Stiefel Manifold Dynamical Systems for Tracking Representational Drift

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The paper studies how to model neural activity when the mapping from latent states to observed neural signals changes gradually across trials, a phenomenon the authors term representational drift. They introduce a Stiefel Manifold Dynamical System (SMDS), in which emission matrices are constrained to be orthonormal and smoothly evolve over trials on the Stiefel manifold while the underlying dynamics parameters are shared. Across simulated data and neural recordings from multiple species, SMDS is reported to outperform linear dynamical systems in log-likelihood and to achieve similar fits using fewer latent dimensions. The authors do not present specific limitations beyond the comparison framework, but they focus on smoother, orthonormal evolution of emissions as the mechanism for capturing non-stationarity. The paper does not explicitly discuss endometriosis or adenomyosis; it was included in the corpus via a keyword match in the upstream search index.

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Abstract

Understanding neural dynamics is crucial for uncovering how the brain processes information and controls behavior. Linear dynamical systems (LDS) are widely used for modeling neural data due to their simplicity and effectiveness in capturing latent dynamics. However, LDS assumes a stable mapping from the latent states to neural activity, limiting its ability to capture representational drift—gradual changes in the brain’s representation of the external world. To address this, we introduce the Stiefel Manifold Dynamical System (SMDS), a new class of model designed to account for drift in neural representations across trials. In SMDS, emission matrices are constrained to be orthonormal and evolve smoothly over trials on the Stiefel manifold—the space of all orthonormal matrices—while the dynamics parameters are shared. This formulation allows SMDS to leverage data across trials while accounting for non-stationarity, thus capturing the underlying neural dynamics more accurately compared to an LDS. We apply SMDS to both simulated datasets and neural recordings across species. Our results consistently show that SMDS outperforms LDS in terms of log-likelihood and requires fewer latent dimensions to capture the same activity. Moreover, SMDS provides a powerful framework for quantifying and interpreting representational drift. It reveals a gradual drift over the course of minutes in the neural recordings and uncovers varying drift rates across dimensions, with slower drift in behaviorally and neurally significant dimensions.
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Abstract Understanding neural dynamics is crucial for uncovering how the brain processes information and controls behavior. Linear dynamical systems (LDS) are widely used for modeling neural data due to their simplicity and effectiveness in capturing latent dynamics. However, LDS assumes a stable mapping from the latent states to neural activity, limiting its ability to capture representational drift—gradual changes in the brain’s representation of the external world. To address this, we introduce the Stiefel Manifold Dynamical System (SMDS), a new class of model designed to account for drift in neural representations across trials. In SMDS, emission matrices are constrained to be orthonormal and evolve smoothly over trials on the Stiefel manifold—the space of all orthonormal matrices—while the dynamics parameters are shared. This formulation allows SMDS to leverage data across trials while accounting for non-stationarity, thus capturing the underlying neural dynamics more accurately compared to an LDS. We apply SMDS to both simulated datasets and neural recordings across species. Our results consistently show that SMDS outperforms LDS in terms of log-likelihood and requires fewer latent dimensions to capture the same activity. Moreover, SMDS provides a powerful framework for quantifying and interpreting representational drift. It reveals a gradual drift over the course of minutes in the neural recordings and uncovers varying drift rates across dimensions, with slower drift in behaviorally and neurally significant dimensions. Competing Interest Statement The authors have declared no competing interest.

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europepmc
last seen: 2026-05-20T01:45:00.602351+00:00
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last seen: 2026-05-27T02:00:06.600101+00:00
License: CC-BY-4.0