Why and how the brain weights contributions from a mixture of experts

When there are a number of stochastic models in the form of probability distributions, one needs to integrate them. Mixtures of distributions are frequently used, but exponential mixtures also provide a good means of integration. This letter proposes a one-parameter family of integration, called α-integration, which includes all of these well-known integrations. These are generalizations of various averages of numbers such as arithmetic, geometric, and harmonic averages. There are psychophysical experiments that suggest that α-integrations are used in the brain. The α-divergence between two distributions is defined, which is a natural generalization of Kullback-Leibler divergence and Hellinger distance, and it is proved that α-integration is optimal in the sense of minimizing α-divergence. The theory is applied to generalize the mixture of experts and the product of experts to the α-mixture of experts. The α-predictive distribution is also stated in the Bayesian framework.

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Why and how the brain weights contributions from a mixture of experts

10.31234/osf.io/ns6kq ◽

2020 ◽

Author(s):

John O'Doherty ◽

Sangwan Lee ◽

Reza Tadayonnejad ◽

Jeffrey Cockburn ◽

Kiyohito Iigaya ◽

...

Keyword(s):

Expert Systems ◽

Control Mechanism ◽

Behavioral Control ◽

Mixture Of Experts ◽

Multiple Systems ◽

Control Behavior ◽

Learning Domains ◽

Anterior Prefrontal Cortex ◽

The Brain ◽

Specific Contribution

It has long been suggested that human behavior reflects the contributions of multiple systems that cooperate or compete for behavioral control. Here we propose that the brain acts as a “Mixture of Experts” in which different expert systems propose strategies for action. It will be argued that the brain determines which experts should control behavior at any one moment in time by keeping track of the reliability of the predictions within each system, and by allocating control over behavior in a manner that depends on the relative reliabilities across experts. fMRI and neurostimulation studies suggest a specific contribution of the anterior prefrontal cortex in this process. Further, such a mechanism also takes into consideration the complexity of the expert, favoring simpler over more cognitively complex experts. Results from the study of different expert systems in both experiential and social-learning domains hint at the possibility that this reliability-based control mechanism is domain general, exerting control over many different expert systems simultaneously in order to produce sophisticated behavior.

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A modeling framework for adaptive lifelong learning with transfer and savings through gating in the prefrontal cortex

10.1101/2020.03.11.984757 ◽

2020 ◽

Author(s):

Ben Tsuda ◽

Kay M. Tye ◽

Hava T. Siegelmann ◽

Terrence J. Sejnowski

Keyword(s):

Neural Network ◽

Neural Networks ◽

Artificial Neural Networks ◽

Prefrontal Cortex ◽

Reinforcement Learning ◽

Mixture Of Experts ◽

Modeling Framework ◽

Simple Neural Network ◽

And Storage ◽

The Brain

AbstractThe prefrontal cortex encodes and stores numerous, often disparate, schemas and flexibly switches between them. Recent research on artificial neural networks trained by reinforcement learning has made it possible to model fundamental processes underlying schema encoding and storage. Yet how the brain is able to create new schemas while preserving and utilizing old schemas remains unclear. Here we propose a simple neural network framework based on a modification of the mixture of experts architecture to model the prefrontal cortex’s ability to flexibly encode and use multiple disparate schemas. We show how incorporation of gating naturally leads to transfer learning and robust memory savings. We then show how phenotypic impairments observed in patients with prefrontal damage are mimicked by lesions of our network. Our architecture, which we call DynaMoE, provides a fundamental framework for how the prefrontal cortex may handle the abundance of schemas necessary to navigate the real world.

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