Eye movements as a model for active inference - <a href="http://www.laconeu.cl">LACONEU2017: 4th Latin-American Summer School in Computational Neuroscience</a> January 20th, 2017 <BR> <a href="https://laurentperrinet.github.io/talk/2017-01-20-laconeu">https://laurentperrinet.github.io/talk/2017-01-20-laconeu</a>

Tutorial: Active inference for eye movements: Bayesian methods, neural inference, dynamics

Laurent U Perrinet, INT

Acknowledgements:

Mina Aliakbari Khoei, Guillaume Masson and Anna Montagnini - FACETS-ITN Marie Curie Training
Rick Adams and Karl Friston @ UCL - Wellcome Trust Centre for Neuroimaging
Wahiba Taouali, Giacomo Benvenuti, Frédéric Chavane - ANR BalaV1

LACONEU2017: 4th Latin-American Summer School in Computational Neuroscience January 20th, 2017
https://laurentperrinet.github.io/talk/2017-01-20-laconeu

(AUTHOR) Hi, I am Laurent Perrinet from (LOGO) the Institute de Neurosciences de la Timone in Marseille, a joint unit from the CNRS and AMU. Using computational models, I am investigating the link between the efficiency of behavioural responses in vision, their underlying neural code and their adaptation to the structure of the world.
(SHOW TITLE - THEME) = In particular, eye movements, that is, motion of the eyeballs targeted at orienting our gaze in the visual field, provide a large repertoire of behaviors at different time scales from fast, reflexive-like saccades to smooth movememnts and even to long-term adaptation.
(SHOW TITLE -OBJECTIVE) today, I will be focusing on the key challenges in modelizing visually guided eye movements and more generally to better understand decision making in biology (the living kingdom). in particular, we will focus on the dynamics of these mechanisms to unravel the sequence of processes which allow the efficient response of motor commands to the environment. As such, my goal here is to show that the solutions proposed by motion perception and EMs provide a generic (and rather unique) framework to finesse models of decision making in the generic theory championned by Karl Friston, active inference (AI)
(ACKNO) this endeavour involves different techniques, tools and... persons. From the head on, I wish to thank the people who collaborated to this project and in particular Rick Adams and Karl Friston and the Wellcome Trust Centre for Neuroimaging for providing the tools for a successful visit / but also Mina, Guillaume and Anna for the great oppportunity to link theories with psychophysical data; Wahiba, Giacomo and Frédéric for the challenging task of linking such models to the neural activity in NHP, and finally Jean-Bernard, Sohir and Laurent Madelain for their essential knowledge in adaptation and reinforcement.

more precisely... what are eye movements and how can they be useful for active inference?

... Eye movements can be of different nature, and I will propose to you now some gentle post-lunch gymnastics by trying to elicit such visually-guided movements with some short movies:

Most simply, saccades are an orienting behavior aiming at catching a specific position in visual space (or vergence movement in depth). if after fixating at the red fixation dot you try to catch the green dot, then you need to do such saccades, which can be very fast (up to 600 deg/s)

When the dot is now moving almong a trajectory, this visual motion can are also responsible for more complex movements such as the reflexive Ocular Following Response or the voluntary Smooth Pursuit EM which aims at stabilizing the visual image on the retina. INterestingly, in this latter case the position of the eye quickly centers on the present, physical position of the dot and we will later see why this is challenging

... Eye movements can be of different nature, and I will propose to you now some gentle post-lunch gymnastics by trying to elicit such visually-guided movements with some short movies:

The Behavioral receptive field

LP and Masson (2012) Bio Behav Reviews, https://laurentperrinet.github.io/publication/masson-12

Montagnini, and Masson (2015) in Biologically Inspired Computer Vision

... we have been busy in the last couple of years to make sense of this repertoire of behaviors, in particular in light with the architecture of the brain areas involved in producing these EMs, for instance for pursuit initiation, ...

