Coding schemes in neural networks learning classification tasks

• Published in: Nature communications Vol. 16; no. 1; pp. 3354 - 12
• Main Authors: van Meegen, Alexander, Sompolinsky, Haim
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 09.04.2025; Nature Publishing Group; Nature Portfolio
• Subjects: 631/378/116/1925; 631/378/116/2395; 639/766/530/2804; Bayesian analysis; Broken symmetry; Classification; Coding; Humanities and Social Sciences; Learning; Machine learning; multidisciplinary; Neural coding; Neural networks; Nonlinear systems; Nonlinearity; Representations; Scaling; Science; Science (multidisciplinary); Supervised learning
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-025-58276-6

Neural networks posses the crucial ability to generate meaningful representations of task-dependent features. Indeed, with appropriate scaling, supervised learning in neural networks can result in strong, task-dependent feature learning. However, the nature of the emergent representations is still unclear. To understand the effect of learning on representations, we investigate fully-connected, wide neural networks learning classification tasks using the Bayesian framework where learning shapes the posterior distribution of the network weights. Consistent with previous findings, our analysis of the feature learning regime (also known as ‘non-lazy’ regime) shows that the networks acquire strong, data-dependent features, denoted as coding schemes, where neuronal responses to each input are dominated by its class membership. Surprisingly, the nature of the coding schemes depends crucially on the neuronal nonlinearity. In linear networks, an analog coding scheme of the task emerges; in nonlinear networks, strong spontaneous symmetry breaking leads to either redundant or sparse coding schemes. Our findings highlight how network properties such as scaling of weights and neuronal nonlinearity can profoundly influence the emergent representations. Neural networks discover meaningful representations of the data through the process of learning. Here, the authors explore how these representations are affected by scaling the network output or modifying the activation functions.