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

TL;DR

The Geometric Reasoner (TGR) is a training-free method that improves long-context reasoning by manifold-informed latent search, balancing computational cost and coverage quality.

Contribution

TGR introduces a novel, training-free framework that performs manifold-informed latent foresight search with memory-efficient chunk-wise processing.

Findings

TGR improves trajectory coverage by up to 13 points on Qwen3-8B.

TGR achieves this with negligible overhead of about 1.1--1.3 times.

TGR enhances robustness on math and code benchmarks.

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.