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.
Convolutional Neural Networks (CNNs) are well established models capable of achieving state-of-the-art classification accuracy for various computer vision tasks. However, they are becoming increasingly larger, using millions of parameters, while they are restricted to handling images of fixed size. In this paper, a quantization-based approach, inspired from the well-known Bag-of-Features model, is proposed to overcome these limitations. The proposed approach, called Convolutional BoF (CBoF), uses RBF neurons to quantize the information extracted from the convolutional layers and it is able to natively classify images of various sizes as well as to significantly reduce the number of parameters in the network. In contrast to other global pooling operators and CNN compression techniques the proposed method utilizes a trainable pooling layer that it is end-to-end differentiable, allowing the network to be trained using regular back-propagation and to achieve greater distribution shift invariance than competitive methods. The ability of the proposed method to reduce the parameters of the network and increase the classification accuracy over other state-of-the-art techniques is demonstrated using three image datasets.