-optimal states. You want something, that is an extension of Monte-Carlo sampling (for estimating an expectation) to problems that alternate maximization (over actions) and expectation (over next states). But you do not want to StOP with exponential running time, you want something simple to implement and computationally efficient. You want it all and you want it now. You want TrailBlazer.

Although large language models (LLMs) have been largely successful in generating functionally correct programs, conditioning models to produce efficient solutions while ensuring correctness remains a challenge. Further, unreliability in benchmarking code efficiency is a hurdle across varying hardware specifications for popular interpreted languages such as Python. In this paper, we present ECCO, a reproducible benchmark for evaluating program efficiency via two paradigms: natural language (NL) based code generation and history-based code editing. On ECCO, we adapt and thoroughly investigate the three most promising existing LLM-based approaches: in-context learning, iterative refinement with execution or NL feedback, and fine-tuning conditioned on execution and editing history. While most methods degrade functional correctness and moderately increase program efficiency, we find that adding execution information often helps maintain functional correctness, and NL feedback enhances more on efficiency. We release our benchmark to support future work on LLM-based generation of efficient code.

Iterative improvement of model architectures is fundamental to deep learning: Transformers first enabled scaling, and recent advances in model hybridization have pushed the quality-efficiency frontier. However, optimizing architectures remains challenging and expensive. Current automated or manual approaches fall short, largely due to limited progress in the design of search spaces and due to the simplicity of resulting patterns and heuristics. In this work, we propose a new approach for the synthesis of tailored architectures (STAR). Our approach combines a novel search space based on the theory of linear input-varying systems, supporting a hierarchical numerical encoding into architecture genomes. STAR genomes are automatically refined and recombined with gradient-free, evolutionary algorithms to optimize for multiple model quality and efficiency metrics. Using STAR, we optimize large populations of new architectures, leveraging diverse computational units and interconnection patterns, improving over highly-optimized Transformers and striped hybrid models on the frontier of quality, parameter size, and inference cache for autoregressive language modeling.

Recent work has explored improving agents by jointly evolving their harnesses and models, but often takes a ''potpourri'' approach that bundles together new tools, new decision-making procedures, and model adaptation to the evolved harness under a single notion of agent improvement. In this paper, we instead investigate how agents can improve their decision-making procedures. In particular, we propose EvoIn, an agent fine-tuning framework that bridges evolution and internalization. EvoIn first analyzes agent execution traces to evolve and validate new decision-making procedures by temporarily instantiating them in the harness. The validated procedures guide the agent to generate improved reasoning traces. These traces are then rewritten into self-contained reasoning traces, removing explicit references to harness instructions while expressing the induced decision logic as the model's own reasoning. Finally, EvoIn fine-tunes the model on the rewritten traces, internalizing these procedures so that the improved decision-making persists without the evolved harness at inference time. We evaluate EvoIn on diverse benchmarks and find that it consistently enables agents to learn stronger decision-making procedures, raising the pass rate by 10.9 points in-domain and by 9.2 points out-of-domain. Results further show that the internalized decision procedures generalize to unseen tasks. Case studies show that agents can learn to decide how to solve a task before solving it, for example by checking a document's length to choose between reading it in full and searching it. EvoIn is also broadly applicable, showing consistent improvements on another model family.

With the advent of large language models (LLMs) like GPT-3, a natural question is the extent to which these models can be utilized for source code optimization. This paper presents methodologically stringent case studies applied to well-known open source python libraries pillow and numpy. We find that contemporary LLM ChatGPT-4 (state September and October 2023) is surprisingly adept at optimizing energy and compute efficiency. However, this is only the case in interactive use, with a human expert in the loop. Aware of experimenter bias, we document our qualitative approach in detail, and provide transcript and source code. We start by providing a detailed description of our approach in conversing with the LLM to optimize the _getextrema function in the pillow library, and a quantitative evaluation of the performance improvement. To demonstrate qualitative replicability, we report further attempts on another locus in the pillow library, and one code locus in the numpy library, to demonstrate generalization within and beyond a library. In all attempts, the performance improvement is significant (factor up to 38). We have also not omitted reporting of failed attempts (there were none). We conclude that LLMs are a promising tool for code optimization in open source libraries, but that the human expert in the loop is essential for success. Nonetheless, we were surprised by how few iterations were required to achieve substantial performance improvements that were not obvious to the expert in the loop. We would like bring attention to the qualitative nature of this study, more robust quantitative studies would need to introduce a layer of selecting experts in a representative sample -- we invite the community to collaborate.

