Generation of Independent Velocity Spaces through Spatiotemporal Asymmetric Neural Networks

The fundamental challenge in visual motion processing is how the brain extracts velocity vectors unambiguously. While the traditional energy models rely on symmetric nonlinear operations to preserve signal energy, they face inherent mathematical constraints in maintaining the independence of velocity information. We present an innovative mathematical framework that uses Wiener kernel expansion and spatiotemporal Jacobians to illustrate how neural networks separately address different velocities and achieve reliable velocity perception. It is shown that our proposed asymmetric network model—characterized by odd/even-order nonlinearities and phase shift in the nonlinear pathway in which spatiotemporal physical velocity is effectively transformed into the phase shifts in the time domain. Our proposals suggest that the biological nuisance of neural variability and structural asymmetry is, in fact, a fundamental computational resource required to resolve mathematical singularities and achieve unambiguous three-dimensional motion perception.