Background and Methodology
Financial institutions operating under data-residency constraints are restricted to open-weight models small enough to locally host, which trail frontier systems on multi-step quantitative reasoning.
On-policy distillation narrows such gaps by supervising a student on its own rollouts, but traditional OPD requires a strong external teacher, and OPSD conditions on a full reference solution.
We ask how much of that signal is necessary.
Introducing Fin-SD
We present Fin-SD, a localized hindsight self-distillation recipe for multi-step reasoning.
Given a problem the student fails, the student itself identifies the first incorrect reasoning step and writes a short critique of that step. We truncate the student's trajectory immediately before the error (aiming to obtain a correct prefix), condition a frozen copy of the student on the same prefix plus the hint, and distill that hint-conditioned teacher into the student over a short rollout under reverse KL. No external model contributes a gradient.
Experimental Setup
We apply Fin-SD to GPT-OSS-20B on a custom multi-step financial reasoning benchmark that requires deriving formula inputs from realistic scenarios via accounting conventions.
Key Findings
We find:
- (i) replacing the critique at the critical step with a generic-feedback control matches Fin-SD's entire 3.03 pp accuracy gain over the base model on the FinanceReasoning Hard subset, suggesting the gain comes from where supervision is applied, not hint content;
- (ii) the model writing the hint does not need to be stronger than the model receiving it: hints from same-family GPT-OSS-120B, at roughly 6x the parameters, yield no materially greater benefits than self-written hints; and
- (iii) Fin-SD matches on-policy self-distillation from full reference solutions on accuracy while generating 9.5% fewer tokens.
Broader Evaluation
With Fin-SD, general reasoning on MMLU-Pro and a fourteen-metric compliance audit on FinTrust show no material regression.