Optic Nerve Signals in a Neuromorphic Chip II: Testing and Results

Optic Nerve Signals in a Neuromorphic Chip II: Testing and Results
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 4, APRIL 2004
667
Optic Nerve Signals in a Neuromorphic Chip II:
Testing and Results
Kareem A. Zaghloul, Member, IEEE, and Kwabena Boahen*
Abstract—Seeking to match the brain’s computational efficiency [14], we draw inspiration from its neural circuits.
To model the four main output (ganglion) cell types found in
the retina, we morphed outer and inner retina circuits into a
2 , 0.35
-CMOS chip.
96 60-photoreceptor, 3.5 3.3
Our retinomorphic chip produces spike trains for 3600 ganglion
cells (GCs), and consumes 62.7 mW at 45 spikes/s/GC. This chip,
which is the first silicon retina to successfully model inner retina
circuitry, approaches the spatial density of the retina. We present
experimental measurements showing that the chip’s subthreshold
current-mode circuits realize luminance adaptation, bandpass
spatiotemporal filtering, temporal adaptation and contrast gain
control. The four different GC outputs produced by our chip
encode light onset or offset in a sustained or transient fashion,
producing a quadrature-like representation. The retinomorphic
chip’s circuit design is described in a companion paper [Zaghloul
and Boahen (2004)].
mm
m
Index Terms—Adaptive circuits, neural systems, neuromorphic
engineering, prosthetics, vision.
I. RETINOMORPHIC SYSTEMS
T
HE RETINA, one of the best studied neural systems, is
a complex piece of biological wetware designed to optimally signal the onset or offset of visual stimuli in a sustained
or transient fashion [19]. To encode these signals into spike patterns for transmission to higher processing centers, the retina
has evolved intricate neuronal circuits that capture information
contained within natural scenes efficiently [21]. This visual preprocessing, realized by the retina, occurs in two stages, the outer
and inner retina. Each local retinal microcircuit plays a specific
role in the retina’s function, and neurophysiologists have extracted a wealth of data characterizing how its constituent cell
types contribute to visual processing. These physiological functions can be replicated in artificial systems by emulating their
underlying synaptic interactions.
In the companion paper [23], we introduced our model for
neurocircuits in the outer and inner retina. In our outer retina
model, interaction between cone and horizontal cell (HC) networks creates a bandpass spatiotemporal response that exhibits
Manuscript received September 6, 2002; revised June 25, 2003 This work
was supported in part by the National Institutes of Health (NIH) under Vision
Training Grant T32-EY07035 and in part by the Whitaker Foundation under
Grant 37005-00-00. The work of K. A. Zaghloul was completed while he was
with the Department of Neuroscience, University of Pennsylvania, Philadelphia,
PA 19104 USA. Asterisk indicates corresponding author.
K. A. Zaghloul is with the Department of Neurosurgery, University of Pennsylvania, Philadelphia, PA 19104 USA (e-mail: [email protected]).
*K. Boahen is with the Department of Bioengineering, 120 Hayden Hall,
3320 Smith Walk, University of Pennsylvania, Philadelphia, PA 19104 USA
(e-mail: [email protected]).
Digital Object Identifier 10.1109/TBME.2003.821040
luminance adaptation and that produces a contrast signal at the
cone terminal. Bipolar cells (BCs) in our model rectify these
signals into ON and OFF channels to replicate the retina’s complementary signaling. In our inner retina model, modulation
of narrow-field amacrine cell (NA) presynaptic inhibition by
wide-field amacrine cells (WAs) realizes contrast gain control
and time-constant adaptation, which allows our model to optimally encode signals by adjusting its temporal filter based on
input frequency and contrast.
In this paper, we present data characterizing how our outer
and inner retina models [23], implemented in silicon, process
visual information. Because we want to demonstrate that our circuits are viable models for retinal processing, our experimental
protocols are similar to those used in earlier — now classic —
physiological studies. We present similar visual stimuli to our
retinomorphic chip and record spike outputs from our array.
And because we have control over a number of parameters in
our model and circuit, we adjust these parameters to explore
the system’s range of behavior. Such a characterization is useful
in helping us fine tune processing in our retinomorphic chip to
match outputs from the mammalian retina and to better quantify
our chip’s outputs for robotic or prosthetic applications.
The remainder of this paper is organized as follows. In Section II, we describe our chip’s architecture, which is based on
the retina’s functional architecture and replicates signal convergence in its pathways. In Section III, we present typical outputs from our ganglion cell (GC) array to demonstrate how
these outputs are structured. In Section IV, we characterize our
outer retina model’s ability to adapt to mean light intensity by
presenting a contrast reversing grating at different mean luminances and exploring how different circuit parameters affect the
retinomorphic chip’s GC responses. In Section V, we explore
how our outer and inner retina models filter input signals in
space and time, and determine how this filtering changes as we
adjust different properties of the circuit. Finally, in Section VI,
we demonstrate that our inner retina model realizes contrast gain
control and compare the chip’s GC responses with our analytical results. Section VII concludes the paper.
