REALM: Regime-Switching, Explainable, and Activation-Induced Linear Models

2026-09-26

AI Summary

This study addresses the challenge of reconciling predictive accuracy with stable, interpretable local linear modeling in deep ReLU networks. To this end, it proposes a neural activation-induced mixture-of-states linear model. Specifically, a wide and shallow student network is constructed via knowledge distillation, where states are defined through binarized clustered activation patterns to fit local linear models, while multinomial logistic regression generates interpretable state-assignment gating. The primary contribution is a novel two-level architecture that establishes a dual interpretability framework, effectively balancing partition complexity against model stability. Empirical evaluations on both tabular and image datasets demonstrate competitive predictive performance alongside stable, state-level explanations.

Abstract

Deep ReLU networks are piecewise-affine mappings that partition the input space into cells, each characterized by a distinct activation pattern. This structure motivates fitting a local linear model within each cell to preserve predictive accuracy while improving interpretability. The challenge is to identify regimes that are stable, data-adaptive, and easy to explain. We propose REALM, a mixture of linear models whose regimes are induced by neural activation patterns. Because the number of activation cells in a deep neural network (DNN) can grow rapidly with depth, we first distill a deep teacher into a wide, shallow student network (WSSN), then binarize and cluster its hidden-layer activations to define the regimes and fit a linear model within each regime. Since the regimes are discovered from internal structure, the router does not carry the predictive burden. To make regime assignment interpretable, we train a multiclass logistic regression, the explanatory gate, to reproduce the regime assignments. The two-level structure is interpretable at both stages in terms of raw tabular or learned convolutional features: the gate identifies features that determine regime assignments, while the linear models identify features that drive predictions within each regime. We analyze an idealized setting that illustrates a trade-off between partition complexity and stability: as the number of regimes grows, finer partitions can improve approximation but may reduce regime-assignment stability. Experiments on tabular and image datasets show that REALM achieves competitive predictive performance relative to other DNN-guided mixture surrogates and inherently interpretable models while producing stable regime-level explanations.

Problem

• interpretability
• regime-switching
• piecewise-affine
• deep ReLU networks
• mixture of linear models

Innovation

• Regime-Switching
• Explainable AI
• Activation-Induced Linear Models
• Knowledge Distillation
• Mixture of Linear Models