๐ค AI Summary
To address inherent dynamic degradation and memory decay in Echo State Networks (ESNs), this paper proposes a closed-loop ESN architecture incorporating learnable nonlinear state feedbackโthe first to embed parameterized, nonlinear feedback directly into the reservoir, thereby overcoming limitations of conventional open-loop designs. Methodologically, the approach integrates a weighted state feedback loop, gradient-assisted output training, and an adaptive spectral radius regulation mechanism, synergistically enhancing temporal representation learning and long-term dependency modeling. Evaluated on multiple time-series forecasting benchmarks, the proposed model achieves a 32% average reduction in prediction error, a 2.1ร improvement in memory capacity, and significantly enhanced generalization stability. This work establishes a novel paradigm for improving the dynamic expressivity and task adaptability of ESNs.