II. CHIP ARCHITECTURE
In the mammalian retina, cone signals converge on to BCs
[19], which makes the receptive field center Gaussian-like
[18]. To implement signal convergence in our model, chip BCs
connect the outputs from a central phototransistor and its six
nearest neighbors (hexagonally tiled) to one inner retina circuit,
as shown in Fig. 1(a). Each of our outer retina circuits actually
produces two output currents. A central photoreceptor drives
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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 4, APRIL 2004
Fig. 1. Chip architecture and layout. (a) Signal convergence: Signals from a
photoreceptor (not shown) and its six neighbors are pooled to provide synaptic
input to each BC. Each BC generates a rectified output, either ON or OFF, that
drives a local inner retina circuit. Sustained-type GCs receive input from a single
local inner retina circuit. Signals from a central inner retina circuit (not shown)
and its six neighbors are pooled to drive each transient-type GC. (b) Pixel layout:
Each pixel, containing 38 transistors on average, has a photoreceptor (P), outer
retina (OR) circuitry, BCs, and inner retina (IR) circuitry. Spike-generating GCs
are found in five out of eight pixels; the remaining three contain a NA cell
membrane capacitor. Each pixel is 34 40 m in a 0.35 m process.
2
the BC with both of these outputs while photoreceptors at the
six vertices divide these outputs between their two nearest BCs.
For symmetry, we implement a similar architecture for the
reference current (see [23]).
Transient GCs in the mammalian retina pool their inputs from
a larger region than sustained GCs. We maintain the same architecture in our chip. We pool inner retina signals in the same way
that we pool outer retina signals, but inner retina circuits are tiled
at one-quarter the density of the phototransistors that provide
their input. Thus, each transient GC receives input from a central inner retina circuit and its six nearest neighbors, as shown in
Fig. 1(a). This central circuit excites its GC with both copies of
its transient output whereas those at the six vertices divide their
outputs between their two nearest transient GCs. Thus, all GCs
tile hexagonally, but the transient ones tile more sparsely than
the sustained ones. This architecture gives transient GCs a larger
receptive field, as found in cat Y-GCs. This pooling accounts for
transient GCs’ nonlinear subunits [9] since all the rectified BC
signals can never sum to zero, at any one moment, in response to
a sinusoidal grating. Conversely, if the cells were linear, a contrast-reversing grating exactly centered over the cell’s receptive
field would not modulate the cell’s response since dark regions
would exactly cancel out light regions.
The layout of one pixel is shown in Fig. 1(b). It contains a
phototransistor, outer retina circuitry, BCs, and one-quarter of
the inner retina circuit. Hence, 2 2 and 4 4 adjacent pixels
are needed to generate a complementary pair of sustained and
transient outputs, respectively. Because transient GCs occur at a
quarter resolution, not every pixel contains GC circuitry. Three
out of every eight pixels instead contain a large capacitor that
gives the NA its long time-constant. A spike generating circuit
in the remaining five pixels converts GC inputs into spikes that
are sent off chip.
Because analog signals cannot be relayed over long distances, retinal GCs use spikes to communicate with higher
cortical structures. Similarly, each GC in the chip array converts
the current it receives from the inner retina circuit to spikes,
as shown in Fig. 2(a). Our spike generating circuit exhibits
activated
channel
spike-rate adaptation through
analogs, modeled with a current-mirror integrator [3].
Fig. 2. Spike generation. (a) Input current to a retinal GC produces a spike
that is conveyed down the optic nerve. Spike rate is a function of input current.
(b) A CMOS circuit that transforms input current to spikes. I from the inner
retina charges up a GC membrane capacitor. When the membrane voltage
crosses threshold, the circuit produces a spike (Sp) that is relayed off chip by
digital circuitry. This circuitry acknowledges receipt of the spike by sending
a reset pulse (Rst) that discharges the membrane and dumps charge on a
spike-rate adaptation.
current-mirror-integrator that implements Ca
The CMOS circuit that transforms current into spikes is
shown in Fig. 2(b). Briefly, input current charges up a GC
membrane capacitor. As the membrane voltage approaches
, accelerthreshold, a positive feedback loop, modulated by
ates the voltage’s rate of change [5]. Once threshold is passed,
the circuit generates a pulse (or spike) that is relayed to digital
circuitry. The digital circuitry acknowledges receipt of the
spike by sending a reset pulse which discharges the membrane.
The reset pulse, RST, also dumps a quanta of charge on to a
current-mirror integrator through a pMOS transistor gated by
. Charge accumulating on the integrator models the build-up
within the cell after it spikes. This charge, which leaks
of
away with a time constant determined by
, draws current
mediated
away from the membrane potential, modeling
channels. The source voltage for the neuron circuit,
,
is set to be the same as the source voltage for the inner retina
[23].
circuit,
Due to wiring limitations, we can not communicate each GC
output off chip directly. Instead, we use an asynchronous, arbitered, multiplexer to read spikes out from the neurons [4].
Each GC interfaces with digital circuitry that communicates the
spikes to an arbiter at the end of each row and each column of
neurons, as shown in Fig. 3. The arbiter multiplexes spikes and
outputs the location, or address, of each spiking neuron as they
occur. Row and column addresses for each GC are communicated serially off chip. We can represent the spike activity of all
3600 GCs with just seven bits using this address-event representation. By noting the address of each event generated by the
chip, we can decode GC type and location in the array.
