February 2026

Recent research shows that Preference Alignment (PA) objectives act as divergence estimators between aligned (chosen) and unaligned (rejected) response distributions. In this work, we extend this divergence-based perspective to general alignment settings, such as reinforcement learning with verifiable rewards (RLVR), where only environmental rewards are available. Within this unified framework, we propose $f$-Group Relative Policy Optimization ($f$-GRPO), a class of on-policy reinforcement learning, and $f$-Hybrid Alignment Loss ($f$-HAL), a hybrid on/off policy objectives, for general LLM alignment based […]

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Suppose I give you a big number F and claim that F is a Fibonacci number. How could you confirm this? Before I go further, let me say what this post is really about. It’s not about Fibonacci numbers so much as it is about proofs and certificates. There’s no market for large Fibonacci numbers, and certainly no need to quickly verify that a number is a Fibonacci number. You could write a program to generate Fibonacci numbers, and run […]

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High-quality kernel is critical for scalable AI systems, and enabling LLMs to generate such code would advance AI development. However, training LLMs for this task requires sufficient data, a robust environment, and the process is often vulnerable to reward hacking and lazy optimization. In these cases, models may hack training rewards and prioritize trivial correctness over meaningful speedup. In this paper, we systematically study reinforcement learning (RL) for kernel generation. We first design KernelGYM, a robust distributed GPU […]

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High-quality kernel is critical for scalable AI systems, and enabling LLMs to generate such code would advance AI development. However, training LLMs for this task requires sufficient data, a robust environment, and the process is often vulnerable to reward hacking and lazy optimization. In these cases, models may hack training rewards and prioritize trivial correctness over meaningful speedup. In this paper, we systematically study reinforcement learning (RL) for kernel generation. We first design KernelGYM, a robust distributed GPU […]

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[Guest post by Salil Vadhan; Boaz’s note: I am thrilled to see this award. Luca’s expository writing on his blog, surveys, and lecture notes was and is an amazing resource. Luca had a knack for explaining some of the most difficult topics in intuitive ways that cut to their heart. I hope it will inspire more people to follow in footsteps.] The Trevisan Award for Expository Work is a new SIGACT award  created in memory of Luca Trevisan (1971-2024), with […]

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In this work, we provide a sharp theory of scaling laws for two-layer neural networks trained on a class of hierarchical multi-index targets, in a genuinely representation-limited regime. We derive exact information-theoretic scaling laws for subspace recovery and prediction error, revealing how the hierarchical features of the target are sequentially learned through a cascade of phase transitions. We further show that these optimal rates are achieved by a simple, target-agnostic spectral estimator, which can be interpreted as the […]

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Floating-point neural networks dominate modern machine learning but incur substantial inference cost, motivating interest in Boolean networks for resource-constrained settings. However, learning compact and accurate Boolean networks is challenging due to their combinatorial nature. In this work, we address this challenge from three different angles: learned connections, compact convolutions and adaptive discretization. First, we propose a novel strategy to learn efficient connections with no additional parameters and negligible computational overhead. Second, we introduce a novel convolutional Boolean architecture […]

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