We posit that hippocampal place cells encode information about future locations under a transition distribution observed as an agent explores a given (physical or conceptual) space. The encoding of information about the current location, usually associated with place cells, then emerges as a necessary step to achieve this broader goal. We formally derive a biologically-inspired neural network from Nystrom kernel approximations and empirically demonstrate that the network successfully approximates transition distributions. The proposed network yields representations that, just like place cells, soft-tile the input space with highly sparse and localized receptive fields. Additionally, we show that the proposed computational motif can be extended to handle supervised problems, creating class-specific place cells while exhibiting low sample complexity.
@cite_25 show that localized receptive fields emerge in similarity-preserving networks of rectifying neurons. These networks learn to represent low-dimensional manifolds populated by sensory inputs and yield localized receptive fields tiling these manifolds.
@cite_25
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Many neurons in the brain, such as place cells in the rodent hippocampus, have localized receptive fields, i.e. they respond to a small neighborhood of stimulus space. What is the functional significance of such representations and how can they arise? Here, we propose that localized receptive fields emerge in similarity-preserving networks of rectifying neurons that learn low-dimensional manifolds populated by sensory inputs. Numerical simulations of such networks on standard datasets yield manifold-tiling localized receptive fields. More generally, we show analytically that, for data lying on symmetric manifolds, optimal solutions of objectives, from which similarity-preserving networks are derived, have localized receptive fields. Therefore, nonnegative similarity-preserving mapping (NSM) implemented by neural networks can model representations of continuous manifolds in the brain. THE receptive fields of simple cells in mammalian primary visual cortex can be characterized as being spatially localized, oriented1–4 and bandpass (selective to structure at different spatial scales), comparable to the basis functions of wavelet transforms5,6. One approach to understanding such response properties of visual neurons has been to consider their relationship to the statistical structure of natural images in terms of efficient coding7–12. Along these lines, a number of studies have attempted to train unsupervised learning algorithms on natural images in the hope of developing receptive fields with similar properties13–18, but none has succeeded in producing a full set that spans the image space and contains all three of the above properties. Here we investigate the proposal8,12 that a coding strategy that maximizes sparseness is sufficient to account for these properties. We show that a learning algorithm that attempts to find sparse linear codes for natural scenes will develop a complete family of localized, oriented, bandpass receptive fields, similar to those found in the primary visual cortex. The resulting sparse image code provides a more efficient representation for later stages of processing because it possesses a higher degree of statistical independence among its outputs. The spatial receptive fields of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive field properties may be accounted for in terms of a strategy for producing a sparse distribution of output activity in response to natural images. Here, in addition to describing this work in a more expansive fashion, we examine the neurobiological implications of sparse coding. Of particular interest is the case when the code is overcomplete--i.e., when the number of code elements is greater than the effective dimensionality of the input space. Because the basis functions are non-orthogonal and not linearly independent of each other, sparsifying the code will recruit only those basis functions necessary for representing a given input, and so the input-output function will deviate from being purely linear. These deviations from linearity provide a potential explanation for the weak forms of non-linearity observed in the response properties of cortical simple cells, and they further make predictions about the expected interactions among units in response to naturalistic stimuli. © 1997 Elsevier Science Ltd A receptive field is defined as the region in an input image space that an output image pixel is looking at. Thus, the receptive field size influences the learning of deep convolution neural networks. Especially, in single image dehazing problems, larger receptive fields often show more effective dehazying by considering the brightness and color of the entire input hazy image without additional information (e.g. scene transmission map, depth map, and atmospheric light). The conventional generative adversarial network (GAN) with small-sized receptive fields cannot be effective for hazy images of ultra-high resolution. Thus, we proposed a fully end-to-end learning based conditional boundary equilibrium generative adversarial network (BEGAN) with the receptive field sizes enlarged for single image dehazing. In our conditional BEGAN, its discriminator is trained ultra-high resolution conditioned on downscale input hazy images, so that the haze can effectively be removed with the original structures of images stably preserved. From this, we can obtain the high PSNR performance (Track 1 - Indoor: top 4th-ranked) and fast computation speeds. Also, we combine an L1 loss, a perceptual loss and a GAN loss as the generator's loss of the proposed conditional BEGAN, which allows to obtain stable dehazing results for various hazy images.