While reinforcement learning with verifiable rewards (RLVR) is widely used to improve the reasoning capabilities of large language models (LLMs), the generalizability of the resulting models remains poorly understood. In this work, we establish the first non-vacuous generalization bounds for parameter-efficient RLVR fine-tuning at the billion-parameter scale. Our approach adapts PAC-Bayes compression bounds to this setting, and addresses the inherent stochasticity of token generation by applying the Gumbel-max reparameterization trick. To operationalize these bounds, we propose the Progressive RLVR framework, which integrates RLVR with on-policy distillation, TinyLoRA, and model quantization. Progressive RLVR empirically retains 84-97% performance of standard LoRA fine-tuning while producing models that are 14,796x more compressible. We show that this framework yields non-vacuous generalization bounds in four domains: mathematical problem-solving, programming, general-knowledge reasoning, and Text-to-SQL. Our bounds exceed the accuracy of the base model by 9-51% and lie within 6-11% of the accuracy of the fine-tuned models.
Partial differential equations (PDEs) are foundational to modeling in science and engineering, but constructing reliable numerical solvers remains labor-intensive, demanding expert knowledge of discretization schemes, stability conditions, and boundary treatments. Recent work has…
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Reinforcement learning with verifiable rewards (RLVR) has been established as a viable paradigm for the post-training of Large Language Models (LLMs), including downstream tasks, such as Neural Machine Translation (NMT). With the latest research indicating that RLVR could be the…
Large language models (LLMs) can generate BPMN process models from natural-language descriptions, yet supervised fine-tuning (SFT) limits their output quality to the patterns present in the training data. Reinforcement learning (RL) can optimize beyond this ceiling using external…
RL with verifiable rewards (RLVR) has emerged as a powerful paradigm for training LMs on tasks with well-defined success metrics, such as code generation and mathematical reasoning. However, current RLVR methods optimize only what can be objectively scored, often neglecting subje…