Related papers: Bounding Embeddings of VC Classes into Maximum Cla…
Embedding the nodes of a large network into an Euclidean space is a common objective in modern machine learning, with a variety of tools available. These embeddings can then be used as features for tasks such as community detection/node…
We propose a way to learn visual features that are compatible with previously computed ones even when they have different dimensions and are learned via different neural network architectures and loss functions. Compatible means that, if…
The well-known Sauer lemma states that a family $\mathcal{F}\subseteq 2^{[n]}$ of VC-dimension at most $d$ has size at most $\sum_{i=0}^d\binom{n}{i}$. We obtain both random and explicit constructions to prove that the corresponding…
Source code representations are key in applying machine learning techniques for processing and analyzing programs. A popular approach in representing source code is neural source code embeddings that represents programs with…
Numerous embedding models have been recently explored to incorporate semantic knowledge into visual recognition. Existing methods typically focus on minimizing the distance between the corresponding images and texts in the embedding space…
Image clustering is one of the most important computer vision applications, which has been extensively studied in literature. However, current clustering methods mostly suffer from lack of efficiency and scalability when dealing with…
Learning a powerful representation from point clouds is a fundamental and challenging problem in the field of computer vision. Different from images where RGB pixels are stored in the regular grid, for point clouds, the underlying semantic…
The VC-dimension of a family of sets is a measure of its combinatorial complexity used in machine learning theory, computational geometry, and even model theory. Computing the VC-dimension of the $k$-fold union of geometric set systems has…
We say that a family ${x_i|i\in[m]}$ of vectors in a Banach space $X$ satisfies the $k$-collapsing condition if $|\sum_{i\in I}x_i|\leq 1$ for all $k$-element subsets $I\subseteq{1,2,...,m}$. Let $C(k,d)$ denote the maximum cardinality of a…
Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…
Graph embedding is a transformation of nodes of a graph into a set of vectors. A~good embedding should capture the graph topology, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes. If these…
The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In…
In this paper, we propose a new deep neural network classifier that simultaneously maximizes the inter-class separation and minimizes the intra-class variation by using the polyhedral conic classification function. The proposed method has…
Feature selection removes redundant features to enhanc performance and computational efficiency in downstream tasks. Existing works often struggle to capture complex feature interactions and adapt to diverse scenarios. Recent advances in…
Given a hypothesis space, the large volume principle by Vladimir Vapnik prioritizes equivalence classes according to their volume in the hypothesis space. The volume approximation has hitherto been successfully applied to binary learning…
Neural networks are widely used as a model for classification in a large variety of tasks. Typically, a learnable transformation (i.e. the classifier) is placed at the end of such models returning a value for each class used for…
Large vision-language contrastive models (VLCMs), such as CLIP, have become foundational, demonstrating remarkable success across a variety of downstream tasks. Despite their advantages, these models, akin to other foundational systems,…
Overparameterized machine learning (ML) methods such as neural networks may be prohibitively resource intensive for devices with limited computational capabilities. Hyperdimensional computing (HDC) is an emerging resource efficient and…
The field of deep visual recognition is undergoing a paradigm shift toward universal representations. The Platonic Representation Hypothesis suggests that diverse architectures trained on massive datasets are converging toward a shared,…
Let U be a monster model and let D be a subset of U. Let (U,D) denote theexpansion of U with a new predicate for D. Write e(D) for the collection of all subsets C of U such that (U,C) is elementary equivalent to (U,D). We prove that if e(D)…