The expressiveness of neural networks highly depends on the nature of the activation function, although these are usually assumed predefined and fixed during the training stage. In this paper we present Expressive Neural Network (ENN), a novel architecture in which the non-linear activation functions are modeled using the Discrete Cosine Transform (DCT) and adapted using backpropagation during training. This parametrization keeps the number of trainable parameters low, is appropriate for gradient-based schemes, and adapts to different learning tasks. This is the first non-linear model for activation functions that relies on a signal processing perspective, providing high flexibility and expressiveness to the network. We contribute with insights in the explainability of the network at convergence by recovering the concept of bump, this is, the response of each activation function in the output space to provide insights. Finally, through exhaustive experiments we show that the model can adapt to classification and regression tasks. The performance of ENN outperforms state of the art benchmarks, providing up to a 40\% gap in accuracy in some scenarios.

翻译：神经网络的表达能力高度依赖于激活函数的性质，尽管这些函数在训练阶段通常被预设为固定形式。本文提出表达性神经网络（ENN），这是一种新型架构，其中非线性激活函数采用离散余弦变换（DCT）建模，并在训练过程中通过反向传播进行自适应调整。该参数化方法使可训练参数数量保持低位，适合基于梯度的优化方案，并能适应不同学习任务。这是首个基于信号处理视角的激活函数非线性模型，为网络提供了高度灵活性与表达能力。我们通过引入"凸包（bump）"概念——即每个激活函数在输出空间中的响应——为网络收敛后的可解释性提供了洞见。最后，通过大量实验表明，该模型可适用于分类与回归任务。ENN的性能超越了当前最先进的基准模型，在某些场景下准确率差距高达40%。