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
https://github.com/koriavinash1/SymbolicInterpretability.

使用超几何来解释深度判别模型的特征重要性和生成层级符号规则的方法，有效提高了模型解释的多级抽象水平。

在双曲空间中进行层次符号推理以用于深度判别模型

Hierarchical Symbolic Reasoning in Hyperbolic Space for Deep Discriminative Models

Deep discriminative models (e.g. deep regression forests, deep neural
decision forests) have achieved remarkable success recently to solve problems
such as facial age estimation and head pose estimation. Most existing methods
pursue robust and unbiased solutions either through learning discriminative
features, or reweighting samples. We argue what is more desirable is learning
gradually to discriminate like our human beings, and hence we resort to
self-paced learning (SPL). Then, a natural question arises: can self-paced
regime lead deep discriminative models to achieve more robust and less biased
solutions? To this end, this paper proposes a new deep discriminative
model--self-paced deep regression forests with consideration on
underrepresented examples (SPUDRFs). It tackles the fundamental ranking and
selecting problem in SPL from a new perspective: fairness. This paradigm is
fundamental and could be easily combined with a variety of deep discriminative
models (DDMs). Extensive experiments on two computer vision tasks, i.e., facial
age estimation and head pose estimation, demonstrate the efficacy of SPUDRFs,
where state-of-the-art performances are achieved.

本文提出了一种新的自我定步深度回归森林模型（SPUDRFs）解决深度识别模型中的排序和选择问题，在人脸年龄估计和头部姿势估计等视觉任务中实现了最先进的表现。