1 Introduction
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Self-Organization, Plasticity, and Low-level Visual Phenomena in a Laterally Connected Map Mo del of the Primary Visual Cortex Risto Miikkulainen, James A. Bednar, Yo onsuck Cho e, and Joseph Sirosh Department of Computer Sciences The UniversityofTexas at Austin, Austin, TX 78712 fristo,jb ednar,yscho e,[email protected] Abstract Based on a Hebbian adaptation pro cess, the a erent and lateral connections in the RF-LISSOM mo del organize simultaneously and co op eratively, and form structures such as those observed in the primary visual cortex. The neurons in the mo del develop lo cal receptive elds that are organized into orientation, o cular dominance, and size selectivity columns. At the same time, patterned lateral connections form b etween neurons that follow the receptive eld organization. This structure is in a continuously-adapting dynamic equilibrium with the external and intrinsic input, and can account for reorganization of the adult cortex following retinal and cortical lesions. The same learning pro cesses may b e resp onsible for a number of low-level functional phenomena such as tilt aftere ects, and combined with the leaky integrator mo del of the spiking neuron, for segmentation and binding. The mo del can also b e used to verify quantitatively the hyp othesis that the visual cortex forms a sparse, redundancy-reduced enco ding of the input, which allows it to pro cess massive amounts of visual information eciently. 1 Intro duction The primary visual cortex, like many other regions of the neo cortex, is a top ographic map, organized so that adjacent neurons resp ond to adjacent regions of the visual eld. In addition, neurons are resp onsive to particular features in the input, such as lines of a particular orientation or o cularity. All neurons in a vertical column in the cortex typically have the same feature preferences. Vertical groups of neurons with the same orientation preference are called orientation columns and vertical groups with the same eye preference are called o cular dominance columns. The feature preferences gradually vary across the surface of the cortex in characteristic spatial patterns that constitute the cortical maps. Cortical maps are shap ed by visual exp erience. Altering the visual environment can drastically change the organization of o cular dominance and orientation columns Hub el and Wiesel 1962, 1968, 1977, 1974. The animal is most susceptible during a critical p erio d of early life, typically a few weeks. For example, if a kitten is raised with b oth eyes sutured shut, the cortex do es not develop a normal organization, and o cular dominance and orientation columns do not form. Even if the eye is op ened after a few weeks, the animal remains blind, even though the eye and the LGN are p erfectly normal. Similarly, if kittens are raised in environments containing only vertical or horizontal contours, their ability to see other orientations su ers signi cantly. In the cortex, Psychology of Learning and Motivation, in press. most cells develop preferences for these particular orientations, and do not resp ond well to the other orientations Hirsch and Spinelli 1970; Blakemore and Co op er 1970; Blakemore and van Sluyters 1975. Such exp eriments indicate that visual inputs are crucial to form a normal cortical organization, and suggest that the cortex tunes itself to the distribution of visual inputs. The discovery byvon der Malsburg 1973; see also Amari 1980 and Grossb erg 1976 that simple computational rules could drive the development of oriented receptive elds from visual input, raised the hop e that much of the structure and development of V1 could b e understo o d in terms of very simple neuronal b ehavior. However, since then substantial new discoveries havechanged our understanding of the primary visual cortex. New evidence indicates that cells in V1 are coupled by highly-sp eci c long-range lateral connections Gilb ert et al. 1990; Gilb ert and Wiesel 1983; Schwark and Jones 1989. These connections are recipro cal and far more numerous than the a erents, and they are b elieved to have a substantial in uence on cortical activity. They grow exub erantly after birth and reach their full extent in a short p erio d. During subsequent development, they get automatically pruned into well-de ned clusters. Pruning happ ens at the same time as the a erent connections organize into top ographic maps Callaway and Katz 1990, 1991,Burkhalter et al. 1993; Katz and Callaway 1992; Luhmann et al. 1986. The nal clustered distribution corresp onds closely to the distribution of a erent connections in the map. For example, in the mature visual cortex, lateral connections primarily run b etween areas with similar resp onse prop erties, such as neurons with the same orientation or eye preference Gilb ert et al. 1990; Gilb ert and Wiesel 1989; Lowel and Singer 1992. Several observations indicate that the lateral connection structure is not de ned genetically, but dep ends on the visual input: 1 When the primary visual cortex of the cat is deprived of visual input during early development, lateral connectivity remains crude and unre ned Callaway and Katz 1991. 