Related papers: Deep Sets
Artificial intelligence, particularly the subfield of machine learning, has seen a paradigm shift towards data-driven models that learn from and adapt to data. This has resulted in unprecedented advancements in various domains such as…
We introduce a novel deep learning algorithm for computing convex conjugates of differentiable convex functions, a fundamental operation in convex analysis with various applications in different fields such as optimization, control theory,…
Deep neural networks have proven to be quite effective in a wide variety of machine learning tasks, ranging from improved speech recognition systems to advancing the development of autonomous vehicles. However, despite their superior…
Modern machine learning algorithms, especially deep learning based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian…
Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal…
Domain generalization aims at training machine learning models to perform robustly across different and unseen domains. Several recent methods use multiple datasets to train models to extract domain-invariant features, hoping to generalize…
The paper discusses the limitations of deep learning models in identifying and utilizing features that remain invariant under a bijective transformation on the data entries, which we refer to as combinatorial patterns. We argue that the…
Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional…
We define the notion of an invariant function on a cluster ensemble with respect to an action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type…
Deep learning models have seen significant successes in numerous applications, but their inner workings remain elusive. The purpose of this work is to quantify the learning process of deep neural networks through the lens of a novel…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Most set prediction models in deep learning use set-equivariant operations, but they actually operate on multisets. We show that set-equivariant functions cannot represent certain functions on multisets, so we introduce the more appropriate…
Neural networks are powerful predictive models, but they provide little insight into the nature of relationships between predictors and outcomes. Although numerous methods have been proposed to quantify the relative contributions of input…
The advent of big data has vast potential for discovery in natural phenomena ranging from climate science to medicine, but overwhelming complexity stymies insight. Existing theory is often not able to succinctly describe salient phenomena,…
In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…
Sorting is a fundamental operation of all computer systems, having been a long-standing significant research topic. Beyond the problem formulation of traditional sorting algorithms, we consider sorting problems for more abstract yet…
Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…
Neural networks that satisfy invariance with respect to input permutations have been widely studied in machine learning literature. However, in many applications, only a subset of all input permutations is of interest. For heterogeneous…
Next generation deep neural networks for classification hosted on embedded platforms will rely on fast, efficient, and accurate learning algorithms. Initialization of weights in learning networks has a great impact on the classification…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…