Recurrent cortical competition: Strengthen or 
weaken? 
P6ter AdorjJn% Lars Schwabe, 
Christian Piepenbrock*, and Klaus Obermayer 
Dept. of Comp. Sci., FR2-1, Technical University Berlin 
Franklinstrasse 28/29 10587 Berlin, Germany 
adorjan @epigenomics.com, { schwabe, oby } @ cs.tu-berlin.de, 
piepenbrock@epigenomics.com 
http://www. ni.cs.tu-berlin.de 
Abstract 
We investigate the short term dynamics of the recurrent competition and 
neural activity in the primary visual cortex in terms of information pro- 
cessing and in the context of orientation selectivity. We propose that af- 
ter stimulus onset, the strength of the recurrent excitation decreases due 
to fast synaptic depression. As a consequence, the network shifts from 
an initially highly nonlinear to a more linear operating regime. Sharp 
orientation tuning is established in the first highly competitive phase. In 
the second and less competitive phase, precise signaling of multiple ori- 
entations and long range modulation, e.g., by intra- and inter-areal con- 
nections becomes possible (surround effects). Thus the network first ex- 
tracts the salient features from the stimulus, and then starts to process 
the details. We show that this signal processing strategy is optimal if 
the neurons have limited bandwidth and their objective is to transmit the 
maximum amount of information in any time interval beginning with the 
stimulus onset. 
1 Introduction 
In the last four decades there has been a vivid and highly polarized discussion about the 
role of recurrent competition in the primary visual cortex (V1) (see [12] for review). The 
main question is whether the recurrent excitation sharpens a weakly orientation tuned feed- 
forward input, or the feed-forward input is already sharply tuned, hence the massive re- 
current circuitry has a different function. Strong cortical recurrency implements a highly 
nonlinear mapping of the feed-forward input, and obtains robust and sharply tuned corti- 
cal response even if only a weak or no feed-forward orientation bias is present [6, 11, 2]. 
However, such a competitive network in most cases fails to process multiple orientations 
within the classical receptive field and may signal spurious orientations [7]. This moti- 
vates the concept that the primary visual cortex maps an already sharply orientation tuned 
feed-forward input in a less competitive (more linear) fashion [9, 13]. 
Although these models for orientation selectivity in V1 vary on a wide scale, they have 
one common feature: each of them assumes that the synaptic strength is constant on the 
short time scale on which the network operates. Given the phenomenon of fast synaptic 
* Current address: Epigenomics GmbH, Kastanienallee 24, D-10435 Berlin, Germany 
90 P Adorjtin, L. Schwabe, C. Piepenbrock and K. Oberrnayer 
dynamics this, however, does not need to be the case. Short term synaptic dynamics, e.g., 
of the recurrent excitatory synapses would allow a cortical network to operate in both-- 
competitive and linear--regimes. We will show below (Section 2) that such a dynamic 
cortical amplifier network can establish sharp contrast invariant orientation tuning from 
a broadly tuned feed-forward input, while it is still able to respond correctly to multiple 
orientations. 
We then show (Section 3) that decreasing the recurrent competition with time naturally fol- 
lows from functional considerations, i.e. from the requirement that the mutual information 
between stimuli and representations is maximal for any time interval beginning with stimu- 
lus onset. We consider a free-viewing scenario, where the cortical layer represents a series 
of static images that are flashed onto the retina for a fixation period (AT -- 200 - 300 ms) 
between saccades. We also assume that the spike count in increasing time windows after 
stimulus onset carries the information. The key observations are that the signal-to-noise 
ratio of the cortical representation increases with time (because more spikes are available) 
and that the optimal strength of the recurrent connections (w.r.t. information transfer) de- 
creases with the decreasing output noise. Consequently the model predicts that the infor- 
mation content per spike (or the SNR for afixed sliding time window) decreases with time 
for a flashed static stimulus in accordance with recent experimental studies. The neural 
system thus adapts to its own internal changes by modifying its coding strategy, a phe- 
nomenon which one may refer to as "dynamic coding" 
2 Cortical amplifier with fast synaptic plasticity 
To investigate our first hypothesis, we set up a model for an orientation-hypercolumn in 
the primary visual cortex with similar structure and parameters as in [7]. The important 
novel feature of our model is that fast synaptic depression is present at the recurrent ex- 
citatory connections. Neurons in the cortical layer receive orientation-tuned feed-forward 
input from the LGN and they are connected via a Mexican-hat shaped recurrent kernel in 
orientation space. In addition, the recurrent and feed-forward excitatory synapses exhibit 
fast depression due to the activity dependent depletion of the synaptic transmitter [1, 14]. 
