These findings position ES as a distinct reasoning post-training paradigm rather than a less effective, memory-efficient alternative to GRPO, and study how hyperparameter design affects the effectiveness of ES, demonstrating that ES requires a smaller population size in a larger LLM.
Abstract
Evolution Strategies (ES) have recently emerged as a memory-efficient post-training paradigm for LLM reasoning. However, the optimization behavior of ES remains understudied, making it hard to define its advantage scope compared to mainstream post-training paradigms (e.g., Group Relative Policy Optimization (GRPO)). By systematically investigating ES dynamics and mechanisms, this paper first identifies a performance advantage of ES over GRPO, theoretically and empirically showing that ES can lead to broader reasoning coverage, thereby better exploiting the reasoning capabilities of pretrained LLMs. Theoretically, we show that verifier-projected Jensen-Shannon diversity across the ES population is helpful to higher Pass@K performances. Empirically, unlike GRPO, which exhibits entropy collapse, ES improves Pass@1 while attaining higher Pass@K than GRPO. We further develop a sequential GRPO-ES training strategy that combines GRPO's strength in Pass@1 with ES's gains in Pass@K. Second, we find that despite substantial whole-model parameter drift, the task-performance gains of ES are only contributed to a sparse subset of larger-magnitude updates. This functional sparsity suggests that large parameter movement need not imply widespread functional change, and held-out evaluations further show that it does not necessarily lead to catastrophic forgetting. Finally, we study how hyperparameter design affects the effectiveness of ES, demonstrating that ES requires a smaller population size in a larger LLM. These findings position ES as a distinct reasoning post-training paradigm rather than a less effective, memory-efficient alternative to GRPO.
Although reinforcement learning with verifiable rewards (RLVR) has improved the performance of large language models (LLMs) across a variety of reasoning tasks, there is significant debate as to whether RLVR expands the reasoning capability boundary, or just improves sampling efficiency. In this paper, we investigate the nature of test-time exploration in RLVR-trained LLMs by employing controlled maze-solving experiments and extracting a tree structure from mathematical reasoning traces (BODHI-Trees) based on semantic equivalence. This helps us delineate between entropy arising from stylistic variations and genuine inferential branching. Our findings demonstrate that the policy entropy collapse observed in RLVR models is not merely syntactic, and is accompanied by a significant reduction in semantic branching entropy. While RLVR improves adherence to environmental constraints and backtracking capabilities, it constricts the space of continuations; we provide evidence suggesting that this might be responsible for the sample efficiency gains of RLVR, albeit at the cost of genuine rollout diversity.
Soumadeep Saha, Krish Sharma, Akshay Chaturvedi et al.· 1 citation
Large Language Models (LLMs) are increasingly deployed in discovery domains such as math and science. The usual approach is to present the problem to the model and use its answer as the proposed solution. However, beyond this best guess, discovery can be enhanced by increasing test-time compute. In a process called pass@k, the model is allowed to explore the solution space and generate diverse candidate solutions. Unfortunately, the standard approach to post-training LLMs through Reinforcement Learning (RL) may limit pass@k: the model's output distribution narrows around high-reward outputs, causing the solution coverage to collapse. The alternative is to use Evolution Strategies (ES), a population-based, gradient-free post-training method that optimizes directly in weight space through random perturbations. As this paper shows, ES achieves consistently higher pass@k than RL and produces a broader output distribution with greater solution coverage. This coverage in turn makes it possible to achieve better results in e.g. standard math benchmarks. Thus, ES provides a better foundation for post-training in discovery problems and other domains where diverse solution coverage is critical.
Conor F. Hayes, Elliot Meyerson, Kajetan Schweighofer et al.· 1 citation
Group Relative Policy Optimization (GRPO) has become a standard reinforcement learning method for post-training language models. Recent work shows that GRPO can reduce the base model's reasoning capacity and underperform it in Pass@k when k is large, indicating reduced coverage of reasoning paths. We find that this reduction is associated with GRPO concentrating on responses that the base model already generates with high probability. We trace this concentration to two mechanisms in the GRPO update. At the response level, high-probability responses dominate the group gradient through repeated occurrence. At the token level, GRPO's importance ratio scales gradients, further reinforcing tokens that become more likely under the current policy. We propose ReCo, a reweighting method that addresses both effects. Response contributions are normalized by their expected occurrence within the rollout group, and the token-level importance ratio is replaced with a variance-based ratio that gives larger update scale to non-saturated decision points where alternative token choices remain plausible. Across Qwen2.5-Math-1.5B/7B and Llama-3.1-8B-Instruct on five mathematical reasoning benchmarks, ReCo improves Pass@k for large values of k and is comparable to GRPO for small values of k.
