Related papers: Mathematical Foundation of Interpretable Equivaria…
The rising adoption of machine learning in high energy physics and lattice field theory necessitates the re-evaluation of common methods that are widely used in computer vision, which, when applied to problems in physics, can lead to…
Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers,…
Generative engines (GEs) are reshaping information access by replacing ranked links with citation-grounded answers, yet current Generative Engine Optimization (GEO) methods optimize each instance in isolation, unable to accumulate or…
Generative Adversarial Networks (GANs) have achieved impressive results for many real-world applications. As an active research topic, many GAN variants have emerged with improvements in sample quality and training stability. However,…
We study spectral graph convolutional neural networks (GCNNs), where filters are defined as continuous functions of the graph shift operator (GSO) through functional calculus. A spectral GCNN is not tailored to one specific graph and can be…
We formalize a novel modeling framework for achieving interpretability in deep learning, anchored in the principle of inference equivariance. While the direct verification of interpretability scales exponentially with the number of…
Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…
As sixth generation (6G) wireless networks evolve, accurate signal-to-interference-noise ratio (SINR) maps are becoming increasingly critical for effective resource management and optimization. However, acquiring such maps at high…
How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…
Understanding how the dynamics in biological and artificial neural networks implement the computations required for a task is a salient open question in machine learning and neuroscience. In particular, computations requiring complex memory…
As Earth science enters the era of big data, artificial intelligence (AI) not only offers great potential for solving geoscience problems, but also plays a critical role in accelerating the understanding of the complex, interactive, and…
This paper introduces Interpretability-Guided Bi-objective Optimization (IGBO), a framework that trains interpretable models by incorporating structured domain knowledge via a bi-objective formulation. IGBO encodes feature importance…
Graph Neural Networks (GNNs) have achieved state-of-the-art performance for link prediction. However, GNNs suffer from poor interpretability, which limits their adoptions in critical scenarios that require knowing why certain links are…
This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source…
Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and transformations of an origin-preserving group $G$, such as reflections and rotations. They rely on…
Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse…
This paper introduces a novel surrogate modeling framework for aerodynamic applications based on Neural Fields. The proposed approach, MARIO (Modulated Aerodynamic Resolution Invariant Operator), addresses non parametric geometric…
Graph neural networks (GNNs) are commonly described as being permutation equivariant with respect to node relabeling in the graph. This symmetry of GNNs is often compared to the translation equivariance of Euclidean convolution neural…
Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…
With the advent of group equivariant convolutions in deep networks literature, spherical CNNs with $\mathsf{SO}(3)$-equivariant layers have been developed to cope with data that are samples of signals on the sphere $S^2$. One can implicitly…