Collins Conference Room
Seminar
  US Mountain Time
Speaker: 
Francesco Caravelli (Los Alamos National Laboratory)

Our campus is closed to the public for this event.

Abstract

Networks with memristive elements (resistors with memory) are being explored for a variety of applications ranging from unconventional computing to brain-computer interface. However, analytical results that highlight the role of the graph connectivity on the memory dynamics are still a few, thus limiting our understanding of these important dynamical systems. In this talk we discuss various aspects of the dynamics which we analyzed in recent works. We derive an exact matrix equation of motion for the internal memory, that takes into account all the network constraints of a purely memristive circuit, and we employ it to derive analytical results regarding its relaxation properties. We are able to describe the memory evolution in terms of orthogonal projection operators onto the subspace of fundamental loop space of the underlying circuit. This orthogonal projection matrix explicitly reveals the coupling between the spatial and temporal sectors of the memristive circuits, compactly describes the circuit topology and encodes the circuit conservation laws. We briefly discuss various analytical results that can be inferred using this dynamical equation.

We conclude by discussing the relationship between learning and memristive circuits. 

In the weak non-linear regime, showing that the internal memory dynamics can be interpreted as a constrained gradient descent, and provide the functional being minimized. We use exact equations to provide a direct connection between purely memristive circuits and the Sherrington-Kirkpatrick Hamiltonian, similarly in spirit to what done in the past decades for the case of neural networks and the Hopfield model.

Purpose: 
Research Collaboration
SFI Host: 
Artemy Kolchinsky

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