Hierarchical Symbolic Reasoning in Hyperbolic Space for Deep Discriminative Models

TL;DR

This paper introduces a hierarchical symbolic reasoning approach in hyperbolic space to generate multi-level explanations for deep discriminative models, enhancing interpretability with symbolic rules and visual semantics.

Contribution

It proposes a novel method combining hyperbolic geometry and vector quantisation to produce hierarchical symbolic explanations from deep models, capturing multiple abstraction levels.

Findings

Effective hierarchical explanations on MNIST and AFHQ datasets

Generation of symbolic rules with visual semantics

Improved interpretability of deep discriminative models

Abstract

Explanations for \emph{black-box} models help us understand model decisions as well as provide information on model biases and inconsistencies. Most of the current explainability techniques provide a single level of explanation, often in terms of feature importance scores or feature attention maps in input space. Our focus is on explaining deep discriminative models at \emph{multiple levels of abstraction}, from fine-grained to fully abstract explanations. We achieve this by using the natural properties of \emph{hyperbolic geometry} to more efficiently model a hierarchy of symbolic features and generate \emph{hierarchical symbolic rules} as part of our explanations. Specifically, for any given deep discriminative model, we distill the underpinning knowledge by discretisation of the continuous latent space using vector quantisation to form symbols, followed by a \emph{hyperbolic reasoning block} to induce an \emph{abstraction tree}. We traverse the tree to extract explanations in terms of symbolic rules and its corresponding visual semantics. We demonstrate the effectiveness of our method on the MNIST and AFHQ high-resolution animal faces dataset. Our framework is available at \url{https://github.com/koriavinash1/SymbolicInterpretability}.