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Accurate modeling and explaining geospatial tabular data (GTD) are critical for understanding geospatial phenomena and their underlying processes. Recent work has proposed a novel transformer-based deep learning model named GeoAggregator…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
A compatible associative algebra is a vector space equipped with two associative multiplication structures that interact in a certain natural way. This article presents the classification of these algebras with dimension less than four, as…
Performing link prediction using knowledge graph embedding models has become a popular approach for knowledge graph completion. Such models employ a transformation function that maps nodes via edges into a vector space in order to measure…
Many complex engineering systems can be represented in a topological form, such as graphs. This paper utilizes a machine learning technique called Geometric Deep Learning (GDL) to aid designers with challenging, graph-centric design…
Existing efforts are dedicated to designing many topologies and graph-aware strategies for the graph Transformer, which greatly improve the model's representation capabilities. However, manually determining the suitable Transformer…
Topological integral transforms have found many applications in shape analysis, from prediction of clinical outcomes in brain cancer to analysis of barley seeds. Using Euler characteristic as a measure, these objects record rich geometric…
Clifford Group Equivariant Neural Networks (CGENNs) leverage Clifford algebras and multivectors as an alternative approach to incorporating group equivariance to ensure symmetry constraints in neural representations. In principle, this…
While numerous approaches have been developed to embed graphs into either Euclidean or hyperbolic spaces, they do not fully utilize the information available in graphs, or lack the flexibility to model intrinsic complex graph geometry. To…
The art of quantum algorithm design is highly nontrivial. Grover's search algorithm constitutes a masterpiece of quantum computational software. In this article, we use methods of geometric algebra (GA) and information geometry (IG) to…
We present GEOPARD, a transformer-based architecture for predicting articulation from a single static snapshot of a 3D shape. The key idea of our method is a pretraining strategy that allows our transformer to learn plausible candidate…
There is an increasing interest in the application of deep learning architectures to tabular data. One of the state-of-the-art solutions is TabTransformer which incorporates an attention mechanism to better track relationships between…
The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…
The Efficient Adaptive Transformer (EAT) framework unifies three adaptive efficiency techniques - progressive token pruning, sparse attention, and dynamic early exiting - into a single, reproducible architecture for input-adaptive…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…
This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…
Circuit representation learning has shown promising results in advancing the field of Electronic Design Automation (EDA). Existing models, such as DeepGate Family, primarily utilize Graph Neural Networks (GNNs) to encode circuit netlists…
The Transformer architecture has gained growing attention in graph representation learning recently, as it naturally overcomes several limitations of graph neural networks (GNNs) by avoiding their strict structural inductive biases and…
Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely…