Sparse optimization in neural computations - <a href="http://www.laconeu.cl">LACONEU2017: 4th Latin-American Summer School in Computational Neuroscience</a> January 19th, 2017 <BR> <a href="https://laurentperrinet.github.io/talk/2017-01-19-laconeu">https://laurentperrinet.github.io/talk/2017-01-19-laconeu</a>

Check-list:

(before) bring miniDVI adaptors, AC plug, remote, pointer
(avoid distractions) turn off airport, screen-saver, mobile, sound, ... other running applications...
(VP) open monitor preferences / calibrate / title page
(timer) start up timer
(look) @ audience

Preparing Effective Presentations

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http://pne.people.si.umich.edu/PDF/howtotalk.pdf

Tutorial: Sparse optimization in neural computations

Laurent U Perrinet, INT

Acknowledgements:

Jim Bednar @ Continuum Analytics & University of Edinburgh
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 19th, 2017
https://laurentperrinet.github.io/talk/2017-01-19-laconeu

(AUTHOR) Hello, I am Laurent Perrinet from the Institute of Neurosciences of la Timone in Marseille, a joint unit from the CNRS and the AMU
(OBJECTIVE) in this short talk, I will be focus in highlighting some key challenges in modelizing visual perception and
(ACKNO) this endeavour involves different techniques and tools ... From the head on, I wish to thanks people who collaborated and in particular .. mostly funded by the ANR bala V1 (hansel wreeiswijk nowak) + ANR TRAJECTORY (o marrre bruno cessac palacios )
LONDON (Jim Bednar, Friston) great thanks to Stéphane for proposing me to present this work
(SHOW TITLE) I am interested in the link between the neural code and the structure of the world. in particular, for vision, I am researching the relation between the functional (in terms of the inferential processes leading to behaviour) organization (anatomy and activity) of low-level visual areas (V1) and the structures of natural scenes, that is of the images that hit the retina and which are relevant to visual perception in general.

so what is visual perception?

LP (2015) "Sparse models" in Biologically Inspired Computer Vision

... by linking to the statistics of natural images:

* (natural) For instance, oriented edges that constitute images of natural scenes
tend to be aligned in co-linear or co-circular arrangements, such as when
💠 you follow the contours of these boulders: lines and smooth curves
are more common than other possible arrangements of edges. See for example
the work of Mariano Sigman on co-circularity in natural images (see Sigman, 2001).

* (neural) The visual system appears to take advantage of this prior
information, and human contour detection and grouping performance is well
predicted by what is coined an "association field" (Field et al., 1993)...

Outline

Learning sparse codes: competition vs cooperation

Sparse codes for real-life images

Categorizing using sparse edges

LP (2015) "Sparse models" in Biologically Inspired Computer Vision

Outline

Learning sparse codes: competition vs cooperation

Sparse codes for real-life images

Categorizing using sparse edges

LP (2015) "Sparse models" in Biologically Inspired Computer Vision

Outline

Learning sparse codes: competition vs cooperation

Sparse codes for real-life images

Categorizing using sparse edges

Bosking et al. (1997) Journal of Neuroscience

... is the set of long-range lateral connections between neurons, which could
act to facilitate detection of contours matching the association field, and/or
inhibit detection of other contours. To fill this role, the lateral connections
would need to be orientation specific and aligned along contours, * (colin) and
indeed such an arrangement has been found in treeshrew's primary visual
cortex  (Bosking et al., J Neurosci 17:2112-27, 1997)
* (neural) if one looks at  the primary visual area in the occipital lobe of the cortex
using optical imaging as here in the treeshrew by Bosking and colleagues under the
supervision of DF, one could represent the distributed, topographical representation
of orientation selectivity. in (A) and (B) the orientation giving the most response
at each cortical position is represented by hue using the code below from orange for
horizontal to blue for verticals, and typical structures are magnified in (C): stripes
(on the periphery) and pinwheels. You can understand this as a packing of a 3D feature
space on the 2D surface of the cortex.
* (method)  Tree shrew orientation preference maps were obtained using optical imaging.
Additionally, 540 nm light was used to map surface blood vessels used for alignment.
Biocytin was then injected into a specific site in V1 and the animal was sacrificed 16
hours later. Slices of V1 were imaged to locate the biocytin bouton and the surface
blood vessels. The blood vessel information was then used to align the orientation
preference maps with the bouton images giving overlaid information on the underlying
connectivity from the injection site on the animal. The original experiment used a total
of ten cases.
* (lateral) we show here one result of Bosking
which overlay over a map or orientation selectivity the network of lateral connectivity
originating froma group of neurons with similar orientations and position. There is
a structure in this connectivity towards locality (more pronounced for site B) +
connecting iso orientations even on long ranges (A). This type of structure tends
to wire together those neurons that have similar orientations, indicating a prior
to colinearities.
*(colin) ... Overall, a typical assumption that the role of lateral interactions is to
enhance the activity of neurons which are collinear : it is the so-called
**association field** formalized in Field 93, as was for instance modeled neurally in
the work from P. Series or in this version for computer vision
* (physio) is there a match of these structures with the statistics of natural images?
 2) Some authors (Kisvarday, 1997, Chavane and Monier) even say it is weak or
inexistent on a the scale of the area... 1:  Hunt & Goodhill have reinterpreted above data and shown that there is more diversity
than that -
* TRANSITION : my goal here will be to tackle this problem at different levels:

LP and Bednar (2015) Scientific Reports, http://www.nature.com/articles/srep11400

We first extracted the edges from images using a scale-space analysis (all OSS
on github) The histogram was computed as a a 4-dimensional function of
distance, (symmetrical) azimuth $\psi$, difference of orientation $ heta$ and
ratio of scale. ... second-order statistics are efficiently computed by using a
the algorithm from Geisler et al. (2001), with a more general edge extraction
algorithm that uses sparse coding %to avoid multiple responses to a single
edge.  * ... Collinearity and co-circularity results for natural images
replicated qualitatively the results from Geisler et al. (2001), confirming
that prior information about continuations appeared consistently in natural
images.

