Consideration Circuits: Depth Separation and Universality Beyond a Single Softmax

תקציר מקורי באנגליתarXiv:2610.04143v2 Announce Type: replace Abstract: Most feature-based choice models, classical and deep, score items and apply a single softmax. We introduce consideration circuits (CC), feature-based models of multi-stage choice defined by directed acyclic graphs of multinomial logit (MNL) units. Source units assign probabilities to menu items, and internal units combine predecessor distributions using MNL weights computed from their probability-weighted feature summaries. On a three-item compromise task with fixed non-collinear features, menu-independent random-utility models (RUM), including a single MNL unit, suffer an error bounded away from zero. For CC, in contrast, we establish a sharp depth--norm separation: increasing depth from $2$ to $3$ reduces the optimal maximum taste-vecto