the Left-side plot (extracted from this review paper) illustrates in primates a sketch of the hierarchy of neuronal population yielding to ocular following responses from the early visual areas (retina, thalamus, primary visual cortex), finessed by processing in motion specific information in downstream sensory areas (MT for speed or MST for global motion) to the brain stem and the oculomotor muscles which tranform this neural activity in a graded motor output. As such, moving stimuli covering the retina are processed by a cascade of neuronal populations, where information is processed through feedforward, lateral and feedback interactions.
in particular, we took advantage of a Bayesian, probabilistic framework to develop an unified theory, the "behavioral receptive field" which encompasses a large range of psychophysical experiments by modeling behavioral responses from population dynamics. Such cascade implements local, context-dependent extraction of motion information…
today, I would like today to focus on a particular problem which will help us unravel the dynamics of decision making: oculomotor delays. Indeed, one challenge for modelling is to understand EMs using AI as a problem of optimal motor control under axonal delays. The central nervous system has to contend with axonal delays, both at the sensory and the motor levels. For instance, in the human visuo-oculomotor system, it takes approximately $ au_s=50~ms$ for the retinal image to reach the visual areas implicated in motion detection, and a further $ au_m=40~ms $ to reach the oculomotor muscles.

The motion energy model

Weiss et al (2002) Nature Neuroscience

Standard Models of Motion detection are the well-known motion energy and Reichhardt models: these local motion detectors take the sequence as an input and give as an output different ``scores'' for a set of velocities.

(proba) in fact these models are equivalent at the functional level to a probabilistic measure. so if it's equivalent, why use probas? first, computation of a likelihood explicitly defines the generative models underlying the definition of motion and thus gives all underlying assumptions of a given model. second, we will see that probabilities are well adapted to manipulate bits of information,
(weiss) I show right the architecture of the model by Weiss02: top, the stimulus (here a rhombus), and in the middle what knowledge as represented in motion space (referenced here by the axis of horizontal and vertical translational velocities). we may extract internal knowledge about the motion in a receptive field and represent it by a subset in motion space, represented here by the "white" colours. In the case of the segment, most information is distributed along the line corresponding to the possible velocities. In the case of a dot or of an edge, motion is unambiguous, information lies on a small concentrated area of motion space.
(merge) information is then assumed to be conditionally independent and probabilities are multiplied to give a global readout. finally, the introduction of a bayesian prior was very successful in describing many behavioural and physiological data ... % however, the question is open concerning as how we may select and merge these measures

Eye movements and Bayes: motion integration

Outline

Eye movements

Motion-based predictive coding

Active inference, EMs & oculomotor delays

Perspectives: Saccadic adaptation

Motion-based predictive coding

Pack and Born (2001) Nature

(pack01) ... that the solution to the aperture problem seems to be dynamical. This data was recorded by Chris Pack and Rick Born in neurones from area MT in macaques: (2.a) the early response of neurones is preferentially tuned to the perpendicular to the line, (2.b) while it shifts to the physical direction (2.c) after approx 60 ms.
(OFR) this is also demonstrated at different levels of the system, and in particular for eye movements. (3) This is data recorded at their lab showing eye tracking to the slanted line a showing the same initial bias as with the neural data. These behavioural results replicate those obtained previously in humans by Guillaume Masson at our lab and show the close causality link from neural to behavioural response.
OBSOLETE (Pack03) as was shown physiologically or behaviorally, the transient response to line or line-ending detector detectors was similar, a difference emerged in their dynamics after few milliseconds. This observations suggest that these different cells have a common excitatory drive but that they integrate contextual information from neighboring neurons differently. It therefore suggests that the response to line-endings is not caused by specialized receptors but rather the consequence of a dynamical integration for which motion-based prediction gives a principled approach. (Figure 7 from Pack, 2003) Timing of V1 End-Stopping (A) The first row shows successive snapshots of the one-bar map for a strongly end-stopped V1 cell, for the preferred bar orientation. The cell initially responds well to a bar placed anywhere in its receptive field, but after $20-30 ms$, it responds only when the endpoints are in the receptive field. The second row shows the time course of the response when the analysis was limited to specific regions of the stimulus range. When the analysis was limited to instances when the bar was centered on the receptive field (green square), the neuron responded transiently (green line). When the analysis was limited to instances when the endpoint of the bar appeared in the receptive field (black square), the cell exhibited a strong maintained discharge (black line). (B) The time course of the response, averaged across the population of 29 neurons for the preferred bar orientation. Dotted lines indicate standard error of the mean.

