<b>Debreu Activation: A Novel Monotonic and Continuous Function Inspired by Economic Theory for Deep Learning</b>

Activation functions are the core components of nonlinear modeling in neural networks. This paper proposes a new activation function inspired by Gérard Debreu's utility theory and verifies its effectiveness in image classification tasks. Unlike traditional activation functions that only focus on mathematical convenience or gradient propagation characteristics, this paper attempts to introduce the concept of "preferring strict incrementality and continuity" in economics into deep learning. By constructing a composite function structure with strict monotonicity and continuity, we design a new universal activation function, Debreu Activation. Experiments show that this activation function can bring a stable and small performance improvement without increasing the complexity of training, and is applicable to a variety of neural network structures.