Vision in Brains and Machines - Redwood Center for Theoretical

Vision in Brains and Machines
Bruno A. Olshausen
Helen Wills Neuroscience Institute, School of Optometry
and Redwood Center for Theoretical Neuroscience
UC Berkeley
Brains vs. machines
“the brain doesn’t do things
the way an engineer would”
“we needn’t be constrained by
the way biology does things”
Brains vs. machines
“the brain doesn’t do things
“we needn’t be constrained by
“brains and machines use a common set of operating principles”
the way an engineer would”
the way biology does things”
Cybernetics/neural networks
Norbert Wiener
Warren McCulloch & Walter Pitts
Frank Rosenblatt
By the study of systems such as the perceptron, it is hoped that those
fundamental laws of organization which are common to all information
handling systems, machines and men included, may eventually be
understood.
— Frank Rosenblatt, Psychological Review, 1958.
Two modern developments that arose from the
confluence of ideas between disciplines
Information
theory
Natural scene
statistics
Signal and image
processing
Feature
detection
Machine
learning
Models of visual
cortex
The ‘Ratio Club’ (1952)
216 YNGVI zonERMAN
Gonloo, G. , R. Kjtchell , L. Strom , and Y.
Zotterman, The response pattern
Redundancy
reduction
I.
(Barlow, 1961)
of taste flbres in the chorda
1959 , 46, 119-- 132.
Jacobs , H. L., and M.
Acta physiol, scand.
tympani of the monkey,
L. Scott.
H.
B.
BARLOW
Physiological Laboratory, Cambridge UniversIty
Factors mediating food and liquid intake in
Studies on the prefct"ellt'c for sucrose or saccharinc solutions,
Poultry Sci. 1957 , 36, ~15.
Kare, M, R., R. Black , and E. G. Allison, The sense of taste in the fowl.
Poultry
. chiekells.
Possible Principles
Sel. 1957 , 36, 129-138.
Kitchell , R. L. ,
L. Strom
, and y, Zotterman. Electrophyslological studies of ther-
mal and taste reception in chickens
and pigeons.
Acta physlol, scand.,
46, 13~151.
Koketsu , K. Impulses from receptors in the tongue of a frog,
mea. Sci. 195 J , 2, 53-61.
Kusano , K. , and M. Sato. Properties of fungiform papillae
la1',
in frog s tongue.
1957
J.
G.
mammals.
Geschmacksinn,
, 2, 1-
impulses. J.
, E. v.
ZottermRn ,
tympani.
Zotterman ,
of Sensory Messages
Kywhu Mem,
The hypothesis
is that sensory relays
PhI/sial.
, 7, 324-338.
, and y, Zotterman. The water taste in
recode
sensory messages so Acta physlol.
,cond. 1954 , 32, 291-303.
Skand, Arch. Phl/slol.
ohrwalJ , H. Untersuchungen tiber den
that
their69.redundancy is reduced
but
IA9l
Pfaffmann , C. Gustatory afferent
243-258.
comparatively
little information is lost.
Handbuch der nlederen
Skrarulik
Li.ljestTand ,
Underlying the Transformations
1959
Y. Aclion
Sinne.
ceU, compo Phl/sIoI. 1941 ,
17,
Bd. 1. Leipzig: Thieme, 1926,
potentials in the glossopharyngeal nerve and in the chorda
Skalla. Arch. PhYstol.
1935, 72, 73-77,
Y. The response of the frog s taste fibres to the application of pure
Acta phI/stolt scand. a way of organizing
...it
constitutes
Experientia
Zotterman
Zotterman
the sensory InformatIon so that, on
the one hand, an internal model of
the environment causing the past
sensory inputs is built up, while on
the other hand the current sensory
situation is represented in a
concise way which simplifies the
task of the parts of the nervous
system responsible for learning and
conditioning.
water,
1949 ,
18, 181- 189,
The water taste in the frog,
Species differences in the water taste,
37, 00-70.
1950
6 (2), 57-58,
Acta physwl. scand.,
1956
A wing would be a most mystifying structure if one did not know
that birds flew. One might observe that it could be extended a considerable distance
, that it had
a smooth covering of feathers with
conspicuous markings ,
that it was operated by powerful muscles , and
that strength and lightness were prominent features of its construction, These are important facts , but by themselves they do not tell
us that birds fly. Yet without knowing this , and without understanding something of the principles of flight, a more detailed examination
of the wing itself would probably be unrewarding, I think that we
may be at an analogous point in our understanding of the sensory
side of the central nervous system, We have got our first batch of
facts from the anatomical , neurophysiological , and psychophysical
study of sensation and perception , and now we need ideas about what
operations are performed by the various structures we have examined.
