Keep your face always toward the sunshine - and shadows will fall behind you. Walt Whitman
Idea Transcript
From Cryptanalysis to Cognitive Neuroscience A hidden legacy of Alan Turing
The Ratio Club
The Ratio Club
An Enigma Machine
Bletchley Park
Hut 8
Bayes‐Laplace “I now send you an essay which I have found among the papers of our deceased friend Mr Bayes, and which, in my opinion, has great merit....” Essay towards solving a problem in the doctrine of chances (1764) Phil. Trans. Roy. Soc.
Rev. Thomas Bayes
Pierre‐Simon Laplace
(1702-1761)
(1749‐1827)
Bayesian statistics
Inference based on uncertain information
Bayesian Inference Data e.g. sensory input
Beliefs Prior knowledge e.g. memory
Probabilities represent degrees of belief – Strength of a belief is given a value between 0 and 1 – P(A) = belief in proposition A – P(dice shows six)=1/6 Conditional probability – P(A|B)= Probability of A being true given that B is true – P (dice shows six| dice is even)=1/3
Decoding under uncertainty The Brain decodes the state of the world Cryptanalysis decodes the Enigma
As for code breakers, a Bayesian perspective on the brain provides a means of starting with a theory of how parameters produce data and inverts it into a theory of how the data can be used to reveal the parameters that caused it
A central concern in systems neuroscience is to formulate precise models of the brain’s model making processes
“The human mind is the equivalent not to
the brain itself, but instead to the pattern of information processing supported by the brain” Alan Turing 1950
Outline
Perceptual inference
Uncertainty and perceptual experience Belief Encoding Models of self and others Inferring what goes on inside the brain (‘a mathematical microscope’)
Sensory Evidence Accumulation •
Random dot motion task: decide between two opposite directions of motion.
Sensory Evidence Accumulation •
Random dot motion task: decide between two opposite directions of motion.
Evidence Accumulation •
Random dot motion task: decide between two opposite directions of motion.
Evidence Accumulation •
Random dot motion: decide between two opposite directions of motion.
Neural Evidence
Decisions are made based on a decision variable (DV), usually log likelihood ratio (log LR12 = log P(e|h1)/P(e|h2) ). Evidence is collected until DV > threshold, then decision is made
Analogy between sensory decoding and cryptanalysis noisy data; sequential sampling; weight of evidence for alternative hypotheses; a criterion to determine acceptance of evidence in favour of one or other hypothesis
Outline
Perceptual inference
Uncertainty and perceptual experience Belief Encoding Models of self and others Inferring what goes on inside the brain (‘a mathematical microscope’)
Low uncertainty
Computational perspectives on psychopathology and ageing
High uncertainty
Uncertainty and pain anticipation in the brain
Uncertainty and brain response to receipt of pain
Outline
Perceptual inference
Uncertainty and perceptual experience Belief Encoding Models of self and others Inferring what goes on inside the brain (‘a mathematical microscope’)
Turing posed a fundamental challenge What algorithm is “the brain” running?
“It would be quite possible for the machine
to try out variations of behaviour and accept or reject them in the manner you describe and I have been hoping to make a machine like this”. Correspondence with Ross Ashby
“If I understand it right, the idea is that by
different training certain of the paths could be made effective and the others ineffective. How much information could be stored in the brain this way? The answer is simply MN binary bits where there are M paths each capable of two states” 8th February 1951, correspondence with JZ Young
The National Hospital for Nervous Diseases circa 1950
“We can only see a short distance ahead, but we can see plenty there that needs to be done” “Computing Machinery and Intelligence”, Mind, October 1950.
Acknowledgements • • • • • • • • •
Karl Friston Peter Dayan Rosalyn Moran Ben Seymour Wako Yoshida Tim Behrens Antoinette Nicolle Miriam Klein‐Flugge Many Others