Maths and memory

 Mathematical model could help in physical therapy and shed light on learning more generally. 

The COIN model may also generalise to many other forms of learning and memory, not just memories underlying our movement

Máté Lengyel

How is it that a chef can control their knife to fillet a fish or peel a grape and can wield a cleaver just as efficiently as a paring knife? Even those of us less proficient in the kitchen learn to skilfully handle an astonishing number of different objects throughout our lives, from shoelaces to tennis rackets.

This ability to continuously acquire new skills, without forgetting or degrading old ones, comes naturally to humans but is a major challenge even for today’s most advanced artificial intelligence systems.

Now, scientists from the University of Cambridge and Columbia University (USA) have developed and experimentally verified a new mathematical theory that explains how the human brain achieves this feat. Called the COntextual INference (COIN) model, it suggests that identifying the current context is key to learning how to move our bodies.

The model describes a mechanism in the brain that is constantly trying to figure out the current context. The theory suggests that these continuously changing beliefs about context determine how to use existing memories — and whether to form new ones. The results are reported in the journal Nature.

“Imagine playing tennis with a different racket than usual or switching from tennis to squash,” said co-senior author Dr Daniel Wolpert from Columbia University. “Our theory explores how your brain adjusts to these situations and whether to treat them as distinct contexts.”

According to the COIN model, the brain maintains a repertoire of motor memories, each associated with the context in which it was created, such as playing squash versus tennis. Even for a single swing of the racket, the brain can draw upon many memories, each in proportion to how much the brain believes it is currently in the context in which that memory was created. 

This goes against the traditional view that only one memory is used at a time. To improve performance on the next swing, the brain also updates all memories, once again depending on its belief about the current context. When the context of the movement is judged to be new (the first time we play squash after years of tennis, for example), the brain automatically creates a new memory for that context. This ensures that we do not overwrite previously established memories, such as the memory for playing tennis.

This research may lead to better physical therapy strategies to help people with injuries use their bodies again. Often the improvements seen in the setting of a physical therapist's office do not transfer to improvements in the real world.

“With a better understanding of how context affects motor learning, you can think about how to nudge the brain to generalise what it learns to contexts outside of the physical therapy session,” said first author Dr James Heald. “A better understanding of the basic mechanisms that underlie the context dependence of memory and learning could have therapeutic consequences in this area.”

“What I find exciting is that the principles of the COIN model may also generalise to many other forms of learning and memory, not just memories underlying our movement,” said co-senior author Professor Máté Lengyel from Cambridge’s Department of Engineering. “For example, the spontaneous recurrence of seemingly forgotten memories, often triggered by a change in our surroundings, has been observed both in motor learning and in post-traumatic stress disorder.”

COINing a new model

Practice with a tennis racket, and the brain forms motor memories of how you moved your arm and the rest of your body that improve your serve over time. But learning isn’t as simple as just making better memories to make movements more precise, the researchers said. Otherwise, a tennis player’s serves might improve to the point at which they never hit a ball out of bounds. The real world and our nervous systems are complex, and the brain has to deal with a lot of variability.

How does the brain distinguish this noise — these random fluctuations — from new situations? And how does it understand that a slightly lighter tennis racket can still be operated using previous tennis racket memories? But that a table tennis paddle is an entirely different kind of object that requires starting from scratch?

The answer, according to the COIN model, may be Bayesian inference, a mathematical technique used to deal with uncertainty. This method statistically weighs new evidence in light of prior experience in order to update one's beliefs in a changeable world. In the COIN model, a context is a simplifying assumption that, in a given set of circumstances, certain actions are more likely to lead to some consequences than others. The new theory's acceptance of the role that uncertainty plays in motor learning is similar t