相关论文: Neural codes, decidability, and a new local obstru…

Our formal understanding of the inductive bias that drives the success of convolutional networks on computer vision tasks is limited. In particular, it is unclear what makes hypotheses spaces born from convolution and pooling operations so…

Model predictive control (MPC) may provide local motion planning for mobile robotic platforms. The challenging aspect is the analytic representation of collision cost for the case when both the obstacle map and robot footprint are…

To evaluate the nature of the neural code in the cerebral cortex, we have used a combination of theory and experiment to assess how information is represented in a realistic cortical population response. We have shown how a sensory stimulus…

It has been shown that the activations invoked by an image within the top layers of a large convolutional neural network provide a high-level descriptor of the visual content of the image. In this paper, we investigate the use of such…

Recent experiments revealed that a certain class of inhibitory neurons in the cerebral cortex make synapses not onto cell bodies but at distal parts of dendrites of the target neurons, mediating highly nonlinear dendritic inhibition. We…

Primary visual cortex (V1) is the first stage of cortical image processing, and a major effort in systems neuroscience is devoted to understanding how it encodes information about visual stimuli. Within V1, many neurons respond selectively…

We show that every convex code realizable by compact sets in the plane admits a realization consisting of polygons, and analogously every open convex code in the plane can be realized by interiors of polygons. We give factorial-type bounds…

Computational intractability has for decades motivated the development of a plethora of methodologies that mainly aimed at a quality-time trade-off. The use of Machine Learning techniques has finally emerged as one of the possible tools to…

Neural networks (NNs) hold great promise for advancing inverse design via topology optimization (TO), yet misconceptions about their application persist. This article focuses on neural topology optimization (neural TO), which leverages NNs…

Soft-thresholding has been widely used in neural networks. Its basic network structure is a two-layer convolution neural network with soft-thresholding. Due to the network's nature of nonlinearity and nonconvexity, the training process…

Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…

Deep Learning is mostly responsible for the surge of interest in Artificial Intelligence in the last decade. So far, deep learning researchers have been particularly successful in the domain of image processing, where Convolutional Neural…

Let $C$ be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps $f\colon C\to\bar{C}$. First we prove that if $f(C)$ is totally bounded, then it has an approximate…

Navigating mobile robots through environments shared with humans is challenging. From the perspective of the robot, humans are dynamic obstacles that must be avoided. These obstacles make the collision-free space nonconvex, which leads to…

A neural code on $ n $ neurons is a collection of subsets of the set $ [n]=\{1,2,\dots,n\} $. In this paper, we study some properties of graphs of neural codes. In particular, we study codeword containment graph (CCG) given by Chan et al.…

The problem of neural coding is to understand how sequences of action potentials (spikes) are related to sensory stimuli, motor outputs, or (ultimately) thoughts and intentions. One clear question is whether the same coding rules are used…

Although it seems counter-intuitive, categorical colours do not exist as external physical entities but are very much the product of our brains. Our cortical machinery segments the world and associate objects to specific colour terms, which…

We study learning problems involving arbitrary classes of functions $F$, distributions $X$ and targets $Y$. Because proper learning procedures, i.e., procedures that are only allowed to select functions in $F$, tend to perform poorly unless…

Error-correcting codes that admit local decoding and correcting algorithms have been the focus of much recent research due to their numerous theoretical and practical applications. An important goal is to obtain the best possible tradeoffs…

Recent work suggests that changing Convolutional Neural Network (CNN) architecture by introducing a bottleneck in the second layer can yield changes in learned function. To understand this relationship fully requires a way of quantitatively…