Title: $$FLAMES2Graph: An Interpretable Federated Multivariate Time Series Classification Framework$$. Abstract: $$Increasing privacy concerns have led to decentralized and federated machine learning techniques that allow individual clients to consult and train models collaboratively without sharing private information. Some of these applications, such as medical and healthcare, require the final decisions to be interpretable. One common form of data in these applications is multivariate time series (MTS), where deep neural networks, especially Convolutional Neural Networks (CNN)-based approaches, have established excellent performance in their classification tasks. However, the promising results and performance of deep learning models are a black box, and their decisions cannot always be guaranteed and trusted. While several approaches address the interpretability of deep learning models for multivariate time series data in a centralized environment, less effort has been made in a federated setting. In this work, We focus on horizontal federated learning and introduce FLAMES2Graph, a new framework designed to interpret the deep learning decisions of each client by extracting and visualizing those input subsequences that highly activate a trained convolutional neural network. These subsequences then form a client evolution graph that captures the temporal dependencies between the extracted unique subsequences. The Federated Learning (FL) clients only share this temporal evolution graph with a centralized server instead of trained model weights to create a global evolution graph. Our extensive experiments on various datasets from well-known multivariate benchmarks indicate the excellent performance of the FLAMES2Graph framework compared to other state-of-the-art federated methods with the advantage of network decision interpretation.$$