Context-Dependent Manifold Learning in Dynamical Systems: A Neuromodulated Constrained Autoencoder Approach

This work introduces a novel approach to context-dependent manifold learning in dynamical systems using a modulated constrained autoencoder (cAE). Classic dimensionality reduction methods often fail to account for context-dependent relationships in data without explicitly reducing the context combined with the original input. However, these relationships are critical when physical parameters or environmental conditions vary. Building on the constrained autoencoder framework, which imposes geometric constraints to ensure smooth manifold representations and proper projections, we incorporate neuromodulation to enable context-dependent learning. Neuromodulation is a fundamental mechanism that uses neuromodulators to tune neuronal properties and circuit function dynamically. It is essential for generating flexible brain states and complex behaviors. Our method effectively integrates contextual information into the constrained autoencoder framework, allowing for context-dependent dimensionality reduction. This advancement has significant implications for learning smooth, context-aware manifolds in dynamical systems.