We compare the response of the cortical amplifier models with and without fast synap- 
tic plasticity at the recurrent excitatory connections to single and multiple bars within the 
classical receptive field. 
The membrane potential V(O, t) of a cortical cell tuned to an orientation 0 decreases due 
to the leakage and the recurrent inhibition, and increases due to the recurrent excitation 
T-tV(O,t ) q- V(0, t) : ILGN(0, t) q- Iexc(0, t) -- Iinh(0, t), 
(1) 
where r = 15 ms is the membrane time constant and IIa(O, t) is the input received from 
the LGN. The recurrent excitatory and inhibitory cortical inputs are given by 
I(O,t) = J(O,O',t) exp 2 ' 
2 
(2) 
where A(O t, O) is arr periodic circular difference between the preferred orientations, 
d(O, 0 , t) are the excitatory and inhibitory connection strengths (with a C {exc, inh}, 
drx --- 0.2 mV/Hz and dh x -- 0.8mV/Hz), and f is the presynaptic firing rate. The ex- 
citatory synaptic efficacy jexc is time dependent due to the fast synaptic depression, while 
the efficacy of inhibitory synapses jinh is assumed to be constant. The recurrent excitation 
is sharply tuned O'exc = 7.5 , while the inhibition has broad tuning O'in h = 90 o . The map- 
ping from the membrane potential to firing rate is approximated by a linear function with 
a threshold at 0 (f(O) =/3max(0, V(O)),/3: 15Hz/mV). Gaussian-noise with variances 
Recurrent Cortical Competition: Strengthen or Weaken? 91 
Feedforward Input 
-45 0 45 
Orientation [deg] 
Static 
15 ' ' ' 
-0906 ']['5 "-0 a 
Orientation [deg] 
Depressing 
15 . , 
 -9'o 
Orientation [deg] 
(a) (b) (c) 
Figure 1: The feed-forward input (a), and the response of the cortical amplifier model with 
static recurrent synaptic strength (b), and a network with fast synaptic depression (c) if the 
stimulus is single bar with different stimulus contrasts (40%dotted; 60%dashed; 80%solid 
line). The cortical response is averaged over the first 100 ms after stimulus onset. 
of 6 Hz and 1.6 Hz is added to the input intensities and to the output of cortical neurons. 
The orientation tuning curves of the feed-forward input I LaN are Gaussians (rrLaN = 18 ) 
resting on a strong additive orientation independent component which would correspond to 
a geniculo-cortical connectivity pattern with an approximate aspect ratio of 1:2. Both, the 
orientation dependent and independent components increase with contrast. Considering a 
free-viewing scenario where the environment is scanned by saccading around and fixating 
for short periods of 200 - 300 ms we model stationary stimuli present for 300 ms. The 
stimuli are one or more bars with different orientations. 
Feed-forward and recurrent excitatory synapses exhibit fast depression. Fast synaptic de- 
p_ression is modeled by the dynamics of the expected synaptic transmitter or "resource" 
R(t) for each synapse. The amount of the available transmitter decreases proportionally to 
the release probability p and to the presynaptic firing rate f, and it recovers exponentially 
_LGN _Ctx pLGN pCtx 
*rec = 120 ms, rrec= 850 ms, = 0.35 and = 0.55), 
t(t) : 1- (t) f(t)p(t)(t) = (t) 1 
r rfr(f(t),p(t)) I-  (3) 
Trec 
The change of the membrane potential on the postsynaptic cell at time t is proportional 
to the released transmitter pR(t). The excitatory connectivity strength between neurons 
tuned to orientations 0 and 0' is expressed as jxc (0, 0', t) = dmxPROo, (t). Similarly this 
applies to the feed-forward synapses. Fast synaptic plasticity at the feed-forward synapses 
has been investigated in more detail in previous studies [3, 4]. 