For the bird' s wing we can say that it accelerates downwards the air
flowing past it and so derives an upward force which supports the
weight of the bird; what would be a similar summary of the most
important operation performed at a sensory relay?
It seems to me vitally important to have in mind possible answers
to this question when investigating these structures , for if one does
not one will get lost in a mass of irrelevant detail and fail to make the
.crucial observations, In this paper I shall discuss three hypotheses
according to which the answers would bc as follows:
1, Sensory relays are for detecting, in the incoming messages , cer-
passwords " that have a particular key significance for the animal.
2, They are filters , or recoding centers , whose "pass characteristics
tain "
217
.........
...
Models and experimentally-tested predictions
arising from the redundancy reduction theory
Notizen
coding characteristic is used in
911
digital image pro-
cessing, and is called " histogram equalization (5).
Note that this coding procedure amplifies inputs in
proportion to their expected frequency of occurrence , using the response range for the better resolution of common events , rather than reserving large
portions for the improbable.
1.0
• Histogram equalization
To
first order
Laughlin (1981); Bell & Sejnowski
use this coding procedure I
blowfly s compound eye (1995)
110m V
50ms
interneurons of the
see if the
0 0.
compared their contrast-response functions with the
contrast levels measured in natural scenes , such as
dry schlerophyll woodland and lakeside vegetation.
Relati ve intensities were measured across these
scenes using a detector which scanned horizontally,
like the ommatidium of a turning fly. It consisted of
a PIN photodiode, operating within its linear range
in the focal plane of a quartz lens. A combination of ....,
coloured glass filters (Schott , KG 3 + BG 38) was
used to givs, the detector a spectral sensitivity
similar to a fly monopolar cell (3). The scans
206were
cumu lative
probability
• Predictive coding
1.0
Srinivasan, Laughlin & Dubs (1982)
digitised at intervals of 0. 070
Joseph J. Atick and A. Norman Redlich
1.4 0
coHesponding to the angular sensitivity of a fly
photoreceptor (6). Contrast values were obtained by
• Whitening
averaged from 6 cells; range bars show total scatter. Inset
shows the averaged responses of an LMC to four contrast
steps (the cell hyperpolarises to increments and depolarises
to 300
decrements). The stimulus , a Siemens LD57C light
emitting diode (LED) subtending 20 and filling the centre
dividing each scan into intervals of 10 , 25 or 500
Within each interval the mean intensity, /, was
found , and substracted from every data point to
give the fluctuation about the mean LlI.
This
of the LMC's receptive field; was mounted in the centre of
the reflecting screen of diameter 160 . LED and screen
difference value was divided by the mean to give
the contrast AI/I.
The cumulative probability dis-
Atick & Redlich (1990; 1992);
levels (Fig. 2) was derived from
tribution of contrast
15000 readings. As expected , the range of contrasts
of the interval
van Hateren (1992; 1993);
used difference between the two larger
intervals
, was small.
Dan, Atick & Reid (1996)measured using thes techniques
contrast-response function was
developed for intraencountered increased with the width
, but the
, 25 0 and 500
The interneuron
+ 1.0
Fig. 2. The contrast-response function of light adapted fly
LMC's compared to the cumulative probability function
for natural contrasts (500 interval). Response is normalised
with the maximum amplitude to light off as 0. , and the
maximum
amplitude to an increment as 1. 0. Data points
1000
and convolved with a
Gaussian point spread function of half-width
contrast cd/I
100
brightnesses
were equalised by setting the mean LED
intensity so that its substitution for the screen in the centre
. of the field generated a negligible response. Contrast steps
...,J
!II
Q.)
were generated by setting the LED driving voltage to a
for 100 ms , and the corresponding contrast
new level
determined by recording the driving voltages and referring
these to the diode
s voltage/intensity curve, determined
Mean light levels where 2. 5 to 3. 0 log units above the
intensity producing a half maximal response from the dark
adapted LMc.
situ.
cellular recording in the intact retina of the blowfly,
Calliphora stygia
, 6). Individual LMC' s were light
adapted by a bright steaqy background and the
responses to sudden increments and decrements
about this level recorded (Fig. 2). Repeated responses to the same stimulus were averaged to
enhance the reliability of the data. The light adapted
contrast-response function approximates to the sig-
sponse equiprobability have a
marginal effect on 100
entropy (4), there should be little redundancy associated with the LMC response to natural scenes.
frequency,
c/deg concept
The successfulSpatial
application
of a central
from information theory,
entropy, to a neuron
V1 is highly overcomplete
Tempo ral recons tructio n o f the image
The homun culus also has to face t'he proble m that the image is often nioving
contin uously , but is only represe nted by impulses a t discret e mome nts in time. I n
these days he often has to deal with visual images derive d from cinema screens and
television sets t h a t repres ent scenes sample d a t quite long interva ls, and we know
LGN
afferents
IVb
layer 4
cortex
Barlow (1981)
C
0 1mm
I
E A tracing of the outlines of the granule cells of area 17 in layers I V b and IVc of
FIGUR8.
monkey cortex, where the incoming geniculate fibres termma te (from fig. 3 c of Hubel &
Wiesel 1972) The dots at the top lndlcate the calct~l atedseparation of the sample points
Sparse,
distributed codes
Dense codes
(e.g., ascii)
(e.g., grandmother cells)
. . .
