High-dimensional neuronal activity from low-dimensional latent dynamics: a solvable model.

Area of Science:

• Computational neuroscience
• Systems neuroscience
• Machine learning

Background:

• Recurrent neural networks (RNNs) are hypothesized to use low-dimensional latent dynamics for computation.
• Large-scale neuronal recordings in mice reveal high-dimensional population activity, seemingly contradicting this hypothesis.
• The relationship between latent dynamics and observable neural activity dimensionality remains unclear, especially with nonlinear neuronal processing.

Purpose of the Study:

• To reconcile the apparent conflict between low-dimensional latent dynamics and high-dimensional neural activity.
• To investigate whether low-dimensional latent variables explain high-dimensional activity in the mouse visual cortex.
• To develop a method for inferring latent dynamics from nonlinear neural population recordings.

Main Methods:

• Developed an analytically solvable RNN model demonstrating how low-dimensional dynamics can generate high-dimensional activity.
• Utilized spectral theory to analyze the limitations of covariance eigenspectra in determining latent dimensionality with nonlinear neurons.
• Introduced Neural Cross-Encoder (NCE), an interpretable nonlinear latent variable model for neuronal recordings.

Main Results:

• The proposed RNN model shows that low-dimensional latent dynamics can indeed produce high-dimensional activity manifolds.
• NCE analysis revealed that high-dimensional neural responses to drifting gratings and spontaneous activity in the visual cortex can be reduced to low-dimensional latents.
• However, neural responses to natural images could not be reduced to low-dimensional latents using this method.

Conclusions:

• High-dimensional neural activity observed in certain conditions (e.g., spontaneous activity) can be explained by low-dimensional latent variables.
• Individual neurons nonlinearly process these low-dimensional latents, leading to the observed high-dimensional population activity.
• The dimensionality of neural processing in the visual cortex may depend on the specific stimulus or behavioral context.