Reinforcement learning (RL) yields substantial improvements in large language models' (LLMs) downstream task performance and alignment with human values. Surprisingly, such large gains result from updating only a small subnetwork comprising just 5%-30% of the parameters, with the rest effectively unchanged. We refer to this phenomenon as parameter update sparsity induced by RL. It is observed across all 7 widely-used RL algorithms (e.g., PPO, GRPO, DPO) and all 10 LLMs from different families in our experiments. This sparsity is intrinsic and occurs without any explicit sparsity-promoting regularizations or architectural constraints.

Unlike the uniform application of asingle penalty,CPR enforces an upper bound on astatistical measure, suchas theL2-norm, ofindividual parameter matrices.

While it has been shown that training such very deep architectures was typically easier than smaller ones [24], it is also well-known that they are highly over-parameterized.

The two-stage fine-tuning paradigm of Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL) has empirically shown better reasoning performance than one-stage SFT for the post-training of Large Language Models (LLMs). However, the evolution and mechanism behind the synergy of SFT and RL are still under-explored and inconclusive. In our study, we find the well-known claim "SFT memorizes, RL generalizes" is over-simplified, and discover that: (1) OOD performance peaks at the early stage of SFT and then declines (OOD forgetting), the best SFT checkpoint cannot be captured by training/test loss; (2) the subsequent RL stage does not generate fundamentally better OOD capability, instead it plays an \textbf{OOD restoration} role, recovering the lost reasoning ability during SFT; (3) The recovery ability has boundaries, \ie{} \textbf{if SFT trains for too short or too long, RL cannot recover the lost OOD ability;} (4) To uncover the underlying mechanisms behind the forgetting and restoration process, we employ SVD analysis on parameter matrices, manually edit them, and observe their impacts on model performance. Unlike the common belief that the shift of model capacity mainly results from the changes of singular values, we find that they are actually quite stable throughout fine-tuning. Instead, the OOD behavior strongly correlates with the \textbf{rotation of singular vectors}. Our findings re-identify the roles of SFT and RL in the two-stage fine-tuning and discover the rotation of singular vectors as the key mechanism. %reversing the rotations induced by SFT, which shows recovery from forgetting, whereas imposing the SFT parameter directions onto a RL-tuned model results in performance degradation. Code is available at https://github.com/xiaodanguoguo/RL_Heals_SFT

Regularization is a critical component in deep learning.

We consider the task of building compact deep learning pipelines suitable for deployment on storage and power constrained mobile devices. We propose a unified framework to learn a broad family of structured parameter matrices that are characterized by the notion of low displacement rank. Our structured transforms admit fast function and gradient evaluation, and span a rich range of parameter sharing configurations whose statistical modeling capacity can be explicitly tuned along a continuum from structured to unstructured. Experimental results show that these transforms can significantly accelerate inference and forward/backward passes during training, and offer superior accuracy-compactness-speed tradeoffs in comparison to a number of existing techniques. In keyword spotting applications in mobile speech recognition, our methods are much more effective than standard linear low-rank bottleneck layers and nearly retain the performance of state of the art models, while providing more than 3.5-fold compression.

Recently, neural network based approaches have achieved significant progress for solving large, complex, graph-structured problems.