. . .
N
2
Local codes
N
K
( )
(From Foldiak & Young, 1995)
N
4.00
d.
3.00
coo
0
I
Field (1987)
X~~~~~~~~~~. Ia
2.00
David J. Field
r~2
0
to
1.01
II
02
> 0.0c11
1,
¢oX 6.OC
ar
01=,
a s.ocII.
more recently by Daugman,1 a Gabor function represents a
minimum in terms of the spread of uncertainty in space and
spatial frequency (actually time and frequency in Gabor's
description). However, the Gabor code is mathematically
pure in only the Cartesian coordinates where all the Gabor
Gi~~~~~~~~~~~~~~~(."
11.,
channels are the same size in frequency and hence have
,)0
Vol.in4,space
No. 12/December
1987/J. Opt. Soc. Am. A
sensors that are all the same size
(i.e., all the rectangles in the diagrams in Fig. 1 are the same size). In such a
case, the Gabor code represents the most effective means of
packing the information space with a minimum of spread
and hence a minimum of overlap between neighboring units
in both space and frequency.
However, modifying the basic structure of the code to
permit a polar distribution such as that shown in our rosettes
(Fig. 3) alters the relative spread and overlap between neighbors. In this section some results are described that were
obtained with a function that partially restores some of the
destructive David
effects J.ofField
the polar mapping. This function will
be called the log Gabor function. It has a frequency rePhysiological Laboratory,
sponse University
described of
byCambridge, Cambridge CB2 3EG, UK
Relations between the statistics of natural images and the
response properties of cortical cells
Image D
2 4.OC
II.
0)
E. 3.OC
2379
Image E
1.0 2.0
3.0
I aatM
2.OC
Simple-cell receptive fields are well suited to encode images
with a small fraction of active units.
1.001
0.0 ,
David J. Field
6.005.00
4.00
d.
3.00
coo
0
I
2.00
to
3.0
1.0 2.0 3.0
G(f) = expi-[log(f/f 0 )]2 /2[log(oi/f0 )]2 I,
Received May 15, 1987; accepted August 14, 1987
(12)
Bandwidth (octaves)
that image-coding
is, the frequency
response is a Gaussian on a log freThe relative efficiency of any particular
scheme should be defined only in relation to the class of
Vol.
4,
No.
12/December
1987/J.
Opt. Soc.
Am.
A
2389 the
Fig. 12. Relative response of the different
subsets
of
sensors
as
a
quency
axis.
Figure
14
a comparison
images that the code is likely to encounter. To understand the provides
representation
of images between
by the mammalian
visual
function of the bandwidth. For example,
plottherefore
labeled 0.01
system, itthe
might
be useful to consider the statistics of images from the natural environment (i.e., images
represents the average response of the
toptrees,
1%ofrocks,
the sensors
relative
with
bushes,
etc). In this study, various coding schemes are compared in relation to how they represent
to the averageresponse of all the sensors.
If we consider
the
sensor
Image
natural
Gabor
codesA of
have
number
Image
Bof interesting
Image C
the information
in such
naturalimages.
images. The
coefficients
suchacodes
are represented
4 by arrays of mechanisms
6.00r
subject
thisrespond
plot
related
to
the
Image A response to be
C cantobelocal
Image
B to noise, thenthat
Image
regions
of space, spatial
mathematical
properties.
As orientation
described
by Gabor1
and For many classes
frequency, and
(Gabor-like
transforms).
signal-to-noise ratio. It suggests that spatial-frequency band2
of image, such codes will
not recently
be an efficient
means of representing
information.
the results
obtained with
more
by5.00
Daugman,1
a Gabor
function However,
represents
a
widths in the range of 1 octave produce
the highest
signal-to-noise
- and the spatial-frequency
six natural
images
suggest that the orientation
tuning
of
mammalian
simple
cells are well
ratio.
insuch
terms
of the
in
0o,0space and
suited for coding the minimum
information in
images
if thespread
goal of of
the uncertainty
code is to convert
higher-order redundancy (e.g.,
002
4.00
-0.0opixels)time
correlation between the
intensities
of neighboring
spatial
frequency
into first-order
(actually
and frequency
in(i.e.,
Gabor's
redundancy
the response distribution
0.02
0.05
of the tocoefficients).
