A Model of Feedback to the Lateral 
Geniculate Nucleus 
Carlos D. Brody 
Computation and Neural Systems Program 
California Institute of Technology 
Pasadena, CA 91125 
Abstract 
Simplified models of the lateral geniculate nucles (LGN) and stri- 
ate cortex illustrate the possibility that feedback to the LGN may 
be used for robust, low-level pattern analysis. The information 
fed back to the LGN is rebroadcast to cortex using the LGN's full 
fan-out, so the cortexLGNcortex pathway mediates extensive 
cortico-cortical communication while keeping the number of neces- 
sary connections small. 
1 INTRODUCTION 
The lateral geniculate nucleus (LGN) in the thalamus is often considered as just a 
relay station on the way from the retina to visual cortex, since receptive field prop- 
erties of neurons in the LGN are very similar to retinal ganglion cell receptive field 
properties. However, there is a massive projection from cortex back to the LGN: 
it is estimated that 3-4 times more synapses in the LGN are due to corticogenicu- 
late connections than those due to retinogeniculate connections [12]. This suggests 
some important processing role for the LGN, but the nature of the computation 
performed has remained far from clear. 
I will first briefly summarize some anatomical facts and physiological results con- 
cerning the corticogeniculate loop, and then present a simplified model in which its 
function is to (usefully) mediate communication between cortical cells. 
409 
410 Brody 
1.1 SOME ANATOMY AND PHYSIOLOGY 
The LGN contains both principal cells, which project to cortex, and inhibitory 
interneurons. The projection to cortex sends collaterals into a sheet of inhibitory 
cells called the perigeniculate nucleus (PGN). PGN cells, in turn, project back to 
the LGN. The geniculocortical projection then proceeds into cortex, terminating 
principally in layers 4 and 6 in the cat [11, 12]. Areas 17, 18, and to a lesser extent, 
19 are all innervated. Layer 6 cells in area 17 of the cat have particularly long, 
non-end-stopped receptive fields [2]. It is from layer 6 that the corticogeniculate 
projection back originates. 1 It, too, passes through the PGN, sending collaterals 
into it, and then contacts both principal cells and interneurons in the LGN, mostly 
in the more distal parts of their dendrites [10, 13]. Both the forward and the 
backward projection are retinotopically ordered. 
Thus there is the possibility of both excitatory and inhibitory effects in the cortico- 
geniculate projection, which is principally what shall be used in the model. 
The first attempts to study the physiology of the corticogeniculate projection in- 
volved inactivating cortex in some way (often cooling cortex) while observing genic- 
ulate responses to simple visual stimuli. The results were somewhat inconclusive: 
some investigators reported that the projection was excitatory, some that it was in- 
hibitory, and still others that it had no observable effect at all. [1, 5, 9] Later studies 
have emphasized the need for using stimuli which optimally excite the cortical cells 
which project to the LGN; inactivating cortex should then make a significant dif- 
ference in the inputs to geniculate cells. This has helped to reveal some effects: 
for example, LGN cells with corticogeniculate feedback are end-stopped (that is, 
respond much less to long bars than to short bars), while the end-stopping is quite 
clearly reduced when the cortical input is removed [8]. 
One study [13] has used cross-correlation analysis between cortical and geniculate 
cells to suggest that there is spatial structure in the corticogeniculate projection: an 
excitatory corticogeniculate interaction was found if cells had receptive field centers 
that were close to each other, while an inhibitory interaction was found if the centers 
were farther apart. ttowever, the precise spatial structure of the projection remains 
unknown. 
2 A FEEDBACK MODEL 
I will now describe a simplified model of the LGN and the corticogeniculate loop. 
The very simple connection scheme shown in fig 1 originated in a suggestion by 
Christof Koch [3] that the long receptive fields in layer 6 might be used to facilitate 
contour completion at the LGN level. In the model, then, striate cortex simple 
cells feed back positively to the LGN, enhancing the conditions which gave rise 
to their firing. This reinforces, or completes, the oriented bar or edge patterns to 
which they are tuned. Assuming that the visual features of interest are for the most 
part oriented, while much of the noise in images may be isotropic and unoriented, 
enhancing the oriented features improves the signal-to-noise ratio. 
aIn all areas innervated by the LGN. 
A Model of Feedback to the Lateral Geniculate Nucleus 411 
RETINA 
LGN 
CELLS 
Vl CELLS 
Figure 1: Basic model connectivity: A schematic diagram showing the connections 
between different pools of units in the single spatial frequency channel model. LGN cells 
first filter the image linearly through a center-surround filter (72G), the result of which 
is then passed through a sigmoid nonlinearity (tanh). (In the simulations presented here 
G was a Gaussian with standard deviation 1.4 pixels.) V1 cells then provide oriented 
filtering, which is also passed through a nonlinearity (logistic; but see details in text) and 
fed back positively to the LGN to reinforce detected oriented edges. V1 cells excite LGN 
cells which have excitatory connections to them, and inhibit those that have inhibitory 
connections to them. Inhibition is implicitly assumed to be mediated by interneurons. 
