A Comedy of Estimators: On KL Regularization in RL Training of LLMs

The reasoning performance of large language models (LLMs) can be substantially improved by training them with reinforcement learning (RL). The RL objective for LLM training involves a regularization term, which is the reverse Kullback-Leibler (KL) divergence between the trained policy and the reference policy. Since computing the KL divergence exactly is intractable, various estimators are used in practice to estimate it from on-policy samples. Despite its wide adoption, including in several open-source libraries, there is no systematic study analyzing the numerous ways of incorporating KL estimators in the objective and their effect on the downstream performance of RL-trained models. Recent works show that prevailing practices for incorporating KL regularization do not provide correct gradients for stated objectives, creating a discrepancy between the objective and its implementation. In this paper, we further analyze these practices and study the gradients of several estimators configurations, revealing how design choices shape gradient bias. We substantiate these findings with empirical observations by RL fine-tuning \texttt{Qwen2.5-7B}, \texttt{Llama-3.1-8B-Instruct} and \texttt{Qwen3-4B-Instruct-2507} with different configurations and evaluating their performance on both in- and out-of-distribution tasks. Through our analysis, we observe that, in on-policy settings: (1) estimator configurations with biased gradients can result in training instabilities; and (2) using estimator configurations resulting in unbiased gradients leads to better performance on in-domain as well as out-of-domain tasks. We also investigate the performance resulting from different KL configurations in off-policy settings and observe that KL regularization can help stabilize off-policy RL training resulting from asynchronous setups.

Sliding Window Recurrences for Sequence Models

Multi-hybrid architectures are poised to take over language modeling due to better quality and performance. We introduce a hierarchical decomposition framework for linear recurrences that allows us to develop algorithms aligned with GPU memory hierarchies, yielding Sliding Window Recurrences. We focus specifically on truncating recurrences to hardware-aligned windows which are naturally jagged, limiting costly inter-warp communication. Using SWR, we develop Phalanx layers that serve as drop-in replacements for windowed attention or linear recurrences. In 1B parameter multi-hybrid models, Phalanx achieves over 10-40% speedup across 4K to 32K context length over optimized Transformers while matching perplexity.

FALCON: Few-step Accurate Likelihoods for Continuous Flows

Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann Generators tackle this problem by pairing a generative model, capable of exact likelihood computation, with importance sampling to obtain consistent samples under the target distribution. Current Boltzmann Generators primarily use continuous normalizing flows (CNFs) trained with flow matching for efficient training of powerful models. However, likelihood calculation for these models is extremely costly, requiring thousands of function evaluations per sample, severely limiting their adoption. In this work, we propose Few-step Accurate Likelihoods for Continuous Flows (FALCON), a method which allows for few-step sampling with a likelihood accurate enough for importance sampling applications by introducing a hybrid training objective that encourages invertibility. We show FALCON outperforms state-of-the-art normalizing flow models for molecular Boltzmann sampling and is two orders of magnitude faster than the equivalently performing CNF model.

Scaling Latent Reasoning via Looped Language Models

Modern LLMs are trained to "think" primarily via explicit text generation, such as chain-of-thought (CoT), which defers reasoning to post-training and under-leverages pre-training data. We present and open-source Ouro, named after the recursive Ouroboros, a family of pre-trained Looped Language Models (LoopLM) that instead build reasoning into the pre-training phase through (i) iterative computation in latent space, (ii) an entropy-regularized objective for learned depth allocation, and (iii) scaling to 7.7T tokens. Ouro 1.4B and 2.6B models enjoy superior performance that match the results of up to 12B SOTA LLMs across a wide range of benchmarks. Through controlled experiments, we show this advantage stems not from increased knowledge capacity, but from superior knowledge manipulation capabilities. We also show that LoopLM yields reasoning traces more aligned with final outputs than explicit CoT. We hope our results show the potential of LoopLM as a novel scaling direction in the reasoning era. Our model could be found in: http://ouro-llm.github.io.

Surrogate-based quantification of policy uncertainty in generative flow networks

Generative flow networks are able to sample, via sequential construction, high-reward, complex objects according to a reward function. However, such reward functions are often estimated approximately from noisy data, leading to epistemic uncertainty in the learnt policy. We present an approach to quantify this uncertainty by constructing a surrogate model composed of a polynomial chaos expansion, fit on a small ensemble of trained flow networks. This model learns the relationship between reward functions, parametrised in a low-dimensional space, and the probability distributions over actions at each step along a trajectory of the flow network. The surrogate model can then be used for inexpensive Monte Carlo sampling to estimate the uncertainty in the policy given uncertain rewards. We illustrate the performance of our approach on a discrete and continuous grid-world, symbolic regression, and a Bayesian structure learning task.

