Data-Driven Reduced Modeling of Recurrent Neural Networks
Marraffa, A.; Krause, R.; Mante, V.; Haller, G.
Show abstract
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.
Matching journals
The top 6 journals account for 50% of the predicted probability mass.
Similar papers in this journal
- Cooperative coding of continuous variables in networks with sparsity constraint 98%
- The covariance perceptron: A new paradigm for classification and processing of time series in recurrent neuronal networks 97%
- Complex spatiotemporal oscillations emerge from transverse instabilities in large-scale brain networks 97%
Similar papers in this journal
- Robustly encoding certainty in a metastable neural circuit model 97%
- Statistically inferred neuronal connections in subsampled neural networks strongly correlate with spike train covariance 96%
- Robust Cortical Criticality and Diverse Neural Network Dynamics Resulting from Functional Specification 96%
"Similar papers" are the closest papers from that journal in the model's embedding space. They show what the match is built on, but the ranking comes mostly from a classifier over the whole training set, not from these examples alone.