Structural Interpretability: Unifying Deep Network Analysis via Piecewise Linear Path Algebras
Abstract
Post-hoc Explainable Artificial Intelligence (XAI) methods provide useful but potentially divergent views of neural-network decisions. We introduce Unified Quiver Analysis of Neural Networks (UQANN), a framework for relating interpretability diagnostics through local path-algebra representations of continuous piecewise-linear (CPWL) networks. Within the interior of a polyhedral linearity cell, fixed activation masks and pooling-selection operators determine an instantiated quiver with invariant combinatorial path support. Under explicit decomposition assumptions, the local Jacobian admits a path-wise expansion compatible with the completeness identity of Integrated Gradients. The framework relates Feature Visualization, semantic alignment through an Algebraic Coherence Index, Topological Data Analysis, and attribution. The empirical implementation uses filter-level visualizations, spatial-support point clouds, morphism-level attribution, and thresholded routing-support proxies rather than exhaustive channel-level path computations. We demonstrate the framework on a VGG16-BN-style classifier trained from scratch on Tiny ImageNet. Across 11 selected comparative pairs, the diagnostics describe differences in routing-support proxies, while targeted channel ablations measure the functional influence of selected channels on the examined logits. A separate feasibility benchmark demonstrates channel-level subgraph and dominant-path extraction on a representative case. These results position UQANN as a proof-of-concept structural auditing framework rather than a complete solution to explanatory disagreement. Future work will compare the operational proxies with channel-level computations on controlled cases and evaluate scalable extraction across larger image sets and multiple target channels. The findings remain conditional on the model, diagnostic datasets, and extraction thresholds.
Related
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BibTeX
@misc{tchietchouang2026structural,
title = {{Structural Interpretability: Unifying Deep Network Analysis via Piecewise Linear Path Algebras}},
author = {Christian Tchietchouang and Louis Fippo Fitime and Thomas Bouetou Bouetou},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05774651v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Structural Interpretability: Unifying Deep Network Analysis via Piecewise Linear Path Algebras
AU - Christian Tchietchouang
AU - Louis Fippo Fitime
AU - Thomas Bouetou Bouetou
PY - 2026
DA - 2026/09/25
PB - HAL
UR - https://hal.science/hal-05774651v1
AB - Post-hoc Explainable Artificial Intelligence (XAI) methods provide useful but potentially divergent views of neural-network decisions. We introduce Unified Quiver Analysis of Neural Networks (UQANN), a framework for relating interpretability diagnostics through local path-algebra representations of continuous piecewise-linear (CPWL) networks. Within the interior of a polyhedral linearity cell, fixed activation masks and pooling-selection operators determine an instantiated quiver with invariant combinatorial path support. Under explicit decomposition assumptions, the local Jacobian admits a path-wise expansion compatible with the completeness identity of Integrated Gradients. The framework relates Feature Visualization, semantic alignment through an Algebraic Coherence Index, Topological Data Analysis, and attribution. The empirical implementation uses filter-level visualizations, spatial-support point clouds, morphism-level attribution, and thresholded routing-support proxies rather than exhaustive channel-level path computations. We demonstrate the framework on a VGG16-BN-style classifier trained from scratch on Tiny ImageNet. Across 11 selected comparative pairs, the diagnostics describe differences in routing-support proxies, while targeted channel ablations measure the functional influence of selected channels on the examined logits. A separate feasibility benchmark demonstrates channel-level subgraph and dominant-path extraction on a representative case. These results position UQANN as a proof-of-concept structural auditing framework rather than a complete solution to explanatory disagreement. Future work will compare the operational proxies with channel-level computations on controlled cases and evaluate scalable extraction across larger image sets and multiple target channels. The findings remain conditional on the model, diagnostic datasets, and extraction thresholds.
ER -