Group-Constrained Hardness Reweighting for Tool-Calling Agents

Structured tool calls connect language-model agents to external systems; a call is actionable only when tool selection, call composition, serialization, and arguments are valid. Offline corpora mix rows with different protocol roles, so a global hardness rule can redistribute optimization mass across roles rather than isolate confusion among candidate schemas. We introduce HARDNESS-SCMD, which combines a protocol-complete row objective with non-uniform weights restricted to fixed candidate-one fine groups. Within each such group, sibling-schema-text confusability defines a Gibbs target, which is contracted toward uniform only as far as the weight-floor, effective-sample-size, and weight-cap constraints require. We establish uniqueness of the groupwise Gibbs target, minimality of this contraction along the Gibbs-to-uniform path, exact preservation of every fine group’s optimization mass, and a global effective-sample-size lower bound. Because a mean-one group weight multiplies the complete row objective, confusable choices receive greater optimization emphasis while aggregate mass at both the fine-group and protocol-role levels remains unchanged. A cross-model continuation study shows that distributional imprints can survive later uniform training, motivating separate control of protocol-role mass and candidate confusability.