Dynamical neural networks: Modeling low-level vision at short latencies

Abstract

Our goal is to understand the dynamics of neural computations in low-level vision. We study how the substrate of this system, that is local biochemical neural processes, could combine to give rise to an efficient and global perception. We will study these neural computations at different scales from the single-cell to the whole visual system to infer generic aspects of the underlying neural code which may help to understand this cognitive ability. In fact, the architecture of cortical areas, such as the Primary Visual Cortex (V1), is massively parallel and we will focus on cortical columns as generic adaptive micro-circuits. To stress on the dynamical aspect of the processing, we will also focus on the transient response, that is during the first milliseconds after the presentation of a stimulus. In a generic model of a visual area, we propose to study the neural code as implementing visual pattern matching, that is as efficiently inverting a known model of image synthesis. A possible solution offered by the architecture of the visual pathways could be to represent at first on the surface of the cortical area how well the prototypical visual features are matched by a combination of inferential mechanisms as ideal observers. We studied the efficiency of this representation by rating the statistics of the output using natural scenes, that is scenes occurring frequently. We show that this may be finally used to provide a behavioral output such as an eye movement. However, constraints specific to the visual system imply that the set of prototypical features is not independent and that the cortical columns should communicate to produce an efficient, sparse solution. We will present efficient algorithms and representations based on the event-based nature of neural computations. By explicitely defining this efficiency, we propose then a simple implementation of Sparse Spike Coding using greedy inference mechanisms but also how the system may adapt in a unsupervised fashion. These computations may be implemented in simple models of neural networks by explicitly setting the lateral connectivity between populations of columns. Using natural scenes, this algorithm provides a model of V1 which exhibit prototypical properties of neural activities in that area. We show simple applications in the field of image processing as a quantitative method to evaluate these different cortical models.

Role of Homeostasis in Learning Sparse Representations

“…This also suggests the extension to representations with some built-in invariances, such as translation and scaling. A gaussian pyramid, for instance, provides a multiscale representation where the set of learned filters would become a dictionary of mother wavelets (Perrinet, 2007). Such an extension leads to a fundamental question: How does representation efficiency evolve with the number M of elements in the dictionary, that is, with the complexity of the representation?…”

“…An effective decoding algorithm is to estimate the analog values of the sparse vector (and thus reconstruct the signal) from the order of neurons' activation in the sparse vector (Perrinet, 2007). In fact, knowing the address of the fiber i 0 corresponding to the maximal value, we may infer that it has been produced by an analog value on the emitter side in the highest quantile of the probability distribution function of a i 0 .…”

Sparse spike coding : applications of neuroscience to the processing of natural images

“…In fact, we restricted us ourselves here to static flashed images, but is easily extendable to causal filters (see Ch. 3.4.1 in (Perrinet, 2007)). It however raises the unsolved problem of a dynamical compromise between precision and rapidity of the code which is still unanswered.…”

“…(Right) The resulting COMP solution gives a similar result than MP in terms of residual energy as a function of pure L 0 sparseness (see inset). In fact, in MP, by taking the maximum absolute, and since the decrease of energy is proportional to the square of the coefficient (see Chapter 3.1.2 of (Perrinet, 2007)) one ensures that the decrease of MSE per coefficient is optimal for MP. These are both better for that purpose than conjugate gradient.…”

“…We will then in a third section pro-pose that this linear information may be optimally coded by a spike list if we apply a point non-linear operation. At least, we will define an improvment over Matching Pursuit (Mallat and Zhang, 1993) by optimizing the efficiency of the ArgMax operator and which finally defines Sparse Spike Coding (Perrinet, 2004(Perrinet, , 2007Perrinet et al, 2002).…”