Unsupervised Learning in Echo State Networks for Input Reconstruction

Conventional echo state networks (ESNs) require supervised learning to train the readout layer, using the desired outputs as training data. In this study, we focus on input reconstruction (IR), which refers to training the readout layer to reproduce the input time series in its output. We reformulate the learning algorithm of the ESN readout layer to perform IR using unsupervised learning (UL). By conducting theoretical analysis and numerical experiments, we demonstrate that IR in ESNs can be effectively implemented under realistic conditions without explicitly using the desired outputs as training data; in this way, UL is enabled. Furthermore, we demonstrate that applications relying on IR, such as dynamical system replication and noise filtering, can be reformulated within the UL framework. Our findings establish a theoretically sound and universally applicable IR formulation, along with its related tasks in ESNs. This work paves the way for novel predictions and highlights unresolved theoretical challenges in ESNs, particularly in the context of time-series processing methods and computational models of the brain.

Diffusion model for relational inference

Dynamical behaviors of complex interacting systems, including brain activities, financial price movements, and physical collective phenomena, are associated with underlying interactions between the system's components. The issue of uncovering interaction relations in such systems using observable dynamics is called relational inference. In this study, we propose a Diffusion model for Relational Inference (DiffRI), inspired by a self-supervised method for probabilistic time series imputation. DiffRI learns to infer the probability of the presence of connections between components through conditional diffusion modeling. Experiments on both simulated and quasi-real datasets show that DiffRI is highly competent compared with other state-of-the-art models in discovering ground truth interactions in an unsupervised manner. Our code will be made public soon.

Dynamical Graph Echo State Networks with Snapshot Merging for Dissemination Process Classification

The Dissemination Process Classification (DPC) is a popular application of temporal graph classification. The aim of DPC is to classify different spreading patterns of information or pestilence within a community represented by discrete-time temporal graphs. Recently, a reservoir computing-based model named Dynamical Graph Echo State Network (DynGESN) has been proposed for processing temporal graphs with relatively high effectiveness and low computational costs. In this study, we propose a novel model which combines a novel data augmentation strategy called snapshot merging with the DynGESN for dealing with DPC tasks. In our model, the snapshot merging strategy is designed for forming new snapshots by merging neighboring snapshots over time, and then multiple reservoir encoders are set for capturing spatiotemporal features from merged snapshots. After those, the logistic regression is adopted for decoding the sum-pooled embeddings into the classification results. Experimental results on six benchmark DPC datasets show that our proposed model has better classification performances than the DynGESN and several kernel-based models.