FIPO: Eliciting Deep Reasoning with Future-KL Influenced Policy Optimization

Chiyu Ma; Shuo Yang; Kexin Huang; Jinda Lu; Haoming Meng; Shangshang Wang; Bolin Ding; Soroush Vosoughi; Guoyin Wang; Jingren Zhou

arXiv · 2603.19835

FIPO: Eliciting Deep Reasoning with Future-KL Influenced Policy Optimization

Chiyu Ma·Shuo Yang·Kexin Huang·Jinda Lu·Haoming Meng·Shangshang Wang·Bolin Ding·Soroush Vosoughi·Guoyin Wang·Jingren Zhou

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Abstract

We present Future-KL Influenced Policy Optimization (FIPO), a reinforcement learning algorithm designed to overcome reasoning bottlenecks in large language models. While GRPO style training scales effectively, it typically relies on outcome-based rewards (ORM) that distribute a global advantage uniformly across every token in a trajectory. We argue that this coarse-grained credit assignment imposes a performance ceiling by failing to distinguish critical logical pivots from trivial tokens. FIPO addresses this by incorporating discounted future-KL divergence into the policy update, creating a dense advantage formulation that re-weights tokens based on their influence on subsequent trajectory behavior. Empirically, FIPO enables models to break through the length stagnation seen in standard baselines. Evaluated on Qwen2.5-32B, FIPO extends the average chain-of-thought length from roughly 4,000 to over 10,000 tokens and increases AIME 2024 Pass@1 accuracy from 50.0% to a peak of 58.0% (converging at approximately 56.0\%). This outperforms both DeepSeek-R1-Zero-Math-32B (around 47.0%) and o1-mini (approximately 56.0%). Our results suggest that establishing dense advantage formulations is a vital path for evolving ORM-based algorithms to unlock the full reasoning potential of base models. We open-source our training system, built on the verl framework.

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BibTeX RIS

Chiyu Ma, Shuo Yang, Kexin Huang, Jinda Lu, Haoming Meng, Shangshang Wang, Bolin Ding, Soroush Vosoughi, Guoyin Wang, Jingren Zhou. 2026-03-31. FIPO: Eliciting Deep Reasoning with Future-KL Influenced Policy Optimization. https://arxiv.org/abs/2603.19835

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