Title:Embedding Foundation Model Predictions in Discrete-Choice Models with Structural Guarantees

Abstract:Tabular foundation models achieve strong accuracy on choice prediction tasks, but their predictions often violate the economic logic those tasks require: raising a price can increase predicted demand, implied willingness-to-pay estimates are frequently negative or implausible, and unavailable alternatives receive nonzero probability. We propose a two-stage adapter that takes a foundation model's predicted choice probabilities as a precomputed feature and embeds them inside a multinomial logit's utility. In Stage 1, we fit the multinomial logit's structural coefficients by maximum likelihood with sign constraints; in Stage 2, we freeze those coefficients and fit a small neural correction operating on the foundation model's predictions. We prove that this composition exactly preserves the multinomial logit's marginal rate of substitution, so analytically computable value-of-time becomes a mathematical guarantee rather than an empirical accident. Across three datasets and two foundation models, the adapter gains 6.4 percentage points (pp) of test accuracy on average over the multinomial logit and up to 12.8 pp, maintains 100% cost monotonicity, and produces values of time within the published transportation-economics range on the transportation datasets. Performance degrades gracefully under foundation-model context restriction, retaining at least 6 pp of accuracy gain even at 10% of the original foundation-model context.

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