Ilias Rentzeperis

The work of Hubel and Wiesel has been instrumental in shaping our understanding of V1, leading to modeling neural responses as cascades of linear and nonlinear processes in what is known as the “standard model” of vision. Under this formulation, however, some dendritic properties cannot be represented in a practical manner, while evidence from both experimental and theoretical work indicates that dendritic processes are an indispensable element of key neural behaviors. As a result, current V1 models fail to explain neural responses in a number of scenarios. In this work, we propose an implicit model for V1 that considers nonlinear dendritic integration and backpropagation of action potentials from the soma to the dendrites. Our model can be viewed as an extension of the standard model that minimizes an energy function, allows for a better conceptual understanding of neural processes, and explains several neurophysiological phenomena that have challenged classical approaches. Significance statement: Most current approaches for modeling neural activity in V1 are data driven; their main goal is to obtain better predictions and are formally equivalent to a deep neural network (DNN). Aside from behaving like a black-box these models ignore a key property of biological neurons, namely, that they integrate their input via their dendrites in a highly nonlinear fashion that includes backpropagating action potentials (bAPs). Here, we propose a model based on dendritic mechanisms, which facilitates conceptual analysis and can explain a number of physiological results that challenge standard approaches. Our results suggest that the proposed model may provide a better understanding of neural processes and be considered as a contribution in the search of a consensus model for 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 theℓ₁norm 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 theℓ₁norm is highly suboptimal compared to other functions suited to approximatingℓ_pwith 0 ≤p< 1 (including recently proposed continuous exact relaxations), in terms of performance. We show thatℓ₁sparsity 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 theℓ₁norm as a penalty requires a dictionary of ten times more units compared to the proposed approach, where a non-convex continuous relaxation of theℓ₀pseudo-norm is used, to reconstruct the external stimulus equally well. At a fixed sparsity level, bothℓ₀- andℓ₁-based regularization develop units with receptive field (RF) shapes similar to biological neurons in V1 (and a subset of neurons in V2), butℓ₀-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 theℓ₀pseudo-norm rather than theℓ₁one, and suggests a similar mode of operation for the sensory cortex in general.

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.

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.

Activity dependent plasticity is the brain’s mechanism for reshaping neural connections. Representing activity by graph diffusion, we model plasticity as adaptive rewiring. The rewiring involves adding shortcut connections where diffusion on the graph is intensive while pruning underused ones. This process robustly steers initially random networks to high-levels of structural complexity reflecting the global characteristics of brain anatomy: modular or centralized small world topologies, depending on overall diffusion rate. We extend this result, known from binary networks, to weighted ones in order to evaluate the flexibility of their evolved states. Both with normally- and lognormally-distributed weights, networks evolve modular or centralized topologies depending on a single control parameter, the diffusion rate, representing a global homeostatic or normalizing regulation mechanism. Once settled, normally weighted networks lock into their topologies, whereas lognormal ones allow flexible switching between them, tuned by the diffusion rate. For a small range of diffusion rates networks evolve the largest variety of topologies: modular, centralized or intermediate. Weighted networks in the transition range show topological but not weighted rich-club structure matching empirical data in the human brain. The simulation results allow us to propose adaptive rewiring based on diffusion as a parsimonious model for activity-dependent reshaping of the brain’s connections. Author Summary: The brain is adapting continuously to a changing environment by strengthening or adding new connections and weakening or pruning existing ones. This forms the basis of flexible and adaptable behaviors. On the other hand, uncontrolled changes to the wiring can compromise the stability of the brain as an adaptive system. We used an abstract model to investigate how this basic problem could be addressed from a graph-theoretical perspective. The model adaptively rewires an initially randomly connected network into a more structured one with properties akin to the human brain, such as small worldness and rich club structure. The adaptive changes made to the network follow the heat diffusion, an abstract representation of brain functional connectivity. Moreover, depending on a parameter of the model, the heat diffusion rate, either modular or centralized connectivity patterns emerge, both found across different regions of the brain. For a narrow range of intermediate heat diffusion rates, networks develop a full range from modular to centralized connectivity patterns. Once settled into a connectivity pattern networks with normally distributed weights lock into that state, whereas networks with lognormally distributed weights show greater flexibility to adjust, while maintaining their small-world and rich club properties. Networks with lognormally distributed weights, therefore, show the combination of stability and flexibility needed to address the fundamental requirements of adaptive networks.

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.

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.