Monday, April 26, 2010

Theories of Everything-The Bayesian Brain

The Director of the Future of Life Research Centre in Australia- David Hunter Tow, proposes that the latest Theory of the Brain based on Bayesian statistical methods, has connections to a wider Theory of Information that underpins the deep nature of the evolutionary process itself.

Theories of Mind provide a framework for investigating the capacity of humans to attribute thoughts, desires, and intentions to others; to explain and predict their actions and infer their intentions. The current theories of the mind and brain, developed over the last few decades, primarily focus on defining the mental behavior of others through mirror neurons. These are a set of specialized brain cells that fire when an animal observes an action performed by another. Therefore, the neurons ‘mirror’ or reflect the behavior of the other, as though the observer was itself acting. Such neurons have been directly observed in primates and now possibly humans and are believed to occur in other species including birds.

However despite an increasing understanding of the role of such mechanisms in shaping the evolution of the brain, previous theories have failed to provide an overarching or unified framework, linking all mental and physical aspects- until recently.
In a breakthrough by a group of researchers from University College London headed by neuroscientist Karl Friston, a mathematical law that may provide the basis for such a holistic theory has been derived.

This is based on Bayesian probability theory, which allows predictions to be made about the validity of a proposition or phenomenon based on the evidence available. Friston’s hypothesis builds on an existing theory known as the “Bayesian Brain”, which postulates the brain is a probability machine that constantly updates its predictions about the world based on its sensory perception and memory.

The crucial element is that these encoded probabilities are based on cumulative experience, which is updated whenever additional relevant data becomes available; such as visual information about an object’s location. Friston’s theory is therefore based on the brain as an inferential agent, continuously refining and optimising its model of the past, present and future. This can be seen as a generic process applied throughout the brain, continually adapting the internal state of its neural connections, as it learns from its experience. In the process it attempts to minimise the gap between its predictions and the actual state of the external world.

This gap or prediction error, can be defined mathematically in terms of the concept of ‘free energy’ used in thermodynamics and statistical mechanics. This is defined as the amount of useful work that can be extracted from a system such as an engine and is roughly equivalent to the difference between the total energy provided by the system and its waste energy or entropy. In this case the prediction error is equated to the free energy of the system, which must be minimised as far as practical. All functions of the brain has therefore evolved to reduce the usage of free energy in relation to prediction errors.

As proof of concept, Friston created a computer simulation of the brain’s cortex or primary cognitive area, with layers of neurons passing signals back and forth. Signals going from higher to lower levels represented the brain’s internal predictions, while signals going the other way represented sensory input. As new information arrived, the higher neurons adjusted their predictions according to Bayesian theory.
When the predictions are right, the brain is rewarded by being able to respond more efficiently. If it is wrong, additional energy is required to find out why it is incorrect and come up with better predictions.

The principle guiding this Bayesian model can be extrapolated to better understand the evolutionary process itself. As further developed in the author's forthcoming book- The Future of Life: A Unified Theory of Evolution, the process of minimizing prediction errors or in this case- useable energy, bears a striking similarity to the process of minimizing the information gap between a system’s environment and own internal state.

The system’s ability to minimize this gap determines its capacity to survive in accordance with an Information Law, first defined in the nineties by physicist Roy Frieden. This is based on Fisher Information, which provides a measure of a system’s accessible information, for deriving the dynamical equations of any process, including the physics of Quantum Mechanics and Relativity.

According to the author, it can also be applied to derive the dynamical equations of Evolution.

Bayesian mechanics can therefore be seen as an agent of the evolutionary process, providing a measure of a system’s capacity, whether a brain or species, to adapt in a changing physical or social landscape, by reducing the gap between its current and required knowledge states.

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