Beyond Softmax: A Natural Parameterization for Categorical Random Variables

arXiv:2509.24728v2 Announce Type: replace Abstract: Latent categorical variables are frequently found in deep learning architectures. They can model actions in discrete reinforcement-learning environments, represent categories in latent-variable models, or express relations in graph neural networks. Despite their widespread use, their discrete nature poses significant challenges to gradient-descent learning algorithms. While a substantial body of work has offered improved gradient estimation techniques, we take a complementary approach. Specifically, we: 1) revisit the ubiquitous extit{softmax} function and demonstrate its limitations from an information-geometric perspective; 2) replace the extit{softmax} with the extit{catnat} function, a function composed of a sequence of hierarchical binary splits; we prove that this choice offers significant advantages to gradient descent due to the resulting diagonal Fisher Information Matrix. A rich set of experiments - including graph structure learning, variational autoencoders, and reinforcement learning - empirically show that the proposed function improves the learning efficiency and yields models characterized by consistently higher test performance. extit{Catnat} is simple to implement and seamlessly integrates into existing codebases. Moreover, it remains compatible with standard training stabilization techniques and, as such, offers a better alternative to the extit{softmax} function.

Source: arXiv cs.LG | 2026-05-14