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arXiv · 2601.18832

The Geometric Reasoner: Manifold-Informed Latent Foresight Search for Long-Context Reasoning

Ren Zhuang·Ben Wang·Shuifa Sun
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Abstract

Scaling test-time compute enhances long chain-of-thought (CoT) reasoning, yet existing approaches face a fundamental trade-off between computational cost and coverage quality: either incurring high training expense or yielding redundant trajectories. We introduce The Geometric Reasoner (TGR), a training-free framework that performs manifold-informed latent foresight search under strict memory bounds. At each chunk boundary, TGR scores candidate latent anchors via a lightweight look-ahead estimate combined with soft geometric regularizers that encourage smooth trajectories and diverse exploration. Chunk-wise KV cache resets keep memory linear in chunk length. On challenging math and code benchmarks, TGR improves robust trajectory coverage, measured by the area under the Pass@k curve (AUC), by up to 13 points on Qwen3-8B, with negligible overhead of about 1.1--1.3 times.

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Ren Zhuang, Ben Wang, Shuifa Sun. 2026-01-25. The Geometric Reasoner: Manifold-Informed Latent Foresight Search for Long-Context Reasoning. https://arxiv.org/abs/2601.18832

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