Motion-based predictive coding

Pack and Born (2001) Nature

(pack01) ... that the solution to the aperture problem seems to be dynamical. This data was recorded by Chris Pack and Rick Born in neurones from area MT in macaques: (2.a) the early response of neurones is preferentially tuned to the perpendicular to the line, (2.b) while it shifts to the physical direction (2.c) after approx 60 ms.
(OFR) this is also demonstrated at different levels of the system, and in particular for eye movements. (3) This is data recorded at their lab showing eye tracking to the slanted line a showing the same initial bias as with the neural data. These behavioural results replicate those obtained previously in humans by Guillaume Masson at our lab and show the close causality link from neural to behavioural response.
OBSOLETE (Pack03) as was shown physiologically or behaviorally, the transient response to line or line-ending detector detectors was similar, a difference emerged in their dynamics after few milliseconds. This observations suggest that these different cells have a common excitatory drive but that they integrate contextual information from neighboring neurons differently. It therefore suggests that the response to line-endings is not caused by specialized receptors but rather the consequence of a dynamical integration for which motion-based prediction gives a principled approach. (Figure 7 from Pack, 2003) Timing of V1 End-Stopping (A) The first row shows successive snapshots of the one-bar map for a strongly end-stopped V1 cell, for the preferred bar orientation. The cell initially responds well to a bar placed anywhere in its receptive field, but after $20-30 ms$, it responds only when the endpoints are in the receptive field. The second row shows the time course of the response when the analysis was limited to specific regions of the stimulus range. When the analysis was limited to instances when the bar was centered on the receptive field (green square), the neuron responded transiently (green line). When the analysis was limited to instances when the endpoint of the bar appeared in the receptive field (black square), the cell exhibited a strong maintained discharge (black line). (B) The time course of the response, averaged across the population of 29 neurons for the preferred bar orientation. Dotted lines indicate standard error of the mean.

Motion-based predictive coding

LP and Masson (2012) Neural Computation, https://laurentperrinet.github.io/publication/perrinet-12-pred

We will now define a probabilistic framework for the representation of predictive motion information.

(prediction) First, we will define motion-based prediction which is adapted to smooth trajectories such as are observed in natural environments
(markov) Seeing this prediction as a prior on motion transition in the probabilistic domain, we then show how information may be pooled using a Hidden Markov Model, merging current information and measurement likelihood
(SMC) Differently to neural approximations that were used previously, we use a particle filtering method to implement this functional model. Prediction will now take the form of an anisotropic, context-dependent diffusion of local information.

But first, how do we define prediction?
In computer vision, one can define the prediction of the trajectory of some distinguished feature of the image (e.g., a local extremum of luminance) using its motion. here we define the feature to track as the motion at a given position and define Motion-based prediction by modelling smoothness in the trajectory of motion:
knowing the velocity $V_{t-dt}$ at one position $x_{t-dt}$, one expects that velocity will be transported to a new location, that is $x_{t} pprox x_{t-dt} + V_{t-dt} dt$ and approximately conserved in amplitude and direction $V_t pprox V_{t-dt} $. Nothing new: if we go to infinitesimal $dt$, this equation is the advection term in the navier-stokes equations.
This "approximately" may be included in our generative model by some random variable. different values for the variance of this state noise quantify the strength or precision of the prediction... it shapes the association fields in motion space similarly with what happens in the space domain with association field in the orientation domain of static images.
Note that contrary to classical models, position becomes an unknown variable instead of being a parameter as in OF. note also that it is auto-referent since prediction is based itself on motion %: neural = Series / models Grzywack, Burgi et al = "motion tracking"
then, we may use a classical Hidden Markov Model to recurrently update knowledge. This uses three steps knowing the probabilistic motion information at a current time and for simplicity I will just represent local probabilistic motion representations:
prediction of motion thanks to the generative model as a prior of motion transition and an integral over all possible motions. note that prediction is always diffusive
estimation of the likelihood of the predicted state,
merging both, we updated our knowledge from time $ t-dt$ to $ t$
repeating the operation, we define a dynamical system.
this theory seems easy on the paper, and there is nothing new here in the definition of the dynamical system . extit{BUT} ...... I have bad news: it is extremely hard to represent \& implement on classical machines: if we allow ourself a rather modest discretisation if the probability space (position and velocities), the very high dimensionality of the problem makes it tedious to represent ($2e9$ dimensions in the previously shown POF)...