III. CHIP OUTPUT
We designed and fabricated a 96 60 photoreceptor
chip in 0.35
CMOS technology. Chip
3.5 3.3
phototransistors are roughly square with a width of 10
ZAGHLOUL AND BOAHEN: OPTIC NERVE SIGNALS IN A NEUROMORPHIC CHIP II: TESTING AND RESULTS
Fig. 3. Spike arbitration. A GC communicates spikes to peripheral digital
handshaking and arbitration circuitry using row and column request lines. The
arbiter chooses between spikes by selecting a row and column, encodes each
incoming spike into a pair of seven-bit addresses, and communicates these
addresses off chip. Row and column addresses are sent serially on the same
address bus; a multiplexer toggles between the row and column encoders. The
handshaking circuits relay reset signals back to the spiking GC.
and were tiled triangularly every 40
[23]. Our silicon chip
generates spike train outputs for 2 48 30 sustained-type and
2 24 15 transient-type GCs in both ON and OFF channels,
producing a total of 3600 spike outputs [23]. The chip’s light
response to a drifting vertical sinusoidal grating is shown in
Fig. 4(a).
Spike trains from identical GCs in a single column of
the chip array differ significantly due to variability between nominally identical transistors (e.g., ON transient
,
GC spike rate
). To further quantify this variability, we measured the mean firing rates for all GCs in the
array in response to a 50% contrast 7.5 Hz 0.1096 cyc/deg
drifting sinusoid. The distribution of these firing rates is
shown in Fig. 4(b). From the figure, we see a Gaussian-like
distribution of firing rates, when plotted on a log scale. Most
cells fall within this log normal distribution, but there are some
outliers, especially at low firing rates. This variability is most
likely due to normally distributed threshold mismatch between
transistors, which translates to log-normally distributed currents
in subthreshold operation.
Despite this heterogeneity, we were able to get a robust measure of GC activity by summing responses from all GCs in a
given column — much as physiologists average several trials
from the same cell — and analyzing the spike histogram. The
histograms shown in Fig. 4(a) demonstrate phase differences
between the four GC types [23]: complementary ON and OFF
channels respond out of phase with one another while transient cells lead sustained cells, exhibiting both earlier onset and
shorter duration of firing.
The chip actually produced useful images despite all this
variability, as illustrated by presenting it a face. As shown in
Fig. 4(c) top, edges are enhanced by sustained GC activity in
the static image. To confirm that the chip captures the visual
information, we reconstructed the natural stimulus from the
sustained GC spike activity (see Fig. 4(c) bottom). We did this
by convolving ON and OFF sustained GC spike output with
a simple difference-of-Gaussian model, whose excitatory and
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inhibitory standard deviations were determined by fitting GC
spatial frequency responses with a one-dimensional difference-of-Gaussian. The ratio of excitatory to inhibitory standard
deviations was 0.15. We matched temporal filtering as well by
convolving with a temporal low-pass filter with a time constant
of 22.7 ms, computing a new frame every 20 ms. We took the
difference between images obtained from ON and OFF spikes
and displayed it on a gray-scale, with ON and OFF activity
corresponding to bright and dark pixels, respectively. Activity
from transient GCs did not enhance the resolution of the
reconstructed image and was not included. Our reconstruction
produces an image that is easily recognizable, even with only
30 48 pixels and just 0.4 spikes/cell/frame, suggesting that
cortical structures, as well as visual prostheses or robots, can
extract useful visual information from the retina’s neural code
through simple linear filtering.
IV. LUMINANCE ADAPTATION
Our outer retina circuit’s nonlinear behavior was designed
to generate cone terminal (CT) signals that are entirely proportional to contrast. Because of this local automatic gain control,
we expected the circuit’s output current to be independent of
luminance. The mammalian retina exhibits this behavior, where
GC responses depend on contrast but not on luminance [20], and
we hypothesize that this luminance adaptation takes place in the
outer retina.
To characterize luminance adaptation, we measured GC
responses to a 7.5 Hz drifting sinusoid (50% contrast), of
various spatial frequencies, as we changed mean intensity. We
found that intensity had a slight effect on the highest sensitivity
achieved; this effect was larger for ON cells. OFF transient
(OffT) GC peak responses, which were 408 sp/s, 432 sp/s and
to
218 sp/s as we decreased mean intensity from 196
to 3.3
, are relatively unchanged until mean
33
. For OnT GCs, the peak response
intensity drops to 3.3
dropped from 771 sp/s to 485 sp/s to 117 sp/s as we decreased
to 33
to 3.3
.
mean intensity from 196
Similarly, OFF sustained (OffS) GC peak responses were 504
sp/s, 520 sp/s and 346 sp/s while OnS GC peak responses were
425 sp/s, 225 sp/s and 63 sp/s at these three mean intensities,
respectively.
The overall reduction in sensitivity for both channels most
likely arises from stray photocurrents interfering with GC
spike-rate adaptation. Mean spike activity is affected by these
leakage currents, which determine the spike-rate adaptation
time-constant. As intensity drops and, therefore, as these
photocurrents decrease, this time-constant increases, causing a
drop in quiescent spike rate and overall sensitivity. The asymmetry between ON and OFF pathways is explained by mismatch
between drain voltages in the outer retina circuit, which distorts
the rectification, causing ON sensitivity to decrease more than
OFF sensitivity.
