Biologists — neuroscientists included — can’t hope for that kind of theory. Biology isn’t elegant the way physics appears to be. The living world is bursting with variety and unpredictable complexity, because biology is the product of historical accidents, with species solving problems based on happenstance that leads them down one evolutionary road rather than another. No overarching theory of neuroscience could predict, for example, that the cerebellum (which is involved in timing and motor control) would have vastly more neurons than the prefrontal cortex (the part of the brain most associated with our advanced intelligence).
Gary Marcus wants to know: what does a theory of the brain look like? The final sentence is a bit troubling – the best predictor of brain size across animals is body mass; given that this suggests motor control is really important, why would it be surprising that the cerebellum would have more neurons than PFC? So I thought I’d try to compile the current “theories of the brain”, or something like it. I know this is very incomplete so please fill in what I’m missing.
1. Sensory neurons maximize information
There are a lot of ways that the neurons that sense the external world could be responding to the world. An influential theory from Horace Barlow is that neurons are trying to represent the world as well as it is physically possible to do. In mathematical terms, they want to maximize the information that they transmit about whatever they are sensing. In successive stages of the nervous system, this happens through decorrelation: neurons at each stage of neural processing are less like others at that stage.
What this also suggests is that the nervous system needs to know the statistics of the natural world, ie the boundary conditions. In fact, the primary sensory neurons tend to act like they are maximizing their information about the world; it’s been pretty successful at describing the sensory nervous system.
2. Value learning happens through reinforcement (Temporal difference learning)
We all know the story of Pavlov’s dog: a man rings a bell every time he gives a dog some food and pretty soon ringing the bell, even in the absence of food, will get the dog salivating. In 1972, Rescorla and Wagner decided to write this down in mathematical form. In a slightly different form, the equation says that you learn how valuable an action or an object or a thing is by updating your guess a little higher when it was better than expected or a little lower when it was worse than expected. This model of behavior has a very clear implementation in the brain – have some set of neurons that are only active when there is an unpredictably high or low reward. And in a structure called the basal ganglia, this is exactly what you see! There are collections of dopamine neurons that send a reinforcing signal that is proportional to how much better or worse something was than expected. And these dopamine neurons, they reinforce the value by changing the activity of the neurons they are talking to. Temporal-difference learning is another pretty successful theory.
3. Predictive coding and the Bayesian Brain
The world is a tough place, full of constant simulation but a whole lot of useless noise. If the brain had to respond to constantly signal every little thing you would be immensely tired. After all, the brain already uses about 20% of your calories and it is immensely energy efficient. In order to save on internal electricity, it often responds to changes in the world rather than the exact details.
This is one way of implementing another popular theory: the Bayesian Brain. The Bayesian Brain hypothesis proposes that the nervous system is implementing Bayes Theorem in order to optimally learn about statistical signals of the environment (this is very related to theory #1). It can even explain many optical illusions!
3. Association happens through Hebbian plasticity
The paragraph in the book proposing Hebb’s rule has been called “the most cited and least read” paragraph in neuroscience, which is probably true (any contenders? Laughlin, maybe?). Hebb’s rule is summed up as, “those that fire together, wire together”. The biological implementation is through spike-timing dependent plasticity (STDP).
4. Decisions are made through accumulation of evidence
When forced to make a quick decision, how do you decide to decide? What’s the best way to combine the evidence that you have and determine – I have enough? The optimal decision-making rule is called Evidence Accumulation, simply enough, and can be well-described by a drift-diffusion model. In simpler terms, evidence slowly accumulates until it hits some sort of ‘threshold’: enough evidence is in there, it’s time to make a decision! This type of rule does a really good job of describing human decisions in a wide range of contexts. Even better, there appears to be just such a signal in various areas of the brain, the most well-studied being area LIP.
5. Hodgkin-Huxley neurons
What would a list of the theories of the brain be without the Hodgkin-Huxley model? The Nobel Prize-winning work from the 50s that – when extended – almost perfectly describes the ionic mechanisms underlying spiking? That predicted the role of ion channels before we knew about ion channels?
Like I said, this is an incredibly incomplete list. What else should we add? Neural sparsity? Divisive normalization?
I’ll admit I was a bit inspired by the equations that explain the world, so I thought I’d try to compile the Equations of the Brain:
I thought about using the backpropagation version of TD-learning but decided against it…