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.

翻译：神经网络输出对其某些输入的单调依赖性是一种关键的归纳偏置，在领域知识要求此类行为的许多场景中尤为重要，尤其是对于可解释性和公平性考量。在更广泛的背景下，金融、医学、物理学及其他学科中均可发现单调性至关重要的情况。因此，构建能够可证明地实现这种归纳偏置的神经网络架构具有重要价值。本文提出一种带有单一残差连接的权重约束架构，可在任意输入子集上实现精确的单调依赖。该权重约束方案直接控制神经网络的Lipschitz常数，从而带来鲁棒性的额外优势。与现有单调性技术相比，我们的方法在实现和理论基础方面更为简单，计算开销可忽略不计，能保证产生单调依赖，且具有高度表达能力。我们展示了该算法如何用于训练强大、鲁棒且可解释的判别器，在从社会应用到欧洲核子研究中心大型强子对撞机产生的亚原子粒子衰变分类等各类基准测试中，其性能均达到与当前最先进方法相媲美的水平。