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The Principle of Least Cognitive Action

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In this talk we introduce the principle of Least Cognitive Action with the purpose of understanding perceptual learning processes. The principle closely parallels related approaches in physics, and suggests to regard neural networks as systems whose weights are Lagrangian variables, namely functions depending on time. Interestingly, neural networks “conquer their own life” and there is no neat distinction between learning and test; their behavior is characterized by the stationarity of the cognitive action, an appropriate functional which contains a potential and a kinetic term. While the potential term is somewhat related to the loss function used in supervised and unsupervised learning, the kinetic term represents the energy connected with the velocity of weight change. Unlike traditional gradient descent, the stationarity of the cognitive action yields differential equations in the connection weights, and gives rise to a dissipative process which is needed to yield ordered configurations. We give conditions under which this learning process reduces to stochastic gradient descent and to Backpropagation. We give examples on supervised and unsupervised learning, and briefly discuss the application to deep convolutional neural networks, where an appropriate Lagrangian term is used to enforce motion invariance in the visual feature extraction.

Video recording available at: https://www.cl.cam.ac.uk/seminars/wednesday/video/lt2-190529-wed-1600-t125104.html (note that the first 2:00 minutes of audio are missing).

This talk is part of the Computer Laboratory Wednesday Seminars series.

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