Normalized Relevance Measure as a Unifying Framework to Explain Neural Network Latent Structures
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913175630249984 |
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| author | Xiong, Ping Schnake, Thomas Montavon, Grégoire Müller, Klaus-Robert Nakajima, Shinichi |
| author_facet | Xiong, Ping Schnake, Thomas Montavon, Grégoire Müller, Klaus-Robert Nakajima, Shinichi |
| contents | To understand how a neural network (NN) functions and makes predictions, it has become increasingly clear that analyzing only the input domain is insufficient -- one must also examine its internal inference mechanisms to capture the complete picture. To explain the internal inference mechanisms of such models, it is essential to analyze the importance of latent representations for a given task. In this paper, we propose the \emph{normalized relevance measure} (NRM) framework -- a novel general explanation procedure that attributes relevance to \emph{arbitrary sets of neurons across layers of arbitrary architectures}. In the NRM framework, relevance of selected neurons is explicitly defined as a normalized signed measure, constructed using simple operations -- marginalization and conditioning based on additive and multiplicative laws -- in analogy to the probability measures. The normalization property further guarantees comparability across layers. The NRM framework subsumes existing propagation-based explanation algorithms by explicitly identifying the underlying quantity being computed. We demonstrate the utility of the framework in computer vision applications, where joint relevance analysis across multiple layers reveals key information flows in VGG16 networks. Overall, the NRM framework provides a general, mathematically grounded approach to understanding how modern NNs propagate information, offering a versatile and broadly applicable foundation for explainable artificial intelligence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_00557 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Normalized Relevance Measure as a Unifying Framework to Explain Neural Network Latent Structures Xiong, Ping Schnake, Thomas Montavon, Grégoire Müller, Klaus-Robert Nakajima, Shinichi Machine Learning To understand how a neural network (NN) functions and makes predictions, it has become increasingly clear that analyzing only the input domain is insufficient -- one must also examine its internal inference mechanisms to capture the complete picture. To explain the internal inference mechanisms of such models, it is essential to analyze the importance of latent representations for a given task. In this paper, we propose the \emph{normalized relevance measure} (NRM) framework -- a novel general explanation procedure that attributes relevance to \emph{arbitrary sets of neurons across layers of arbitrary architectures}. In the NRM framework, relevance of selected neurons is explicitly defined as a normalized signed measure, constructed using simple operations -- marginalization and conditioning based on additive and multiplicative laws -- in analogy to the probability measures. The normalization property further guarantees comparability across layers. The NRM framework subsumes existing propagation-based explanation algorithms by explicitly identifying the underlying quantity being computed. We demonstrate the utility of the framework in computer vision applications, where joint relevance analysis across multiple layers reveals key information flows in VGG16 networks. Overall, the NRM framework provides a general, mathematically grounded approach to understanding how modern NNs propagate information, offering a versatile and broadly applicable foundation for explainable artificial intelligence. |
| title | Normalized Relevance Measure as a Unifying Framework to Explain Neural Network Latent Structures |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2606.00557 |