We propose a novel way to improve the generalisation capacity of deep learning models by reducing high correlations between neurons. For this, we present two regularisation terms computed from the weights of a minimum spanning tree of the clique whose vertices are the neurons of a given network (or a sample of those), where weights on edges are correlation dissimilarities. We provide an extensive set of experiments to validate the effectiveness of our terms, showing that they outperform popular ones. Also, we demonstrate that naive minimisation of all correlations between neurons obtains lower accuracies than our regularisation terms, suggesting that redundancies play a significant role in artificial neural networks, as evidenced by some studies in neuroscience for real networks. We include a proof of differentiability of our regularisers, thus developing the first effective topological persistence-based regularisation terms that consider the whole set of neurons and that can be applied to a feedforward architecture in any deep learning task such as classification, data generation, or regression.

翻译：我们提出了一种新颖的方法，通过减少神经元之间的高相关性来提升深度学习模型的泛化能力。为此，我们引入了两个正则化项，这些正则化项基于给定网络（或其样本）中所有神经元构成的完全图的权值最小生成树计算得出，其中边权定义为相关性差异。我们通过大量实验验证了所提正则化项的有效性，结果表明其性能优于主流方法。此外，我们证明了对所有神经元之间的相关性进行直接最小化所获得的准确率低于我们的正则化项，这表明冗余在人工神经网络中扮演着重要角色——这与现实神经网络的部分神经科学研究结论一致。我们提供了正则化项可微性的证明，从而首次开发了基于拓扑持久性且适用于全连接架构的有效正则化项，该技术可应用于分类、数据生成或回归等任意深度学习任务。