Such
coding produces
a relatively
active sensors have a high response
the average.
If we
high
signal-to-noise
ratio
and permits information
to be
description).
However,
the
Gabor
code is mathematically
0.02
transmitted
with
only
a
subset
of
the
total
number
of
cells.
3.00
0.05
These
results support Barlow's theory that
the
goal
of
consider the fact that cortical neurones
are
inherently
rather
0.05
0.10
0.) Cartesian
pure intheonly
the
coordinates
where
all0.20the redundancy.
Gabor
G
i~~~~~~~~~~~~~~~(."
natural
vision
3
is toplot
represent
information
in
the
natural
X~~~~~~~~~~. Ia
environment
with
minimal
noisy in their response to a stimulus,
' this
can
be
0.10
11.,
channels are 0~0the2.00same size in frequency and hence have _~~0.20
,)0
considered a measure of the signal-to-noise ratio
of different
sensors
VI) all the same size in space (i.e., all the rectantypes of sensors. INTRODUCTION
Coding information into channels
with that are
to
2
2why
behave
1.00 in Fig. 1 are
gles in the diagrams
thecortical
sameneurons
size). might
In such
a in this way. Daugman'
approximately 1-octave bandwidths produces a representa02
points out that the Gabor coderepresents an effective means
Since Hubel and the cells classic
experiments
oncode
neurons
in
case,
the
represents
the most effective means of
tion in which a small proportion of Weisel'sl
represents
a Gabor
0.00
of filling the information space with functions that extend in
the visual cortex, we have moved a great deal0) closer to an
packing the information
spaceboth
withspace
a minimum
of spread
large proportion of the information with a high signal-to2and frequency.
However, this does not necessarunderstanding
of
the
behavior
and
connections
of
visual
noise ratio.
and
hence
a
minimum
of
overlap
between
neighboring
units
ily
imply
that
mustF be an efficient means of
cortical neurons.
A number
recent
Image D
Image Esuch a codeImage
0 early visual
Image D We have Image
so far Econsidered
only channels
for of
which
themodels of
C,,
r~2
0
I.1.0 2.0
1.01
II
02
> 0.0c11
1,
¢oX 6.OC
ar
0
a s.ocII.
1=,
in both spaceC,and6.00
frequency. representing the information in any
image. As we shall see,
processing bandwidth
have been quite
in accounting
ratio of the spatial-frequency
to theeffective
orientation
0 for a wide
2 4the basic
However,
modifying
structure
of
the
code
to
the efficiency of a code will depend on the statistics of the
range
of physiological
and psychophysical
observations.
0.) 5.0 - bandwidth is constant
(AF/AO
= 1.0). Figure
13 shows reinput
the images).
permit
a
polar
distribution
such
as that(i.e.,
shown
in our rosettes
For a wide variety of images, a
2However,
although
we
know
much
more about
how the
2 4.OC
II.
sults with various
different
aspect
ratios.
One
of
the
diffi0.)
1.0 2.0 early
3.0 stages of the visual system (Fig.
codewillbetween
be quite an
inefficient means of representing
3)information,
altersV)
the4.00k
relative
and overlap
neigh0)
process
there isspreadGabor
culties of such an analysis
is that the two-dimensional
Gabor
Ca.
0.02
0.01
information.
E
E. 3.OC
still
a
great
deal
0.02
of
disagreement
bors.
In
this
section
some
results
are
described
that
were
about
the
reasons
why
the
functions
are
not
polar
separable.
That
is,
the
spatial-fre0.02
c
__ _~ 0.02
I aatM
0.05
Clearly,
the definition
visual
an efficient, or optimal, code
system works
as it does.obtained
Theorieswith
of why
3.00ccortical that partially
a function
restores
some ofofthe
quency tuning is not
independent
of the orientation
tuning
0.0
0.05
0.20
depends
on
two
parameters:
the goal
neurons
of the code and the
behave
as
they
do havedestructive
varied widely
\ function
0.10
from Fourier
2.OC
(in degrees). Extending the5 orientation
bandwidth
actually
effects
of
the
polar
mapping.
This
will
0.20
6
0.20
7
0.20
statistics
of thea input.
analysis
to edge todetection.
However,
theory function.
extends the response
of the' channel
higher frequencies.
be
called no
thegeneral
log2.00Gabor
It has
frequency rehas emerged
a clear
With few exceptions (e.g., Refs. 15-18), theories of why
favorite.
