Geometry for a Brain. Optimal Control in a Network of Adaptive Memristors

Adv. Studies Theor. Phys., (no.10):479-513 (2013)
Download Edit this record How to cite View on PhilPapers
In the brain the relations between free neurons and the conditioned ones establish the constraints for the informational neural processes. These constraints reflect the systemenvironment state, i.e. the dynamics of homeocognitive activities. The constraints allow us to define the cost function in the phase space of free neurons so as to trace the trajectories of the possible configurations at minimal cost while respecting the constraints imposed. Since the space of the free states is a manifold or a non orthogonal space, the minimum distance is not a straight line but a geodesic. The minimum condition is expressed by a set of ordinary differential equation ( ODE ) that in general are not linear. In the brain there is not an algorithm or a physical field that regulates the computation, then we must consider an emergent process coming out of the neural collective behavior triggered by synaptic variability. We define the neural computation as the study of the classes of trajectories on a manifold geometry defined under suitable constraints. The cost function supervises pseudo equilibrium thermodynamics effects that manage the computational activities from beginning to end and realizes an optimal control through constraints and geodetics. The task of this work is to establish a connection between the geometry of neural computation and cost functions. To illustrate the essential mathematical aspects we will use as toy model a Network Resistor with Adaptive Memory (Memristors).The information geometry here defined is an analog computation, therefore it does not suffer the limits of the Turing computation and it seems to respond to the demand for a greater biological plausibility. The model of brain optimal control proposed here can be a good foundation for implementing the concept of "intentionality",according to the suggestion of W. Freeman. Indeed, the geodesic in the brain states can produce suitable behavior to realize wanted functions and invariants as neural expressionsof cognitive intentions.
PhilPapers/Archive ID
Revision history
Archival date: 2013-06-11
View upload history
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Added to PP index

Total views
330 ( #8,613 of 39,660 )

Recent downloads (6 months)
22 ( #21,109 of 39,660 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.