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

Deep learning researchers commonly suggest that converged models are stuck in local minima. More recently, some researchers observed that under reasonable assumptions, the vast majority of critical points are saddle points, not true minima.…

In general, approximating classes of functions defined over high-dimensional input spaces by linear combinations of a fixed set of basis functions or ``features'' is known to be hard. Typically, the worst-case error of the best basis set…

Since the beginning of this decade, CNN has been a very successful tool in the field of Computer Vision tasks.The invention of CNN was inspired from neuroscience and it shares a lot of anatomical similarities with our visual system.Inspired…

Motivated by a wide-spread use of convex optimization techniques, convexity properties of bit error rate of the maximum likelihood detector operating in the AWGN channel are studied for arbitrary constellations and bit mappings, which also…

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases---including common classes of causal or graphical models, as well as time series models---distinct models may…

Neural systems, artificial and biological, show similar representations of inputs when optimized to perform similar tasks. In visual systems optimized for tasks similar to object recognition, we propose that representation similarities…

Many supervised machine learning methods are naturally cast as optimization problems. For prediction models which are linear in their parameters, this often leads to convex problems for which many mathematical guarantees exist. Models which…

Neural circuits exhibit remarkable computational flexibility, enabling adaptive responses to noisy and ever-changing environmental cues. A fundamental question in neuroscience concerns how a wide range of behaviors can emerge from a…

In this paper, we design explicit codes for strong coordination in two-node networks. Specifically, we consider a two-node network in which the action imposed by nature is binary and uniform, and the action to coordinate is obtained via a…

Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that…

Local robustness ensures that a model classifies all inputs within an $\ell_2$-ball consistently, which precludes various forms of adversarial inputs. In this paper, we present a fast procedure for checking local robustness in feed-forward…

Deep convolutional neural networks (CNNs) trained on objects and scenes have shown intriguing ability to predict some response properties of visual cortical neurons. However, the factors and computations that give rise to such ability, and…

In this paper, we investigate the geometric structure of activation spaces of fully connected layers in neural networks and then show applications of this study. We propose an efficient approximation algorithm to characterize the convex…

We prove that free boundary incompressible Euler equations are locally well posed in a class of solutions in which the interfaces can exhibit corners and cusps. Contrary to what happens in all the previously known non-$C^1$ water waves, the…

The LOCAL model is among the main models for studying locality in the framework of distributed network computing. This model is however subject to pertinent criticisms, including the facts that all nodes wake up simultaneously, perform in…

In this paper, we introduce curve-lifted codes over fields of arbitrary characteristic, inspired by Hermitian-lifted codes over $\mathbb{F}_{2^r}$. These codes are designed for locality and availability, and their particular parameters…

Inspired by "predictive coding" - a theory in neuroscience, we develop a bi-directional and dynamic neural network with local recurrent processing, namely predictive coding network (PCN). Unlike feedforward-only convolutional neural…

The goal of this paper is to analyze the geometric properties of deep neural network classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision…

Sparse coding algorithms trained on natural images can accurately predict the features that excite visual cortical neurons, but it is not known whether such codes can be learned using biologically realistic plasticity rules. We have…

Combinatorial optimization problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral…