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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.14619 |
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| _version_ | 1866917495510663168 |
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| author | Chen, Kang Nian, Junjie Cao, Yixin Jiang, Yugang |
| author_facet | Chen, Kang Nian, Junjie Cao, Yixin Jiang, Yugang |
| contents | Multi-run chain-of-thought reasoning is usually collapsed to final-answer aggregates, which discard howsampled trajectories share, split, and rejoin through intermediate computation. We propose SliceGraph, a post-hoc problem-model-cell graph built by mutual-kNN over sparse activation-key Jaccard similarity between CoT slices, and treat it as a measurement object for process geometry rather than as a decoding program. Across sampled CoT ensembles from three primary 4B/8B models on math and science benchmarks, blinded annotation supports SliceGraph biconnected components as shared reasoning-state units and process families as within-family strategy-coherent route units. In 85.5% of 954 problem-model cells, correct CoTs sharing the same normalized answer split into multiple process families; among cells with at least two such runs, 76.6% of run pairs are cross-family on average. We call such same-answer, family-divergent correct trajectories process isomers. A label-seeded reward field provides a separate value-landscape layer: success-associated regions often split into disconnected high-value cores, and route families specialize over these core footprints rather than merely duplicating one another. A typed-state transition analysis further shows that process families navigate the same atlas with distinct transition kernels under matched null controls. Representation ablations, a cross-architecture replication, and two cross-scale replications support the robustness of the route-family scaffold, showing that final-answer aggregation overlooks this structured multi-route process geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14619 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SliceGraph: Mapping Process Isomers in Multi-Run Chain-of-Thought Reasoning Chen, Kang Nian, Junjie Cao, Yixin Jiang, Yugang Artificial Intelligence Multi-run chain-of-thought reasoning is usually collapsed to final-answer aggregates, which discard howsampled trajectories share, split, and rejoin through intermediate computation. We propose SliceGraph, a post-hoc problem-model-cell graph built by mutual-kNN over sparse activation-key Jaccard similarity between CoT slices, and treat it as a measurement object for process geometry rather than as a decoding program. Across sampled CoT ensembles from three primary 4B/8B models on math and science benchmarks, blinded annotation supports SliceGraph biconnected components as shared reasoning-state units and process families as within-family strategy-coherent route units. In 85.5% of 954 problem-model cells, correct CoTs sharing the same normalized answer split into multiple process families; among cells with at least two such runs, 76.6% of run pairs are cross-family on average. We call such same-answer, family-divergent correct trajectories process isomers. A label-seeded reward field provides a separate value-landscape layer: success-associated regions often split into disconnected high-value cores, and route families specialize over these core footprints rather than merely duplicating one another. A typed-state transition analysis further shows that process families navigate the same atlas with distinct transition kernels under matched null controls. Representation ablations, a cross-architecture replication, and two cross-scale replications support the robustness of the route-family scaffold, showing that final-answer aggregation overlooks this structured multi-route process geometry. |
| title | SliceGraph: Mapping Process Isomers in Multi-Run Chain-of-Thought Reasoning |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2605.14619 |