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Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large…
Spatial self-attention layers, in the form of Non-Local blocks, introduce long-range dependencies in Convolutional Neural Networks by computing pairwise similarities among all possible positions. Such pairwise functions underpin the…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
We show that passing input points through a simple Fourier feature mapping enables a multilayer perceptron (MLP) to learn high-frequency functions in low-dimensional problem domains. These results shed light on recent advances in computer…
In this effort we propose a novel approach for reconstructing multivariate functions from training data, by identifying both a suitable network architecture and an initialization using polynomial-based approximations. Training deep neural…
Interest point descriptors have fueled progress on almost every problem in computer vision. Recent advances in deep neural networks have enabled task-specific learned descriptors that outperform hand-crafted descriptors on many problems. We…
Deep dictionary learning seeks multiple dictionaries at different image scales to capture complementary coherent characteristics. We propose a method for learning a hierarchy of synthesis dictionaries with an image classification goal. The…
Natural target functions and tasks typically exhibit hierarchical modularity -- they can be broken down into simpler sub-functions that are organized in a hierarchy. Such sub-functions have two important features: they have a distinct set…
Multi-index models - functions which only depend on the covariates through a non-linear transformation of their projection on a subspace - are a useful benchmark for investigating feature learning with neural nets. This paper examines the…
Polynomial functions have plenty of useful analytical properties, but they are rarely used as learning models because their function class is considered to be restricted. This work shows that when trained properly polynomial functions can…
This paper presents a general graph representation learning framework called DeepGL for learning deep node and edge representations from large (attributed) graphs. In particular, DeepGL begins by deriving a set of base features (e.g.,…
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…
This paper presents a deep machine learning architecture, the "polyharmonic cascade" -- a sequence of packages of polyharmonic splines, where each layer is rigorously derived from the theory of random functions and the principles of…
This paper aims at bringing some light and understanding to the field of deep learning for dynamic point cloud processing. Specifically, we focus on the hierarchical features learning aspect, with the ultimate goal of understanding which…
Graph Neural Networks (GNNs) exploit signals from node features and the input graph topology to improve node classification task performance. However, these models tend to perform poorly on heterophilic graphs, where connected nodes have…
We introduce the hierarchical compositional network (HCN), a directed generative model able to discover and disentangle, without supervision, the building blocks of a set of binary images. The building blocks are binary features defined…
We study the computational and sample complexity of learning a target function $f_*:\mathbb{R}^d\to\mathbb{R}$ with additive structure, that is, $f_*(x) = \frac{1}{\sqrt{M}}\sum_{m=1}^M f_m(\langle x, v_m\rangle)$, where…
Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such…
Deep Convolutional Neural Networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful…
Nonsmooth Nonnegative Matrix Factorization (nsNMF) is capable of producing more localized, less overlapped feature representations than other variants of NMF while keeping satisfactory fit to data. However, nsNMF as well as other existing…