Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.18832 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917476213719040 |
|---|---|
| author | Zhuang, Ren Wang, Ben Sun, Shuifa |
| author_facet | Zhuang, Ren Wang, Ben Sun, Shuifa |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18832 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Geometric Reasoner: Manifold-Informed Latent Foresight Search for Long-Context Reasoning Zhuang, Ren Wang, Ben Sun, Shuifa Machine Learning Artificial Intelligence 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. |
| title | The Geometric Reasoner: Manifold-Informed Latent Foresight Search for Long-Context Reasoning |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2601.18832 |