November 2000 Volume 3 Number Supp P 1168

November 2000 Volume 3 Number Supp p1168

Models of motion detection

Alexander Borst
The author is at the ESPM-Division of Insect Biology, 201 Wellman Hall, Univ. of California Berkeley, Berkeley, California 94720, USA.
e-mail:

Visual motion detection is one of the most active areas in systems neuroscience today1, 2, and the cellular mechanisms of directional selectivity may soon be understood in unprecedented biophysical detail. Alongside undeniable technical advances such as whole-cell patch-clamp recording and the retinal slice preparation, a major determinant of this recent progress is the conceptual foundation laid almost half a century ago.

Curiously, the story began with two young soldiers during World War II. A biology student, Bernhard Hassenstein, then 21, met a 19-year-old aspiring physicist, Werner Reichardt. In the craziness of wartime, they promised each other that, if they survived, they would do something great together: start the first institute of physics and biology. In 1958 they founded the Research Group of Cybernetics at the Max-Planck-Institute of Biology in Tübingen, Germany. In a congenial collaboration, which still sounds like the goal of every summer school in computational neuroscience, they did a series of elegant experiments, using the optomotor response of the beetle Cholorphanus as a behavioral measure. This response is the animal's tendency to follow the movement of the visual surround to compensate for its mistaken perception of self-motion in the opposite direction. The beetle was glued to a rod so it could not move its body, head or eyes relative to the surround, but could express its behavior at decision points by rotating a 'Y-maze globe' under its feet (Fig. 1).

/ Their results3 led to the development of a model for motion detection that became known as the 'correlation-type motion detector', the 'Hassenstein-Reichardt model' or briefly—omitting half the original team—the 'Reichardt detector' (Fig. 2). The core computation in this model is a delay-and-compare mechanism: delaying the brightness signal as measured by one photoreceptor by a low-pass filter and comparing it by multiplication with the instantaneous signal derived from a neighboring location. Doing this twice in a mirror-symmetrical fashion and subtracting the output signals of both subunits leads to a response that is fully directionally selective. The strict mathematical treatment of this model4 led to many counterintuitive predictions, which nevertheless were experimentally verified in many species' behavior and in many types of neurons (for review, see ref. 5). For example, the model predicted that the response, unlike a speedometer, should not increase continuously with increasing velocity; instead, going beyond an optimum velocity should decrease the response. The model also predicted that the optimum velocity should vary with the pattern's spatial wavelength so that their ratio remains constant.
The theory's influence can hardly be overestimated. It inspired work on motion vision in many animals, including humans. In some cases, filters and parameters of the original model were modified to fit experimental observations6. In others, researchers approaching the problem from a different angle arrived at similar solutions, such as the 'motion energy model', which despite a different internal architecture is identical to the original model at its output7. Some of these studies became famous under their own name, like the 'Barlow-Levick-model' of motion detection, arising from ex-periments on rabbit retinal ganglion cells8 that were stimulated, not by smooth motion, but by a sequence of discrete illumination steps in two neighboring locations, in either the preferred or null direction for the cell. Barlow and Levick found that the response to the null direction sequence was significantly reduced compared to the sum of the individual responses, whereas the response to the preferred direction sequence was roughly equal to the sum of individual responses. The authors proposed a veto-mechanism or 'null-direction inhibition' as the basis for direction selectivity. From this study, the historical thread leads to the proposal that a shunting inhibition is the cellular implementation of the veto operation9, and from there directly to the current 'pre or post' debate over directionally selective ganglion cells1.
Thus, the Hassenstein-Reichardt model set the standard for how researchers thought about visual motion detection and how they designed experiments. In a more general sense, it introduced mathematical techniques and quantitative modeling to biology, clearly demonstrating that our intuition does not reach very far; instead we soon reach the point where the 'pen starts getting smarter than the person holding it'. Far beyond the question of whether the particular Hassenstein-Reichardt model is correct or not, this has probably been its most significant contribution to neuroscience.



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1. Barinaga, M. Science289, 2256–2257 ( 2000). MEDLINE
2. Taylor, W. R., He, S., Levick, W. R. & Vaney, D. I. Science289, 2347–2350 (2000). MEDLINE
3. Hassenstein, B. & Reichardt, W. Z. Naturforsch. 11b, 513–524 ( 1956).
4. Reichardt, W. in Sensory Communication (ed. Rosenblith, W. A.) 303– 317 (MIT Press, Cambridge, Massachusetts, 1961).
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Figure 1: Tethered Chlorophanus walking on the Y-maze globe (from ref. 10).

