Beyond ℓ1 sparse coding in V1.

Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using the ℓ1 norm as a penalty due to its convexity, which makes it amenable to fast and simple algorithmic solvers. In this work, we use biological vision as a test-bed and show that the soft thresholding operation associated to the use of the ℓ1 norm is highly suboptimal compared to other functions suited to approximating ℓp with 0 ≤ p < 1 (including recently proposed continuous exact relaxations), in terms of performance. We show that ℓ1 sparsity employs a pool with more neurons, i.e. has a higher degree of overcompleteness, in order to maintain the same reconstruction error as the other methods considered. More specifically, at the same sparsity level, the thresholding algorithm using the ℓ1 norm as a penalty requires a dictionary of ten times more units compared to the proposed approach, where a non-convex continuous relaxation of the ℓ0 pseudo-norm is used, to reconstruct the external stimulus equally well. At a fixed sparsity level, both ℓ0- and ℓ1-based regularization develop units with receptive field (RF) shapes similar to biological neurons in V1 (and a subset of neurons in V2), but ℓ0-based regularization shows approximately five times better reconstruction of the stimulus. Our results in conjunction with recent metabolic findings indicate that for V1 to operate efficiently it should follow a coding regime which uses a regularization that is closer to the ℓ0 pseudo-norm rather than the ℓ1 one, and suggests a similar mode of operation for the sensory cortex in general.

Functional and spatial rewiring principles jointly regulate context-sensitive computation.

Adaptive rewiring provides a basic principle of self-organizing connectivity in evolving neural network topology. By selectively adding connections to regions with intense signal flow and deleting underutilized connections, adaptive rewiring generates optimized brain-like, i.e. modular, small-world, and rich club connectivity structures. Besides topology, neural self-organization also follows spatial optimization principles, such as minimizing the neural wiring distance and topographic alignment of neural pathways. We simulated the interplay of these spatial principles and adaptive rewiring in evolving neural networks with weighted and directed connections. The neural traffic flow within the network is represented by the equivalent of diffusion dynamics for directed edges: consensus and advection. We observe a constructive synergy between adaptive and spatial rewiring, which contributes to network connectedness. In particular, wiring distance minimization facilitates adaptive rewiring in creating convergent-divergent units. These units support the flow of neural information and enable context-sensitive information processing in the sensory cortex and elsewhere. Convergent-divergent units consist of convergent hub nodes, which collect inputs from pools of nodes and project these signals via a densely interconnected set of intermediate nodes onto divergent hub nodes, which broadcast their output back to the network. Convergent-divergent units vary in the degree to which their intermediate nodes are isolated from the rest of the network. This degree, and hence the context-sensitivity of the network's processing style, is parametrically determined in the evolving network model by the relative prominence of spatial versus adaptive rewiring.

Adaptive Rewiring in Weighted Networks Shows Specificity, Robustness, and Flexibility.

Brain network connections rewire adaptively in response to neural activity. Adaptive rewiring may be understood as a process which, at its every step, is aimed at optimizing the efficiency of signal diffusion. In evolving model networks, this amounts to creating shortcut connections in regions with high diffusion and pruning where diffusion is low. Adaptive rewiring leads over time to topologies akin to brain anatomy: small worlds with rich club and modular or centralized structures. We continue our investigation of adaptive rewiring by focusing on three desiderata: specificity of evolving model network architectures, robustness of dynamically maintained architectures, and flexibility of network evolution to stochastically deviate from specificity and robustness. Our adaptive rewiring model simulations show that specificity and robustness characterize alternative modes of network operation, controlled by a single parameter, the rewiring interval. Small control parameter shifts across a critical transition zone allow switching between the two modes. Adaptive rewiring exhibits greater flexibility for skewed, lognormal connection weight distributions than for normally distributed ones. The results qualify adaptive rewiring as a key principle of self-organized complexity in network architectures, in particular of those that characterize the variety of functional architectures in the brain.

Adaptive rewiring evolves brain-like structure in weighted networks.