In the following, we compare the predictions of the cortical amplifier model with and with- 
out fast synaptic depression at the recurrent excitatory connections. In both cases fast 
synaptic depression is present at the feed-forward connections limiting the duration of the 
effective feed-forward input to 200 - 400 ms. Figure 1 shows the orientation tuning curves 
at different stimulus contrasts. The feed-forward input is noisy and broadly tuned (Fig. 
la). Both models exhibit contrast invariant tuning (Fig. lb, c). If fast synaptic depression 
is present at the recurrent excitation, the cortical network sharpens the broadly tuned feed- 
forward input in the initial response phase. Once sharply tuned input is established, the 
tuning width does not change, only the response amplitude decreases in time. 
The predictions of the two models differ substantially if multiple orientations are present 
(Fig. 2). At first, we test the cortical response to two bars separated by 60 o with differ- 
ent intensities (Figs. 2a, b). If the recurrent synaptic weights are static and strong enough 
(Fig. 2a), then only one orientation is signaled. The cortical network selects the orientation 
92 P Adorjdn, L. Schwabe, C. Piepenbrock and K. Obermayer 
(a) 
(b) 
(c) 
(d) 
Feedforward Input 
10 
090 -45 0 45 90  0 
Orientation [deg] wlO 
5 
ZO 
09 90 
Orientation [deg] 
Average Cortical Response 
20 ,;. 
10 
z _09 ""  '"" ./ 
0 -45 0 45 90 
Orientation [deg] 
90 
-90 
90 
o 
-90 
9o 
io 
-90 
9O 
o 
-900 
Activity Profile 
150 300 
Time [ms] 
Figure 2: The response of the cortical amplifier model with static (a,c) and fast depressing 
recurrent synapses (b, d). In both models the feed-forward synapses are fast depressing. In 
the left column the feed-forward input is shown, that is same for both models. Two types 
of stimuli were applied. The first stimulus consists of a stronger (c = -30 ) and a weaker 
bar (a -- +30 ) (a, b); the second stimulus consists of three equal intensity bars with 
orientations that are separated by 60 o (c, d). In the middle column the cortical response is 
shown averaged for different time windows ([0..30] dotted; [0..80] dashed; [200..300] solid 
line). In the right column the cortical activity profile is plotted as a function of time. Gray 
values indicate the activity with bright denoting high activities. 
with the highest amplitude in a winner-take-all fashion. In contrast, if synaptic depression 
is present at the recurrent excitatory synapses, both bars are signaled in parallel (at low 
release probability, Fig. 2b) or after each other (high release probability, data not shown). 
First, those cells fire which are tuned to the orientation of the bar with the stronger inten- 
sity, and a sharply tuned response emerges at a single orientation--the network operates in 
a winner-take-all regime. The synapses of these highly active cells then become strongly 
depressed and cortical competition decreases. As the network is shifted to a more linear 
operation regime, the second orientation is signaled too. Note that this phenomenon-- 
together with the observed contrast invariant tuning-cannot be reproduced by simply de- 
creasing the static synaptic weights in the cortical amplifier model. The recurrent synap- 
tic efficacy changes inhomogeneously in the network depending on the activity. Only the 
synapses of the highly active cells depress strongly, and therefore a sharply tuned response 
can be evoked by a bar with weak intensity. Fast synaptic depression thus behaves as a lo- 
cal self-regulation that modulates competition with a certain delay. This delay, and there- 
fore the delay of the rise of the response to the second bar depends on the efftive time 
constant ref(f(t),p) = free/(1 + pf(t)rrec) of the synaptic depression at the recurrent 
connections. If the depression becomes faster due to an increase in the release probabil- 
ity p, then the delay decreases. The delay also scales with the difference between the bar 
intensities. The closer to each other they are, the shorter the delay will be. 
