Related papers: Data-driven Construction of Hierarchical Matrices …

Recurrent neural networks can be large and compute-intensive, yet many applications that benefit from RNNs run on small devices with very limited compute and storage capabilities while still having run-time constraints. As a result, there…

This paper studies the use of kernel density estimation (KDE) for linear algebraic tasks involving the kernel matrix of a collection of $n$ data points in $\mathbb R^d$. In particular, we improve upon existing algorithms for computing the…

In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great significance for improving the computational efficiency and…

We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…

Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…

Directional interpolation is a fast and efficient compression technique for high-frequency Helmholtz boundary integral equations, but it requires a very large amount of storage in its original form. Algebraic recompression can significantly…

In this work we introduce a new multiscale artificial neural network based on the structure of $\mathcal{H}$-matrices. This network generalizes the latter to the nonlinear case by introducing a local deep neural network at each spatial…

In our previous work [arXiv:2202.10042], the complexity of Sinkhorn iteration is reduced from $O(N^2)$ to the optimal $O(N)$ by leveraging the special structure of the kernel matrix. In this paper, we explore the special structure of kernel…

In-memory database query processing frequently involves substantial data transfers between the CPU and memory, leading to inefficiencies due to Von Neumann bottleneck. Processing-in-Memory (PIM) architectures offer a viable solution to…

Existing approaches for synthetic tabular data generation are based on either purely generative models or LLMs, both of which struggle with data heterogeneity, logical consistency, rare-event coverage, and robustness in low-data regimes. In…

The implementation difficulties of combining distribution matching (DM) and dematching (invDM) for probabilistic shaping (PS) with soft-decision forward error correction (FEC) coding can be relaxed by reverse concatenation, for which the…

We present a hierarchical optimization architecture for large-scale power networks that overcomes limitations of fully centralized and fully decentralized architectures. The architecture leverages principles of multigrid computing schemes,…

High Energy Physics (HEP) experiments, for example at the Large Hadron Collider (LHC) at CERN, store data at exabyte scale in sets of files. They use a binary columnar data format by the ROOT framework, that also transparently compresses…

With the rapid growth of deep neural networks (DNNs), compute-in-memory (CIM) has emerged as a promising energy-efficient paradigm for accelerating multiply-and-accumulate (MAC) operations. Yet, current CIM architectures are largely limited…

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central…

In this paper, we propose a new neural network architecture based on the H2 matrix. Even though networks with H2-inspired architecture already exist, and our approach is designed to reduce memory costs and improve performance by taking into…

Trajectory planning for quadrotors in cluttered environments has been challenging in recent years. While many trajectory planning frameworks have been successful, there still exists potential for improvements, particularly in enhancing the…

Work introduces a hierarchical binary tree-based reduction that replaces standard self-attention. The core idea is to use a recursive Gated Linear Unit merge operation, achieving O(n) total merge operations O(log n) parallel depth O(n d^2)…

To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as…

Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…