Additive Coupling of Liquid Neural Networks and Modern Hopfield Layer for Regression

ICLR 2026 Conference Submission25581 Authors

Keywords: liquid neural networks, modern hopfield network, biologically inspired neural models

Abstract: Regression tasks on complex datasets often involve diverse feature interactions, long-range dependencies, and structured patterns that must be recalled across examples for accurate prediction. Conventional models—such as MLPs, tree ensembles, or standard continuous-time networks, struggle to maintain predictions and stability over extended horizons, especially when patterns must be reused. To address these challenges, we introduce a hybrid architecture that couples Liquid Neural Networks (LNNs) with Modern Hopfield Networks (MHNs) using additive fusion. The LNN component delivers input-adaptive continuous dynamics, while the associative memory enables retrieval and correction using previously encountered global structures. This biologically-inspired design preserves adaptability and stability, while leveraging memory-based recall for consistent predictions. On the OpenML-CTR23 regression benchmark, our approach consistently improved performance, with mean and median gains of 10.42\% and 5.37\%. These results demonstrate the effectiveness of integrating continuous dynamics and content-addressable memory for complex regression scenarios.

Primary Area: learning on time series and dynamical systems

Submission Number: 25581