Edge
detection
has
proved
With the 1/f amplitude
spectrum,asthe
response
of the
chan1.001
sponse described1.0C
by
to beprimarily
an effective
visual neurons behave as they do have failed to give serious
of coding
many types of images, but
nel will be dependent
on means
the lower
frequencies,
2
the evidence
that
cortical neurons
can generally
classified 0 )]consideration
with little effect produced
by the
extension.
Nonetheless,
(12) of the natural environment.
/2[log(oi/f0 )]2toI, the properties
G(f) =beexpi-[log(f/f
0.00'
0.0 ,
I.1.0 2.0 3.0
1.0 2.0 as3.0
0.25
1.00
4.00
0.25
1.00
4.00
0.25
4.00
edge
detectors
is
lacking
Our
present theories about the1.00
Refs.
the results of such an analysis are shown in Fig.(e.g.,
13. As
can8 and 9).
function
of cortical neurons
Bandwidth
(octaves)
Theofnotion
thatoptiis, the frequency
response
is based
a Gaussian
onona the
log bandwidth
frethe is
are
frequency
bandwidth
/ Orientation
visual
cortex
primarily
performs
be seen, an aspect
ratio
about that
0.5-1.0
somewhat
a globalSpatial
Fouriresponse
of such neurons to stimer transform
no longer
uli asuch
Fig. 12. Relative response
of the different
subsets
of is
sensors
as a given quency
serious consideration.
checkerboards,
mal, although
the effects
are small.
Theprovides
axis. Fig.
Figure
14
comparison
between
the
13. Relative
response
of
theasdifferent
subsets
as asine-wave
function ofgratings, long straight
-
.
..-------
0.10
Field (1994)
Simple-cell receptive fields
are well suited to maximize
non-Gaussianity (kurtosis) of
response histograms.
Internal
model
External
world
.
.
.
Sparse coding
image model
(Olshausen & Field, 1996;
Chen, Donoho & Saunders 1995)
I(x,y)
φi(x,y)
I(⇤x) =
M
X
ai
ai ⇥i (⇤x) + (⇤x)
i=1
image
neural
activities
(sparse)
features
other
stuff
Learned dictionary { i }
spatial frequency (cycles/window)
2.5 5.0
1.2 2.5
0 1.2
y
x
Olshausen & Field (1996)
Non-linear encoding
Outputs of sparse coding network (a i)
Pixel values
Image I(x,y)
Many other developments
• Divisive normalization Schwartz & Simoncelli (2001); Lyu (2011)
• Non-Gaussian, elliptically symmetric distributions
Zetzsche et al. (1999); Sinz & Bethge (2010); Lyu & Simoncelli (2009)
• Contours
Geisler et al. (2001, 2009); Sigman et al. (2001); Hoyer & Hyvarinen (2002)
• Complex cells, higher-order structure
Hyvarinen & Hoyer (2000); Karklin & Lewicki (2003, 2009); Berkes et al. (2009); Cadieu & Olshausen (2012)
Natural Scene Statistics
(Hancock, MA 1997)
Barlow Donoho Li
Applications of sparse coding
Denoising / Inpainting / Deblurring
Compressed sensing
Computer vision
Deep learning
building blocks,
staggering them
present
appropriately
Up toover
the two mechanisms
the an
and conversely).
wide region. have
' off'-centre,
A
complexgeniculate
units. One
only of
simple fields
useopposite
the corresponding
type ('on '-centre
instead
as of
by ones
sponding
cellsneed
mayinhibitory
Similarendings
schemes by
explain thewebehaviour
be proposed
replace of
ones,to provided
corretheother
excitatory
complex
field, and
this would tend
higher-order
to excite 19
thewe
cell. any of the
may replace
connexions.
direct inhibitory
In Text-fig.
activate scheme
one or more
ofshould,
these simple
cells wherever
fellpossibility
itthe
within the of
however,
consider
proposed
In would
the
one
280 and staggeredexcitatory
H. HUBEL
AND
T. N. WIESEL
axis orientation,
along aD.
horizontal
light
line. An&edge
of
1961).
Wiesel,
(Hubel
suppression
afferent
firing
of
in
its
main
of simple cortical cells with fields of type C, Text-fig. 2, all with vertical
because
of FIG. 38. Wiring
centrefrom
its field
an of
'off'-centre
on illuminating
Text-figs. 5cell
One may imagine
andis6.suppressed
that it receives
afferents
a set
diagrams
that
visual system is clear from studies of the lateral geniculate body, where
account
for the properties
of hypercomple
the
mechanisms
occur
in
place
level.
such
takes
That
inhibition
at
a
lower
order cell.
cells. A: hypercomplex
cell responding
tonic excitation,
field isofpresumed
to be
result
of withdrawal
thesome
its position, will
excite
simple-field
cells, leadingof
to excitation
of the higher-i.e. the
single
stopped
edge (as in Figs. 8 th
rupted lines.
