Introduction

The tilt aftereffect (TAE, Gibson and Radner 1937) is a simple but intriguing visual phenomenon. After staring at a pattern of tilted lines or gratings, subsequent lines appear to have a slight tilt in the opposite direction (Figure 1). The effect resembles an afterimage from staring at a bright light, but it reflects changes in orientation perception rather than in color or brightness.

Most modern explanations of the TAE are based on the feature-detector model of the visual cortex (Hubel and Wiesel, 1968). Individual orientation detectors become more difficult to excite during repeated presentation of oriented stimuli, and the desensitization persists for some time afterwards. This observation forms the basis of the fatigue theory of the TAE: if active neurons become fatigued over time, the set of neurons activated for a test figure will shift away from the adaptation orientation. Assuming the perceived orientation is some sort of average over the orientation preferences of the activated neurons, the perceived orientation would thus show the direct TAE (Coltheart, 1971).

The fatigue theory has been discredited because it has become apparent that the adaptation is mediated by the lateral connections between neurons, rather than changes occurring within the neurons themselves (Bednar, 1997; Vidyasagar, 1990). The now-popular inhibition theory postulates that tilt aftereffects result from changing inhibition between neurons (Tolhurst and Thompson, 1975), perhaps by increases in the strength of lateral connections between them.

**Figure 1:** **Tilt aftereffect patterns.**
Fixate your gaze upon the circle inside the square at the center for at least thirty seconds, moving your eye slightly inside the circle to avoid developing strong afterimages. Now fixate upon the figure at the left. The vertical lines should appear slightly tilted to the right; this phenomenon is called the direct tilt aftereffect. If you fixate upon the horizontal lines at the right, they should appear barely tilted counterclockwise, demonstrating the indirect tilt aftereffect. (Adapted from Campbell and Maffei 1971.)
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Although the inhibition theory was first proposed in the 1970s, only recently has it become computationally feasible to test in a detailed model of cortical function. A Hebbian self-organizing process (the Receptive-Field Laterally Interconnected Synergetically Self-Organizing Map, or RF-LISSOM; Miikkulainen, Bednar, Choe, and Sirosh 1997; Sirosh and Miikkulainen 1994a; Sirosh and Miikkulainen 1996, 1997; Sirosh, Miikkulainen, and Bednar 1996; Sirosh 1995) has been shown to develop feature detectors and specific lateral connections that could produce such aftereffects. The RF-LISSOM model gives rise to anatomical and functional characteristics of the cortex such as topographic maps, ocular dominance, orientation, and size preference columns, and the patterned lateral connections between them. Although other models exist that explain how the feature-detectors and afferent connections could develop by input-driven self-organization, RF-LISSOM is the only model that also shows how the lateral connections can self-organize as an integral part of the process. The laterally connected model has also been shown to account for many of the dynamic aspects of the visual cortex, such as reorganization following retinal and cortical lesions (Miikkulainen et al. 1997; Sirosh and Miikkulainen 1994b; Sirosh 1995; Sirosh, Miikkulainen, and Bednar 1996).

The current work is a first study of the functional behavior of the model, specifically the response to stimuli similar to those known to cause the TAE in humans. The RF-LISSOM model allows observing activation and connection patterns between large numbers of neurons simultaneously, making it possible to relate higher-level phenomena to low-level events, which is difficult to do experimentally. The results suggest that tilt aftereffects are not flaws in an otherwise well-designed system, but an unavoidable result of a self-organizing process that aims at producing an efficient, sparse encoding of the input through decorrelation (as proposed by Barlow 1990; see also Dong 1994; Földiák 1990; Field 1994; Miikkulainen et al. 1997; Sirosh, Miikkulainen, and Bednar 1996).