From Neural Network Decisions to Training Cases: An Exact Account via Case-Based Decision Theory

2026-07-13

AI Summary

This work addresses the lack of auditability in neural networks within high-stakes decision-making by establishing an interpretable mapping between model decisions and individual training examples. Drawing on Case-Based Decision Theory (CBDT), it introduces a method that fits an ordinary least squares (OLS) action readout layer atop fixed neural representations, enabling each predicted action score to be exactly decomposed as a weighted sum of training-case returns. The authors propose a coefficient interpretation mechanism grounded in the geometry of the empirical Gram matrix and provide sufficient conditions under which CBDT’s semantic similarity holds. Requiring neither retraining nor access to the original optimization trajectory, the approach effectively recovers case-level preference structures across multiple datasets, achieving superior Top-30 consistency over existing attribution methods while maintaining competitive performance in reconstruction tasks and delivering auditable decision provenance signals.

Abstract

Neural networks increasingly guide decisions in high-stakes domains such as medical diagnosis, credit approval, and energy bidding. Audit in these settings requires case-level evidence: which training cases support an action and what outcomes they carried. Case-based decision theory (CBDT) formalizes this reasoning by aggregating outcome support from remembered cases. We show that an OLS action readout fitted on a fixed neural representation admits an exact case-based decomposition. Each action score is a weighted sum of training-case returns, with coefficients determined by empirical Gram geometry. We identify a sufficient regime for CBDT similarity semantics; outside it, the coefficients should generally be treated as signed Gram-geometric influence. The decomposition yields audit signals that trace scores to training cases, measure action coherence, and identify weak support. Across synthetic CBDT, PJM, Adult Income, and Default Credit tasks, the method recovers case-level preference structure and achieves the highest mean Top-30 consistency among compared attribution baselines, while remaining competitive on support reconstruction. The audit requires only fitting an OLS top-layer probe, without retraining the representation or accessing the original optimization trajectory; probe fidelity is measured by score reconstruction.

Problem

• auditability
• case-based decision theory
• neural network decisions
• training cases
• high-stakes domains

Innovation

• case-based decision theory
• exact decomposition
• Gram geometry
• auditability
• OLS probe