Junoh Park, Junseong Hwang, Won-Yong Cho et al.· 0 citations
Inference-time search with large language models (LLMs) often concentrates on a small set of structurally or semantically similar trajectories, leaving alternatives underexplored---a failure mode we call \textit{reasoning basin collapse}. We introduce BASIN, a training-free, structure-aware selection method that groups reasoning states into basins and penalizes repeated visits to the same strategy, thereby reallocating search across genuinely distinct reasoning paths under a fixed compute budget. Under matched inference budgets, BASIN improves over Tree of Thoughts (ToT) by up to $+22$pp on Game of 24 and $+6.7$pp on MuSR. A quality-aware variant, QA-BASIN, further improves robustness by preserving high-quality basins when unconditional diversification over-explores. To explain when basin-aware selection helps, we introduce the redundancy gap $\Delta$, which measures how differently search concentrates for correct versus incorrect predictions: standard ToT often operates near $\Delta \approx 0$, while BASIN consistently shifts $\Delta$ positive. More broadly, BASIN suggests structure-aware selection as a simple and general approach to improving inference-time reasoning. Code can be found at https://github.com/GitHubLuCheng/basin.
Evolution Strategy (ES) is a promising alternative to gradient-based fine-tuning for resource-constrained Large Language Model (LLM) reasoning. However, directly applying ES to billion-parameter LLMs is highly ineffective. In such high-dimensional parameter spaces, most random perturbations are nearly orthogonal to useful update directions, leading to unstable optimization. We propose Hyper-ES, a subspace-based ES framework that avoids the weakness of ES in full-parameter search while exploiting its strength in low-dimensional optimization. Instead of asking ES to discover useful directions from random perturbations in the LLM parameter space, Hyper-ES first performs a small number of inexpensive gradient-based fine-tuning runs to obtain descent directions. Although each direction may provide only a limited improvement on its own, their span forms a compact adaptation subspace that captures useful reasoning updates. Hyper-ES then applies CMA-ES to optimize layer-wise DARE-TIES merging coefficients within this subspace, allowing ES to search over combinations of meaningful descent directions rather than over arbitrary full-model perturbations. We evaluate Hyper-ES on three Qwen2.5-Instruct and DeepSeek-R1-Distill backbones across six mathematical reasoning datasets. Results show that Hyper-ES consistently outperforms GRPO-LoRA by 1% while requiring 10% fewer space-consuming gradient updates. Code at https://github.com/kuangrepi/Hyper-ES.
Yuntian Gu, Zhi Zheng, Yunpeng Ba et al.· 0 citations
Diffusion large language models (dLLMs) have emerged as a promising alternative to autoregressive LLMs, offering efficient generation through block-wise progressive unmasking. However, their strong general-purpose performance does not necessarily translate into reliable mathematical reasoning, where correctness depends on preserving coherent numerical-symbolic reasoning trajectories. In this work, we analyze the decoding trajectories of LLaDA 2.0 and identify a recurring diffusion confidence trap: local token confidence can become misaligned with global reasoning correctness during progressive block decoding. Our analysis reveals two representative failure regimes: sampling-sensitive failures, where correct paths exist but are unstable, and sampling-consistent failures, where repeated sampling converges to repetitive high-confidence but incorrect continuations. Motivated by this observation, we propose Evolutionary Decoding, a training-free test-time scaling framework that views diffusion decoding as an evolutionary process over candidate reasoning states. The framework combines step-wise selection, which preserves useful numerical-symbolic signals and suppresses repetitive patterns, with block-wise mutation, which introduces structured alternatives to escape incorrect high-confidence basins. Experiments on multiple benchmarks show that Evolutionary Decoding improves LLaDA 2.0 over confidence-based decoding, leading to more reliable mathematical reasoning.
Zhenhong Sun, Hanqing Zhao, Yatao Bian et al.· 0 citations
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
MIT News · Artificial Intelligence· news.mit.eduAug 24, 2026
