Context-dependent manifold learning: A neuromodulated constrained autoencoder approach
This work addresses the need for more flexible, physics-informed representations in systems with non-stationary environmental constraints, offering an incremental improvement over standard constrained autoencoders.
The paper tackled the problem of constrained autoencoders conflating contextual shifts with primary input by introducing a neuromodulated constrained autoencoder (NcAE) that adapts geometric constraints based on context, resulting in accurate capture of manifold geometry variations across regimes while maintaining projection properties.
Constrained autoencoders (cAE) provide a successful path towards interpretable dimensionality reduction by enforcing geometric structure on latent spaces. However, standard cAEs cannot adapt to varying physical parameters or environmental conditions without conflating these contextual shifts with the primary input. To address this, we integrated a neuromodulatory mechanism into the cAE framework to allow for context-dependent manifold learning. This paper introduces the Neuromodulated Constrained Autoencoder (NcAE), which adaptively parameterizes geometric constraints via gain and bias tuning conditioned on static contextual information. Experimental results on dynamical systems show that the NcAE accurately captures how manifold geometry varies across different regimes while maintaining rigorous projection properties. These results demonstrate that neuromodulation effectively decouples global contextual parameters from local manifold representations. This architecture provides a foundation for developing more flexible, physics-informed representations in systems subject to (non-stationary) environmental constraints.