The scientific scale-up of large language models (LLMs) necessitates a comprehensive understanding of their scaling properties. However, the existing literature on the scaling properties only yields an incomplete answer: optimization loss decreases predictably as the model size increases, in line with established scaling law; yet no scaling law for task has been established and the task performances are far from predictable during scaling. Task performances typically show minor gains on small models until they improve dramatically once models exceed a size threshold, exemplifying the ``emergent abilities''. In this study, we discover that small models, although they exhibit minor performance, demonstrate critical and consistent task performance improvements that are not captured by conventional evaluation strategies due to insufficient measurement resolution. To measure such improvements, we introduce PassUntil, an evaluation strategy through massive sampling in the decoding phase. We conduct quantitative investigations into the scaling law of task performance. Firstly, a strict task scaling law is identified, enhancing the predictability of task performances. Remarkably, we are able to predict the performance of the 2.4B model on code generation with merely 0.05\% deviation before training starts. Secondly, underpinned by PassUntil, we observe concrete evidence of emergent abilities and ascertain that they are not in conflict with the continuity of performance improvement. Their semblance to break-through is that their scaling curve cannot be fitted by standard scaling law function. We then introduce a mathematical definition for the emergent abilities. Through the definition, we refute a prevalent ``multi-step reasoning hypothesis'' regarding the genesis of emergent abilities and propose a new hypothesis with a satisfying fit to the observed scaling curve.

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a (delta,epsilon)-stationary point from O(epsilon^{-4}delta^{-1}) stochastic gradient queries to O(epsilon^{-3}delta^{-1}), which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to online learning, after which our results follow from standard regret bounds in online learning. For deterministic and second-order smooth objectives, applying more advanced optimistic online learning techniques enables a new complexity of O(epsilon^{-1.5}delta^{-0.5}). Our techniques also recover all optimal or best-known results for finding epsilon stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings.

Harness evolution automatically optimizes the prompts, skills, tools, and orchestration code around a fixed-weight model, offering a way to improve agentic systems without updating model weights. The agent harness is iteratively optimized to achieve higher performance on the search set. But how much of this gain reflects benchmark-specific overfitting or additional inference-time compute, and how much may generalize beyond the search set? In this work, we introduce Harness-Delta Attribution (HDA), an evaluation protocol that dissects an evolution gain into artifact-driven overfitting, gains explained by test-time scaling, and the remainder, which gives an upper bound on residual generalizable improvement. We apply HDA to 11 executor models and three harness-evolution frameworks across math, coding, creativity, and agentic tasks. In 21 of these settings that show statistically significant search-set gains, we find that a large share of the improvement is explained by overfitting or test-time scaling. Specifically, among these 21 settings, overfitting and test-time scaling account for 54% and 14% of the gain on average; their combined share exceeds 50% in 14 settings. The residual and held-out transfer vary substantially across tasks, models, and frameworks. Importantly, search-set gains often fail to transfer to held-out tasks, and provide limited evidence that they will persist under practical distribution shifts. Moreover, validation-based signals are insufficient to prevent overfitting. These results motivate attribution-aware evaluation in future harness evolution research.

