Training-Free Few-Shot Adaptation via Exponential Tilting of Latent Representations

Adapting frozen foundation models to new few-shot tasks is often infeasible when parameters cannot be modified e.g., under shared checkpoints or deployment policies barring mutation. We study few-shot classification under this fully frozen-model regime: no gradients, no parameter updates, no upstream data. We show that under these constraints, adaptation reduces to choosing a weighting over the support embeddings used to form class prototypes, and that exponential (Gibbs) tilting is the unique such weighting minimizing KL divergence from the empirical support distribution subject to a task-relevance constraint. We instantiate this constraint with simple support-set scores label consistency, geometric alignment, or classifier confidence yielding closed-form tilted prototypes with no backward pass or iterative solving. Across three frozen encoders (DINOv3, I-JEPA, CLIP) and several few-shot and cross-domain benchmarks, tilted prototypes improve over uniform-average baselines in most settings and are competitive with training-free adaptation methods that use strictly more information (query streams, upstream statistics), while gradient-based fine-tuning remains an upper bound under weaker constraints. This positions principled latent-distribution reweighting as a lightweight, gradient-free alternative to parameter-based few-shot adaptation.