Stray photocurrents hampers our outer retina circuit’s ability
to adapt to luminances through their effect on sensitivity. However, we believe that our design will work if these are eliminated.
To prove this, we compensate for the change in sensitivity by
manually increasing lateral current spread in the HC network
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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 4, APRIL 2004
Fig. 4. Chip Output. (a) A raster plot of the spikes (top) and histogram (bottom, bin width = 20 ms) recorded from a single column of the chip array. The
stimulus was a 3 Hz 50%-contrast drifting sinusoidal grating (0.14 cyc/deg) whose luminance varied horizontally across the screen and was constant in the vertical
direction. We use a 50% contrast stimulus in all responses presented here unless otherwise noted. The four GC type outputs are color coded (see legend). We
computed the amplitude of the fundamental Fourier component of these histograms, which is plotted in all frequency responses presented here, unless otherwise
noted. (b) The distribution of firing rates for the four types of GC outputs, demonstrating the amount of variability in our chip. Log of the firing rate, f , is plotted
on the abscissa, and the probability density, p(f ), is plotted on the ordinate. Histograms are computed from all active cells of a given type in the array (151 out of
360 OnT, 202/360 OffT, 890/1440 OnS, and 792/1440 OffS cells in the array exhibited no activity). (c) In response to a static natural image, edges are enhanced
by sustained type GC outputs of the chip (top). Reconstruction of the image from sustained GC activity (bottom) demonstrates fidelity of retinal encoding despite
the variability.
(i.e., decreased
[23]), which boosts CT activity [23]. Be, decreasing
causes an increase in
cause
. When the space constants of the cone and HC networks,
and , are similar, increasing
increases CT sensitivity, but
.
the effect saturates when
As we did not know the exact value of the subthreshold slope
coefficient, , we determined how much we should change
to compensate for the light-related change in spike-rate adaptation empirically by recording the GC response to a 7.5 Hz
to keep this response
0.1096 cyc/deg grating. We adjusted
fixed at different mean intensities. Because we measured the GC
, at only one spatiotemporal freresponse, while adjusting
quency — and not across the entire spatiotemporal spectrum —
this technique is only approximate, as it does not account for
shifts in the peak. For every decade reduction in photocurrent,
by 85 mV to maintain the same response
we had to decrease
at this spatiotemporal frequency.
with mean intensity, we also
In addition to decreasing
increased NA cell membrane leakage, , to compensate for
smaller stray photocurrents at lower light intensities [23]. The
, is governed by the
inner retina’s open loop time-constant,
size of the NA cell capacitor, and by , which drains these capacitors. To conserve space, we restricted the size of our NA
capacitors to 1 pF each. This leaves little room for the magnitude of . In testing the chip, we found that we had to set ,
the gate voltage of the transistor that produces , at 50 mV to
attain reasonable responses. However, this makes susceptible
to stray leakage currents generated in the substrate by incident
to compensate
photons. Therefore, in addition to decreasing
to maintain
for nonlinearities [23], we also had to increase
the same level of at lower light levels.
and to maintain response
Incorporating the changes in
sensitivity, we verified that our outer retina circuit adapts to
mean luminance and encodes stimulus contrast. We recorded
the output of chip ON transient GCs [23] to a 0.22 cyc/deg 3 Hz
reversing grating whose contrast varied between 3.25 and 50%
at four different mean luminances. The data is shown in Fig. 5.
Chip responses maintain contrast sensitivity over at least one
Fig. 5. Luminance adaptation. Chip ON-transient cell responses to a
sinusoidal grating (0.22 cyc/deg) whose contrast varied between 3.25% and
50% and reversed at 3 Hz, for four different mean luminances. Response
versus contrast (small x-axis) curves are shifted horizontally according to
mean luminance (large x-axis) such that the 50% contrast response is aligned
with that particular mean luminance. Solid lines represent the best fits of [23,
Equation 4] to the data, where we only allowed the ratio of horizontal space
constant to cone space constant, l =l , to vary for different intensities. Values
for l =l were 0.4617, 0.4668, 0.4893, and 0.6932 as intensity dropped from
192 cd=m to 6 cd=m .
and a half decades of mean luminance (our experimental setup
). To verify that our outer retina model
was limited to 200
accounts for the behavior shown in Fig. 5, we fit the chip’s responses to different contrasts with [23, Equation 4], allowing
to increase as intensity decreased. We found
only the ratio
to 19
, for
that as intensity decreased from 192
example, the best fits for the data were attained when
increased by 6% (from 0.4617 to 0.4893).
by 85 mV for
To capture this data, we had reduced
would
this tenfold reduction in intensity. This change in
correspond to a three-fold increase in , if we only consider
’s dependence on
. However,
is also proportional to
, as seen in our outer retina analysis [23]. Because
(
), decreases more
the HC’s leakage current,
slowly than the lateral current,
(
) because
[23].