Any vertical-edge
stimulus an
falling
across this rectangle,
part of regardless
inhibitory
the receptive
firing
suppression
of
on illuminating
The boundaries of the fields are staggered within an area outlined by the inter11) receives
projections
from
two co
the
excitatory
synapses.
Here
Text-fig.
model
of
is
based
on
The the
19
left and an inhibitory region to the right of a vertical straight-line boundary.
cells, one excitatory
to the hypercomple
neurone has a receptive field arranged as shown to the left: an excitatory region to
afferents.
cell (E),
the other
inhibitory
(I). Th
are imagined
to project
to a single
cortical
cell of higher
order. Eachby
projecting
'on'-centre
unequally
reinforced
be produced
were
the
two
flanks
if
fields. A number of cells with simple fields, of which three are shown schematically,
citatory
complex
cell has iti receptive
E, would
regions, as
flanking
asymmetry
in field
left. 20.
An Possible
to the Text-fig.
scheme forofexplaining
the organization
of complex
receptive
in the region
indicated
by the left
region below and to the right of the boundary, and 'on' centres above and
tinuous)
rectangle;
the inhibitory
ce
be formed by having geniculate afferents with 'off' centres situated in the
its field in the area indicated
by the
their field centres appropriately placed. For example, field-type G could
(interrupted)
rectangle.
The hypercomple
by supposing that the afferent 'on'- or 'off'-centre geniculate cells have
field thus includes
both areas, one bein
In a similar way, the simple fields of Text-fig. 2D-G may be constructed
Hubel & Wiesel (1962, 1965)
Hypercomplex
Complex
activating
region,
the other the antagonis
receptive-field diagram to the left of the figure.
Stimulating
the left region
alone resu
then have an elongated 'on' centre indicated by the interrupted lines in the excitation
of the cell, whereas
stimulat
synapses are supposed to be excitatory. The receptive field of the cortical cell will
regions
together
is without
effec
a straight line on the retina. All of these project upon a single cortical cell, and the both
proposed
to explain
the prope
the upper right in the figure, have receptive fields with 'on' centres arranged along scheme
fields. A large number of lateral geniculate cells, of which four are illustrated in of a hypercomplex
cell responding
Text-fig.
receptive
20.
hypothetical
simple
The
of
organization
illustrated
explaining
the
has a complex field like thatdouble-stopped
Text-fig. 19. Possible scheme for cell
slit (such as that desc
their exact retinal positions. An example of such a scheme is given in
for the differ
all have identical axis orientation, but would differ from one another inin Figs. 16 and 17, except
or the hypercomplex
ce
having cells with simple fields as their afferents. These simple fields wouldin orientation,
in Fig. 27). The cell re
noted in Part I suggests that cells with complex fields are of higher order,small spikes
input
from
a complex
cell
body. Rather, the correspondence between simple and complex fieldsexcitatory
posing that these cells receive afferents directly from the lateral geniculate vertically
oriented
field is indicated
The properties of complex fields are not easily accounted for by sup-left by a continuous
rectangle;
two
occur.
tional
complex
cells inhibitory
to the
not been distinguished, but there is no reason to think that both do not
complex
cell have
vertically
oriented
CAT VISUAL CORTEX1
143flanking
cortical fields.
the first
one above
and
Simple
Neocognitron
(Fukushima 1980)
image
feature pooling feature pooling
objects
extraction
extraction
“LeNet”
(Yann LeCun et al., 1989)
articles
‘HMAX’
(Riesenhuber & Poggio, 1999; Serre, Wolf & Poggio, 2005)
n extension of
simple cells4,
‘S’ units in the
matching, solid
nits6, performonlinear MAX
he cell’s inputs
odel’s propersummation of
e two types of
invariance to
different posiover afferents
ap in space
e ‘complex’
mulus size,
nvariance!
a simplified
View-tuned cells
Complex composite cells (C2)
Composite feature cells (S2)
Complex cells (C1)
Simple cells (S1)
weighted sum
MAX
network to recover the data from the code.
minimizing the discrepancy between the original data and its reconstruction. The required
gradients are easily obtained by using the chain
rule to backpropagate error derivatives first
through the decoder network and then through
the encoder network (1). The whole system is
Deep Belief Networks
Department of Computer Science, University of Toronto, 6
King’s College Road, Toronto, Ontario M5S 3G4, Canada.
