Related papers: Deep Sets

We use deep learning to model interactions across two or more sets of objects, such as user-movie ratings, protein-drug bindings, or ternary user-item-tag interactions. The canonical representation of such interactions is a matrix (or 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…

The paper aims to investigate relevant computational issues of deep neural network architectures with an eye to the interaction between the optimization algorithm and the classification performance. In particular, we aim to analyze the…

It is often said that a deep learning model is "invariant" to some specific type of transformation. However, what is meant by this statement strongly depends on the context in which it is made. In this paper we explore the nature of…

A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…

Learning generative models for graph-structured data is challenging because graphs are discrete, combinatorial, and the underlying data distribution is invariant to the ordering of nodes. However, most of the existing generative models for…

Using deep neural networks that are either invariant or equivariant to permutations in order to learn functions on unordered sets has become prevalent. The most popular, basic models are DeepSets [Zaheer et al. 2017] and PointNet [Qi et al.…

We address the challenging problem of deep representation learning--the efficient adaption of a pre-trained deep network to different tasks. Specifically, we propose to explore gradient-based features. These features are gradients of the…

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nevertheless, the majority of these studies examine how well deep…

We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…

Deep neural networks (DNNs) achieve remarkable performance on a wide range of tasks, yet their mathematical analysis remains fragmented: stability and generalization are typically studied in disparate frameworks and on a case-by-case basis.…

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…

The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…

Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

Unordered feature sets are a nonstandard data structure that traditional neural networks are incapable of addressing in a principled manner. Providing a concatenation of features in an arbitrary order may lead to the learning of spurious…

Ou et al. (2022) introduce the problem of learning set functions from data generated by a so-called optimal subset oracle. Their approach approximates the underlying utility function with an energy-based model, whose parameters are…

This work studies the design of neural networks that can process the weights or gradients of other neural networks, which we refer to as neural functional networks (NFNs). Despite a wide range of potential applications, including learned…

Incorporating permutation equivariance into neural networks has proven to be useful in ensuring that models respect symmetries that exist in data. Symmetric tensors, which naturally appear in statistics, machine learning, and graph theory,…