Categorization is an important topic both for biological and artificial neural networks. Here, we take an information theoretic approach to assess the efficiency of the representations induced by category learning. We show that one can decompose the relevant Bayesian cost into two components, one for the coding part and one for the decoding part. Minimizing the coding cost implies maximizing the mutual information between the set of categories and the neural activities. We analytically show that this mutual information can be written as the sum of two terms that can be interpreted as (i) finding an appropriate representation space, and, (ii) building a representation with the appropriate metrics, based on the neural Fisher information on this space. One main consequence is that category learning induces an expansion of neural space near decision boundaries. Finally, we provide numerical illustrations that show how Fisher information of the coding neural population aligns with the boundaries between categories.

翻译：类别化是生物与人工神经网络研究的重要课题。本文采用信息论方法评估类别学习所诱导的表征效率。研究表明，相关贝叶斯代价可分解为两部分：编码代价与解码代价。最小化编码代价意味着最大化类别集合与神经活动之间的互信息。我们通过解析证明，该互信息可表示为两项之和，其分别对应：(i) 寻找合适的表征空间，(ii) 基于该空间上的神经Fisher信息构建具有恰当度量的表征。这一结论的重要推论是：类别学习会在决策边界附近引发神经空间扩张。最后，我们通过数值仿真展示了编码神经群体的Fisher信息如何与类别边界实现对齐。