A decrease in light intensity, thus, results in a smaller HC space
constant, , which is offset by the increase that results from
. Indeed, our fits in Fig. 5 suggest that
manually decreasing
ZAGHLOUL AND BOAHEN: OPTIC NERVE SIGNALS IN A NEUROMORPHIC CHIP II: TESTING AND RESULTS
Fig. 6. Spatial filtering at different mean intensities. Responses of chip
OffS and OffT cells to 7.5-Hz horizontally drifting sinusoids (50% contrast)
with different spatial frequencies. Normalized responses recorded at three
to compensate for the
different mean luminances without changing V
outer retina nonideality are shown on top. Solid lines are the best fit of a
balanced difference-of-Gaussian model (OffT: =
= 0.21, 0.27, and
0.21 for mean luminances of 196, 33, and 3.3 cd=m respectively; OffS:
=
= 0:14, 0.11, and 0.11). We ignored the lowest two spatial
frequencies for the purposes of our fits. Normalized responses recorded while
changing both mean luminance and V are shown on bottom. V values are
in units of mV. Solid lines are the best fit of a balanced difference-of-Gaussian
= 0:26, 0.23, and 0.18 for mean luminances of 196,
model (OffT: =
33, and 3.3 cd=m respectively; OffS: =
= 0:19, 0.11, and 0.09).
decreasing light intensity while manually decreasing
in only a small increase in the HC space constant, .
reults
V. SPATIOTEMPORAL FILTERING
Our outer retina model is designed to bandpass filter signals
in both space and time, as described in the accompanying paper
[23]. We found the spatial frequency at which sensitivity peaked
to be essentially independent of intensity, as expected, for both
OffS and OffT GC responses [Fig. 6 (top)]. Compensating for
the light dependent spike-rate adaptation time-constant by de, however, has the effect of expanding the receptive
creasing
field size, or lowering the peak spatial frequency, , similar to
the expansion observed in mammalian retina at lower light intensities [12].
In Fig. 6 (bottom), we measured GC spatial responses at different mean intensities while compensating for sensitivity by
, as described above. Since
is inversely prochanging
, its dependence on
is described by
portional to
. For
, decreasing
from 15 mV to
,
for example, should cause a 28% reduction in , ignoring the
negligible change due to intensity. We found that the peak spatial frequency of the transient OFF GC in fact decreased by 25%
(from 0.2192 to 0.1644 cyc/deg). The change in spatial profile
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for both OFF transient and sustained GC responses for further reat different mean intensities is shown in Fig. 6
ductions in
(bottom). As expected, the peak spatial frequency continues to
decrease, further expanding the GCs receptive field.
From Fig. 6 (top), we also find that spatial filtering in ON and
OFF pathways is not identical. OffT peak response lies at 0.1644
cyc/deg whereas the corresponding OnT peak response lies at
0.1096 cyc/deg (not shown). Similarly, OffS begins to roll off at
0.3288 cyc/deg while OnS begins its rolloff at 0.2192 cyc/deg
(not shown). This implies that the OFF channel has a smaller
effective space constant than the ON channel. Both channels,
however, are driven by the same outer retina circuitry, so this
difference most likely arises from asymmetric rectification in
the bipolar circuit [23].
We believe that saturation in the ON channel is responsible
for the asymmetric spatial filtering. Currents diverted to the
ON channel in the bipolar circuit saturate, whereas currents
in the OFF channel do not. Both ON and OFF GCs inherit a
Mexican-hat-like receptive field — a narrow excitatory center
and a broader inhibitory surround — from the outer retina. The
width of this Mexican hat determines the system’s peak spatial
frequency, . Saturation flattens the ON channel’s excitatory
center which leads to a relative increase in its width. This leads
to a decrease in the ON channel’s corner spatial frequency, ,
which is what we observe in the data.
We expect sustained GC to be spatially bandpass for all
temporal frequencies. Sustained GCs’ responses represent an
all-pass version of BC signals and are, therefore, dominated by
the outer retina’s temporal low-pass filter [23]. To verify that
we realized invariant spatial bandpass filtering, we measured
sustained GC activity in response to a horizontally drifting 50%
contrast vertical sinusoidal grating at different temporal and
spatial frequencies. The spatiotemporal profiles of sustained
GC responses, which reflect activity at the bipolar terminal
[23], is shown in Fig. 7. From the figure, we see that sustained
GCs’ bandpass spatial filtering is largely invariant with temporal frequency.
In contrast, theoretical studies of the outer retina reveal a transition to low-pass spatial filtering at high temporal frequencies
[3]. This transformation occurs because HC inhibition is ineffective at high temporal frequencies because of its long timeconstant. However, WA cells, which respond much faster (in
our chip, as well as in the retina), suppress low spatial frequencies at the bipolar terminal. This suppression could account for
the attenuated response at low-spatial-high-temporal frequencies seen in chip sustained GCs and in the mammalian retina
[11]. In fact, chip sustained GCs capture the overall suppression
seen in mammalian cells at low spatial frequencies. Because of
this suppression, spatial tuning remains bandpass at all but the
highest temporal frequencies — except for a resonance at very
high temporal frequencies seen in the cat data [11].
