A Spatiotemporal Perspective on Dynamical Computation in Neural Information Processing Systems

Area of Science:

• Neuroscience
• Computational Neuroscience
• Machine Learning Theory

Background:

• Spatiotemporal neural activity, including traveling waves, is widespread in the brain.
• The functional role of these neural dynamics remains debated, especially concerning standard models of neural processing.
• Existing links between traveling waves and motion are difficult to integrate with current theories of neural selectivity and receptive fields.

Purpose of the Study:

• To introduce a theoretical framework connecting neural 'motion' and flowing dynamics using equivariant neural network theory.
• To generalize the concept of motion beyond physical or visual spaces to abstract representational spaces.
• To demonstrate the necessity of recurrent traveling-wave dynamics for stable and accurate signal processing under flow transformations.

Main Methods:

• Formalizing the relationship between signal flow and neural dynamics within equivariant neural network theory.
• Analyzing the requirements for recurrent neural networks to process flow transformations in an equivariant manner.
• Developing a 'spatiotemporal perspective on dynamical computation'.

Main Results:

• Recurrent neural network dynamics must realize a homomorphic representation of stimulus flow for structured, equivariant processing.
• Traveling waves and related neural flows serve as faithful dynamic representations of stimulus flows.
• Biological systems' tendency towards such dynamics suggests an innate inductive bias for efficient, generalized processing.

Conclusions:

• Traveling waves are not merely epiphenomena but are fundamental to how the brain processes dynamic, flowing information.
• The framework provides a unified view of neural dynamics, motion processing, and equivariant computation.
• This perspective highlights the brain's inherent efficiency and generalization capabilities shaped by its spatiotemporal environment.