Interpreting Neural Networks through Mahalanobis Distance

• URL: http://arxiv.org/abs/2410.19352v1
• Date: Fri, 25 Oct 2024 07:21:44 GMT
• Title: Interpreting Neural Networks through Mahalanobis Distance
• Authors: Alan Oursland,
• Abstract summary: This paper introduces a theoretical framework that connects neural network linear layers with the Mahalanobis distance. 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.
• Score: 0.0
• License:
• Abstract: 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.

Related papers

• Deep Learning Through A Telescoping Lens: A Simple Model Provides Empirical Insights On Grokking, Gradient Boosting & Beyond [61.18736646013446]
  In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network. Across three case studies, we illustrate how it can be applied to derive new empirical insights on a diverse range of prominent phenomena.
  arXiv  Detail & Related papers  (2024-10-31T22:54:34Z)
• Statistical tuning of artificial neural network [0.0]
  This study introduces methods to enhance the understanding of neural networks, focusing specifically on models with a single hidden layer. We propose statistical tests to assess the significance of input neurons and introduce algorithms for dimensionality reduction. This research advances the field of Explainable Artificial Intelligence by presenting robust statistical frameworks for interpreting neural networks.
  arXiv  Detail & Related papers  (2024-09-24T19:47:03Z)
• Understanding polysemanticity in neural networks through coding theory [0.8702432681310401]
  We propose a novel practical approach to network interpretability and theoretical insights into polysemanticity and the density of codes. We show how random projections can reveal whether a network exhibits a smooth or non-differentiable code and hence how interpretable the code is. Our approach advances the pursuit of interpretability in neural networks, providing insights into their underlying structure and suggesting new avenues for circuit-level interpretability.
  arXiv  Detail & Related papers  (2024-01-31T16:31:54Z)
• Automated Natural Language Explanation of Deep Visual Neurons with Large Models [43.178568768100305]
  This paper proposes a novel post-hoc framework for generating semantic explanations of neurons with large foundation models. Our framework is designed to be compatible with various model architectures and datasets, automated and scalable neuron interpretation.
  arXiv  Detail & Related papers  (2023-10-16T17:04:51Z)
• Addressing caveats of neural persistence with deep graph persistence [54.424983583720675]
  We find that the variance of network weights and spatial concentration of large weights are the main factors that impact neural persistence. We propose an extension of the filtration underlying neural persistence to the whole neural network instead of single layers. This yields our deep graph persistence measure, which implicitly incorporates persistent paths through the network and alleviates variance-related issues.
  arXiv  Detail & Related papers  (2023-07-20T13:34:11Z)
• Statistical Physics of Deep Neural Networks: Initialization toward Optimal Channels [6.144858413112823]
  In deep learning, neural networks serve as noisy channels between input data and its representation. We study a frequently overlooked possibility that neural networks can be intrinsic toward optimal channels.
  arXiv  Detail & Related papers  (2022-12-04T05:13:01Z)
• Data-driven emergence of convolutional structure in neural networks [83.4920717252233]
  We show how fully-connected neural networks solving a discrimination task can learn a convolutional structure directly from their inputs. By carefully designing data models, we show that the emergence of this pattern is triggered by the non-Gaussian, higher-order local structure of the inputs.
  arXiv  Detail & Related papers  (2022-02-01T17:11:13Z)
• What can linearized neural networks actually say about generalization? [67.83999394554621]
  In certain infinitely-wide neural networks, the neural tangent kernel (NTK) theory fully characterizes generalization. We show that the linear approximations can indeed rank the learning complexity of certain tasks for neural networks. Our work provides concrete examples of novel deep learning phenomena which can inspire future theoretical research.
  arXiv  Detail & Related papers  (2021-06-12T13:05:11Z)
• Learning Connectivity of Neural Networks from a Topological Perspective [80.35103711638548]
  We propose a topological perspective to represent a network into a complete graph for analysis. By assigning learnable parameters to the edges which reflect the magnitude of connections, the learning process can be performed in a differentiable manner. This learning process is compatible with existing networks and owns adaptability to larger search spaces and different tasks.
  arXiv  Detail & Related papers  (2020-08-19T04:53:31Z)
• Network Diffusions via Neural Mean-Field Dynamics [52.091487866968286]
  We propose a novel learning framework for inference and estimation problems of diffusion on networks. Our framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node infection probabilities. Our approach is versatile and robust to variations of the underlying diffusion network models.
  arXiv  Detail & Related papers  (2020-06-16T18:45:20Z)
• Consistent feature selection for neural networks via Adaptive Group Lasso [3.42658286826597]
  We propose and establish a theoretical guarantee for the use of the adaptive group for selecting important features of neural networks. Specifically, we show that our feature selection method is consistent for single-output feed-forward neural networks with one hidden layer and hyperbolic tangent activation function.
  arXiv  Detail & Related papers  (2020-05-30T18:50:56Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.