(Note that there are no intracortical or intrageniculate connections: communication takes 
place entirely through the feedback loop.) See text for further details. 
For simplicity, only striate cortex simple "edge-detecting" cells were modeled. Two 
models are presented. In the first one, all cortical cells have the same spatial 
frequency characteristics. In the second one, two channels, a high frequency channel 
and a low frequency channel, interact simultaneously. 
2.1 SINGLE SPATIAL FREQUENCY CHANNEL MODEL 
A schematic diagram of the model is shown in figure 1. The retina is used simply 
as an input layer. To each input position (pixel) in the retina there corresponds 
one LGN unit. Linear weights from the retina to the LGN implement a 7G 
filter, where G(x, y) is a two-dimensional Gaussian. The LGN units then project to 
eight different pools of "orientation-tuned" cells in V1. Each of these pools has as 
many units as there are pixels in the input "retina". The weights in the projection 
forward to V1 represent eight rotations of the template shown in figure 2a, covering 
360 degrees. This simulates basic orientation tuning in V1. Cortical cells then feed 
412 Brody 
back positively to the geniculus, using rotations of the template shown in fig 2(b). 
The precise dynamics of the model are as follows: Ri are real-valued retinal inputs, 
Li are geniculate unit outputs, and V/are cortical cell outputs. Gji represent weights 
from retina  LGN, Fji forward weights from LGN  V1, and Bji backward 
weights from V1  LGN. a,O,7,Tc and T2 are all constants. For geniculate 
units: 
dlj 
dt = -71j + y] GiPq + y. BkVk 
i k 
Lj = tanh(/,/) 
While for cortical cell units: 
/ ..- { g(tj -- TC1) 
ifvj > T2 
otherwise 
Here g() is the logistic function. 
"receptke field lenK(b" 
OOOOOOO 
OOOOOOO 
OOOOOOO 
0000000 
0000000 
0000000 
       
       
OOOOOOO 
0000000 
0 0 0 0 0 0 0 
0 0 0 0 0 0 0 
(,) (b) 
Figure 2: Weights between the LGN and V1. Figure 2(a): Forward weights, from the 
LGN to V1. Each circle represents the weight from a cell in the LGN; dark circles represent 
positive weights, light circles negative weights (assumed mediated by interneurons). The 
radius of each circle represents the strength of the corresponding weight. These weights 
create "edge-detecting" neurons in V1. Figure 2(b): Backwards weights, from V1 back to 
the LGN. Only cells close to the contrast edge receive strong feedback. 
In the scheme described above many cortical cells have overlapping receptive fields, 
both in the forward projection from the geniculus and in the backwards projection 
from cortex. A cell which is reinforcing an edge within its receptive field will also 
partially reinforce the edge for retinotopically nearby cortical cells. For nearby cells 
with similar orientation tuning, the reinforcement will enhance their own firing; 
they will then enhance the firing of other, similar, cells farther along; and so on. 
That is, the overlapping feedback fields allow the edge detection process to follow 
contours (note that the process is tempered at the geniculate level by actual input 
from the retina). This is illustrated in figure 3. 
A Model of Feedback to the Lateral Geniculate Nucleus 413 
Figure 3: Following contours: This figure shows the effect on the LGN of the feedback 
enhancement. The image on the left is the retinal input: a very weak, noisy horizontal edge. 
The center image is the LGN after two iterations of the simulation. Note that initially 
only certain sectors of the edge are detected (and hence enhanced). The rightmost image 
is the LGN after 8 iterations: the enhanced region has spread to cover the entire edge 
through the effect of horizontally oriented, overlapping receptive fields. This is the final 
stable point of the dynamics. 
2.2 MULTIPLE SPATIAL FREQUENCY CHANNELS MODEL 
In the model described above the LGN is integrating and summarizing the informa- 
tion provided by each of the orientation-tuned pools of cortical cells? It does so in 
a way which would easily extend to cover other types of cortical cells (bar or grat- 
ing "detectors", or varying spatial frequency channels). To experiment simply with 
this possibility, an extra set of eight pools of orientation-tuned "edge-detecting" 
cortical cells was added. The new set's weights were similar to the original weights 
described above, except they had a "receptive field length" (see figure 2) of 3 pixels: 
the original set had a "receptive field length" of 9 pixels. 
Thus one set was tuned for detecting short edges, while the other was tuned for 
detecting long edges. The effect of using both of these sets is illustrated in figure 4. 
Both sets interact nonlinearly to produce edge detection rather more robust than 
either set used alone: the image produced using both simultaneously is not a linear 
addition of those produced using each set separately. Note how little noise is ac- 
cepted as an edge. The same model, running with the same parameters but more 
pixels, was also tested on a real image. This is shown in figure 5. 
