相关论文: From DNF compression to sunflower theorems via reg…

Regularization methods are often employed in deep learning neural networks (DNNs) to prevent overfitting. For penalty based DNN regularization methods, convex penalties are typically considered because of their optimization guarantees.…

Given a family $\mathcal F$ of $k$-element sets, $S_1,\ldots,S_r\in\mathcal F$ form an {\em $r$-sunflower} if $S_i \cap S_j =S_{i'} \cap S_{j'}$ for all $i \neq j$ and $i' \neq j'$. According to a famous conjecture of Erd\H os and Rado…

Counterfactual Explanations are becoming a de-facto standard in post-hoc interpretable machine learning. For a given classifier and an instance classified in an undesired class, its counterfactual explanation corresponds to small…

We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…

Classical neural network approximation results take the form: for every function $f$ and every error tolerance $\epsilon > 0$, one constructs a neural network whose architecture and weights depend on $\epsilon$. This paper introduces a…

Despite the impressive performance of deep neural networks (DNNs), their computational complexity and storage space consumption have led to the concept of network compression. While DNN compression techniques such as pruning and low-rank…

In this paper, we investigate the relative power of several conjectures that attracted recently lot of interest. We establish a connection between the Network Coding Conjecture (NCC) of Li and Li and several data structure like problems…

Tensor decomposition is one of the fundamental technique for model compression of deep convolution neural networks owing to its ability to reveal the latent relations among complex structures. However, most existing methods compress the…

Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…

Deep neural networks (DNNs) have been widely used in many artificial intelligence (AI) tasks. However, deploying them brings significant challenges due to the huge cost of memory, energy, and computation. To address these challenges,…

In recent years numerous methods have been developed to formally verify the robustness of deep neural networks (DNNs). Though the proposed techniques are effective in providing mathematical guarantees about the DNNs behavior, it is not…

Knuth (1990) introduced the class of nested formulas and showed that their satisfiability can be decided in polynomial time. We show that, parameterized by the size of a smallest strong backdoor set to the target class of nested formulas,…

Recurrent neural networks (RNNs) are important class of architectures among neural networks useful for language modeling and sequential prediction. However, optimizing RNNs is known to be harder compared to feed-forward neural networks. A…

In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…

Entropic regularization provides a generalization of the original optimal transport problem. It introduces a penalty term defined by the Kullback-Leibler divergence, making the problem more tractable via the celebrated Sinkhorn algorithm.…

Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory,…

A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change…

The big breakthrough on the ImageNet challenge in 2012 was partially due to the `dropout' technique used to avoid overfitting. Here, we introduce a new approach called `Spectral Dropout' to improve the generalization ability of deep neural…

The challenge of speeding up deep learning models during the deployment phase has been a large, expensive bottleneck in the modern tech industry. In this paper, we examine the use of both regularization and pruning for reduced computational…

The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…