Neurons in the input layer of primary visual cortex in primates develop edge-like receptive fields. One approach to understanding the emergence of this response is to state that neural activity has to efficiently represent sensory data with respect t
o the statistics of natural scenes. Furthermore, it is believed that such an efficient coding is achieved using a competition across neurons so as to generate a sparse representation, that is, where a relatively small number of neurons are simultaneously active. Indeed, different models of sparse coding, coupled with Hebbian learning and homeostasis, have been proposed that successfully match the observed emergent response. However, the specific role of homeostasis in learning such sparse representations is still largely unknown. By quantitatively assessing the efficiency of the neural representation during learning, we derive a cooperative homeostasis mechanism that optimally tunes the competition between neurons within the sparse coding algorithm. We apply this homeostasis while learning small patches taken from natural images and compare its efficiency with state-of-the-art algorithms. Results show that while different sparse coding algorithms give similar coding results, the homeostasis provides an optimal balance for the representation of natural images within the population of neurons. Competition in sparse coding is optimized when it is fair. By contributing to optimizing statistical competition across neurons, homeostasis is crucial in providing a more efficient solution to the emergence of independent components.
If modern computers are sometimes superior to humans in some specialized tasks such as playing chess or browsing a large database, they cant beat the efficiency of biological vision for such simple tasks as recognizing and following an object in a co
mplex cluttered background. We present in this paper our attempt at outlining the dynamical, parallel and event-based representation for vision in the architecture of the central nervous system. We will illustrate this on static natural images by showing that in a signal matching framework, a L/LN (linear/non-linear) cascade may efficiently transform a sensory signal into a neural spiking signal and we will apply this framework to a model retina. However, this code gets redundant when using an over-complete basis as is necessary for modeling the primary visual cortex: we therefore optimize the efficiency cost by increasing the sparseness of the code. This is implemented by propagating and canceling redundant information using lateral interactions. We compare the efficiency of this representation in terms of compression as the reconstruction quality as a function of the coding length. This will correspond to a modification of the Matching Pursuit algorithm where the ArgMax function is optimized for competition, or Competition Optimized Matching Pursuit (COMP). We will in particular focus on bridging neuroscience and image processing and on the advantages of such an interdisciplinary approach.