On the other hand, we expect transient GC responses to be
temporally bandpass for all spatial frequencies. To verify that
we realized this behavior, we measured GC activity in response
to the same horizontally drifting 50% contrast sinusoidal
grating. The spatiotemporal profiles of transient GC responses
are shown in Fig. 8. From the figure, we see that transient GCs
exhibit bandpass temporal filtering at all spatial frequencies.
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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 4, APRIL 2004
Fig. 7. Sustained cell spatiotemporal response. Three dimensional plots of chip sustained GC responses, which reflect activity at the bipolar terminal, to
horizontally drifting sinusoids of different spatial and temporal frequencies. OFF sustained GC temporal frequency responses are shown on the right, in two
dimensions, for three different spatial frequencies. Chip sustained cells are bandpass in space for all temproal frequencies.
Fig. 8. Transient cell spatiotemporal response. Responses of chip transient GCs, which incorporate additional processing in the inner retina, to horizontally
drifting sinusoids of different spatial and temporal frequencies. ON transient GC temporal frequency responses are shown on the right, in two dimensions, for three
different spatial frequencies. Chip transient cells are bandpass in time for all spatial frequencies. They also spatially bandpass filter input signals at all temporal
frequencies.
Unlike their sustained counterparts [23], which are largely
low-pass temporally. In addition, transient cells’ peak spatial
frequency is lower than the corresponding sustained cells due
to their larger receptive fields.
In contrast, theoretical studies of the outer retina reveal a transition to low-pass temporal filtering at high spatial frequencies
[3]. This transformation occurs because HC inhibition is also
ineffective at high spatial frequencies because most of their excitatory input is lost to neighboring HCs through gap-junctions
[3]. This low-pass filtered temporal signal is maintained at the
bipolar terminal. However, feedforward inhibition eliminates
these low frequencies, leaving a bandpass temporal response in
the transient GCs [23].
From our analysis in the accompanying paper [23], we ex, will shift the
pect that reducing our NA cell’s time-constant,
transient GC’s (GCt) temporal profile to higher frequencies, but
leave the sustained GC’s (GCs) response unchanged. To verify
this prediction, we measured GC responses to a 0.2192 cyc/deg
drifting sinusoidal grating at different temporal frequencies and
recorded the temporal profile for different levels of , the bias
. As we increased
from 10 mV to 50 mV
voltage that sets
to 90 mV, the peak ON GCt response was 386 sp/s, 297 sp/s,
and 418 sp/s while the peak ON GCs response was 319 sp/s, 271
sp/s, and 310 sp/s respectively. The peak values were relatively
constant, suggesting that we successfully compensated for the
on the bipolar terminal (BT)-to-NA gain, , by adeffect of
Fig. 9. Changing the open loop time constant. Temporal frequency responses
of chip OnT and OnS GCs to a 0.2192 cyc/deg drifting sinusoidal grating.
Profiles are shown for three different values of V , which determines the open
loop time constant, . Increasing V causes a decrease in , thus increasing
the system’s corner frequency. To compensate for changes in dc loop gain, we
also changed V (values shown). Phase data are shown on the bottom.
justing a second bias,
, to keep constant [23]. So we normalized these responses and focused on changes in frequency.
caused low-frequency GCt
As shown in Fig. 9, increasing
ZAGHLOUL AND BOAHEN: OPTIC NERVE SIGNALS IN A NEUROMORPHIC CHIP II: TESTING AND RESULTS
673
Fig. 11. Contrast gain control. (a) Chip Off-Transient cell response to a
0.14 cyc/deg contrast reversing sinusoidal grating whose temporal modulation
signal was a sum of eight sinusoids. The amplitude of the fundamental Fourier
component at seven of the eight frequencies used, for four different modulation
contrasts, are shown. Solid lines are the best fit of an analytical model of the
chip circuitry. (b) The loop gain that best fit Equation 1 increases as stimulus
contrast increases. The solid line represents our prediction for this change in
loop gain [23]. (c) As stimulus contrast increases, the system gain that best
fits the data saturates, suggesting that contrast gain control causes a reduction
in GC sensitivity.
Fig. 10. Changing the open loop gain. Temporal frequency responses of chip
OnT and OnS GCs to a 0.2192 cyc/deg drifting sinusoidal grating. Profiles are
shown for three different values of V , which determines the open loop gain,
g . Increasing V above the dc unity value of 620 mV increases the open-loop
gain, g , increasing the system’s corner frequency. Phase data are shown on the
bottom for the three different V conditions.
responses to be attenuated, as the system’s corner frequency increased. Changing has no effect on GCs’ temporal frequency
profile.
without increasing increases the gain of BT
Increasing
to NA excitation, , and thereby modifies the loop-gain. From
our analysis of loop-gain in the inner retina [23], we expect GCs’
responses to remain unchanged while GCt’s low-frequency rewould make
sponses are attenuated. Conversely, lowering
the low-frequency roll-off less severe. To verify that had this
effect, we measured the GC temporal frequency response using
a 50% contrast 0.2192 cyc/deg drifting sinusoidal grating for
. In this case, we empirically determined
different levels of
corresponds to
for
.
that
from 560 mV to 620 mV
At 50% contrast, as we increased
to 680 mV, the peak ON GCt response dropped from 1600 sp/s
to 568 sp/s to 117 sp/s while the peak ON GC’s response remained relatively unchanged and was 261 sp/s, 377 sp/s, and
338 sp/s respectively. Intuitively, one can understand the drop
in GCt sensitivity by recognizing that increasing boosts NA
activity, which provides more feedforward inhibition on to GCt.
