The monotonic dependence of the outputs of a neural network on some of its
inputs is a crucial inductive bias in many scenarios where domain knowledge
dictates such behavior. This is especially important for interpretability and
fairness considerations. In a broader context, scenarios in which monotonicity
is important can be found in finance, medicine, physics, and other disciplines.
It is thus desirable to build neural network architectures that implement this
inductive bias provably. In this work, we propose a weight-constrained
architecture with a single residual connection to achieve exact monotonic
dependence in any subset of the inputs. The weight constraint scheme directly
controls the Lipschitz constant of the neural network and thus provides the
additional benefit of robustness. Compared to currently existing techniques
used for monotonicity, our method is simpler in implementation and in theory
foundations, has negligible computational overhead, is guaranteed to produce
monotonic dependence, and is highly expressive. We show how the algorithm is
used to train powerful, robust, and interpretable discriminators that achieve
competitive performance compared to current state-of-the-art methods across
various benchmarks, from social applications to the classification of the
decays of subatomic particles produced at the CERN Large Hadron Collider.

本文提出一种基于神经网络的单残差连接的加权受限架构，以实现对神经网络输入的任何子集的确切单调依赖，同时控制了神经网络的 Lipschitz 常数，从而提供了鲁棒性，该算法被用于训练强大，鲁棒和可解释的鉴别器，在多个基准测试中均取得了与当前最先进方法相媲美的性能。

表达性单调神经网络

Expressive Monotonic Neural Networks

We consider the problem of combining machine learning models to perform
higher-level cognitive tasks with clear specifications. We propose the novel
problem of Visual Discrimination Puzzles (VDP) that requires finding
interpretable discriminators that classify images according to a logical
specification. Humans can solve these puzzles with ease and they give robust,
verifiable, and interpretable discriminators as answers. We propose a
compositional neurosymbolic framework that combines a neural network to detect
objects and relationships with a symbolic learner that finds interpretable
discriminators. We create large classes of VDP datasets involving natural and
artificial images and show that our neurosymbolic framework performs favorably
compared to several purely neural approaches.

提出一种新的问题，即视觉鉴别谜题（VDP），要求发现可解释的鉴别器以按照逻辑规范对图像进行分类，用组合的神经符号框架结合神经网络和符号学习器，实现机器学习模型的合并来处理高级认知任务。