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 Brain SECTION 4: CRITICAL GAPS IN MODELS JOINING THE DOTS IN THEORETICAL NEUROBIOLOGY Karl Friston, University College London

Does the brain use continuous or discrete state space models? Does the brain encode beliefs with ensemble densities or sufficient statistics?

Does the brain use continuous or discrete state-space models? States and their Sufficient statistics

Approximate Bayesian inference for continuous states: Bayesian filtering States and their Sufficient statistics Free energy Model evidence

“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” - von Helmholtz Richard Gregory Hermann von Helmholtz Impressions on the Markov blanket…

Bayesian filtering and predictive coding prediction update prediction error

Making our own sensations Changing sensations sensations – predictions Prediction error Changing predictions Action Perception

the Descending predictions Descending predictions Ascending prediction errors A simple hierarchy whatwhere Sensory fluctuations Hierarchical generative models

What does Bayesian filtering explain?

Cross frequency coupling Perceptual categorisation Violation (P300) responses Oddball (MMN) responses Omission responses Attentional cueing (Posner paradigm) Biased competition Visual illusions Dissociative symptoms Sensory attenuation Sensorimotor integration Optimal motor control Motor gain control Oculomotor control and smooth pursuit Visual searches and saccades Action observation and mirror neuron responses Dopamine and affordance Action sequences (reversal learning) Interoceptive inference Communication and hermeneutics

What does Bayesian filtering explain? Cross frequency coupling Perceptual categorisation Violation (P300) responses Oddball (MMN) responses Omission responses Attentional cueing (Posner paradigm) Biased competition Visual illusions Dissociative symptoms Sensory attenuation Sensorimotor integration Optimal motor control Motor gain control Oculomotor control and smooth pursuit Visual searches and saccades Action observation and mirror neuron responses Dopamine and affordance Action sequences (reversal learning) Interoceptive inference Communication and hermeneutics

What does Bayesian filtering explain? Cross frequency coupling Perceptual categorisation Violation (P300) responses Oddball (MMN) responses Omission responses Attentional cueing (Posner paradigm) Biased competition Visual illusions Dissociative symptoms Sensory attenuation Sensorimotor integration Optimal motor control Motor gain control Oculomotor control and smooth pursuit Visual searches and saccades Action observation and mirror neuron responses Dopamine and affordance Action sequences (reversal learning) Interoceptive inference Communication and hermeneutics  Specify a deep (hierarchical) generative model  Simulate approximate (active) Bayesian inference by solving: prediction update

An example: Visual searches and saccades

Frontal eye fields Pulvinar salience map Fusiform (what) Superior colliculus Visual cortex oculomotor reflex arc Parietal (where) Deep (hierarchical) generative model

Saccadic fixation and salience maps Visual samples Conditional expectations about hidden (visual) states And corresponding percept Saccadic eye movements Hidden (oculomotor) states vs.

Is Bayesian filtering the only process theory for approximate Bayesian inference in the brain? What about state space models?

Full priors – control states Empirical priors – hidden states Likelihood A (Markovian) generative model Hidden states Control states

Generative models Hidden states Control states Continuous states Discrete states Bayesian filtering (predictive coding) Variational Bayes (belief updating)

Variational updates Perception Action selection Incentive salience Functional anatomy 00.20.40.60.81 0 20 40 60 80 Performance Prior preference success rate (%) FE KL RL DA Simulated behaviour VTA/SN motor Cortex occipital Cortex striatum prefrontal Cortex hippocampus

Variational updating Perception Action selection Incentive salience Functional anatomy Simulated neuronal behaviour VTA/SN motor Cortex occipital Cortex striatum prefrontal Cortex hippocampus

What does believe updating explain? Cross frequency coupling Perceptual categorisation Violation (P300) responses Oddball (MMN) responses Omission responses Attentional cueing (Posner paradigm) Biased competition Visual illusions Dissociative symptoms Sensory attenuation Sensorimotor integration Optimal motor control Motor gain control Oculomotor control and smooth pursuit Visual searches and saccades Action observation and mirror neuron responses Dopamine and affordance Action sequences (reversal learning) Interoceptive inference Communication and hermeneutics  Specify a deep (hierarchical) generative model  Simulate approximate (active) Bayesian inference by solving:

What does Bayesian filtering explain? Cross frequency coupling (phase precession) Perceptual categorisation Violation (P300) responses Oddball (MMN) responses Omission responses Attentional cueing (Posner paradigm) Biased competition Visual illusions Dissociative symptoms Sensory attenuation Sensorimotor integration Optimal motor control Motor gain control Oculomotor control and smooth pursuit Visual searches and saccades Action observation and mirror neuron responses Dopamine and affordance Action sequences (reversal learning) Interoceptive inference Communication and hermeneutics