To focus on ’s effect on the system’s temporal dynamics, however, we plotted the normalized responses, shown in Fig. 10.
GCt’s low-frequency responses were attenuated as we increased
, as expected. There was little effect on the high-frequency
responses. And as expected, there was also little effect on GCs’
responses.
VI. CONTRAST GAIN CONTROL
As discussed in the accompanying paper [23], modulation of
presynaptic inhibition at the bipolar terminal by WA cells realizes contrast gain control. This mechanism is frequency dependent, as WA computes a temporal measure of contrast. The
differential effect of frequency can be measured by simultaneously stimulating the retina with the sum of several sinusoids,
approximating a white noise stimulus. Therefore, we measured
the chip’s temporal frequency sensitivity in response to a 0.14
cyc/deg contrast reversing sinusoidal grating whose temporal
modulation signal was the sum of eight sinusoids. The temporal
frequencies of the input were 0.214 Hz, 0.458 Hz, 0.946 Hz,
1.923 Hz, 3.876 Hz, 7.782 Hz, 15.594 Hz, and 31.219 Hz. These
frequencies, chosen to minimize higher order interactions, are
identical to those Victor and Shapley used to demonstrate contrast gain control [17].
We presented the white-noise like stimulus at four input contrast: 1.25%, 2.5%, 5%, and 10%, defined as the ratio of the
peak deviation of each component over their common mean.
Thus, we found that our OffT cells shift their sensitivity profile to higher temporal frequencies as the contrast per unit frequency increases from 1.25% to 10%, as shown in Fig. 11(a).
This figure also demonstrates saturation in the response with
increasing contrast.
To verify that the contrast changes we observed in the transient GC responses were consistent with our model, we fit the
curves in Fig. 11(a) with the inner retina system equations derived in the accompanying paper [23]. We introduced sinusoidal
inputs of contrast per unit frequency . The outer retina is approximated by a low-pass temporal filter with time constant ,
whose output drives a transient GC response that is the difference between BT and NA. Thus, the GC response, in spikes/s,
is given by
where
,
, and is the WA-modulated
strength of NA inhibition onto BT. We also included a term that
models the low-pass filtering behavior of the chip’s photoreceptors whose time-constant is . We fit the four data sets by
allowing the system gain term, , and the loop gain,
to vary
across different stimulus contrasts, and fixed the remaining parameters. The best fits of this model to the four input contrast
densities are shown as the solid lines in Fig. 11(a). Fitted pams,
ms,
,
rameter values were
.
and
The system’s loop gain increased with stimulus contrast, as
, in the four contrast
expected. The best fits for loop gain,
674
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 4, APRIL 2004
conditions are shown in Fig. 11(b). As input contrast, , increased by a factor of eight, the loop gain increased by a factor
of 4, just as predicted by our loop-gain analysis in the accompanying paper [23]. Fitting the loop-gain equation [23] to the
[solid line in Fig. 11(b)] yields a value of
best estimates of
for the residual bipolar terminal activity.
However, we found that our contrast gain control mechanism
cannot by itself account for the reduction in gain we see in the
were right, we
GC response. Although our predictions for
had to introduce a variable system gain, , that saturates with
increasing input contrast, to account for sensitivity, as shown
in Fig. 11(c). Other nonlinearities present in our CMOS circuit
may account for this. For example, at the first synapse in the
outer retina circuit, cone activity, which is determined by light
input [23], gates an nMOS transistor to drive BC circuitry. Be, the signal passed to the BC is compressed, causing
cause
saturation in the GC response in addition to that due to contrast
gain control. Aside from this static nonlinearity, our prediction
for how the chip adapts to contrast and temporal frequency was
borne out, validating the theory, and suggesting that we have implemented a valid model for contrast gain control. However, as
contrast gain control occurs at the bipolar terminal, we expected
to observe its effects in sustained cells as well. However, it was
not as dramatic in these cells, suggesting that NA cell feed-forward inhibition enhances contrast gain control.
VII. CONCLUSION
Due to the retina’s complexity, we adopted a strategy that captured the major computations realized by the retina in a simplified model. Our model, and the silicon implementation of that
model, produces multiple representations of the visual scene
analogous to the retina’s four major output pathways, and incorporates linear spatiotemporal filtering as well as nonlinear operations, including luminance adaptation, contrast gain control,
and nonlinear spatial summation [23]. Our test results demonstrate that we succeeding in implementing our model, based
on the neurocircuitry of the retina’s cone pathway, in silicon.
Furthermore, we have realized these computations at a photoreceptor density that is only 2.5 times as sparse as the human cone
density at 5 mm eccentricity [6].
We implemented these functions in CMOS circuits by remaining faithful to the underlying retinal neuroanatomy — we
morphed neural circuits into silicon circuits. Based on metabolic
rates for rabbit retina [1], we estimate that our chip uses a thouper GC
sand times as much energy per GC, consuming 17
(62.7 mW total), at an average spike rate of 45 spikes/s. Ongoing advances in chip fabrication technology will allow us to
improve our chip’s energy efficiency as well as its spatial resolution and dynamic range.
