Data-Driven Reduced Modeling of Recurrent Neural Networks
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908595274121216 |
|---|---|
| author | Marraffa, Alice Krause, Renate Mante, Valerio Haller, George |
| author_facet | Marraffa, Alice Krause, Renate Mante, Valerio Haller, George |
| contents | Artificial Recurrent Neural Networks (RNNs) are widely used in neuroscience to model the collective activity of neurons during behavioral tasks. The high dimensionality of their parameter and activity spaces, however, often make it challenging to infer and interpret the fundamental features of their dynamics.
In this study, we employ recent nonlinear dynamical system techniques to uncover the core dynamics of several RNNs used in contemporary neuroscience. Specifically, using a data-driven approach, we identify Spectral Submanifolds (SSMs), i.e., low-dimensional attracting invariant manifolds tangent to the eigenspaces of fixed points. The internal dynamics of SSMs serve as nonlinear models that reduce the dimensionality of the full RNNs by orders of magnitude.
Through low-dimensional, SSM-reduced models, we give mathematically precise definitions of line and ring attractors, which are intuitive concepts commonly used to explain decision-making and working memory. The new level of understanding of RNNs obtained from SSM reduction enables the interpretation of mathematically well-defined and robust structures in neuronal dynamics, leading to novel predictions about the neural computations underlying behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data-Driven Reduced Modeling of Recurrent Neural Networks Marraffa, Alice Krause, Renate Mante, Valerio Haller, George Dynamical Systems Neurons and Cognition Artificial Recurrent Neural Networks (RNNs) are widely used in neuroscience to model the collective activity of neurons during behavioral tasks. The high dimensionality of their parameter and activity spaces, however, often make it challenging to infer and interpret the fundamental features of their dynamics. In this study, we employ recent nonlinear dynamical system techniques to uncover the core dynamics of several RNNs used in contemporary neuroscience. Specifically, using a data-driven approach, we identify Spectral Submanifolds (SSMs), i.e., low-dimensional attracting invariant manifolds tangent to the eigenspaces of fixed points. The internal dynamics of SSMs serve as nonlinear models that reduce the dimensionality of the full RNNs by orders of magnitude. Through low-dimensional, SSM-reduced models, we give mathematically precise definitions of line and ring attractors, which are intuitive concepts commonly used to explain decision-making and working memory. The new level of understanding of RNNs obtained from SSM reduction enables the interpretation of mathematically well-defined and robust structures in neuronal dynamics, leading to novel predictions about the neural computations underlying behavior. |
| title | Data-Driven Reduced Modeling of Recurrent Neural Networks |
| topic | Dynamical Systems Neurons and Cognition |
| url | https://arxiv.org/abs/2510.13519 |