Motion-based predictive coding

LP and Masson (2012) Neural Computation, https://laurentperrinet.github.io/publication/perrinet-12-pred

We will now define a probabilistic framework for the representation of predictive motion information.

(prediction) First, we will define motion-based prediction which is adapted to smooth trajectories such as are observed in natural environments
(markov) Seeing this prediction as a prior on motion transition in the probabilistic domain, we then show how information may be pooled using a Hidden Markov Model, merging current information and measurement likelihood
(SMC) Differently to neural approximations that were used previously, we use a particle filtering method to implement this functional model. Prediction will now take the form of an anisotropic, context-dependent diffusion of local information.

But first, how do we define prediction?
In computer vision, one can define the prediction of the trajectory of some distinguished feature of the image (e.g., a local extremum of luminance) using its motion. here we define the feature to track as the motion at a given position and define Motion-based prediction by modelling smoothness in the trajectory of motion:
knowing the velocity $V_{t-dt}$ at one position $x_{t-dt}$, one expects that velocity will be transported to a new location, that is $x_{t} pprox x_{t-dt} + V_{t-dt} dt$ and approximately conserved in amplitude and direction $V_t pprox V_{t-dt} $. Nothing new: if we go to infinitesimal $dt$, this equation is the advection term in the navier-stokes equations.
This "approximately" may be included in our generative model by some random variable. different values for the variance of this state noise quantify the strength or precision of the prediction... it shapes the association fields in motion space similarly with what happens in the space domain with association field in the orientation domain of static images.
Note that contrary to classical models, position becomes an unknown variable instead of being a parameter as in OF. note also that it is auto-referent since prediction is based itself on motion %: neural = Series / models Grzywack, Burgi et al = "motion tracking"
then, we may use a classical Hidden Markov Model to recurrently update knowledge. This uses three steps knowing the probabilistic motion information at a current time and for simplicity I will just represent local probabilistic motion representations:
prediction of motion thanks to the generative model as a prior of motion transition and an integral over all possible motions. note that prediction is always diffusive
estimation of the likelihood of the predicted state,
merging both, we updated our knowledge from time $ t-dt$ to $ t$
repeating the operation, we define a dynamical system.
this theory seems easy on the paper, and there is nothing new here in the definition of the dynamical system . extit{BUT} ...... I have bad news: it is extremely hard to represent \& implement on classical machines: if we allow ourself a rather modest discretisation if the probability space (position and velocities), the very high dimensionality of the problem makes it tedious to represent ($2e9$ dimensions in the previously shown POF)...

Tutorial: Active inference for eye movements: Bayesian methods, neural inference, dynamics

Laurent U Perrinet, INT

Acknowledgements:

LACONEU2017: 4th Latin-American Summer School in Computational Neuroscience January 20th, 2017 https://laurentperrinet.github.io/talk/2017-01-20-laconeu

The Behavioral receptive field

The motion energy model

Eye movements and Bayes: motion integration

Outline

Eye movements

Motion-based predictive coding

Active inference, EMs & oculomotor delays

Perspectives: Saccadic adaptation

Motion-based predictive coding

Motion-based predictive coding

Motion-based predictive coding

Motion-based predictive coding

Particle filtering (Sequential Monte-Carlo)

LACONEU2017: 4th Latin-American Summer School in Computational Neuroscience January 20th, 2017
https://laurentperrinet.github.io/talk/2017-01-20-laconeu