Related papers: Tensor Computation of Euler Characteristic Functio…
We study $\mathbb{S}_n$-equivariant weight-graded and topological Euler characteristics of the universal Picard stack $\mathrm{Pic}_{g, n}^d \to \mathcal{M}_{g, n}$ of degree-$d$ line bundles over $\mathcal{M}_{g, n}$. We prove that in the…
Continuous Wavelet Transform (CWT) is frequently used for waveform analysis. For example, in the field of neuroscience research, CWT is performed to analyze electroencephalograms (EEG) and calculate the index of brain activity. Recent…
The Euler tour technique is a classical tool for designing parallel graph algorithms, originally proposed for the PRAM model. We ask whether it can be adapted to run efficiently on GPU. We focus on two established applications of the…
We present e3nn, a generalized framework for creating E(3) equivariant trainable functions, also known as Euclidean neural networks. e3nn naturally operates on geometry and geometric tensors that describe systems in 3D and transform…
This paper explains how to use quantum field theory techniques to find formal power series that encode the virtual Euler characteristics of $\mathrm{Out}(F_n)$ and related graph complexes. Finding such power series was a necessary step in…
In this paper, we propose a flexible notion of characteristic functions defined on graph vertices to describe the distribution of vertex features at multiple scales. We introduce FEATHER, a computationally efficient algorithm to calculate a…
Evolutionary computing (EC) has proven to be effective in solving complex optimization and robotics problems. Unfortunately, typical Evolutionary Algorithms (EAs) are constrained by the computational capacity available to researchers. More…
Higher-order interactions beyond pairwise relationships in large complex networks are often modeled as hypergraphs. Analyzing hypergraph properties such as triad counts is essential, as hypergraphs can reveal intricate group interaction…
Reliable weather forecasting is of great importance in science, business, and society. The best performing data-driven models for weather prediction tasks rely on recurrent or convolutional neural networks, where some of which incorporate…
In the last decade, Expression Templates (ET) have gained a reputation as an efficient performance optimization tool for C++ codes. This reputation builds on several ET-based linear algebra frameworks focused on combining both elegant and…
In this paper we obtain some explicit expressions for the Euler characteristic of a rank n coherent sheaf F on P^N and of its twists F(t) as polynomials in the Chern classes c_i(F), also giving algorithms for the computation. The employed…
Most advanced visual grounding methods rely on Transformers for visual-linguistic feature fusion. However, these Transformer-based approaches encounter a significant drawback: the computational costs escalate quadratically due to the…
Electrocardiogram (ECG) has been widely used for emotion recognition. This paper presents a deep neural network based on convolutional layers and a transformer mechanism to detect stress using ECG signals. We perform leave-one-subject-out…
To capture user preference, transformer models have been widely applied to model sequential user behavior data. The core of transformer architecture lies in the self-attention mechanism, which computes the pairwise attention scores in a…
Message-passing neural networks (MPNN) have shown extremely high efficiency and accuracy in predicting the physical properties of molecules and crystals, and are expected to become the next-generation material simulation tool after the…
In finite element calculations, the integral forms are usually evaluated using nested loops over elements, and over quadrature points. Many such forms (e.g. linear or multi-linear) can be expressed in a compact way, without the explicit…
This study proposes a novel approach to extract topological properties, specifically the Euler characteristic, from input images using neural networks without relying on large pre-existing datasets but with a single geometric image.…
The large models, as predicted by scaling raw forecasts, have made groundbreaking progress in many fields, particularly in natural language generation tasks, where they have approached or even surpassed human levels. However, the…
Tuning tensor program generation involves searching for various possible program transformation combinations for a given program on target hardware to optimize the tensor program execution. It is already a complex process because of the…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…