Competition in High Dimensional Spaces Using a Sparse Approximation of Neural Fields

Abstract

The Continuum Neural Field Theory implements competition within topologically organized neural networks with lateral inhibitory connections. However, due to the polynomial complexity of matrix-based implementations, updating dense representations of the activity becomes computationally intractable when an adaptive resolution or an arbitrary number of input dimensions is required. This paper proposes an alternative to self-organizing maps with a sparse implementation based on Gaussian mixture models, promoting a trade-off in redundancy for higher computational efficiency and alleviating constraints on the underlying substrate.This version reproduces the emergent attentional properties of the original equations, by directly applying them within a continuous approximation of a high dimensional neural field. The model is compatible with preprocessed sensory flows but can also be interfaced with artificial systems. This is particularly important for sensorimotor systems, where decisions and motor actions must be taken and updated in real-time. Preliminary tests are performed on a reactive color tracking application, using spatially distributed color features.

The Cat is on the Mat. or is it a Dog? Dynamic Competition in Perceptual Decision Making

“…Indeed, attentional capabilities and increased robustness are required when the set of potentialities offered to the system increases. Committing to neuro-inspired models, dynamic neural field models allow such properties to emerge and can be applied to the sensory signals and categories [56] or directly to the predictors by using a high dimensional implementation [57]. Finally, the command sent for moving the pointer is a linear combination of the normalized vectors v {1,2} aiming at the two visible targets from the current mouse position (see Fig.…”