# Hierarchical Symbolic Reasoning in Hyperbolic Space for Deep Discriminative Models

arXiv: https://arxiv.org/abs/2207.01916 · HTML: https://mlsanity.com/paper/2207.01916/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 33 of its 54 references that are in the map.
- First posted on arXiv 5 Jul 2022.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)

## Builds on (most cited first, 30 of 33)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [AI safety via debate](https://mlsanity.com/paper/1805.00899/) (2018)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [Neural-Symbolic VQA: Disentangling Reasoning from Vision and Language Understanding](https://mlsanity.com/paper/1810.02338/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Explaining Image Classifiers by Counterfactual Generation](https://mlsanity.com/paper/1807.08024/) (2018)
- [Explaining in Style: Training a GAN to explain a classifier in StyleSpace](https://mlsanity.com/paper/2104.13369/) (2021)
- [Learning by Abstraction: The Neural State Machine](https://mlsanity.com/paper/1907.03950/) (2019)
- [Counterfactual Generative Networks](https://mlsanity.com/paper/2101.06046/) (2021)
- [Right for the Right Concept: Revising Neuro-Symbolic Concepts by Interacting with their Explanations](https://mlsanity.com/paper/2011.12854/) (2020)
- [Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifolds](https://mlsanity.com/paper/1605.07147/) (2016)
- [Latent Weights Do Not Exist: Rethinking Binarized Neural Network Optimization](https://mlsanity.com/paper/1906.02107/) (2019)
- [Probabilistic Neural-symbolic Models for Interpretable Visual Question Answering](https://mlsanity.com/paper/1902.07864/) (2019)
- [DISSECT: Disentangled Simultaneous Explanations via Concept Traversals](https://mlsanity.com/paper/2105.15164/) (2021)
- [Tell me why! Explanations support learning relational and causal structure](https://mlsanity.com/paper/2112.03753/) (2021)
- [CounteRGAN: Generating Realistic Counterfactuals with Residual Generative Adversarial Nets](https://mlsanity.com/paper/2009.05199/) (2020)

## Built on by (most cited first, 3 of 3)

- [Grounded Object Centric Learning](https://mlsanity.com/paper/2307.09437/) (2023)
- [A survey on Concept-based Approaches For Model Improvement](https://mlsanity.com/paper/2403.14566/) (2024)
- [Explaining Image Classification with Visual Debates](https://mlsanity.com/paper/2210.09015/) (2022)

## Abstract (arXiv)

Explanations for 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 multiple levels of abstraction, from fine-grained to fully abstract explanations. We achieve this by using the natural properties of hyperbolic geometry to more efficiently model a hierarchy of symbolic features and generate 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 hyperbolic reasoning block to induce an 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 urlhttps://github.com/koriavinash1/SymbolicInterpretability.