LaPha: A New Approach to Math Reasoning in Hyperbolic Space

jiqizhixin · x · 2026-07-13

A Shanghai AI for Science team and collaborators proposed **LaPha**: a method for training mathematical reasoning agents in the **Poincaré hyperbolic latent space**. ### Core Ideas - Models the search process as a tree "growing outward" in hyperbolic geometry, leveraging the exponential growth of space with radius for exploration. - Provides **dense process rewards** based on the geodesic distance to "rule-verified correctness," helping the agent learn reasoning trajectories more stably. - Integrates a lightweight **value head** for self-guided search expansion during testing. ### Performance - Boosted **Qwen2.5-Math-1.5B** on **MATH500** from **66.0%** to **88.2%**. - Using value-head-guided search, **LaPha-1.5B** achieved **56.7%** on **AIME'24**. - **LaPha-7B** reached **60.0%** on **AIME'24** and **53.3%** on **AIME'25**. The post also mentions another paper, **T\\*: Progressive Block Scaling for Masked Diffusion Language Models Through Trajectory Aware Reinforcement Learning**, along with links to the paper and an explanation.

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