Artificial Neural Networks (ANNs) require significant amounts of data and computational resources to achieve high effectiveness in performing the tasks for which they are trained. To reduce resource demands, various techniques, such as Neuron Pruning, are applied. Due to the complex structure of ANNs, interpreting the behavior of hidden layers and the features they recognize in the data is challenging. A lack of comprehensive understanding of which information is utilized during inference can lead to inefficient use of available data, thereby lowering the overall performance of the models. In this paper, we introduce a method for integrating Topological Data Analysis (TDA) with Convolutional Neural Networks (CNN) in the context of image recognition. This method significantly enhances the performance of neural networks by leveraging a broader range of information present in the data, enabling the model to make more informed and accurate predictions. Our approach, further referred to as Vector Stitching, involves combining raw image data with additional topological information derived through TDA methods. This approach enables the neural network to train on an enriched dataset, incorporating topological features that might otherwise remain unexploited or not captured by the network's inherent mechanisms. The results of our experiments highlight the potential of incorporating results of additional data analysis into the network's inference process, resulting in enhanced performance in pattern recognition tasks in digital images, particularly when using limited datasets. This work contributes to the development of methods for integrating TDA with deep learning and explores how concepts from Information Theory can explain the performance of such hybrid methods in practical implementation environments.

翻译：人工神经网络（ANN）在执行其训练任务时，需要大量数据和计算资源才能达到高效能。为降低资源需求，人们采用了诸如神经元剪枝等多种技术。由于ANN结构复杂，解释隐藏层的行为及其在数据中识别的特征具有挑战性。若对推理过程中所利用的信息缺乏全面理解，可能导致可用数据使用效率低下，从而降低模型的整体性能。本文提出了一种在图像识别背景下将拓扑数据分析（TDA）与卷积神经网络（CNN）相结合的方法。该方法通过利用数据中更广泛的信息，显著提升了神经网络的性能，使模型能够做出更明智、更准确的预测。我们的方法（后文称为向量缝合）将原始图像数据与通过TDA方法提取的额外拓扑信息相结合。这种方法使神经网络能够在增强的数据集上进行训练，融入拓扑特征——这些特征若不如此处理，可能仍未被利用或未被网络固有机制捕获。实验结果表明，将额外数据分析结果融入网络推理过程具有巨大潜力，特别是在使用有限数据集时，能显著提升数字图像模式识别任务的性能。本研究为TDA与深度学习的融合方法发展做出了贡献，并探讨了信息论概念如何在实际应用环境中解释此类混合方法的性能表现。