3 DISCUSSION ON CONNECTIVITY 
A major function fulfilled by the LGN in this model is that of providing a communi- 
cations pathway between cortical cells, both between cells of similar orientation but 
different location or spatial frequency tuning, and between cells of different orienta- 
2A function not unlike that suggested by Mumford [7], except that here the "experts" 
are extremely low-level orientation-tuned channels. 
414 Brody 
Figure 4: Combined spatial frequency channels: The leftmost image is the retinal 
input, a weak noisy edge. (The other three images are "summary outputs", obtained as 
follows: the model produces activations in many pools of cortical cell units; the activations 
from all V1 units corresponding to a particular retinotopic position are added together to 
form a real-valued number corresponding to that position; and this is then displayed as 
a grey-scale pixel. Since only "edge-detecting" units were used, this provides a rough 
estimate of the certainty of there being an edge at that point.) Second from left we see the 
summary output of the model after 20 iterations (by which time it has stabilized), using 
only the low spatial frequency channel. Only a single segment of the edge is detected. 
Third from left is the output after 20 iterations using only the high frequency channel. 
Only isolated, short, segments of the edge are detected. The rightmost image is the output 
using both channels simultaneously. Now the segments detected by the high frequency 
channel can combine with the original image to provide edges long enough for the low 
frequency channel to detect and complete into a single, long continuous edge. 
tion tuning: for example, these last compete to reinforce their particular orientation 
preference on the geniculus. The model qualitatively shows that such a pathway, 
while mediated by a low-level representation like that of the LGN, can neverthe- 
less be used effectively, producing contour-following and robust edge-detection. We 
must now ask whether such a function could not be performed without feedback. 
Clearly, it could be done without feedback to the LGN, purely through intracortical 
connections, since any feedback network can in principle be "unfolded in time" into 
a feedforward network which performs the same computation- provided we have 
enough units and connections available. 
In other words, any suggested functional role for corticogeniculate feedback must not 
only include an account of the proposed computation performed, but also an account 
of why it is preferable to perform that computation through a feedback process, in 
terms of some efficiency measure (like the number of cells or synapses necessary, 
for example). There can be no other rationale, apart from fortuitous coincidence, 
for constructing an elaborate feedback mechanism to perform a computation that 
could just as well be done without it. 
With this view in mind, it is worth re-stating that in this model any two cortical cells 
whose receptive fields overlap are connected (disynaptically) through the LGN. How 
many connections would we require in order to achieve similar communication if we 
only used direct connections between cortical orientation-tuned cells instead? In 
monkey, each cell's receptive field overlaps with approximately 10 6 others [4]- thus, 
A Model of Feedback to the Lateral Geniculate Nucleus 415 
 K.;4:::: - ,:: :-;-.-:--:-.-:.-:-:.:-:.:-:.-:......:'-:-:.:':-:':-:.:-:' ..:-.'.'.,-.---.-.'.--'--.:-----:-:-'.'-'-'-v:. 
:...:..:.:.:.:..:::.::.:.:.:.:. ::.:..:.:.;.:.::::.:::-::: :::::::::::::::::::::::.:;::.:.::::.:::::.:.: 
Figure 5: A real image: The top image is the retinal input. Stippling is due to printing 
only. The center image is that obtained through detecting the zero-crossings of X7G. 
To reduce spurious edges, a minimum slope threshold was placed on the point of the 
zero-crossing below which edges were not accepted. The image shown here was the best 
that could be obtained through varying both the width of the Gaussian G and the slope 
threshold value. The last image shows the summary output from the model, using two 
simultaneous spatial frequency channels. Note how noise is reduced compared to the center 
image, straight lines are smoother, and resolution is not impaired, but is better in places 
(group of people at lower left, or "smoke stacks" atop launcher). 
416 Brody 
any cortical cell would need to synapse onto at least 10  cells. If the information 
can be sent via the LGN, geniculate cell fan-out can reduce the number of necessary 
synapses by a significant factor. It is estimated that geniculate cells (in the cat) 
synapse onto at least 200 cortical cells (probably more) [6], reducing the number of 
necessary connections considerably. 
4 BIOLOGY AND CONCLUSIONS 
In section 1.1 I noted one important study [8] which established that corticogenic- 
ulate input reduces firing of geniculate cells for long bars; this is in direct contra- 
diction to the prediction which would be made by this model, where the feedback 
enhances firing for long features (here, edges). Thus, the model does not agree with 
known physiology. 
However, the model's value lies simply in clearly illustrating the possibility 
that feedback in a hierarchical processing scheme like the corticogeniculate loop 
can be utilized for robust, low-level pattern analysis, through the use of the 
cortexLGNcortex communications pathway. The possibility that a great deal 
of different types of information could be flowing through this pathway for this 
purpose should not be left unconsidered. 
Acknowledgements 
The author is supported by fellowships from the Parsons Foundation and from 
CONACYT (Mexico). Thanks are due to Michael Lyons for careful reading of the 
manuscript. 
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