ABSTRACT: My treatment of critical gaps in models of probabilistic inference will focus on the potential of unified theories to “close the gaps” between

ABSTRACT: My treatment of critical gaps in models of probabilistic inference will focus on the potential of unified theories to close the gaps between probabilistic models of perception and evidence accumulation - and how these models can be understood in terms of embodied inference and action. Formally speaking, models of motor control and choice behaviour can be cast in terms of (active) probabilistic inference; however, there are two key outstanding issues. Both pertain to the implementation of active inference in the brain. The first speaks to the distinction between discrete and continuous state-space models and the requisite message passing schemes (e.g., variational Bayes versus predictive coding). The second key distinction is between mean field descriptions in terms of population dynamics (i.e., sufficient statistics) and their microscopic implementation in terms of spiking neurons (i.e., sampling approaches to probabilistic inference). These are potentially important issues that constrain the interpretation of empirical data and how these data can be used to adjudicate among different models of the Bayesian brain. .

Probabilistic Inference and the BrainSECTION 4: CRITICAL GAPS IN MODELSJOINING THE DOTS IN THEORETICAL NEUROBIOLOGY Karl Friston, University College London

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Does the brain use continuous or discrete state space models?

Does the brain encode beliefs with ensemble densities or sufficient statistics?

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Does the brain use continuous or discrete state-space models?

States and theirSufficient statistics

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Approximate Bayesian inference for continuous states: Bayesian filtering

States and theirSufficient statistics

Free energy Model evidence4Objects 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 - von Helmholtz Richard Gregory

Hermann von Helmholtz Impressions on the Markov blanket

5Bayesian filtering and predictive coding

prediction update

prediction error

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Making our own sensations

Changing sensationssensations predictionsPrediction errorChanging predictionsActionPerception7

the

DescendingpredictionsAscending prediction errors

A simple hierarchy

whatwhereSensory fluctuations

Hierarchical generative models

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What does Bayesian filtering explain?

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What does Bayesian filtering explain?Cross frequency couplingPerceptual categorisation Violation (P300) responsesOddball (MMN) responsesOmission responses Attentional cueing (Posner paradigm)Biased competitionVisual illusionsDissociative symptomsSensory attenuationSensorimotor integrationOptimal motor controlMotor gain controlOculomotor control and smooth pursuitVisual searches and saccadesAction observation and mirror neuron responsesDopamine and affordanceAction sequences (reversal learning)Interoceptive inferenceCommunication and hermeneutics

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Cross frequency couplingPerceptual categorisation Violation (P300) responsesOddball (MMN) responsesOmission responses Attentional cueing (Posner paradigm)Biased competitionVisual illusionsDissociative symptomsSensory attenuationSensorimotor integrationOptimal motor controlMotor gain controlOculomotor control and smooth pursuitVisual searches and saccadesAction observation and mirror neuron responsesDopamine and affordanceAction sequences (reversal learning)Interoceptive inferenceCommunication and hermeneutics12














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Specify a deep (hierarchical) generative model

Simulate approximate (active) Bayesian inference by solving:

prediction update31

An example: Visual searches and saccades

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Frontal eye fields

Pulvinar salience mapFusiform (what)Superior colliculusVisual cortexoculomotor reflex arc

Parietal (where)

Deep (hierarchical) generative model33

Saccadic fixation and salience mapsVisual samplesConditional expectations about hidden (visual) statesAnd corresponding perceptSaccadic eye movementsHidden (oculomotor) states

vs.vs.

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Is Bayesian filtering the only process theory for approximate Bayesian inference in the brain?

What about state space models?

35Full priors control statesEmpirical priors hidden statesLikelihoodA (Markovian) generative modelHidden states

Control states

36Generative modelsHidden states

Control states

Continuous statesDiscrete statesBayesian filtering (predictive coding)Variational Bayes(belief updating)

37Variational updatesPerception

Action selection

Incentive salienceFunctional anatomy

00.20.40.60.81020406080PerformancePrior preferencesuccess rate (%) FEKLRLDASimulated behaviour

VTA/SNmotor Cortexoccipital Cortexstriatum

prefrontal Cortex

hippocampus38Variational updatingPerception

Action selection

Incentive salienceFunctional anatomy

Simulated neuronal behaviour

0.20.40.60.811.21.4510152025300.250.50.7511.251.5-0.0200.020.040.060.08102030405060708090-0.0500.050.10.150.2

VTA/SNmotor Cortexoccipital Cortexstriatum

prefrontal Cortex

hippocampus39

What does believe updating explain?Cross frequency couplingPerceptual categorisation Violation (P300) responsesOddball (MMN) responsesOmission responses Attentional cueing (Posner paradigm)Biased competitionVisual illusionsDissociative symptomsSensory attenuationSensorimotor integrationOptimal motor controlMotor gain controlOculomotor control and smooth pursuitVisual searches and saccadesAction observation and mirror neuron responsesDopamine and affordanceAction sequences (reversal learning)Interoceptive inferenceCommunication and hermeneutics

Specify a deep (hierarchical) generative model

Simulate approximate (active) Bayesian inference by solving:

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Unit responsestime (seconds)0.250.50.75816240.250.50.75-0.0200.020.040.060.080.10.120.14Local field potentialstime (seconds)ResponseCross frequency coupling (phase precession)Perceptual categorisation Violation (P300) responsesOddball (MMN) responsesOmission responses Attentional cueing (Posner paradigm)Biased competitionVisual illusionsDissociative symptomsSensory attenuationSensorimotor integrationOptimal motor controlMotor gain controlOculomotor control and smooth pursuitVisual searches and saccadesAction observation and mirror neuron responsesDopamine and affordanceAction sequences (reversal learning)Interoceptive inferenceCommunication and hermeneutics

