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cs.LG updates on arXiv.org

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Context-dependent manifold learning: A neuromodulated con...
J\'er\^ome A · 2026-05-20 · via cs.LG updates on arXiv.org

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Abstract:Many physical systems exhibit a low-dimensional structure that varies with external parameters: link lengths in a robot, forcing constants in a fluid, or Reynolds numbers in a flow shift the underlying manifold while preserving its intrinsic dimension. Constrained AutoEncoders (cAEs) learn such manifolds through an idempotent encoder-decoder projection, a property that unconstrained autoencoders cannot match and that is essential whenever the model is applied iteratively. However, the standard strategies for making a cAE context-dependent, namely concatenating the context to the input or affinely modulating hidden activations, break the encoder-decoder idempotency, sacrificing the projection guarantee precisely in the setting where it would be most valuable. To restore this guarantee under context variation, we developed the Neuromodulated Constrained Autoencoder (NcAE), which modulates the activation slope and bias of a cAE through a context-driven hyper-network. This paper presents the NcAE, its theoretical foundation, and its empirical validation. We prove that for every context, including contexts unseen at training time, the reconstruction map remains an idempotent projection, the topology of the learned manifold is invariant, and context perturbations induce smooth changes in the manifold. We evaluated our approach on a 16-DoF pendulum with context-dependent coupling and the Lorenz96 system across a bifurcation. The NcAE matched or exceeded the best of six baselines on reconstruction, idempotency, and latent-geometry metrics, while being the only architecture that preserves geometric consistency by construction. The NcAE thereby provides a stable, geometry-preserving coordinate system across families of physical regimes.
Comments: 26 pages, 5 figures, 24 Tables
Subjects: Machine Learning (cs.LG)
MSC classes: 68T07 (Primary), 53Z50 (Secondary)
ACM classes: I.2.6; I.5.2; G.1.6
Cite as: arXiv:2603.11673 [cs.LG]
  (or arXiv:2603.11673v2 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2603.11673

arXiv-issued DOI via DataCite

Submission history

From: Jérôme Adriaens [view email]
[v1] Thu, 12 Mar 2026 08:39:52 UTC (7,599 KB)
[v2] Mon, 18 May 2026 14:23:12 UTC (2,139 KB)

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