Variational Reasoning for Language Models
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arXiv
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| Autori principali: | , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908595134660608 |
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| author | Zhou, Xiangxin Liu, Zichen Wang, Haonan Du, Chao Lin, Min Li, Chongxuan Wang, Liang Pang, Tianyu |
| author_facet | Zhou, Xiangxin Liu, Zichen Wang, Haonan Du, Chao Lin, Min Li, Chongxuan Wang, Liang Pang, Tianyu |
| contents | We introduce a variational reasoning framework for language models that treats thinking traces as latent variables and optimizes them through variational inference. Starting from the evidence lower bound (ELBO), we extend it to a multi-trace objective for tighter bounds and propose a forward-KL formulation that stabilizes the training of the variational posterior. We further show that rejection sampling finetuning and binary-reward RL, including GRPO, can be interpreted as local forward-KL objectives, where an implicit weighting by model accuracy naturally arises from the derivation and reveals a previously unnoticed bias toward easier questions. We empirically validate our method on the Qwen 2.5 and Qwen 3 model families across a wide range of reasoning tasks. Overall, our work provides a principled probabilistic perspective that unifies variational inference with RL-style methods and yields stable objectives for improving the reasoning ability of language models. Our code is available at https://github.com/sail-sg/variational-reasoning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22637 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational Reasoning for Language Models Zhou, Xiangxin Liu, Zichen Wang, Haonan Du, Chao Lin, Min Li, Chongxuan Wang, Liang Pang, Tianyu Computation and Language Artificial Intelligence Machine Learning We introduce a variational reasoning framework for language models that treats thinking traces as latent variables and optimizes them through variational inference. Starting from the evidence lower bound (ELBO), we extend it to a multi-trace objective for tighter bounds and propose a forward-KL formulation that stabilizes the training of the variational posterior. We further show that rejection sampling finetuning and binary-reward RL, including GRPO, can be interpreted as local forward-KL objectives, where an implicit weighting by model accuracy naturally arises from the derivation and reveals a previously unnoticed bias toward easier questions. We empirically validate our method on the Qwen 2.5 and Qwen 3 model families across a wide range of reasoning tasks. Overall, our work provides a principled probabilistic perspective that unifies variational inference with RL-style methods and yields stable objectives for improving the reasoning ability of language models. Our code is available at https://github.com/sail-sg/variational-reasoning. |
| title | Variational Reasoning for Language Models |
| topic | Computation and Language Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2509.22637 |