Activity-dependent plasticity refers to a range of mechanisms for adaptively reshaping neuronal connections. We model their common principle in terms of adaptive rewiring of network connectivity, while representing neural activity by diffusion on the network: Where diffusion is intensive, shortcut connections are established, while underused connections are pruned. In binary networks, this process is known to steer initially random networks robustly to high levels of structural complexity, reflecting the global characteristics of brain anatomy: modular or centralized small world topologies. We investigate whether this result extends to more realistic, weighted networks. Both normally- and lognormally-distributed weighted networks evolve either modular or centralized topologies. Which of these prevails depends on a single control parameter, representing global homeostatic or normalizing regulation mechanisms. Intermediate control parameter values exhibit the greatest levels of network complexity, incorporating both modular and centralized tendencies. The simulation results allow us to propose diffusion based adaptive rewiring as a parsimonious model for activity-dependent reshaping of brain connectivity structure.

Orientation perception anisotropies indicate functional segregation within the color system.

When stimuli are luminance-defined, the visual system is known to prefer those that are radially oriented with respect to the point of fixation over tangentially oriented ones (the radial bias effect). In two contrast detection experiments and an orientation discrimination experiment, we investigated whether the radial bias effect also exists for chromatic stimuli. The contrast detection experiments revealed the radial bias effect to be color-specific; the effect was present for isoluminant red-green stimuli but absent or in the opposite direction for blue-yellow stimuli with, respectively, low (0.4 c/°) and medium (1 c/°) spatial frequencies. In agreement with previous results, we also found distinct sensitivity distributions for red-green and blue-yellow signals as a function of eccentricity. The results, thus, demonstrate a functional segregation between red-green and blue-yellow signals not only in local but also in nonlocal signal processing.

Distributed processing of color and form in the visual cortex.

To what extent does the visual system process color and form separately? Proponents of the segregation view claim that distinct regions of the cortex are dedicated to each of these two dimensions separately. However, evidence is accumulating that color and form processing may, at least to some extent, be intertwined in the brain. In this perspective, we review psychophysical and neurophysiological studies on color and form perception and evaluate their results in light of recent developments in population coding.

Relationship between neural response and adaptation selectivity to form and color: an ERP study.

Adaptation is widely used as a tool for studying selectivity to visual features. In these studies it is usually assumed that the loci of feature selective neural responses and adaptation coincide. We used an adaptation paradigm to investigate the relationship between response and adaptation selectivity in event-related potentials (ERPs). ERPs were evoked by the presentation of colored Glass patterns in a form discrimination task. Response selectivities to form and, to some extent, color of the patterns were reflected in the C1 and N1 ERP components. Adaptation selectivity to color was reflected in N1 and was followed by a late (300-500 ms after stimulus onset) effect of form adaptation. Thus for form, response and adaptation selectivity were manifested in non-overlapping intervals. These results indicate that adaptation and response selectivity can be associated with different processes. Therefore, inferring selectivity from an adaptation paradigm requires analysis of both adaptation and neural response data.

Evidence for color and luminance invariance of global form mechanisms.

Human visual cortex contains mechanisms that pool local orientation information over large areas of visual space to support percepts of global form. Initial studies concluded that some of these mechanisms are cue invariant, in that they yield form percepts irrespective of whether the visual signals contain luminance or chromatic information. Later studies reported that these mechanisms are chromatically selective, albeit with a broad tuning in color space. We used Glass patterns and the phenomenon of adaptation to determine whether Glass pattern perception is mediated by mechanisms that are color and/or luminance selective, or not. Subjects were adapted to either a radial or concentric Glass pattern of a given color or luminance polarity. We measured the effect of adaptation on subsequent detection of Glass patterns with the same or different visual attributes. Our results show that adapting to a concentric or radial pattern significantly elevates threshold for the subsequent detection of patterns of the same form, irrespective of their color or luminance polarity, but that adaptation to luminance leads to higher threshold elevations than adaptation to color. We conclude that Glass pattern perception is mediated by perceptual mechanisms that are color invariant but not totally insensitive to the difference between color and luminance information.