Catalyst GFlowNet for electrocatalyst design: A hydrogen evolution reaction case study

Efficient and inexpensive energy storage is essential for accelerating the adoption of renewable energy and ensuring a stable supply, despite fluctuations in sources such as wind and solar. Electrocatalysts play a key role in hydrogen energy storage (HES), allowing the energy to be stored as hydrogen. However, the development of affordable and high-performance catalysts for this process remains a significant challenge. We introduce Catalyst GFlowNet, a generative model that leverages machine learning-based predictors of formation and adsorption energy to design crystal surfaces that act as efficient catalysts. We demonstrate the performance of the model through a proof-of-concept application to the hydrogen evolution reaction, a key reaction in HES, for which we successfully identified platinum as the most efficient known catalyst. In future work, we aim to extend this approach to the oxygen evolution reaction, where current optimal catalysts are expensive metal oxides, and open the search space to discover new materials. This generative modeling framework offers a promising pathway for accelerating the search for novel and efficient catalysts.

Recursive Self-Aggregation Unlocks Deep Thinking in Large Language Models

Test-time scaling methods improve the capabilities of large language models (LLMs) by increasing the amount of compute used during inference to make a prediction. Inference-time compute can be scaled in parallel by choosing among multiple independent solutions or sequentially through self-refinement. We propose Recursive Self-Aggregation (RSA), a test-time scaling method inspired by evolutionary methods that combines the benefits of both parallel and sequential scaling. Each step of RSA refines a population of candidate reasoning chains through aggregation of subsets to yield a population of improved solutions, which are then used as the candidate pool for the next iteration. RSA exploits the rich information embedded in the reasoning chains -- not just the final answers -- and enables bootstrapping from partially correct intermediate steps within different chains of thought. Empirically, RSA delivers substantial performance gains with increasing compute budgets across diverse tasks, model families and sizes. Notably, RSA enables Qwen3-4B-Instruct-2507 to achieve competitive performance with larger reasoning models, including DeepSeek-R1 and o3-mini (high), while outperforming purely parallel and sequential scaling strategies across AIME-25, HMMT-25, Reasoning Gym, LiveCodeBench-v6, and SuperGPQA. We further demonstrate that training the model to combine solutions via a novel aggregation-aware reinforcement learning approach yields significant performance gains. Code available at https://github.com/HyperPotatoNeo/RSA.

Active Attacks: Red-teaming LLMs via Adaptive Environments

We address the challenge of generating diverse attack prompts for large language models (LLMs) that elicit harmful behaviors (e.g., insults, sexual content) and are used for safety fine-tuning. Rather than relying on manual prompt engineering, attacker LLMs can be trained with reinforcement learning (RL) to automatically generate such prompts using only a toxicity classifier as a reward. However, capturing a wide range of harmful behaviors is a significant challenge that requires explicit diversity objectives. Existing diversity-seeking RL methods often collapse to limited modes: once high-reward prompts are found, exploration of new regions is discouraged. Inspired by the active learning paradigm that encourages adaptive exploration, we introduce \textit{Active Attacks}, a novel RL-based red-teaming algorithm that adapts its attacks as the victim evolves. By periodically safety fine-tuning the victim LLM with collected attack prompts, rewards in exploited regions diminish, which forces the attacker to seek unexplored vulnerabilities. This process naturally induces an easy-to-hard exploration curriculum, where the attacker progresses beyond easy modes toward increasingly difficult ones. As a result, Active Attacks uncovers a wide range of local attack modes step by step, and their combination achieves wide coverage of the multi-mode distribution. Active Attacks, a simple plug-and-play module that seamlessly integrates into existing RL objectives, unexpectedly outperformed prior RL-based methods -- including GFlowNets, PPO, and REINFORCE -- by improving cross-attack success rates against GFlowNets, the previous state-of-the-art, from 0.07% to 31.28% (a relative gain greater than $400\ \times$) with only a 6% increase in computation. Our code is publicly available \href{https://github.com/dbsxodud-11/active_attacks}{here}.

Chain of Thought Monitorability: A New and Fragile Opportunity for AI Safety

AI systems that "think" in human language offer a unique opportunity for AI safety: we can monitor their chains of thought (CoT) for the intent to misbehave. Like all other known AI oversight methods, CoT monitoring is imperfect and allows some misbehavior to go unnoticed. Nevertheless, it shows promise and we recommend further research into CoT monitorability and investment in CoT monitoring alongside existing safety methods. Because CoT monitorability may be fragile, we recommend that frontier model developers consider the impact of development decisions on CoT monitorability.

Torsional-GFN: a conditional conformation generator for small molecules

Generating stable molecular conformations is crucial in several drug discovery applications, such as estimating the binding affinity of a molecule to a target. Recently, generative machine learning methods have emerged as a promising, more efficient method than molecular dynamics for sampling of conformations from the Boltzmann distribution. In this paper, we introduce Torsional-GFN, a conditional GFlowNet specifically designed to sample conformations of molecules proportionally to their Boltzmann distribution, using only a reward function as training signal. Conditioned on a molecular graph and its local structure (bond lengths and angles), Torsional-GFN samples rotations of its torsion angles. Our results demonstrate that Torsional-GFN is able to sample conformations approximately proportional to the Boltzmann distribution for multiple molecules with a single model, and allows for zero-shot generalization to unseen bond lengths and angles coming from the MD simulations for such molecules. Our work presents a promising avenue for scaling the proposed approach to larger molecular systems, achieving zero-shot generalization to unseen molecules, and including the generation of the local structure into the GFlowNet model.