Conceptual model of a cognitive system

  • 13 February 2019
  • 14.00-15.00
  • Loughborough University campus

Dynamical system with plastic self-organising velocity vector field

Presented by Dr. Natalia Janson (Loughborough University)


Possibly the greatest challenge of modern science is to understand how the brain creates the mind, which should help create human-like artificial intelligence. Traditionally, in the hope to achieve understanding, brain scientists have been observing the behaviour of various parts of the brain and looking for correlations and emerging patterns. The dominating paradigm asserts that in order to be intelligent, the system needs to be made as a neural network. In this context, mathematics is used primarily as a tool to model the brain as a device, or the phenomena occurring in the brain. The focus of modern brain research is on the behaviour of the neural circuits, possibly in connection with the higher cognitive functions and bodily movements. With this, there is no definitive conceptual model of the brain.

In [1] we look at the brain from the viewpoint of dynamical systems theory and shift the focus from the behaviour to the reasons behind the behavior. It is well appreciated that the brain can mathematically be described as a dynamical system. Assuming that an accurate dynamical brain model exists in principle (which is the basis of much of brain-related research), the force dictating every neuron what to do next would be the velocity vector field of this model. The unique feature of the brain is its spontaneous self-organising plasticity which enables learning.  Since the velocity vector field of a device’s dynamical model is a mathematical image of its physical architecture, we point out that the brain’s time-evolving architecture implies that its velocity field de-facto evolves with time.  Moreover, since the architecture changes spontaneously in a self-organised manner with some account of sensory stimuli, we hypothesize that the brain’s velocity field also self-organises according to some deterministic rules. Dynamical systems with self-organising velocity fields have not been considered previously, so we introduce them in order to describe cognition. We suggest that the condition for being intelligent is the ability to create a velocity field, which would spontaneously evolve according to some appropriate laws, which also incorporate sensory information. With this, having an architecture of a plastic neural network is not the necessary condition for intelligence, but rather the means to create the velocity field with the required properties. To support this hypothesis, we construct a simple non-neuromorphic dynamical system with a self-organising velocity field and demonstrate how it performs basic cognition in line with what is expected of artificial neural networks.

The mathematical consistency of the newly introduced dynamical systems is studied in [2], where the existence and uniqueness of solutions is proved under certain conditions, together with the existence of pullback attractors.

In terms of neurophysiology, looking at the brain through the prism of its velocity field could help combine a variety of conflicting notions about memory representation and acquisition into a single picture. Also, the velocity field could serve as the sought-after explicit link between the brain substance and bodily behaviour and cognition.

We suggest that understanding how the brain works could amount to revealing the laws of its velocity field evolution. At the same time, one could construct dynamical systems with a variety of such laws, which would lead to cognition of different types. Implementing such laws in hardware could potentially lead to creation of novel Artificial Intelligence.

[1] Janson, N.B. & Marsden, C.J. Dynamical system with plastic self-organized velocity field as an alternative conceptual model of a cognitive system. Scientific Reports 7, 17007 (2017).

[2] Janson, N.B. & Kloeden, P.E. Asymptotic behaviour of dynamical systems with plastic self-organising vector fields, arXiv:1812.05205 (2018)

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