Probability distribution function of "chevrons" * (angles)  By computing
measures of the independence of the different variables, we found that the
probability density function of the second-order statistics of edges factorizes
with on one side distance and scale and on the other side the 2 angles.  The
first component proved to be quite similar across both classes and the greater
difference is seen for different angle configuration. As it can be reduced to 2
dimensions, we can plot the full probability as shown here by different
contrast values assigned to all possible chevrons configurations, for all
possible "azimuth" values $\psi$ on the horizontal axis and difference of
orientation $   heta$ on the vertical axis. Such a plot most strikingly shows
the difference between these 2 classes.  one issue now that we can show the 2nd
order statistics is to know if it would be possible to quantify such
difference...

* (colin)  let's first replicate the result from Geisler by showing that
relative to a given edge (segment in the center), what is the Here I show for
each distance and angle the most probable difference of angle, showing that
collinear and parallel edges predominate.  (cocir) a similar pattern is observed the
cocircular plot. it reproduces the results from Geisler on natural images, but
laboratory environment shows a strong bias to colinearity. If we believe
bosking link, obviously, this should have a consequence on antomy. thus we test
whether these AF were different across different image classes.

LP and Bednar (2015) Scientific Reports, http://www.nature.com/articles/srep11400

* we computed the statistics of edge co-occurrences for different categories
(natural, man-made, or containing an animal) . These differed strongly, with
animal images having more curved configurations. Here we show that the
statistics of edge co-occurrences alone are sufficient to perform a rough yet
robust (translation, scale, and rotation invariant) scene categorization.  This
seems a bit crazy (in particular with the current trend for deep learning)
especially, knowing that most model (like the one from Serre 07) would rather
consider that it is better done in 10 processing layers.
* Classification results for different sets of natural images (50\% is chance
level) and different classification methods. Note that for SVM, we controlled
for different feature choice: first-order statistics (SVM 1), full second-order
statistics (SVM 2) or the chevron map only (SVM C). Surprisingly, the results
are very similar to the results of Serre 07, and we do not lose much
performance by choosing the simple chevron map. First, this has direct
application in machine learning as this translation- and rotation-independent
classifier performs as well as more complicated networks (that is they have
more parameters) - and could be imported to existing architectures

LP and Bednar (2015) Scientific Reports, http://www.nature.com/articles/srep11400

 We show that this geometry alone is sufficient for categorization, and that
 the pattern of errors made by humans is consistent with this procedure.  * To
 see whether the patterns of errors made by humans are consistent with our
 model, we studied the second-order statistics of the 50 non-animal images that
 human subjects in Serre et al. (2007) most commonly falsely reported as having
 an animal. We call this set of images the false-alarm image dataset. (Left)
 This chevron map plot shows the ratio between the second-order statistics of
 the false-alarm images and the full non-animal natural image dataset, computed
 as in Figure 3 (left). Just as for the images that actually do contain animals
 , the images falsely reported as having
 animals have more co-circular and converging (red chevrons) and fewer
 collinear and orthogonal configurations (blue chevrons). (Right) To quantify
 this similarity, we computed the Kullback-Leibler distance between the
 histogram of each of these images from the false-alarm image dataset, and the
 average histogram of each class. The difference between these two distances
 gives a quantitative measure of how close each image is to the average
 histograms for each class. Consistent with the idea that humans are using edge
 co-occurences to do rapid image categorization, the 50 non-animal images that
 were worst classified are biased toward the animal histogram ($d' = 1.04$),
     while the 550 best classified non-animal images are closer to the
     non-animal histogram.

LP and Bednar (2015) Scientific Reports, http://www.nature.com/articles/srep11400

Tutorial: Sparse optimization in neural computations

Laurent U Perrinet, INT

Acknowledgements:

Jim Bednar @ Continuum Analytics & University of Edinburgh
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 19th, 2017
https://laurentperrinet.github.io/talk/2017-01-19-laconeu

Tutorial: Sparse optimization in neural computations

Laurent U Perrinet, INT

Acknowledgements:

LACONEU2017: 4th Latin-American Summer School in Computational Neuroscience January 19th, 2017 https://laurentperrinet.github.io/talk/2017-01-19-laconeu

Outline

Learning sparse codes: competition vs cooperation

Sparse codes for real-life images

Categorizing using sparse edges

Outline

Learning sparse codes: competition vs cooperation

Sparse codes for real-life images

Categorizing using sparse edges

Outline

Learning sparse codes: competition vs cooperation

Sparse codes for real-life images

Categorizing using sparse edges

Tutorial: Sparse optimization in neural computations

Laurent U Perrinet, INT

Acknowledgements:

LACONEU2017: 4th Latin-American Summer School in Computational Neuroscience January 19th, 2017 https://laurentperrinet.github.io/talk/2017-01-19-laconeu

LACONEU2017: 4th Latin-American Summer School in Computational Neuroscience January 19th, 2017
https://laurentperrinet.github.io/talk/2017-01-19-laconeu

LACONEU2017: 4th Latin-American Summer School in Computational Neuroscience January 19th, 2017
https://laurentperrinet.github.io/talk/2017-01-19-laconeu