Figure 2: Correlation-type motion detector (from ref. 4).
November 2000 Volume 3 Number Supp p1170
/
Computation by neural networks
Geoffrey E. Hinton
The author is in the Gatsby Computational Neuroscience Unit, University College London, 17 Queen Square, London WC1N 3AR, UK.
e-mail:
Networks of neurons can perform computations that have proved very difficult to emulate in conventional computers. In trying to understand how real nervous systems achieve their remarkable computational abilities, researchers have been confronted with three major theoretical issues. How can we characterize the dynamics of neural networks with recurrent connections? How do the time-varying activities of populations of neurons represent things? How are synapse strengths adjusted to learn these representations? To gain insight into these difficult theoretical issues, it has proved necessary to study grossly idealized models that are as different from real biological neural networks as apples are from planets.


/ The 1980s saw major progress on all three fronts. In a classic 1982 paper1, Hopfield showed that asynchronous networks with symmetrically connected neurons would settle to locally stable states, known as 'point attractors', which could be viewed as content-addressable memories. Although these networks were both computationally inefficient and biologically unrealistic, Hopfield's work inspired a new generation of recurrent network models; one early example was a learning algorithm that could automatically construct efficient and robust population codes in 'hidden' neurons whose activities were never explicitly specified by the training environment2.
The 1980s also saw the widespread use of the backpropagation algorithm for training the synaptic weights in both feedforward and recurrent neural networks. Backpropagation is simply an efficient method for computing how changing the weight of any given synapse would affect the difference between the way the network actually behaves in response to a particular training input and the way a teacher desires it to behave3. Backpropagation is not a plausible model of how real synapses learn, because it requires a teacher to specify the desired behavior of the network, it uses connections backward, and it is very slow in large networks. However, backpropagation did demonstrate the impressive power of adjusting synapses to optimize a performance measure. It also allowed psychologists to design neural networks that could perform interesting computations in unexpected ways. For example, a recurrent network that is trained to derive the meaning of words from their spelling makes very surprising errors when damaged, and these errors are remarkably similar to those made by adults with dyslexia4.
The practical success of backpropagation led researchers to look for an alternative performance measure that did not involve a teacher and that could easily be optimized using information that was locally available at a synapse. A measure with all the right properties emerges from thinking about perception in a peculiar way: the widespread existence of top-down connections in the brain, coupled with our ability to generate mental images, suggests that the perceptual system may literally contain a generative model of sensory data. A generative model stands in the same relationship to perception as do computer graphics to computer vision. It allows the sensory data to be generated from a high-level description of the scene. Perception can be seen as the process of inverting the generative model—inferring a high-level description from sensory data under the assumption that the data were produced by the generative model. Learning then is the process of updating the parameters of the generative model so as to maximize the likelihood that it would generate the observed sensory data.
Many neuroscientists find this way of thinking unappealing because the obvious function of the perceptual system is to go from the sensory data to a high-level representation, not vice versa. But to understand how we extract the causes from a particular image sequence, or how we learn the classes of things that might be causes, it is very helpful to think in terms of a top-down, stochastic, generative model. This is exactly the approach that statisticians take to modeling data, and recent advances in the complexity of such statistical models5 provide a rich source of ideas for understanding neural computation. All the best speech recognition programs now work by fitting a probabilistic generative model.
If the generative model is linear, the fitting is relatively straightforward but can nevertheless lead to impressive results6, 7. There is good empirical evidence that the brain uses generative models with temporal dynamics for motor control8 (see also ref. 9, this issue). If the generative model is non-linear and allows multiple causes, it can be very difficult to compute the likely causes of a pattern of sensory inputs. When exact inference is unfeasible, it is possible to use bottom-up, feedforward connections to activate approximately the right causes, and this leads to a learning algorithm for fitting hierarchical nonlinear models that requires only information that is locally available at synapses10. So far, theoretical neuroscientists have considered only a few simple types of nonlinear generative model. Although these have produced impressive results, it seems likely that more sophisticated models and better fitting techniques will be required to make detailed contact with neural reality.


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2. Hinton, G. E. & Sejnowski, T. J. in Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Vol. 1Foundations (eds. Rumelhart, D. E. & McClelland, J. L.) 282 –317 (MIT Press, Cambridge, Massachusetts, 1986).
3. Rumelhart, D. E., Hinton, G. E. & Williams, R. J. Nature323, 533– 536 (1986).
4. Plaut, D. C. & Shallice, T. Cognit. Neuropsychol.10, 377–500 (1993).
5. Cowell, R. G., Dawid, A. P., Lauritzen, S. L. & Spiegelhalter, D. J. Probabilistic Networks and Expert Systems (Springer, New York, 1999).
6. Bell, A. J. & Sejnowski, T. J. Neural Comput.7, 1129–1159 (1995). MEDLINE
7. Olshausen, B. A. & Field. D. J. Nature381, 607–609 (1996). MEDLINE
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9. Wolpert, D. M. & Ghahramani, Z. Nat. Neurosci.3, 1212–1217 (2000).
10. Hinton, G. E., Dayan, P., Frey, B. J. & Neal, R. Science268, 1158–1161 (1995). MEDLINE