Memory-Induced Attractor Dynamics in Liquid Time-Constant Networks

Continuous-time neural networks provide adaptive temporal dynamics for sequential data. However, their hidden state must simultaneously respond to rapidly changing inputs and preserve longer-range context within a single evolving representation. This creates a representational bottleneck, as newly arriving observations can interfere with previously accumulated temporal information. To alleviate this limitation, we propose Memory-Induced Attractor Dynamics in Liquid Time-Constant Networks (AM-LTC), a continuous-time sequence model that integrates trainable memory directly into the hidden-state update. At each time step, the model computes a provisional LTC state, retrieves a memory state through a Modern Hopfield Network, and updates the hidden state through a learned pull toward the retrieved pattern. This allows memory to shape the recurrent transition itself rather than acting only as a representation-level augmentation. Across six classification and three regression benchmarks, AM-LTC improves the average classification accuracy from 87.18 to 89.43 and reduces the average regression MAE from 0.251 to 0.243 relative to LTC. We also demonstrate robustness of AM-LTC under increasing sparsity where it retains highest accuracy compared baseline methods. These results show that memory-based state modulation can improve both robustness and predictive performance in continuous-time sequence models.