2 The pattern of lateral connection clusters can b e altered bychanging the input to the developing cortex. The resulting patterns re ect correlations in the input Lowel and Singer 1992. 3 In the mouse somatosensory barrel cortex, sensory deprivation by sectioning the input nerve causes drastic decreases in the extent and density of lateral connections McCasland et al. 1992. These observations suggest that the development of lateral connections, like that of a erent connections, dep ends on cortical activity driven by external input. New discoveries have also changed the notion that the a erent structures and lateral connections are essentially static after a critical p erio d of early development. Recent results show that the adult cortex can undergo signi cant, often reversible, reorganization in resp onse to various sensory and cortical manipulations such as lesions in the receptive surface and the cortex Gilb ert 1992; Kaas 1991; Merzenich et al. 1990; Kapadia et al. 1994; Pettet and Gilb ert 1992. Based on the ab ove results, a new theory of the visual cortex has started to emerge. The cortex app ears to b e a continuously-adapting structure in a dynamic equilibrium with b oth the external and intrinsic input. This equilibrium is maintained by co op erative and comp etitive lateral interactions within the cortex, mediated by lateral connections Gilb ert et al. 1990. The a erent and lateral connection patterns develop synergetically and simultaneously, based on the same un- derlying pro cess. The primary function of the a erent and lateral structures is to form a sparse, redundancy-reduced enco ding of the visual input Barlow 1972; Field 1994. By integrating infor- mation over large p ortions of the cortex, lateral connections assist in grouping simple features into p erceptual ob jects Singer et al. 1990; von der Malsburg and Singer 1988, and may b e resp onsible for low-level visual phenomena such as tilt illusions and aftere ects. The exact mechanisms of such self-organization, plasticity, and function are still not completely understo o d. Computational mo dels can play a fundamental role in this research. With the advent 2 of massively parallel computers in the last veyears, it has b ecome p ossible to simulate large numb ers of neural units and their connections. At the same time, neurobiological techniques for mapping the resp onse prop erties and connectivity of neurons have b ecome sophisticated enough to constrain and validate such mo dels. This technological con uence provides a timely opp ortunity to test hyp otheses ab out cortical mechanisms through large-scale computational exp eriments. One of the most p owerful computational abstractions of biological learning is the Hebb rule Gustafsson and Wigstrom 1988; Hebb 1949, where synaptic ecacies are adjusted based on coin- cident pre- and p ostsynaptic activity.Iftwo neurons are active at the same time, their connection is deemed useful and is strengthened. Hebbian learning is usually coupled with normalization so that the ecacies do not grow without b ounds but only their relative strengths change Miller 1994b. A network of such units and connections may develop a globally ordered structure where units represent sp eci c inputs, such as lines of di erent orientation. Such a pro cess is called self- organization: there is no global sup ervisor directing the pro cess, but learning is based on a lo cal rule and driven by the input. Several computational mo dels have already shown how receptive elds and their global organi- zation in the cortical network can develop through Hebbian self-organization of a erent synapses Erwin et al. 1995; Go o dhill 1993; Kohonen 1982; Miller 1994a; Miller et al. 1989; Ob ermayer et al. 1990b; von der Malsburg 1973. Some of these mo dels have also shown that asp ects of cortical plasticity, such as remapping of cortical top ography following p eripheral lesions, can b e explained with similar mechanisms Ob ermayer et al. 1990a; Ritter et al. 1992. However, these mo dels have not taken the lateral interactions b etween cells into account, or have assumed that they are pre- set and xed and have a regular pro le. Therefore, the simultaneous self-organization of lateral connections and a erent structures, and many asp ects of cortical plasticity such as reorganization of the map in resp onse to cortical lesions and reshaping of mature receptive elds in resp onse to retinal lesions, cannot b e explained by these mo dels.