Post-training has become the dominant recipe for turning a language model into a competent search-augmented reasoning agent. A line of recent work pushes its performance further by adding elaborate machinery on top of this standard pipeline. These augmentations import external supervision from stronger external systems, attach auxiliary modules such as process reward models or retrospective critics, restructure the rollout itself with tree search or multi-stage curricula, or shape the reward with hand-crafted bonuses and penalties. Each addition delivers a measurable gain, but each also inflates the training pipeline and ties the recipe to resources or designs that may not always be available. We take a step back and ask whether any of this machinery is actually necessary, and propose Search-E1, a self-evolution method that lets a search-augmented agent improve through only vanilla GRPO interleaved with on-policy self-distillation (OPSD). After each GRPO round, the policy rolls out on its own training questions. A token-level forward KL objective then aligns the policy's inference-time distribution to its own distribution under a privileged context that exposes a more efficient sibling trajectory. Despite this simplicity, the procedure naturally provides dense per-step supervision. On seven QA benchmarks, Search-E1 reaches 0.440 average EM with Qwen2.5-3B, surpassing all open-source baselines at both scales. Code and complete version will be made public soon.

Recent advances in large language models (LLMs) have enabled breakthroughs in mathematical discovery, exemplified by AlphaEvolve, a closed-source system that evolves programs to improve bounds on open problems. However, it relies on ensembles of frontier LLMs to achieve new bounds and is a pure inference system that models cannot internalize the evolving strategies. We introduce ThetaEvolve, an open-source framework that simplifies and extends AlphaEvolve to efficiently scale both in-context learning and Reinforcement Learning (RL) at test time, allowing models to continually learn from their experiences in improving open optimization problems. ThetaEvolve features a single LLM, a large program database for enhanced exploration, batch sampling for higher throughput, lazy penalties to discourage stagnant outputs, and optional reward shaping for stable training signals, etc. ThetaEvolve is the first evolving framework that enable a small open-source model, like DeepSeek-R1-0528-Qwen3-8B, to achieve new best-known bounds on open problems (circle packing and first auto-correlation inequality) mentioned in AlphaEvolve. Besides, across two models and four open tasks, we find that ThetaEvolve with RL at test-time consistently outperforms inference-only baselines, and the model indeed learns evolving capabilities, as the RL-trained checkpoints demonstrate faster progress and better final performance on both trained target task and other unseen tasks. We release our code publicly: https://github.com/ypwang61/ThetaEvolve

We introduce Post-Optimization Model Edit (POME), a new algorithm that enhances the performance of fine-tuned large language models using only their pretrained and fine-tuned checkpoints, without requiring extra data or further optimization. The core idea is to apply a muon-style projection to ΔW, the difference between the fine-tuned and pretrained weights. This projection uses truncated singular value decomposition (SVD) to equalize the influence of dominant update directions and prune small singular values, which often represent noise. As a simple post-processing step, POME is completely decoupled from the training pipeline. It requires zero modifications and imposes no overhead, making it universally compatible with any optimizer or distributed framework. POME delivers consistent gains, boosting average performance by +2.5\% on GSM8K and +1.0\% on code generation. Its broad applicability -- from 7B foundation models to 72B RLHF-instructed models -- establishes it as a practical, zero-cost enhancement for any fine-tuning pipeline. Code is available at https://github.com/NUS-HPC-AI-Lab/POME.

Diffusion models currently dominate the field of data-driven image synthesis with their unparalleled scaling to large datasets. In this paper, we identify and rectify several causes for uneven and ineffective training in the popular ADM diffusion model architecture, without altering its high-level structure. Observing uncontrolled magnitude changes and imbalances in both the network activations and weights over the course of training, we redesign the network layers to preserve activation, weight, and update magnitudes on expectation. We find that systematic application of this philosophy eliminates the observed drifts and imbalances, resulting in considerably better networks at equal computational complexity. Our modifications improve the previous record FID of 2.41 in ImageNet-512 synthesis to 1.81, achieved using fast deterministic sampling. As an independent contribution, we present a method for setting the exponential moving average (EMA) parameters post-hoc, i.e., after completing the training run. This allows precise tuning of EMA length without the cost of performing several training runs, and reveals its surprising interactions with network architecture, training time, and guidance.