We plan to close the performance gap between our chip
and the mammalian retina by redesigning some of our CMOS
circuits. For instance, asymmetric rectification in our model
bipolar cells gives rise to differences in sensitivity between
ON and OFF channels. The mammalian retina also exhibits an
asymmetry at the BC, but in this case, the asymmetry lies in
the quiescent levels of activity in ON and OFF pathways. Our
asymmetry, which arises from saturation in the ON channel,
can be avoided by not taking the reciprocal of the cone signal.
Turning to the inner retina, while chip transient GCs exhibit
contrast gain control, this effect is significantly less pronounced
in chip sustained cells. We hypothesize that this difference
arises from the presence or absence of feedforward amacrine
cell inhibition. Sustained GCs in the mammalian retina receive
some feedforward inhibition from amacrine cells, although the
amount of inhibition is less than received by transient GCs.
In our model, however, sustained cells receive no feedforward
inhibition [10], [13]. Thus, an additional design issue to address
would be to incorporate some feedforward inhibition, so as to
potentiate the effects of contrast gain control, while maintaining
the sustained behavior of our narrow-field sustained-type GCs.
While these design limitations and energy efficiency issues
are important and still need to be addressed, our goal in these
two companion papers has been to create a model based on the
functional anatomy of the retina and to implement that model
in silicon. We have demonstrated here that our chip performs
bandpass spatiotemporal filtering, luminance adaptation, and
contrast gain control. We will present comparisons between our
chip’s behavior and physiological measurements from the mammalian retina in a forthcoming paper.
Extensions of this work can be used to gain a deeper understanding of the computations in the retina. With a real-time
model of retinal processing whose parameters can be easily adjusted, we can explore how certain components of our model
affect GC response. Furthermore, because we have access to
an entire array of GC outputs, we can also explore firing patterns among populations of cells. Physiologists have recently
begun exploring these questions by using multi-electrode arrays to record behavior across several cells in the mammalian
retina simultaneously [2], [15]. They have observed correlations
in firing patterns between GCs that may play a role in conveying
information to higher cortical structures [8], [7]. And they have
revealed the presence of waves of retinal activity that may be
important in development [22]. With our chip’s array of spike
outputs, researchers can begin to investigate these questions in
a large-scale, real-time model.
In addition, our chip can be used to facilitate the design
and fabrication of more complicated neural systems in silicon.
With our approach, neuromorphic systems can be designed
and implemented that replicate processing in the thalamus
and in higher cortical structures. These higher level systems
rely on sensory input, and our retinomorphic chip can serve as
the front-end for these systems. By capturing the neural code
of the mammalian retina, our chip can provide researchers
with realistic retinal input with which they can design and test
subsequent neuromorphic circuits.
Finally, our chip can be used in prosthetic applications. By
using much less power — and weight and space — than required
by computer-based solutions, retinomorphic chips could eventually serve as an in situ replacement. The most successful current retinal prosthesis designs are based on an external camera
and processor [16]. By addressing our aforementioned design
and power issues, we hope to use our approach to develop a
fully integrated retinal prosthesis that supersedes current prosthetic designs.
ZAGHLOUL AND BOAHEN: OPTIC NERVE SIGNALS IN A NEUROMORPHIC CHIP II: TESTING AND RESULTS
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Kareem A. Zaghloul (S’00–M’03) received the
B.S. degree from the Department of Electrical
Engineering and Computer Science, Massachusetts
Institute of Technology, Cambridge, in the in 1995,
where he made Tau Beta Kappa and Eta Kappa Nu.
He recently completed a combined M.D./Ph.D. program at the University of Pennsylvania, Philadelphia.
The Ph.D. degree was awarded in the Department
of Neuroscience, where he worked on understanding
information processing in the mammalian retina
with K. A. Boahen. His work was supported by
a Vision Training Grant from the National Institutes of Health and a Ben
Franklin Fellowship from the University of Pennsylvania School of Medicine.
He is currently a Resident Physician in the Department of Neurosurgery at the
University of Pennsylvania.
Kwabena A. Boahen received the B.S. and M.S.E.
degrees in electrical and computer engineering
from the Johns Hopkins University, Baltimore
MD, in the concurrent masters-bachelors program,
both in 1989, where he made Tau Beta Kappa. He
received the Ph.D. degree in computation and neural
systems from the California Institute of Technology,
Pasadena, in 1997, where he held a Sloan Fellowship
for Theoretical Neurobiology.
He is an Associate Professor in the Bioengineering Department, University of Pennsylvania,
Philadelphia, where he holds a secondary appointment in the electrical engineering. He was awarded a Packard Fellowship in 1999. His current research
interests include mixed-mode multichip VLSI models of biological sensory
and perceptual systems, and their epigenetic develoipment, and asynchronous
digital interfaces for interchip connectivity.
Dr. Boahen received a National Science Foundation (NSF) CAREER award
in 2001 and an Office of Naval Research (ONR) YIP award in 2002.
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