Title: Echo State Transformer: Attention over Finite Memories
Primary area: learning on time series and dynamical systems
Keywords: Echo State Transformer, EST, reservoir computing, echo state networks, ESN, attention, working memory, linear-time sequence modeling, fixed-size memory, transformers, state space models, SSM, time series, short-term forecasting, time-series classification, anomaly detection, leak rate, spectral radius, FLOPs, TSL, TSLib

Abstract: While Large Language Models and their underlying Transformer architecture are remarkably efficient, they do not reflect how our brain processes and learns a diversity of cognitive tasks such as language and working memory. Furthermore, sequential data processing with Transformers encounters a fundamental barrier: quadratic complexity growth with sequence length. Motivated by these limitations, our ambition is to create more efficient models that are less reliant on intensive computations. We introduce Echo State Transformers (EST), a hybrid architecture that elegantly resolves this challenge while demonstrating exceptional performance in classification and detection tasks. EST integrates the Transformer attention mechanisms with principles from Reservoir Computing to create a fixed-size window distributed memory system. Drawing inspiration from Echo State Networks, the most prominent instance of the Reservoir Computing paradigm, our approach leverages reservoirs (random recurrent networks) as a lightweight and efficient memory. Our architecture integrates a new module called "Working Memory" based on several reservoirs working in parallel. These reservoirs work as independent working memory units with distinct internal dynamics. A novelty here is that the classical reservoir hyperparameters, controlling the dynamics, are now trained. Thus, the EST dynamically adapts the reservoir memory/non-linearity trade-off. Thanks to these working memory units, EST achieves constant computational complexity at each processing step, effectively breaking the quadratic scaling problem of standard Transformers. We evaluate ESTs on a recent challenging timeseries benchmark: the Time Series Library, which comprises 69 tasks across five categories. Results show that ESTs ranks first overall in two of five categories, outperforming strong state-of-the-art baselines on classification and anomaly detection tasks, while remaining competitive on short-term forecasting. These results position ESTs as a compelling alternative for time-series classification and anomaly detection, and a practical complement to transformer-style models in applications that prioritize robust representations and sensitive event detection.

TL;DR: The Echo State Transformer (EST) is a memory-augmented architecture that uses reservoir-based working memory with attention, achieving linear-time scaling and SOTA performance on time-series tasks including classification and anomaly detection.