Long-horizon agent runs generate experience that can improve both the current run and future work. Most self-improvement methods process this experience only after execution ends, so they cannot redirect the active run or immediately apply and validate lessons learned from it. We argue that self-improvement should instead be live, using emerging experience both to redirect the active run and to update the persistent harness. Existing agent architectures do not fully support this goal. Single-agent self-correction combines task execution and trajectory assessment within one context, while subagent delegation separates execution but typically cannot redirect an active subagent. We present PILOT, a supervisor-worker harness for live self-improvement through two coupled mechanisms: (1) live steering lets a separate supervisor redirect or abort the active worker during execution; and (2) live self-evolution distils procedures and failure modes revealed during execution into reusable skills and memory. Across two frozen backbones and three benchmarks, PILOT ranks first in five of six configurations. On Terminal-Bench 2.0, PILOT outperforms counterpart harnesses by up to 9.8 percentage points. In the self-improvement setting, PILOT gains 14.6 points with GLM-5.1 and 12.4 points with Kimi-K2.6. Mean output tokens fall by 42.9% and 47.4%, while successful evaluations per million output tokens rise by 110.3% and 134.0%, respectively.

AI is increasingly used in the R\&D process that produces future AI systems. We study the conditions under which this feedback becomes self-amplifying. Our model describes how the rate of AI capability growth depends on baseline research productivity, recursive feedback, and the increasing difficulty of research progress. We derive a recursive reproduction number, R_{AI}, that determines whether improvements are amplified or damped across development cycles. This quantity compares the strength of feedback with the rate at which further progress becomes more difficult. When R_{AI}>1, the effects of improvements compound across development cycles, placing the system in a self-amplifying regime. When R_{AI}<1, their effects weaken across cycles. The transition depends on the structure of the AI R\&D feedback loop and need not occur at any particular level of model capability. A system can therefore enter a self-amplifying regime before acceleration becomes visible, while rapid progress can also occur without self-amplification. Higher baseline research productivity can accelerate progress without changing whether the system is self-amplifying, but the duration of the development cycle becomes a limiting timescale for amplification. Increasing research difficulty can end a period of self-amplification. Extending the model to multiple research actors shows that improvements shared across organizations can make the overall research ecosystem self-amplifying even when no individual actor is. The framework identifies measurable properties of AI R\&D systems that can help distinguish recursive amplification from rapid progress driven by other sources, including the strength of recursive feedback, how effectively improvements propagate into successor systems, cycle duration, and the increasing difficulty of further progress.

Exponential moving average (EMA) has recently gained significant popularity in training modern deep learning models, especially diffusion-based generative models. However, there have been few theoretical results explaining the effectiveness of EMA. In this paper, to better understand EMA, we establish the risk bound of online SGD with EMA for high-dimensional linear regression, one of the simplest overparameterized learning tasks that shares similarities with neural networks. Our results indicate that (i) the variance error of SGD with EMA is always smaller than that of SGD without averaging, and (ii) unlike SGD with iterate averaging from the beginning, the bias error of SGD with EMA decays exponentially in every eigen-subspace of the data covariance matrix. Additionally, we develop proof techniques applicable to the analysis of a broad class of averaging schemes.

We study compute efficiency of LLM training when using different parameterizations, i.e., rules for adjusting model and optimizer hyperparameters (HPs) as model size changes. Some parameterizations fail to transfer optimal base HPs (such as learning rate) across changes in model depth, requiring practitioners to either re-tune these HPs as they scale up (expensive), or accept sub-optimal training when re-tuning is prohibitive. Even when they achieve HP transfer, we develop theory to show parameterizations may still exist in the lazy learning regime where layers learn only features close to their linearization, preventing effective use of depth and nonlinearity. Finally, we identify and adopt the parameterization we call CompleteP that achieves both depth-wise HP transfer and non-lazy learning in all layers. CompleteP enables a wider range of model width/depth ratios to remain compute-efficient, unlocking shapes better suited for different hardware settings and operational contexts. Moreover, CompleteP enables 12-34% compute efficiency improvements over the prior state-of-the-art.

