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Local-to-Global Logical Explanations for Deep Vision Models

Bhavan Vasu, Giuseppe Raffa, Prasad Tadepalli

TL;DR

This work tackles the opacity of deep vision models by introducing local and global explanations grounded in human-interpretable object parts. Local explanations for individual images are formulated as complete monotone $MDNF$ expressions over minimally sufficient object-part subsets $P_{ ext{min}}(x,y)$, enabling instance-level transparency. Global explanations aggregate these locals via greedy covering to form a compact class-level $MDNF$, and via an explanation list to jointly explain multiple classes without retraining. Empirical results on ADE20K and Pascal-Parts with both CNN and ViT backbones show strong fidelity and substantial coverage (e.g., ~85% of decisions explained with ~20 clauses) and a competitive multi-class explanation accuracy (e.g., 75.69% on ADE20K with ViT-B), supporting GDPR-aligned, model-agnostic interpretability for deep vision systems. The framework offers practical, scalable insights for auditing and deploying complex models while preserving protection of proprietary components.

Abstract

While deep neural networks are extremely effective at classifying images, they remain opaque and hard to interpret. We introduce local and global explanation methods for black-box models that generate explanations in terms of human-recognizable primitive concepts. Both the local explanations for a single image and the global explanations for a set of images are cast as logical formulas in monotone disjunctive-normal-form (MDNF), whose satisfaction guarantees that the model yields a high score on a given class. We also present an algorithm for explaining the classification of examples into multiple classes in the form of a monotone explanation list over primitive concepts. Despite their simplicity and interpretability we show that the explanations maintain high fidelity and coverage with respect to the blackbox models they seek to explain in challenging vision datasets.

Local-to-Global Logical Explanations for Deep Vision Models

TL;DR

This work tackles the opacity of deep vision models by introducing local and global explanations grounded in human-interpretable object parts. Local explanations for individual images are formulated as complete monotone expressions over minimally sufficient object-part subsets , enabling instance-level transparency. Global explanations aggregate these locals via greedy covering to form a compact class-level , and via an explanation list to jointly explain multiple classes without retraining. Empirical results on ADE20K and Pascal-Parts with both CNN and ViT backbones show strong fidelity and substantial coverage (e.g., ~85% of decisions explained with ~20 clauses) and a competitive multi-class explanation accuracy (e.g., 75.69% on ADE20K with ViT-B), supporting GDPR-aligned, model-agnostic interpretability for deep vision systems. The framework offers practical, scalable insights for auditing and deploying complex models while preserving protection of proprietary components.

Abstract

While deep neural networks are extremely effective at classifying images, they remain opaque and hard to interpret. We introduce local and global explanation methods for black-box models that generate explanations in terms of human-recognizable primitive concepts. Both the local explanations for a single image and the global explanations for a set of images are cast as logical formulas in monotone disjunctive-normal-form (MDNF), whose satisfaction guarantees that the model yields a high score on a given class. We also present an algorithm for explaining the classification of examples into multiple classes in the form of a monotone explanation list over primitive concepts. Despite their simplicity and interpretability we show that the explanations maintain high fidelity and coverage with respect to the blackbox models they seek to explain in challenging vision datasets.
Paper Structure (9 sections, 3 theorems, 5 equations, 3 figures, 1 table, 3 algorithms)

This paper contains 9 sections, 3 theorems, 5 equations, 3 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Sufficient and Complete Local Explanations
  4. Computing Complete Explanations
  5. Computing Global Explanations
  6. Finding Covering Explanations
  7. Global Multi-Class Explanations
  8. Experimental Setup and Results
  9. Conclusion and Future Work

Key Result

theorem thmcountertheorem

Every member of the list returned by Algorithm 1 satisfies the sufficiency test and is non-redundant. Further, if $f_y(x_S)$ is monotonic and the beam width is sufficiently large, then the algorithm correctly computes $P_{min}(x,y)$.

Figures (3)

  • Figure 1: Figure shows the visualization of multiple minimally sufficient concept based local explanations (MSCX) $P^{min}(x, y)$ for two images from the classes Living Room and Dining Room from the ADE20k dataset. Different local explanations focus on different sets of objects.
  • Figure 2: Local explanations across multiple images are used to generate global covering explanations that cover a given class i.e., Covering explanations (left-top) vs Multi-class Explanations (left-bottom) that explain all classes. (Right) The size (number of literals) of the MSCX vs the number of MSCXs of that size.
  • Figure 3: Percentage of images covered vs. number of clauses in the covering explanations for class 'Street' and 'Bedroom' from ADE20k dataset.

Theorems & Definitions (3)

  • theorem thmcountertheorem
  • theorem thmcountertheorem
  • theorem thmcountertheorem