(Hinton & Salakhutdinov, 2006)
*To whom correspondence should be addressed; E-mail:
[email protected]
Decoder
30
W4
500
Top
RBM
T
T
W 1 +ε 8
W1
2000
2000
T
500
1000
1000
W3
1000
T
W 2 +ε 7
W2
T
T
W 3 +ε 6
W3
RBM
500
500
T
W4
30
1000
W4
W2
2000
Code layer
500
RBM
W3
1000
W2
2000
2000
W1
W1
T
W 4 +ε 5
30
W 4 +ε 4
500
W 3 +ε 3
1000
W 2 +ε 2
2000
W 1 +ε 1
It is difficult
nonlinear autoen
hidden layers (2–
autoencoders typi
with small initial
early layers are
train autoencoder
the initial weights
gradient descent
initial weights req
algorithm that lea
time. We introduc
for binary data, ge
and show that it
data sets.
An ensemble
ages) can be mo
work called a Bre
(RBM) (5, 6) in w
are connected t
detectors using s
nections. The pi
units of the RB
observed; the fea
Bhidden[ units. A
the visible and h
given by
X
Eðv, hÞ 0 j
iZpix
j
RBM
Pretraining
X
i, j
Encoder
Unrolling
Fine-tuning
Fig. 1. Pretraining consists of learning a stack of restricted Boltzmann machines (RBMs), each
where vi and hj a
and feature j, bi a
the cortex. They also demonstrate that convolutional
DBNs (Lee et al., 2009), trained on aligned images of
faces, can learn a face detector. This result is interesting, but unfortunately requires a certain degree of
Le etconstruction:
al. 2012)their training
supervision(Quoc
during dataset
images (i.e., Caltech 101 images) are aligned, homogeneous and belong to one selected category.
‘Google Brain’
logical and co
Lyu & Simonc
As mentioned
of local conne
ments, the fir
pixels and the
lapping neighb
The neurons in
input channel
second sublay
(or map).3 W
responses, the
the sum of th
is known as L
normalization
Our style of
ules, switch
ance layers,
HMAX (Fuk
1998; Riesenh
been argued t
brain (DiCarlo
pooling
sparse coding
Figure 1. The architecture and parameters in one layer of
Although we
not convoluti
across differe
We visualize histograms of activation values for face
images and random images in Figure 2. It can be seen,
even with exclusively unlabeled data, the neuron learns
to differentiate between faces and random distractors.
Specifically, when we give a face as an input image, the
neuron tends to output value larger than the threshold,
0. In contrast, if we give a random image as an input
image, the neuron tends to output value less than 0.
‘Google Brain’
(Quoc Le et al. 2012)
Figure 2. Histograms of faces (red) vs. no faces (blue).
The test set is subsampled such that the ratio between
faces and no faces is one.
Figure 3. Top: Top 48 stimuli of the best neuron from
test set. Bottom: The optimal stimulus according t
merical constraint optimization.
4.5. Invariance properties
We would like to assess the robustness of the fac
tector against common object transformations,
logical and computational models (Pinto
the cortex. They also demonstrate that convolutional
et al., 2008;
translation,
scaling and out-of-plane rotation. F
2
In
this
section,
we
will
present
two
visualization
techLyu & Simoncelli, 2008; Jarrett et al.,we2009).
DBNs (Lee et al., 2009), trained on aligned images of
chose a set of 10 face images and perform di
niques
verify
the optimal stimulus of the neuron is
faces, can learn a face detector.
Thisto
result
is if
interAs mentioned above, central to our approach
use e.g., scaling and translating. For
tions tois the
them,
esting, but unfortunately requires
a certain
of method is visualizing the most
indeed
a face.degree
The first
of local connectivity between neurons.
In
our
experiof-plane rotation, we used 10 images of faces rota
supervision during dataset construction:
their
training
responsive
stimuli
in thements,
test set.
Since
the test
the first
sublayer
has set
receptive
of 18x18
infields
3D (“out-of-plane”)
as the test set. To check th
images (i.e., Caltech 101 images)
are aligned,
homoge- can reliably detect near optimal
is large,
this method
pixels and the second sub-layer poolsbustness
over 5x5ofoverthe neuron, we plot its averaged resp
neous and belong to one selected
category.
stimuli
of the tested neuron.
second approach
lapping The
neighborhoods
of features (i.e., pooling size).
over the small test set with respect to changes in s
is to perform numerical The
optimization
to first
findsublayer
the op-connect to pixels in all
neurons in the
3D rotation (Figure 4), and translation (Figure 5
channels
(orErhan
maps) et
whereas
timal stimulus (Berkes &input
Wiskott,
2005;
al., the neurons in the
sublayer
pixels of only6 Scaled,
one channel
2009; Le et al., 2010). Insecond
particular,
we connect
find thetonormtranslated faces are generated by stan
3
While
the
first
sublayer
outputs
linear
filter
(or
map).
cubic interpolation. For 3D rotated faces, we used 1
bounded input x which maximizes the output f of the
Building high-level features using large-scale unsupervised learning
4.4. Visualization
responses, the pooling layer outputs the square root of
the sum of the squares of its inputs, and therefore, it
is known as L2 pooling.
