相关论文: Convexity of Neural Codes with Four Maximal Codewo…

Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum…

Convolutional neural networks (CNNs) have had great success in many real-world applications and have also been used to model visual processing in the brain. However, these networks are quite brittle - small changes in the input image can…

We are interested in assigning a pre-specified number of nodes as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. This problem arises in several applications including control of…

When neural networks are trained to classify a dataset, one finds a set of weights from which the network produces a label for each data point. We study the algorithmic complexity of finding a collision in a single-layer neural net, where a…

It is commonly recognized that the expressiveness of deep neural networks is contingent upon a range of factors, encompassing their depth, width, and other relevant considerations. Currently, the practical performance of the majority of…

The Local-to-Global-Principle used in the proof of convexity theorems for momentum maps has been extracted as a statement of pure topology enriched with a structure of convexity. We extend this principle to not necessarily closed maps…

Finding point configurations, that yield the maximum polarization (Chebyshev constant) is gaining interest in the field of geometric optimization. In the present article, we study the problem of unconstrained maximum polarization on compact…

Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…

The central problem with understanding brain and mind is the neural code issue: understanding the matter of our brain as basis for the phenomena of our mind. The richness with which our mind represents our environment, the parsimony of…

Neural networks can be fragile to input noise and adversarial attacks. In this work, we consider Convolutional Neural Ordinary Differential Equations (NODEs), a family of continuous-depth neural networks represented by dynamical systems,…

Convolutional Neural Networks (CNNs) are the state of the art solution for many computer vision problems, and many researchers have explored optimized implementations. Most implementations heuristically block the computation to deal with…

Many neural network (NN) verification systems represent the network's input-output relation as a constraint program. Sound and complete, representations involve integer constraints, for simulating the activations. Recent works convexly…

Understanding what individual neurons encode is a core question in neuroscience. In primary visual cortex (V1), mathematical models (e.g., Gabor functions) capture neural selectivity, but no comparable framework exists for higher areas. We…

Incorporating geometric inductive biases into models can aid interpretability and generalization, but encoding to a specific geometric structure can be challenging due to the imposed topological constraints. In this paper, we theoretically…

Neurons in the visual cortex are correlated in their variability. The presence of correlation impacts cortical processing because noise cannot be averaged out over many neurons. In an effort to understand the functional purpose of…

Convex functions and their gradients play a critical role in mathematical imaging, from proximal optimization to Optimal Transport. The successes of deep learning has led many to use learning-based methods, where fixed functions or…

The cardinality constrained optimization problem (CCOP) is an optimization problem where the maximum number of nonzero components of any feasible point is bounded. In this paper, we consider CCOP as a mathematical program with disjunctive…

The metric capacitated facility location is a well-studied problem for which, while constant factor approximations are known, no efficient relaxation with constant integrality gap is known. The question whether there is such a relaxation is…

Conditional text generation often requires lexical constraints, i.e., which words should or shouldn't be included in the output text. While the dominant recipe for conditional text generation has been large-scale pretrained language models…

Convex codes were recently introduced as models for neural codes in the brain. Any convex code $\C$ has an associated minimal embedding dimension $d(\C)$, which is the minimal Euclidean space dimension such that the code can be realized by…