In Figs. 2c, d the cortical response to three bars with equal intensities is presented. Cells 
tuned to the presented three orientations respond in parallel if fast synaptic depression at 
the recurrent excitation is present (Figs. 2d). The cortical network with strong static recur- 
rent synapses again fails to signal faithfully its feed-forward input. Additive noise on the 
Recurrent Cortical Competition: Strengthen or Weaken? 93 
feed-forward input introduces a slight symmetry breaking and the network with static re- 
current weights responds strongly at the orientation of only one of the presented bars (Fig. 
2c). 
In summary, our simulations revealed that a recurrent network with fast synaptic depres- 
sion is capable of obtaining robust sharpening of its feed-forward input and it also re- 
sponds correctly to multiple orientations. Note that other local activity dependent adapta- 
tion mechanisms, such as slow potassium current, would have similar effects as the synap- 
tic depression on the highly orientation specific excitatory connections. An experimentally 
testable prediction of our model is that the response to a flashed bar with lower contrast 
can be delayed by masking it with a second bar with higher contrast (Fig. 2b, right). We 
also suggest that long range integration from outside of the classical receptive field could 
emerge with a similar delay. In the initial phase of the cortical response, strong local fea- 
tures are amplified. In the longer, second phase, recurrent competition decreases and then 
weak modulatory recurrent or feed-forward input has a stronger relative effect. In the fol- 
lowing, we investigate whether this strategy is favorable from the point of view of cortical 
encoding. 
3 Dynamic coding 
In the previous section we have proposed that during cortical processing a highly nonlin- 
ear phase is followed by a more linear mode if we consider a short stimulus presentation 
or a fixation period. The simulations demonstrated that unless the recurrent competition 
is modulated in time, the network fails to account for more than one feature in its input. 
From a strictly functional point of view the question arises, why not to use weak recurrent 
competition during the whole processing period. We investigate this problem in an abstract 
signal-encoder framework 
!7 = g() + q, (4) 
where  is the input to the "cortical network", g() is a nonlinear mapping and--for the 
sake of simplicity--r/is additive Gaussian noise. Naturally, in a real recurrent network 
output noise becomes input noise because of the feedback. Here we use the simplifying 
assumption that only output noise is present on the transformed input signal (input noise 
would lead to different predictions that should be further investigated). Output noise can 
be interpreted as a noisy channel that projects out from, e.g., the primary visual cortex. 
The nonlinear transformation g(') here is considered as a functional description of a cor- 
tical amplifier network without analyzing how actually it is "implemented". Considering 
orientation selectivity, the signal ' can be interpreted as a vector of intensities (or contrasts) 
of edges with different orientations. Edges which are not present have zero intensity. The 
coding capacity of a realistic neural network is limited. Among several other noise sources, 
this limitation could arise from imprecision in spike timing and a constraint on the maximal 
or average firing rate. 
The input-output mapping g() of a cortical amplifier network is approximated with the 
soft-max function 
exp(flxi) (5) 
gi(') = 4 exp(flxi) ' 
The fi parameter can be interpreted as the level of recurrent competition. As fi - 0 the 
network operates in a more linear mode, while  -+ oo puts it into a highly nonlinear 
winner-take-all mode. In all cases the average activity in the network is constrained which 
has been suggested to minimize metabolic costs [5]. Let us consider a factorizing input 
distribution, 
1II. exp (--) forx> 0, (6) 
z - 
94 P Adorjdn, L. Schwabe, C. Piepenbrock and K. Obermayer 
6 
0.05 0.1 0.15 
Noise (stdev) 
Figure 3: The optimal competition 
parameter /3 as a function of the 
standard deviation of the Gaussian 
output noise r/. The optimal/3 is cal- 
culated for highly super-Gaussian, 
Gaussian, and sub-Gaussian stimu- 
lus densities. The sparsity parame- 
ter a is indicated in the legend. 
where the exponent a determines the sparsity of the probability density function, Z is a 
normalizing constant, and  determines the variance. If a = 2, the input density is the 
positive half of a multivariate Gaussian distribution. With c > 2 the signal distribution 
becomes sub-Gaussian, and with a < 2 it becomes super-Gaussian. 
