Artificial neural networks (ANNs) are powerful tools capable of approximating
any arbitrary mathematical function, but their interpretability remains
limited, rendering them as black box models. To address this issue, numerous
methods have been proposed to enhance the explainability and interpretability
of ANNs. In this study, we introduce the application of information geometric
framework to investigate phase transition-like behavior during the training of
ANNs and relate these transitions to overfitting in certain models.
The evolution of ANNs during training is studied by looking at the
probability distribution of its parameters. Information geometry utilizing the
principles of differential geometry, offers a unique perspective on probability
and statistics by considering probability density functions as points on a
Riemannian manifold. We create this manifold using a metric based on Fisher
information to define a distance and a velocity. By parameterizing this
distance and velocity with training steps, we study how the ANN evolves as
training progresses. Utilizing standard datasets like MNIST, FMNIST and
CIFAR-10, we observe a transition in the motion on the manifold while training
the ANN and this transition is identified with over-fitting in the ANN models
considered. The information geometric transitions observed is shown to be
mathematically similar to the phase transitions in physics. Preliminary results
showing finite-size scaling behavior is also provided. This work contributes to
the development of robust tools for improving the explainability and
interpretability of ANNs, aiding in our understanding of the variability of the
parameters these complex models exhibit during training.

应用信息几何框架研究人工神经网络（ANN）训练过程中的相变行为与过拟合之间的关联，通过研究 ANN 参数的概率分布，利用差分几何原理构建概率分布函数的黎曼流形，观察到 ANN 在训练过程中在流形上的运动发生相变，该相变与 ANN 模型的过拟合有数学上的相似性，为增强 ANN 的解释能力和可解释性提供了有用的工具。