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Neural Interpretable Reasoning

Pietro Barbiero, Giuseppe Marra, Gabriele Ciravegna, David Debot, Francesco De Santis, Michelangelo Diligenti, Mateo Espinosa Zarlenga, Francesco Giannini

TL;DR

A novel modeling framework for achieving interpretability in deep learning is formalized, anchored in the principle of inference equivariance, and a new modeling paradigm -- neural generation and interpretable execution -- is proposed that enables scalable verification of equivariance.

Abstract

We formalize a novel modeling framework for achieving interpretability in deep learning, anchored in the principle of inference equivariance. While the direct verification of interpretability scales exponentially with the number of variables of the system, we show that this complexity can be mitigated by treating interpretability as a Markovian property and employing neural re-parametrization techniques. Building on these insights, we propose a new modeling paradigm -- neural generation and interpretable execution -- that enables scalable verification of equivariance. This paradigm provides a general approach for designing Neural Interpretable Reasoners that are not only expressive but also transparent.

Neural Interpretable Reasoning

TL;DR

A novel modeling framework for achieving interpretability in deep learning is formalized, anchored in the principle of inference equivariance, and a new modeling paradigm -- neural generation and interpretable execution -- is proposed that enables scalable verification of equivariance.

Abstract

We formalize a novel modeling framework for achieving interpretability in deep learning, anchored in the principle of inference equivariance. While the direct verification of interpretability scales exponentially with the number of variables of the system, we show that this complexity can be mitigated by treating interpretability as a Markovian property and employing neural re-parametrization techniques. Building on these insights, we propose a new modeling paradigm -- neural generation and interpretable execution -- that enables scalable verification of equivariance. This paradigm provides a general approach for designing Neural Interpretable Reasoners that are not only expressive but also transparent.

Paper Structure

This paper contains 17 sections, 8 equations, 2 figures.

Table of Contents

  1. A Turing test for interpretability
  2. Contributions
  3. Interpretability & equivariance
  4. Interpretability as inference equivariance
  5. Preliminaries: Transformation of Random Variables
  6. Inference equivariance
  7. Verify interpretability via inference equivariance is intractable
  8. Properties of interpretability through the lenses of inference equivariance
  9. Semantic and functional equivariances
  10. Breaking combinatorial complexity in verifying interpretability
  11. Interpretability is a Markovian property
  12. Re-parametrizations break equivariance complexity while guaranteeing expressivity and interpretability
  13. Functional Mixtures
  14. Functional and semantic re-parametrizations
  15. Neural Interpretable Reasoning
  16. ...and 2 more sections

Figures (2)

  • Figure 1: Example of inference equivariance.
  • Figure 2: Neural Interpretable Reasoning.

Theorems & Definitions (4)

  • Example 1
  • Example 2: The Donald Duck Comfort Problem (Fig. \ref{['fig:equiv_example']})
  • Example 3
  • Example 4: Thermostat with Many Knobs