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Interpreting Neural Networks through Mahalanobis Distance

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arxiv 2410.19352 v1 pith:6LDK2DLG submitted 2024-10-25 cs.LG cs.AIstat.ML

Alan Oursland This is my paper · ORCID
classification cs.LGcs.AIstat.ML
keywords neuralnetworkdistanceexploredfunctionsmahalanobistheoreticalwork
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This paper introduces a theoretical framework that connects neural network linear layers with the Mahalanobis distance, offering a new perspective on neural network interpretability. While previous studies have explored activation functions primarily for performance optimization, our work interprets these functions through statistical distance measures, a less explored area in neural network research. By establishing this connection, we provide a foundation for developing more interpretable neural network models, which is crucial for applications requiring transparency. Although this work is theoretical and does not include empirical data, the proposed distance-based interpretation has the potential to enhance model robustness, improve generalization, and provide more intuitive explanations of neural network decisions.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Neural Networks Use Distance Metrics

    cs.LG 2024-11 reject novelty 4.0 of 10

    A small MNIST classifier is far more sensitive to shifts of internal decision boundaries than to scaling or clipping of activations, supporting the author's claim that such networks use distance-like representations.

  2. Gradient Descent as Implicit EM in Distance-Based Neural Models

    cs.LG 2025-12 reject novelty 3.0 of 10

    For log-sum-exp objectives, the gradient with respect to each distance is the negative softmax responsibility; the paper interprets this as implicit expectation-maximization in neural training.

  3. Neural Networks Learn Distance Metrics

    cs.LG 2025-02 reject novelty 3.0 of 10

    A two-layer MNIST study argues that networks prefer distance-based representations, but the evidence is mostly architecture-specific and the OffsetL2 layer resembles known RBF units.

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