Recent advancements in diffusion-based generative image editing have sparked a profound revolution, reshaping the landscape of image outpainting and inpainting tasks. Despite these strides, the field grapples with inherent challenges, including: i) inferior quality; ii) poor consistency; iii) insufficient instrcution adherence; iv) suboptimal generation efficiency. To address these obstacles, we present ByteEdit, an innovative feedback learning framework meticulously designed to Boost, Comply, and Accelerate Generative Image Editing tasks. ByteEdit seamlessly integrates image reward models dedicated to enhancing aesthetics and image-text alignment, while also introducing a dense, pixel-level reward model tailored to foster coherence in the output. Furthermore, we propose a pioneering adversarial and progressive feedback learning strategy to expedite the model's inference speed. Through extensive large-scale user evaluations, we demonstrate that ByteEdit surpasses leading generative image editing products, including Adobe, Canva, and MeiTu, in both generation quality and consistency. ByteEdit-Outpainting exhibits a remarkable enhancement of 388% and 135% in quality and consistency, respectively, when compared to the baseline model. Experiments also verfied that our acceleration models maintains excellent performance results in terms of quality and consistency.

We present EGN, a stochastic second-order optimization algorithm that combines the generalized Gauss-Newton (GN) Hessian approximation with low-rank linear algebra to compute the descent direction. Leveraging the Duncan-Guttman matrix identity, the parameter update is obtained by factorizing a matrix which has the size of the mini-batch. This is particularly advantageous for large-scale machine learning problems where the dimension of the neural network parameter vector is several orders of magnitude larger than the batch size. Additionally, we show how improvements such as line search, adaptive regularization, and momentum can be seamlessly added to EGN to further accelerate the algorithm. Moreover, under mild assumptions, we prove that our algorithm converges to an epsilon-stationary point at a linear rate. Finally, our numerical experiments demonstrate that EGN consistently exceeds, or at most matches the generalization performance of well-tuned SGD, Adam, and SGN optimizers across various supervised and reinforcement learning tasks.

Recent text-to-image (T2I) diffusion models achieve remarkable realism, yet faithful prompt-image alignment remains challenging, particularly for complex prompts with multiple objects, relations, and fine-grained attributes. Existing training-free inference-time scaling methods rely on fixed iteration budgets that cannot adapt to prompt difficulty, while reflection-tuned models require carefully curated reflection datasets and extensive joint fine-tuning of diffusion and vision-language models, often overfitting to reflection paths data and lacking transferability across models. We introduce RAISE (Requirement-Adaptive Self-Improving Evolution), a training-free, requirement-driven evolutionary framework for adaptive T2I generation. RAISE formulates image generation as a requirement-driven adaptive scaling process, evolving a population of candidates at inference time through a diverse set of refinement actions-including prompt rewriting, noise resampling, and instructional editing. Each generation is verified against a structured checklist of requirements, enabling the system to dynamically identify unsatisfied items and allocate further computation only where needed. This achieves adaptive test-time scaling that aligns computational effort with semantic query complexity. On GenEval and DrawBench, RAISE attains state-of-the-art alignment (0.94 overall GenEval) while incurring fewer generated samples (reduced by 30-40%) and VLM calls (reduced by 80%) than prior scaling and reflection-tuned baselines, demonstrating efficient, generalizable, and model-agnostic multi-round self-improvement. Code is available at https://github.com/LiyaoJiang1998/RAISE.

We study online maximization of non-monotone Diminishing-Return(DR)-submodular functions over down-closed convex sets, a regime where existing projection-free online methods suffer from suboptimal regret and limited feedback guarantees. Our main contribution is a new structural result showing that this class is 1/e-linearizable under carefully designed exponential reparametrization, scaling parameter, and surrogate potential, enabling a reduction to online linear optimization. As a result, we obtain O(T^{1/2}) static regret with a single gradient query per round and unlock adaptive and dynamic regret guarantees, together with improved rates under semi-bandit, bandit, and zeroth-order feedback. Across all feedback models, our bounds strictly improve the state of the art.

