Energy Gradient Specification: Provable Generalization Guarantees for Learnware Identification and Reuse

The learnware paradigm enables reusing well-established models on new tasks without retraining or exposing private training data, and a learnware dock system identifies reusable candidates through the compact specification stored with each model. However, existing specifications primarily capture statistical information, which may discard predictive information under tight storage budgets and make specification similarity an unreliable indicator of reuse compatibility. In an attempt to address this limitation, we propose Energy Gradient Specification (Egs), which characterizes and compares well-established models and user tasks in a shared one-step energy gradient space. Specifically, Egs optimizes compact proxy sets to match their gradient responses and uses the resulting gradients as specifications. We further establish a capacity-based generalization bound with only logarithmic dependency on the learnware size, together with an excess-risk decomposition explaining why reuse accuracy rises and then saturates as the dock system expands. Our theoretical results offer new insights into understanding how the learnware size affects reuse performance. Extensive experiments on image and text benchmarks show that Egs outperforms existing distribution-based specification methods across multiple learnware reuse scenarios.