Hidden State-Space Decomposition for Long-Term Retention in Liquid Time-Constant Networks

Continuous-time recurrent models naturally handle irregularly sampled data by evolving hidden states as a function of elapsed time. Among these models, Liquid Time-Constant (LTC) networks adapt the rate of state evolution based on the current input, allowing their dynamics to change over time. This adaptability comes with an inherent decay of their hidden state, where information is progressively attenuated from earlier observations. Writing new information and preserving earlier information depend on the same state dynamics. Rapid writing requires the state to change quickly, while long-term retention requires the state to decay slowly. We introduce State-Space Decomposed Liquid Time-Constant Networks (SSD-LTC), where we decompose the LTC hidden state into an adaptive liquid subspace and a controlled persistent subspace. The adaptive liquid component follows the LTC dynamics, while the persistent component uses an input-dependent write rate to balance writing new information with preserving its previous state. We theoretically characterize state attenuation and the writing–retention trade-off in LTCs, and establish boundedness and stability properties of SSD-LTC. Across ten regularly sampled and eight irregularly sampled benchmarks, SSD-LTC improves classification accuracy by 2.2 to 8.0 percentage points and reduces regression and forecasting errors by up to 30% compared with the baseline LTC. We further show through controlled recall and component-exchange experiments that the learned persistent component acts as memory. These results demonstrate that separating adaptive state evolution from persistent information retention improves temporal modeling while retaining the continuous-time dynamics of LTCs.