Adaptive Semantic Branching: Disagreement-Localized Cross-Trajectory Regeneration for Reasoning Candidate Expansion

Jeong-Yoon Kim; Tae-Yoon Lee

cs.AINov 5, 2026

Adaptive Semantic Branching: Disagreement-Localized Cross-Trajectory Regeneration for Reasoning Candidate Expansion

Authors: Jeong-Yoon Kim, Tae-Yoon Lee

Organizations: Department of Electronic Engineering, Hanbat National University

Abstract

Reasoning trajectories generated for the same problem often arrive at conflicting answers. These disagreements reveal alternative intermediate decisions that can be reused to explore new solutions. We introduce Adaptive Semantic Branching (ASB), a training-free inference procedure that turns cross-trajectory disagreement into targeted candidate generation. ASB first groups independently sampled trajectories by extracted final answer, selects a representative from each group, and aligns their reasoning steps with a monotonic dynamic program. A persistent-divergence objective identifies the point at which initially similar reasoning paths develop different continuations. For each selected directed pair, ASB retains the source trajectory's textual prefix, extracts a short reasoning window from a competing donor trajectory, and generates a fresh solution conditioned on both. A diversity-aware policy allocates up to three additional generations according to the answer-cluster structure. In a 500-problem MATH evaluation with Qwen2.5-7B-Instruct, ASB increases oracle candidate coverage from 445/500 (89.0%) with seven initial samples to 455/500 (91.0%), recovering correct candidates for 10 of the 55 initially uncovered problems. The method uses 576 additional generation calls across the evaluation set, averaging 8.152 calls per problem. We provide a precise specification of the branching operator, alignment objective, generation policy, and experimental configuration.

Figures & tables

Panel of Figure 1 — Figure 1: Adaptive Semantic Branching. (a) The inference pipeline groups seven independent trajectories by answer, aligns cross-cluster representatives, locates the persistent divergence boundary, and selects directed exchanges. (b) In $A\leftarrow B$ , source prefix $P_{A}$ and donor insight $I_{B}$ condition a newly generated trajectory $T^{\prime}_{A\leftarrow B}$ . The $k^{*}=0$ case uses an empty source prefix and a fresh start.

Metric	Value
Initial candidate coverage	$445/500$ (89.0%)
ASB candidate coverage	$455/500$ (91.0%)
Additional problems recovered	$10/500$ (+2.0 pp)
Recovery among 55 initial misses	$10/55$ (18.18%)
Initial model generation calls	3,500
Additional branch calls	576

Table 1: Oracle candidate coverage and generation counts for the stored MATH-500 run (Qwen2.5-7B-Instruct; base seed 100).

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Parameter	Configuration
Model	Qwen2.5-7B-Instruct
Benchmark	fixed MATH-500 manifest
Initial trajectories	7 per problem
Maximum branches	3 per problem
Temperature / top- $p$	0.7 / 1.0
Max completion tokens	2,048

Appendix

Table 2: Reference implementation settings for the MATH-500 seed-100 run.

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Abstract

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