Value functions and normalizers

Coalition utility is distinct from cooperative-game value (Shapley/Banzhaf attributions). Value functions map model outputs to scalar payoffs; normalizers reshape aggregated attributions for display only.

Utility families

Plugin key

Utility

Mechanism

tfidf_cosine

Lexical similarity

Hashed token rows → frozen-corpus TF-IDF → cosine similarity

embedding_cosine

Semantic similarity

Cosine similarity of static or contextual embeddings

embedding_euclidean

Embedding distance

1 / (1 + L2 distance) between embeddings

logprob

Model confidence

\(v(S) = \frac{1}{|y_S|}\sum_t \log p(y_{S,t} \mid x_S, y_{S,<t})\), the mean log probability of the coalition’s own generation \(y_S\) given its prompt \(x_S\)

Coming from legacy MLLM-Shap maps these to the U1–U4 labels of legacy MLLM-Shap.

Frozen TF-IDF

tfidf_cosine freezes IDF weights on the full run corpus (the base generation and every coalition output) before scoring. Every coalition comparison reuses those weights, so payoffs within one run are on one scale.

Normalizers

Applied after ShapleyAggregator (or Banzhaf) aggregation:

  • Identity — raw attributions

  • AbsSum — divide by sum of absolute values

  • PowerShift — shift to non-negative, power transform, scale to sum 1

  • MinMax — scale to [0, 1], then scale to sum 1

Archives store generations (the base generation and every coalition output), not payoffs or attributions. reanalyze recomputes payoffs with the runner’s value function and attributions with its normalizer, so either can be swapped without new model calls.