Slide 1
Workshop on Mathematical Models of Cognitive Architectures December 5-9, 2011CIRM, Marseille
Abstract
This presentation will look at action, perception and cognition as emergent phenomena under a unifying perspective: This Helmholtzian perspective regards the brain as a (generative) model of its environment. The imperative for any brain is then to optimize a free energy bound on the (Bayesian) evidence for its model of the world. We will see that this is not just mandated for the brain but for any self-organizing system that resists a natural tendency to disorder in a changing environment. More specifically, maximizing Bayesian evidence leads in a fairly straightforward way to an understanding of action as active inference, and perception in terms of predictive coding. I hope to illustrate these points using simulations of perceptual categorization and action observation.
Active inference, free energy and the Bayesian brain
Karl FristonUniversity College London
Objects are always imagined as being present in the field of vision as would have to be there in order to produce the same impression on the nervous mechanism - Hermann Ludwig Ferdinand von Helmholtz
Thomas BayesGeoffrey HintonRichard FeynmanFrom the Helmholtz machine to the Bayesian brain and self-organizationHermann Haken
Richard Gregory
Gerry EdelmanStephen Grossberg
Overview
Ensemble dynamicsEntropy and equilibriaFree-energy and surprise
Free-energy principleAction and perceptionHierarchies and generative models
PerceptionBirdsong and categorizationSimulated lesions
ActionActive inferenceAction observation
temperatureWhat is the difference between a snowflake and a bird?
Phase-boundary
a bird can move (to avoid surprises)
4What is the difference between snowfall and a flock of birds?Ensemble dynamics, clumping and swarming
birds (biological agents) stay in the same place They resist the second law of thermodynamics, which says that their entropy should increase
This means biological agents must self-organize to minimize surprise - to ensure they occupy a limited number of states (cf homeostasis).
But what is the entropy?
entropy is just average surpriseLow surprise (we are usually here)High surprise (I am never here)
But there is a small problem agents cannot measure their surpriseBut they can measure their free-energy, which is always bigger than surprise
This means agents should minimize their free-energy?
Change sensory inputsensations predictionsPrediction errorChange predictionsActionPerceptionaction and perception to suppress prediction errors and minimise surpriseWhat is free-energy?free-energy is basically prediction error
Action to minimise a bound on surprisePerception to optimise the bound
Action
External states in the worldInternal states of the agent (m)Sensations
More formally,
Free-energy is a function of sensations and a proposal density over hidden causes
and can be evaluated, given a generative model comprising a likelihood and prior:
So what models might the brain use?
Action
External states in the worldInternal states of the agent (m)Sensations
Backward(modulatory)Forward(driving)lateral
Hierarchal models in the brainAnd their hidden states, causes and parameters
Synaptic gainSynaptic activitySynaptic efficacyActivity-dependent plasticityFunctional specializationAttentional gainEnabling of plasticity
Perception and inferenceLearning and memoryThe proposal density and its sufficient statistics
Laplace approximation:Attention and salience
Synaptic activity
Synaptic plasticity
Synaptic gaincf Hebb's Lawcf Rescorla-Wagnercf Bayesian filtering or Predictive coding
Laplace code assumption
Free energy minimisation
Generative model
Backward predictionsForward prediction error
Synaptic activity and message-passing
David MumfordPredictive coding
Adjust hypothesessensory inputBackward connections return predictionsby hierarchical message passing in the brain
prediction
Forward connections convey feedbackPerceptual inference hierarchical message passingPrediction errorsPredictions
Summary
Biological agents resist the second law of thermodynamics
They must minimize their average surprise (entropy)
They minimize surprise by suppressing prediction error (free-energy)
Prediction error can be reduced by changing predictions (perception)
Prediction error can be reduced by changing sensations (action)
Perception entails recurrent message passing in the brain to optimise predictions
Action makes predictions come true (and minimises surprise)Overview
Ensemble dynamicsEntropy and equilibriaFree-energy and surprise
Free-energy principleAction and perceptionHierarchies and generative models
PerceptionBirdsong and categorizationSimulated lesions
ActionActive inferenceAction observation
Generating bird songs with attractorsSyrinxHVC
time (sec)FrequencySonogram0.511.5
causal stateshidden states
102030405060-505101520prediction and error102030405060-505101520hidden statesBackward predictionsForward prediction error102030405060-10-505101520causal statesPerception and message passing
stimulus0.20.40.60.82000250030003500400045005000time (seconds)
Perceptual categorization
Frequency (Hz)Song a
time (seconds)Song b
Song c
Hierarchical (deep) birdsong: sequences of sequencesSyrinxNeuronal hierarchy
Time (sec)Frequency (KHz)sonogram0.511.5
Christoph vonder Malsburg
Frequency (Hz)perceptFrequency (Hz)no top-down messagestime (seconds)Frequency (Hz)no lateral messages0.511.5-40-200204060LFP (micro-volts)LFP-60-40-200204060LFP (micro-volts)LFP0500100015002000-60-40-200204060peristimulus time (ms)LFP (micro-volts)LFP
Simulated lesions and false inference
no structural priorsno dynamical priorsOverview
Ensemble dynamicsEntropy and equilibriaFree-energy and surprise
Free-energy principleAction and perceptionHierarchies and generative models
PerceptionBirdsong and categorizationSimulated lesions
ActionActive inferenceAction observation
predictionsReflexes to action
action
dorsal rootventral hornsensory errorActive inferenceAction can only suppress (sensory) prediction error. This means action fulfils our (sensory) predictions
Descendingproprioceptive predictionsvisual inputproprioceptive inputAction, predictions and priors
Exteroceptive predictions
Autonomous behavior and action-observation00.20.40.60.811.21.40.40.60.811.21.4actionposition (x)position (y)00.20.40.60.811.21.4observationposition (x)Descending predictionshidden attractor states(Lotka-Volterra)
Thank you
And thanks to collaborators:
Rick AdamsSven BestmannJean DaunizeauHarriet BrownLee HarrisonStefan KiebelJames KilnerJrmie MattoutKlaas Stephan
And colleagues:
Peter DayanJrn DiedrichsenPaul VerschureFlorentin Wrgtter
And many others
Perception and Action: The optimisation of neuronal and neuromuscular activity to suppress prediction errors (or free-energy) based on generative models of sensory data.
Learning and attention: The optimisation of synaptic gain and efficacy over seconds to hours, to encode the precisions of prediction errors and causal structure in the sensorium. This entails suppression of free-energy over time.
Neurodevelopment: Model optimisation through activity-dependent pruning and maintenance of neuronal connections that are specified epigenetically
Evolution: Optimisation of the average free-energy (free-fitness) over time and individuals of a given class (e.g., conspecifics) by selective pressure on the epigenetic specification of their generative models.
Time-scaleFree-energy minimisation leading to