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Many scientific and geometric problems exhibit general linear symmetries, yet most equivariant neural networks are built for compact groups or simple vector features, limiting their reuse on matrix-valued data such as covariances, inertias,…

This paper studies four Graph Neural Network architectures (GNNs) for a graph classification task on a synthetic dataset created using classic generative models of Network Science. Since the synthetic networks do not contain (node or edge)…

One popular way for lifted inference in probabilistic graphical models is to first merge symmetric states into a single cluster (orbit) and then use these for downstream inference, via variations of orbital MCMC [Niepert, 2012]. These…

We investigate the optimization of neural networks on symmetric data, and compare the strategy of constraining the architecture to be equivariant to that of using data augmentation. Our analysis reveals that that the relative geometry of…

Recognizing precise geometrical configurations of groups of objects is a key capability of human spatial cognition, yet little studied in the deep learning literature so far. In particular, a fundamental problem is how a machine can learn…

This paper discusses and evaluates ideas of data balancing and data augmentation in the context of mathematical objects: an important topic for both the symbolic computation and satisfiability checking communities, when they are making use…

Artificial neural networks (ANNs) are powerful tools capable of approximating any arbitrary mathematical function, but their interpretability remains limited, rendering them as black box models. To address this issue, numerous methods have…

Machine learning techniques offer a precious tool box for use within astronomy to solve problems involving so-called big data. They provide a means to make accurate predictions about a particular system without prior knowledge of the…

Learning to reason about relations and dynamics over multiple interacting objects is a challenging topic in machine learning. The challenges mainly stem from that the interacting systems are exponentially-compositional, symmetrical, and…

In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…

From the perspective of expressive power, this work compares multi-layer Graph Neural Networks (GNNs) with a simplified alternative that we call Graph-Augmented Multi-Layer Perceptrons (GA-MLPs), which first augments node features with…

Underlying data structures, such as symmetries or invariances to transformations, are often exploited to improve the solution of learning tasks. However, embedding these properties in models or learning algorithms can be challenging and…

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…

Graph neural networks (GNNs) have emerged as a powerful tool for nonlinear processing of graph signals, exhibiting success in recommender systems, power outage prediction, and motion planning, among others. GNNs consists of a cascade of…

Steerable convolutional neural networks (SCNNs) enhance task performance by modelling geometric symmetries through equivariance constraints on weights. Yet, unknown or varying symmetries can lead to overconstrained weights and decreased…

Generalized nonlinear programming is considered without any convexity assumption, capturing a variety of problems that include nonsmooth objectives, combinatorial structures, and set-membership nonlinear constraints. We extend the augmented…

In the feature space, the collapse between features invokes critical problems in representation learning by remaining the features undistinguished. Interpolation-based augmentation methods such as mixup have shown their effectiveness in…

We introduce new families of Integral Probability Metrics (IPM) for training Generative Adversarial Networks (GAN). Our IPMs are based on matching statistics of distributions embedded in a finite dimensional feature space. Mean and…

The use of large language models (LLMs) as feature enhancers to optimize node representations, which are then used as inputs for graph neural networks (GNNs), has shown significant potential in graph representation learning. However, the…

For a given linear program (LP) a permutation of its variables that sends feasible points to feasible points and preserves the objective function value of each of its feasible points is a symmetry of the LP. The set of all symmetries of an…