For optimal processing in time one needs to gain the maximal information about the signal 
for any increasing time window. Let us assume that the stimulus is static and it is pre- 
sented for a limited time. As time goes ahead after stimulus onset, the time window for the 
encoding and the read-out mechanism increases. During a longer period more samples of 
the noisy network output are available, and thus the output noise level decreases with time. 
We suggest that the optimal competition parameter/3Pt--at which the mutual informa- 
tion between input  and output ff (Eq. 4) is maximized--depends on the noise level. As 
the noise decreases with time,/3 or the recurrent cortical competition should also change 
during cortical processing. To demonstrate this idea, the mutual information is calculated 
numerically for a three-dimensional state space. 
One might expect that at higher noise levels the highest information transfer can be ob- 
tained if the typical and salient features are strongly amplified. Note that this is only true 
if the standard deviation of the noise scales sub-linearly with activity, which is true for an 
additive noise process as well as Poisson firing. As noise decreases (e.g., with increas- 
ing the time window for estimation), the level of competition should decrease distributing 
the available resources (e.g., spikes) among more units and letting the network respond to 
finer details at the input. Investigating the level of optimal competition/3 as a function of 
the standard deviation of the output noise (Fig. 3) this intuition is indeed justified. The 
optimal/3 scales with the standard deviation of the additive noise process. Comparing sig- 
nal distributions with the same variance but with different sparsity exponents a, we find 
that the sparser the signal distribution is, the higher the optimal competition becomes, be- 
cause multiple features are unlikely to be present at the same time if the input distribution 
is sparse. By enforcing competition, the optimal encoding strategy also generates an ac- 
tivity distribution where only few units fire for a presented stimulus. Since edges with dif- 
ferent orientations form a sparse distributed representation of natural scenes [8], our work 
suggests that a strongly competitive visual cortical network could achieve a better perfor- 
mance on our visual environment than a simple linear network would do. 
We can now interpret our simulation results presented in the Section 2 from a functional 
point of view and give a prediction for the dynamics of the recurrent cortical competition. 
Noting that the output noise is decreasing with increasing time-window for encoding, the 
cortical competition should also decrease following a similar trajectory as presented in Fig. 
3. If competition is low and static, then the cumulative mutual information between input 
and output would converge only slowly towards the overall information that is available 
in the stimulus. If the competition is high during the whole observation period, then af- 
ter a fast rise the cumulative mutual information would saturate well below the possible 
Recurrent Cortical Competition: Strengthen or Weaken? 95 
maximum. If the level of competition is dynamic, and it decreases from an initially highly 
competitive state, then the network obtains maximal information transfer in time. 
One may argue that the valuable information about the signals mainly depends on the in- 
terest of the observer. Considering an encoding system for one variable it has been sug- 
gested that in a highly attentive state the recurrent competition increases [10]. In the view 
of our results we would refine this statement by suggesting that competition increases or 
decreases depending on the level of visual detail the observer pays attention to. Whenever 
representation of small details is also required, reducing competition is the optimal strategy 
given enough bandwidth. 
In summary, using a detailed model for an orientation hypercolumn in V1 we have demon- 
strated that sharp contrast invariant tuning and faithful representation of multiple features 
can be achieved by a recurrent network if the recurrent competition decreases in time after 
stimulus onset. The model predicts that the cortical response to weak details in the stim- 
ulus emerges with a delay if a second stronger feature is also present. The modulation 
from, e.g., outside of the classical receptive field also has a delayed effect on cortical activ- 
ity. Our study within an abstract framework revealed that weakening the recurrent cortical 
competition on a fast time scale is functionally advantageous, because a maximal amount 
of information can be transmitted in any time window after stimulus onset. 
Acknowledgments Supported by the Boehringer Ingelheim Fonds (C. P.), by the Ger- 
man Science Foundation (DFG grant GK 120-2) and by Wellcome Trust 050080/Z/97. 
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