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.
Our work takes inspiration from convolutional kernel networks (CKN) @cite_15 @cite_19 . CKNs replace the matrix-vector multiplications used in convolutional networks by kernel feature maps and are used for supervised classification. Their feature maps use Nystr "om-like approximations. CKNs are also related to radial basis function networks @cite_31 and self-organizing maps @cite_27 .
@cite_19 @cite_15 @cite_31 @cite_27
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In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with supervision. We proceed by first proposing improvements of the recently-introduced convolutional kernel networks (CKNs) in the context of unsupervised learning; then, we derive backpropagation rules to take advantage of labeled training data. The resulting model is a new type of convolutional neural network, where optimizing the filters at each layer is equivalent to learning a linear subspace in a reproducing kernel Hilbert space (RKHS). We show that our method achieves reasonably competitive performance for image classification on some standard " deep learning " datasets such as CIFAR-10 and SVHN, and also for image super-resolution, demonstrating the applicability of our approach to a large variety of image-related tasks. Convolutional Neural Networks (CNNs) with Bilinear Pooling, initially in their full form and later using compact representations, have yielded impressive performance gains on a wide range of visual tasks, including fine-grained visual categorization, visual question answering, face recognition, and description of texture and style. The key to their success lies in the spatially invariant modeling of pairwise (2nd order) feature interactions. In this work, we propose a general pooling framework that captures higher order interactions of features in the form of kernels. We demonstrate how to approximate kernels such as Gaussian RBF up to a given order using compact explicit feature maps in a parameter-free manner. Combined with CNNs, the composition of the kernel can be learned from data in an end-to-end fashion via error back-propagation. The proposed kernel pooling scheme is evaluated in terms of both kernel approximation error and visual recognition accuracy. Experimental evaluations demonstrate state-of-the-art performance on commonly used fine-grained recognition datasets. Convolutional neural networks (CNNs) are able to model local stationary structures in natural images in a multi-scale fashion, when learning all model parameters with supervision. While excellent performance was achieved for image classification when large amounts of labeled visual data are available, their success for unsupervised tasks such as image retrieval has been moderate so far.Our paper focuses on this latter setting and explores several methods for learning patch descriptors without supervision with application to matching and instance-level retrieval. To that effect, we propose a new family of patch representations, based on the recently introduced convolutional kernel networks. We show that our descriptor, named Patch-CKN, performs better than SIFT as well as other convolutional networks learned by artificially introducing supervision and is significantly faster to train. To demonstrate its effectiveness, we perform an extensive evaluation on standard benchmarks for patch and image retrieval where we obtain state-of-the-art results. We also introduce a new dataset called RomePatches, which allows to simultaneously study descriptor performance for patch and image retrieval. Convolutional neural networks have shown great success on feature extraction from raw input data such as images. Although convolutional neural networks are invariant to translations on the inputs, they are not invariant to other transformations, including rotation and flip. Recent attempts have been made to incorporate more invariance in image recognition applications, but they are not applicable to dense prediction tasks, such as image segmentation. In this paper, we propose a set of methods based on kernel rotation and flip to enable rotation and flip invariance in convolutional neural networks. The kernel rotation can be achieved on kernels of 3 × 3, while kernel flip can be applied on kernels of any size. By rotating in eight or four angles, the convolutional layers could produce the corresponding number of feature maps based on eight or four different kernels. By using flip, the convolution layer can produce three feature maps. By combining produced feature maps using maxout, the resource requirement could be significantly reduced while still retain the invariance properties. Experimental results demonstrate that the proposed methods can achieve various invariance at reasonable resource requirements in terms of both memory and time.