Training-Free Cross-Domain Learning Transfer in Reasoning Models

Abstract

Large language models often solve problems within familiar domains but struggle to transfer the same reasoning strategy across domains with different surface vocabularies. We present COMETS (Cross-domain Memory Enrichment and Transfer System), a training-free framework for cross-domain reasoning transfer through explicit structural pattern matching. COMETS abstracts solved source-domain problems into typed reasoning graphs over domain-agnostic operations such as assign, filter, divide, loop, and return. At inference time, it first generates a zero-shot target-domain solution. If the solution fails validation, COMETS retrieves structurally similar source patterns using the Weisfeiler–Lehman graph kernel and injects them into a corrective prompt. This selective baseline-first strategy avoids pattern-distraction failures that arise when structural hints are applied unconditionally to problems the model can already solve. We evaluate COMETS on MBPP code generation using reasoning patterns extracted from GSM8K and SVAMP arithmetic problems. COMETS achieves 87.5% Pass@1, compared with 71.5% for zero-shot prompting and 76.0% for semantic retrieval. The gains are largest on complex problems, where accuracy improves from 37.2% to 76.7%. Ablations show that the improvement comes from the combination of graph-based abstraction, WL-kernel structural retrieval, and verifier-controlled selective transfer. These results demonstrate that explicit structural pattern matching can enable zero-shot cross-domain reasoning transfer without target-domain labels or model-weight updates.