Our style of stacking a series of uniform modules, switching between selectivity and tolerance layers, is reminiscent of Neocognition and
HMAX (Fukushima & Miyake, 1982; LeCun et al.,
1998; Riesenhuber & Poggio, 1999).
It has also
been argued to be an architecture employed by the
brain (DiCarlo et al., 2012).
Although we use local receptive fields, they are
not convolutional: the parameters are not shared
across different locations in the image.
This is
Deep learning
(Krizhevsky, Sutskever & Hinton, 2012)
0
image layer 1
layer 2
(96x55x55) (256x27x27)
layer 3
layer 4
layer 5 layer 6
(384x13x13) (384x13x13) (256x13x13) (4096)
60 million weights!
layer 7
(4096)
classification
(1000)
Performance
graph credit Matt
Zeiler, Clarifai
place cells
grid cells
.
.
face cells
.
.
.
?
.
.
.
.
‘Gabor filters’
0
Can deep learning provide insights into cortical representation?
(and vice-versa)
?
Deep learning
(Krizhevsky, Sustkever & Hinton, 2012)
Learned first-layer filters
Visualization
filters
learned at intermediate
layers
Visualizing of
and
Understanding
Convolutional
Neur
(Zeiler & Fergus 2013)
Layer 2
Visualization
filters
learned at intermediate
layers
Visualizing of
and
Understanding
Convolutional
Neur
(Zeiler & Fergus 2013)
LayerLayer
3
2
Visualization
filters
learned at intermediate
layers
Visualizing of
and
Understanding
Convolutional
Neur
(Zeiler & Fergus 2013)
LayerLayer
34
Layer
2
Layer 5
http://cs.stanford.edu/people/karpathy/cnnembed/
Visual metamers of a deep neural network
(Nguyen,Yosinki & Clune 2014)
Figure 1.
Evolved images that are unrecognizable to humans,
Figure 5. Simple segmentation
from
(a) The 3-shapes set consisted of b
Binding
byphases.
synchrony
shapes (square, triangle, rotated triangle). (b) Visible states after synchronizatio
(Reichert & Serre, 2014)
image in the MNIST+shape dataset, a MNIST digit and a shape were drawn each w
decode
0
/2
phase
mask
input
3/2
2
eceives input from a recurrent neural network. The system is trained end-to-end using
backpropagation to minimize classification error on a modified MNIST dataset. Remarkably, the
model learns to perform a visual search over the image, correcting mistaken movements
caused by distractors. Furthermore, the cone cells tile themselves in a similar fashion to those
ound in the human retinae. This layout is composed of a high acuity region at the center (low
variance gaussians) surrounded by low acuity (high variance gaussians). These initial results
ndicate the possibility of using deep learning as a mechanism to discover the optimal tiling cone
cells in a data driven manner. With the emergent visual search behavior learned by our model,
we can also investigate the optimal saliency map features for selecting where to attend next.
Learning how and where to attend
(Cheung, Weiss & Olshausen, work in progress)
Classification
Network
Location
Network
Recurrent
Network
Glimpse
Network
Image
Diagram of our neural network attention model
Red line shows the movements (saccades) by our attention model over the MNIST d
modified for visual search
The goal of computer vision
In order to gain new insights about visual representation
we must consider the tasks that vision needs to solve.
• How and why did vision evolve?
• What do animals use vision for?
Visual Navigation in Box Jellyfish
799
jumping spider
sand wasp
Figure 1. Rh
of the Upper
box jellyfish
(A and B) In f
lia maintain
the medusa
heavy crysta
rhopalium c
such that
oriented. Th
straight upw
body orienta
ated on the
eyes directe
(C) Modelin
peripheral p
angular sen
ceptors are
What do you see?
not
ect(s)
ect(s)
not
Lorenceau & Shiffrar (1992);
Murray, Kersten, Schrater, Olshausen & Woods (2002)
Perceptual “explaining away”
(d)
or
or not
Target object(s)
Occlusion object(s)
?
Image measurements Auxilliary image measurements
(Kersten"Explaining
& Yuille, 2003)Away"
Perceptual
Just as principles of
optics govern the
design of eyes,
so do principles of
information processing
govern the design of
brains.