相关论文: Symmetry-Preserving Paths in Integrated Gradients

Learning transformation invariant representations of visual data is an important problem in computer vision. Deep convolutional networks have demonstrated remarkable results for image and video classification tasks. However, they have…

These notes follow my articles [1, 6], and give some new important details. We propose here a new combinatorial method of encoding of measure spaces with measure preserving transformations, (or groups of transformations) in order to give…

Deep neural networks achieve state-of-the-art and sometimes super-human performance across various domains. However, when learning tasks sequentially, the networks easily forget the knowledge of previous tasks, known as "catastrophic…

The seminal book of Gusfield and Irving [GI89] provides a compact and algorithmically useful way to represent the collection of stable matches corresponding to a given set of preferences. In this paper, we reinterpret the main results of…

Let $G$ be a graph of order $n$. The path decomposition of $G$ is a set of disjoint paths, say $\mathcal{P}$, which cover all vertices of $G$. If all paths are induced paths in $G$, then we say $\mathcal{P}$ is an induced path decomposition…

Diffusion has shown great success in improving accuracy of unsupervised image retrieval systems by utilizing high-order structures of image manifold. However, existing diffusion methods suffer from three major limitations: 1) they usually…

We give a formula for the v-number of a graded ideal that can be used to compute this number. Then we show that for the edge ideal $I(G)$ of a graph $G$ the induced matching number of $G$ is an upper bound for the v-number of $I(G)$ when…

Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…

Neural network parameterizations exhibit inherent symmetries that yield multiple equivalent minima within the loss landscape. Scale Graph Metanetworks (ScaleGMNs) explicitly leverage these symmetries by proposing an architecture equivariant…

As deep learning models and datasets rapidly scale up, network training is extremely time-consuming and resource-costly. Instead of training on the entire dataset, learning with a small synthetic dataset becomes an efficient solution.…

Although theoretical properties such as expressive power and over-smoothing of graph neural networks (GNN) have been extensively studied recently, its convergence property is a relatively new direction. In this paper, we investigate the…

Stochastic gradient (SG) methods are fundamental to system identification and machine learning, enabling online parameter estimation in large-scale and streaming-data settings. As a classical identification method, the SG algorithm has been…

We propose a novel iterative method to adapt a a graph to d-dimensional image data. The method drives the nodes of the graph towards image features. The adaptation process naturally lends itself to a measure of feature saliency which can…

Gradient dynamics play a central role in determining the stability and generalization of deep neural networks. In this work, we provide an empirical analysis of how variance and standard deviation of gradients evolve during training,…

This work explores the relationship between sensing accuracy and precoding coefficients for edge artificial intelligence (AI) inference in integrated sensing, communication and computation (ISCC) networks. We start by constructing a system…

Learning to generate neural network parameters conditioned on task descriptions and architecture specifications is pivotal for advancing model adaptability and transfer learning. Existing methods especially those based on diffusion models…

With the vigorous development of artificial intelligence technology, various engineering technology applications have been implemented one after another. The gradient descent method plays an important role in solving various optimization…

This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…

Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of…

The independence equivalence class of a graph $G$ is the set of graphs that have the same independence polynomial as $G$. A graph whose independence equivalence class contains only itself, up to isomorphism, is independence unique. Beaton,…