Orthogonality-based optimizers, such as Muon, have recently shown strong performance across large-scale training and community-driven efficiency challenges. However, these methods rely on a costly gradient orthogonalization step. Even efficient iterative approximations such as Newton-Schulz remain expensive, typically requiring dozens of matrix multiplications to converge. We introduce a preconditioning procedure that accelerates Newton-Schulz convergence and reduces its computational cost. We evaluate its impact and show that the overhead of our preconditioning can be made negligible. Furthermore, the faster convergence it enables allows us to remove one iteration out of the usual five without degrading approximation quality. Our publicly available implementation achieves up to a 2.8x speedup in the Newton-Schulz approximation. We also show that this has a direct impact on end-to-end training runtime with 5-10% improvement in realistic training scenarios across two efficiency-focused tasks. On challenging language or vision tasks, we validate that our method maintains equal or superior model performance while improving runtime. Crucially, these improvements require no hyperparameter tuning and can be adopted as a simple drop-in replacement. Our code is publicly available on github.

The evolving sophistication and intricacies of Large Language Models (LLMs) yield unprecedented advancements, yet they simultaneously demand considerable computational resources and incur significant costs. To alleviate these challenges, this paper introduces a novel, simple, and effective method named ``\growlength'' to accelerate the pretraining process of LLMs. Our method progressively increases the training length throughout the pretraining phase, thereby mitigating computational costs and enhancing efficiency. For instance, it begins with a sequence length of 128 and progressively extends to 4096. This approach enables models to process a larger number of tokens within limited time frames, potentially boosting their performance. In other words, the efficiency gain is derived from training with shorter sequences optimizing the utilization of resources. Our extensive experiments with various state-of-the-art LLMs have revealed that models trained using our method not only converge more swiftly but also exhibit superior performance metrics compared to those trained with existing methods. Furthermore, our method for LLMs pretraining acceleration does not require any additional engineering efforts, making it a practical solution in the realm of LLMs.

We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret performance compared to existing approaches. The first algorithm, although computationally inefficient, ensures a regret of mathcal{O}left(Kright), where K is the number of episodes. This is the first result with the optimal K dependence in the considered setting. The second algorithm, which is based on the policy optimization framework, guarantees a regret of mathcal{O}left(K^{3{4}} right) and is computationally efficient. Both our results significantly improve over the state-of-the-art: a computationally inefficient algorithm by Kong et al. [2023] with mathcal{O}left(K^{4{5}}+polyleft(1{lambda_{min}}right) right) regret, for some problem-dependent constant lambda_{min} that can be arbitrarily close to zero, and a computationally efficient algorithm by Sherman et al. [2023b] with mathcal{O}left(K^{6{7}} right) regret.

There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman. We show how to generalize this to a large class of hierarchical graphs in which the vertices are grouped into "supervertices" which are arranged according to a d-dimensional lattice. Supervertices can have different sizes, and edges between supervertices correspond to random connections between their constituent vertices. The hitting times of quantum walks on these graphs are related to the localization properties of zero modes in certain disordered tight binding Hamiltonians. The speedups range from superpolynomial to exponential, depending on the underlying dimension and the random graph model. We also provide concrete realizations of these hierarchical graphs, and introduce a general method for constructing graphs with efficient quantum traversal times using graph sparsification.

Large language models (LLMs) have shown remarkable progress in code generation, but their generated code often suffers from inefficiency, resulting in longer execution times and higher memory consumption. To address this issue, we propose EffiLearner, a self-optimization framework that utilizes execution overhead profiles to improve the efficiency of LLM-generated code. EffiLearner first generates code using an LLM, then executes it locally to capture execution time and memory usage profiles. These profiles are fed back to the LLM, which then revises the code to reduce overhead. To evaluate the effectiveness of EffiLearner, we conduct extensive experiments on the EffiBench, HumanEval, and MBPP with 16 open-source and 6 closed-source models. Our evaluation results demonstrate that through iterative self-optimization, EffiLearner significantly enhances the efficiency of LLM-generated code. For example, the execution time (ET) of StarCoder2-15B for the EffiBench decreases from 0.93 (s) to 0.12 (s) which reduces 87.1% the execution time requirement compared with the initial code. The total memory usage (TMU) of StarCoder2-15B also decreases from 22.02 (Mb*s) to 2.03 (Mb*s), which decreases 90.8% of total memory consumption during the execution process. The source code of EffiLearner was released in https://github.com/huangd1999/EffiLearner