Scalable Monotonic Neural Networks

In this research, we focus on the problem of learning monotonic neural networks, as preserving the monotonicity of a model with respect to a subset of inputs is crucial for practical applications across various domains. Although several methods have recently been proposed to address this problem, they have limitations such as not guaranteeing monotonicity in certain cases, requiring additional inference time, lacking scalability with increasing network size and number of monotonic inputs, and manipulating network weights during training. To overcome these limitations, we introduce a simple but novel architecture of the partially connected network which incorporates a 'scalable monotonic hidden layer' comprising three units: the exponentiated unit, ReLU unit, and confluence unit. This allows for the repetitive integration of the scalable monotonic hidden layers without other structural constraints. Consequently, our method offers ease of implementation and rapid training through the conventional error-backpropagation algorithm. We accordingly term this method as Scalable Monotonic Neural Networks (SMNN). Numerical experiments demonstrated that our method achieved comparable prediction accuracy to the state-of-the-art approaches while effectively addressing the aforementioned weaknesses.