What does Bayesian filtering explain? Cross frequency coupling (phase synchronisation) Perceptual categorisation Violation (P300) responses Oddball (MMN) responses Omission responses Attentional cueing (Posner paradigm) Biased competition Visual illusions Dissociative symptoms Sensory attenuation Sensorimotor integration Optimal motor control Motor gain control Oculomotor control and smooth pursuit Visual searches and saccades Action observation and mirror neuron responses Dopamine and affordance Action sequences (reversal learning) Interoceptive inference Communication and hermeneutics

What does Bayesian filtering explain? 50100150200250300350 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Time (ms) LFP Difference waveform (MMN) oddball standard MMN Cross frequency coupling Perceptual categorisation Violation (P300) responses Oddball (MMN) responses Omission responses Attentional cueing (Posner paradigm) Biased competition Visual illusions Dissociative symptoms Sensory attenuation Sensorimotor integration Optimal motor control Motor gain control Oculomotor control and smooth pursuit Visual searches and saccades Action observation and mirror neuron responses Dopamine and affordance Action sequences (reversal learning) Interoceptive inference Communication and hermeneutics

What does Bayesian filtering explain? Cross frequency coupling Perceptual categorisation Violation (P300) responses Oddball (MMN) responses Omission responses Attentional cueing (Posner paradigm) Biased competition Visual illusions Dissociative symptoms Sensory attenuation Sensorimotor integration Optimal motor control Motor gain control Oculomotor control and smooth pursuit Visual searches and saccades Action observation and mirror neuron responses Dopamine and affordance (transfer of responses) Action sequences (reversal learning) Interoceptive inference Communication and hermeneutics

What does Bayesian filtering explain? Cross frequency coupling Perceptual categorisation Violation (P300) responses Oddball (MMN) responses Omission responses Attentional cueing (Posner paradigm) Biased competition Visual illusions Dissociative symptoms Sensory attenuation Sensorimotor integration Optimal motor control Motor gain control Oculomotor control and smooth pursuit Visual searches and saccades Action observation and mirror neuron responses Dopamine and affordance Action sequences (devaluation) Interoceptive inference Communication and hermeneutics

Does the brain use continuous or discrete state space models or both? Does the brain encode beliefs with ensemble densities or sufficient statistics?

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

Does the brain use continuous or discrete state space models or both? Does the brain encode beliefs with ensemble densities or sufficient statistics? Ensemble code Laplace code Ensemble density Parametric density or

Variational filtering with ensembles

51015202530 -0.5 0 0.5 1 1.5 hidden states 51015202530 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 cause time {bins} time cause Variational filtering

Taking 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)

Deconvolution with variational filtering (SDE) – free-form Deconvolution with Bayesian filtering (ODE) – fixed-form

Does the brain use continuous or discrete state space models or both? Does the brain encode beliefs with ensemble densities or sufficient statistics or both?

Does the brain use continuous or discrete state space models or both? Does the brain encode beliefs with ensemble densities or sufficient statistics or both? Ensemble code Laplace code Parametric description of ensemble density

Ensemble code Laplace code Parametric description of ensemble density An approximate description of (nearly) exact Bayesian inference A (nearly) exact description of approximate Bayesian inference or In other words, do we have:

And thanks to collaborators: Rick Adams Ryszard Auksztulewicz Andre Bastos Sven Bestmann Harriet Brown Jean Daunizeau Mark Edwards Chris Frith Thomas FitzGerald Xiaosi Gu Stefan Kiebel James Kilner Christoph Mathys Jérémie Mattout Rosalyn Moran Dimitri Ognibene Sasha Ondobaka Will Penny Giovanni Pezzulo Lisa Quattrocki Knight Francesco Rigoli Klaas Stephan Philipp Schwartenbeck And colleagues: Micah Allen Felix Blankenburg Andy Clark Peter Dayan Ray Dolan Allan Hobson Paul Fletcher Pascal Fries Geoffrey Hinton James Hopkins Jakob Hohwy Mateus Joffily Henry Kennedy Simon McGregor Read Montague Tobias Nolte Anil Seth Mark Solms Paul Verschure And many others Thank you

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

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

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Presentation on theme: "ABSTRACT: My treatment of critical gaps in models of probabilistic inference will focus on the potential of unified theories to “close the gaps” between."— Presentation transcript:

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