Persistence Infused Random Walk Positional Encoding for Graph Transformers on Handwritten Character Graphs

Positional encoding is a critical component in graph transformers for capturing structural information. This paper, propose a novel persistence-infused random-walk positional encoding, designed to improve the performance of graph transformers on handwritten character recognition. This method integrates persistence values into the random walk with an exponential decay function, thereby yielding more discriminative node representations. The experiments show that the model performs superior than the baseline random walk model with improved accuracy. This approach is further validated through visualizations of the adjacency matrix and comprehensive statistical tests. The results suggest that persistence-enhanced positional encoding can effectively capture complex graph structures and provides an efficient pathway for graph representation learning.