# Logical Reasoning

On-policy self-distillation lets one model act as a problem-only student and as a teacher given a reference solution, but the reference pushes the teacher toward short, answer-conditioned derivations that omit exploration and self-correction. TeachBack injects a trailing slice of the reference reasoning as optional working notes and optimizes preferences in both directions: teacher trajectories should win under the problem-only prompt, while student trajectories reshape future privileged teacher rollouts. Across Qwen3-1.7B, 4B and 8B, math averages rise by 4.3, 2.2 and 2.5 points over base, and Knight-and-Knaves averages by 6.1, 3.9 and 7.5 points.

On-policy self-distillation lets one model act as a problem-only student and as a teacher given a reference solution, but the reference pushes the teacher toward short, answer-conditioned derivations that omit exploration and self-correction. TeachBack injects a trailing slice of the reference reasoning as optional working notes and optimizes preferences in both directions: teacher trajectories should win under the problem-only prompt, while student trajectories reshape future privileged teacher rollouts. Across Qwen3-1.7B, 4B and 8B, math averages rise by 4.3, 2.2 and 2.5 points over base, and Knight-and-Knaves averages by 6.1, 3.9 and 7.5 points.

LoOPSD builds a stronger self-teacher by repeating a searched block of a model's own layers without changing any weights, then distills that teacher's predictions into a standard-path student, lifting Qwen3-1.7B on GSM8K from 42.30% to 79.61% under a 400-token thinking budget.

LoOPSD builds a stronger self-teacher by repeating a searched block of a model's own layers without changing any weights, then distills that teacher's predictions into a standard-path student, lifting Qwen3-1.7B on GSM8K from 42.30% to 79.61% under a 400-token thinking budget.

This work first shows through controlled experiments on PRMBench and ROSCOE that supplying the correct answer does not consistently improve reasoning quality, locating the flaws in the structure of reasoning traces rather than in answer awareness, and then proposes CRAFT: it rolls out K candidate traces per sample, extracts consensus terms via TF-IRF and filters steps by z-score, converts each trace into a Reasoning Knowledge Graph with steps as nodes and logical relations as edges, aggregates them into a consensus graph, and synthesizes one new trace by traversing that graph in topological order; across FLD, FOLIO, GSM8K and OlympiadBench with GPT-5.

This work first shows through controlled experiments on PRMBench and ROSCOE that supplying the correct answer does not consistently improve reasoning quality, locating the flaws in the structure of reasoning traces rather than in answer awareness, and then proposes CRAFT: it rolls out K candidate traces per sample, extracts consensus terms via TF-IRF and filters steps by z-score, converts each trace into a Reasoning Knowledge Graph with steps as nodes and logical relations as edges, aggregates them into a consensus graph, and synthesizes one new trace by traversing that graph in topological order; across FLD, FOLIO, GSM8K and OlympiadBench with GPT-5.