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Time-frequency (and phase) responsetime (seconds)frequency123456510152025300.250.50.7511.251.51.7522.252.52.7533.253.53.7544.254.54.7555.255.55.756-0.200.20.4Local field potentialstime (seconds)Response5010015020025030035000.050.10.15Phasic dopamine responsestime (updates)change in precisionCross frequency coupling (phase synchronisation)Perceptual categorisation Violation (P300) responsesOddball (MMN) responsesOmission responses Attentional cueing (Posner paradigm)Biased competitionVisual illusionsDissociative symptomsSensory attenuationSensorimotor integrationOptimal motor controlMotor gain controlOculomotor control and smooth pursuitVisual searches and saccadesAction observation and mirror neuron responsesDopamine and affordanceAction sequences (reversal learning)Interoceptive inferenceCommunication and hermeneutics42


Time-frequency (and phase) responsetime (seconds)frequency0.20.40.60.811.21.4510152025300.250.50.7511.251.5-0.0200.020.040.060.08Local field potentialstime (seconds)Response102030405060708090-0.0500.050.10.150.2Phasic dopamine responsestime (updates)change in precisionCross frequency couplingPerceptual categorisation Violation (P300) responsesOddball (MMN) responsesOmission responses Attentional cueing (Posner paradigm)Biased competitionVisual illusionsDissociative symptomsSensory attenuationSensorimotor integrationOptimal motor controlMotor gain controlOculomotor control and smooth pursuitVisual searches and saccadesAction observation and mirror neuron responsesDopamine and affordanceAction sequences (reversal learning)Interoceptive inferenceCommunication and hermeneutics43

What does Bayesian filtering explain?0.250.50.7511.251.5-0.100.10.20.30.4Local field potentialstime (seconds)Response10203040506070809000.050.10.150.2Phasic dopamine responsestime (updates)change in precision50100150200250300350-0.06-0.04-0.0200.020.040.060.080.10.120.14Time (ms)LFPDifference waveform (MMN) oddballstandardMMNCross frequency couplingPerceptual categorisation Violation (P300) responsesOddball (MMN) responsesOmission responses Attentional cueing (Posner paradigm)Biased competitionVisual illusionsDissociative symptomsSensory attenuationSensorimotor integrationOptimal motor controlMotor gain controlOculomotor control and smooth pursuitVisual searches and saccadesAction observation and mirror neuron responsesDopamine and affordanceAction sequences (reversal learning)Interoceptive inferenceCommunication and hermeneutics44

What does Bayesian filtering explain?Cross frequency couplingPerceptual categorisation Violation (P300) responsesOddball (MMN) responsesOmission responses Attentional cueing (Posner paradigm)Biased competitionVisual illusionsDissociative symptomsSensory attenuationSensorimotor integrationOptimal motor controlMotor gain controlOculomotor control and smooth pursuitVisual searches and saccadesAction observation and mirror neuron responsesDopamine and affordance (transfer of responses)Action sequences (reversal learning)Interoceptive inferenceCommunication and hermeneutics

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Cross frequency couplingPerceptual categorisation Violation (P300) responsesOddball (MMN) responsesOmission responses Attentional cueing (Posner paradigm)Biased competitionVisual illusionsDissociative symptomsSensory attenuationSensorimotor integrationOptimal motor controlMotor gain controlOculomotor control and smooth pursuitVisual searches and saccadesAction observation and mirror neuron responsesDopamine and affordanceAction sequences (devaluation)Interoceptive inferenceCommunication and hermeneutics47

Does the brain use continuous or discrete state space models or both?


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Hidden states

Control states

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Ensemble code

Laplace code

Ensemble densityParametric densityor50Variational filtering with ensembles

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51015202530-1-0.500.511.5hidden states51015202530-0.4-0.200.20.40.60.811.2causetime {bins}timecause

Variational filtering

52Taking the expectation of the ensemble dynamics, under the Laplace assumption,we get:

This can be regarded as a gradient ascent in a frame of reference that moves along the trajectory encoded in generalised coordinates. The stationary solution, in this moving frame of reference, maximises variational action by the Fundamental lemma.

c.f., Hamilton's principle of stationary action.

From ensemble coding to predictive coding (Bayesian filtering)

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Deconvolution with variational filtering (SDE) free-form

Deconvolution with Bayesian filtering (ODE) fixed-form

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Does the brain encode beliefs with ensemble densities or sufficient statistics or both?

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Does the brain encode beliefs with ensemble densities or sufficient statistics or both?

Ensemble code

Laplace codeParametric description of ensemble density

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Ensemble code

Laplace codeParametric description of ensemble density

An approximate description of (nearly) exact Bayesian inferenceA (nearly) exact description of approximate Bayesian inferenceorIn other words, do we have:57And thanks to collaborators:

Rick AdamsRyszard AuksztulewiczAndre BastosSven BestmannHarriet BrownJean DaunizeauMark EdwardsChris FrithThomas FitzGeraldXiaosi GuStefan KiebelJames KilnerChristoph MathysJrmie MattoutRosalyn MoranDimitri OgnibeneSasha Ondobaka Will PennyGiovanni PezzuloLisa Quattrocki KnightFrancesco Rigoli Klaas StephanPhilipp Schwartenbeck

And colleagues:

Micah AllenFelix BlankenburgAndy ClarkPeter DayanRay DolanAllan HobsonPaul FletcherPascal FriesGeoffrey HintonJames HopkinsJakob HohwyMateus JoffilyHenry KennedySimon McGregorRead MontagueTobias NolteAnil SethMark SolmsPaul Verschure

And many othersThank you58

Documents

ABSTRACT: My treatment of critical gaps in models of probabilistic inference will focus on the potential of unified theories to “close the gaps” between