TriADA: Massively Parallel Trilinear Matrix-by-Tensor Multiply-Add Algorithm and Device Architecture for the Acceleration of 3D Discrete Transformations

• URL: http://arxiv.org/abs/2506.22818v1
• Date: Sat, 28 Jun 2025 08:42:01 GMT
• Title: TriADA: Massively Parallel Trilinear Matrix-by-Tensor Multiply-Add Algorithm and Device Architecture for the Acceleration of 3D Discrete Transformations
• Abstract summary: Multilinear transformations are key in high-performance computing ( HPC) and artificial intelligence (AI) workloads.<n> scaling computation by enlarging the number of parallel processing units substantially increases energy consumption.<n>TriADA is capable of performing a variety of trilinear transformations with hypercubic arithmetic complexity in a linear number of time-steps.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multilinear transformations are key in high-performance computing (HPC) and artificial intelligence (AI) workloads, where data is represented as tensors. However, their high computational and memory demands, which grow with dimensionality, often slow down critical tasks. Moreover, scaling computation by enlarging the number of parallel processing units substantially increases energy consumption, limiting widespread adoption, especially for sparse data, which is common in HPC and AI applications. This paper introduces the Trilinear Algorithm and isomorphic to algorithm Device Architecture (TriADA) to address these challenges with the following innovations: (1) a massively parallel, low-rank algorithm for computing a family of trilinear (3D) discrete orthogonal transformations (3D-DXTs), which is a special case of the more general 3-mode matrix-by-tensor multiplication (3D-GEMT); (2) a new outer-product-based GEMM kernel with decoupled streaming active memory, specially designed to accelerate 3D-GEMT operation; (3) an isomorphic to the proposed algorithm, fully distributed 3D network of mesh interconnected processing elements or cells with a coordinate-free, data-driven local processing activity, which is independent of problem size; (4) an elastic sparse outer-product (ESOP) method that avoids unnecessary computing and communication operations with zero-valued operands, thereby enhancing energy efficiency, computational accuracy, and stability. TriADA is capable of performing a variety of trilinear transformations with hypercubic arithmetic complexity in a linear number of time-steps. The massively parallel, scalable, and energy-efficient architecture of TriADA is ideal for accelerating multilinear tensor operations, which are the most demanding parts of AI and HPC workloads.

Related papers

• Fast and Stable Triangular Inversion for Delta-Rule Linear Transformers [35.36704326614983]
  Models that incorporate linear attention layers with the so-called Delta-Rule involve the inversion of triangular matrices as a core sub-routine.<n>This work provides a systematic analysis of both direct and iterative triangular inversion algorithms, targeting methods that are rich in matrix products.<n>Performance benchmarks on NPUs reveal up to $4.3times$ speed-up against the state-of-the-art implementations of SGLang for triangular matrix inversion.
  arXiv  Detail & Related papers  (2026-05-20T15:51:32Z)
• Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometries [51.028432812178266]
  Transolver-3 is a new member of the Transolver family designed for high-fidelity physics simulations.<n>We show that Transolver-3 is capable of handling meshes with over 160 million cells, achieving impressive performance across three challenging simulation benchmarks.
  arXiv  Detail & Related papers  (2026-02-04T16:52:44Z)
• Tail-Aware Post-Training Quantization for 3D Geometry Models [58.79500829118265]
  Post-Training Quantization (PTQ) enables efficient inference without retraining.<n>PTQ fails to transfer effectively to 3D models due to intricate feature distributions and prohibitive calibration overhead.<n>We propose TAPTQ, a Tail-Aware Post-Training Quantization pipeline for 3D geometric learning.
  arXiv  Detail & Related papers  (2026-02-02T07:21:15Z)
• NeuMatC: A General Neural Framework for Fast Parametric Matrix Operation [75.91285900600549]
  We propose textbftextitNeural Matrix Computation Framework (NeuMatC), which elegantly tackles general parametric matrix operation tasks.<n>NeuMatC unsupervisedly learns a low-rank and continuous mapping from parameters to their corresponding matrix operation results.<n> Experimental results on both synthetic and real-world datasets demonstrate the promising performance of NeuMatC.
  arXiv  Detail & Related papers  (2025-11-28T07:21:17Z)
• Geometric Operator Learning with Optimal Transport [77.16909146519227]
  We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries.<n>For 3D simulations focused on surfaces, our OT-based neural operator embeds the surface geometry into a 2D parameterized latent space.<n> Experiments with Reynolds-averaged Navier-Stokes equations (RANS) on the ShapeNet-Car and DrivAerNet-Car datasets show that our method achieves better accuracy and also reduces computational expenses.
  arXiv  Detail & Related papers  (2025-07-26T21:28:25Z)
• Fused3S: Fast Sparse Attention on Tensor Cores [3.6068301267188]
  This paper introduces Fused3S, the first fused 3S algorithm that jointly maximizes tensor core utilization and minimizes data movement.<n>Across real-world graph datasets, Fused3S $1.6- 16.3times$ and $1.5-14times$ speedup over state-of-the-art on H100 and A30 GPU.
  arXiv  Detail & Related papers  (2025-05-12T22:09:05Z)
• Higher Order Transformers: Efficient Attention Mechanism for Tensor Structured Data [10.327160288730125]
  Higher-Order Transformers (HOT) are designed to process data with more than two axes, i.e. higher-order tensors.<n>To address the computational challenges associated with high-order tensor attention, we introduce a novel Kronecker factorized attention mechanism.<n>We validate the effectiveness of HOT on two high-dimensional tasks, including multivariate time series forecasting, and 3D medical image classification.
  arXiv  Detail & Related papers  (2024-12-04T00:10:47Z)
• Scaling Studies for Efficient Parameter Search and Parallelism for Large Language Model Pre-training [2.875838666718042]
  We focus on parallel and distributed machine learning algorithm development, specifically for optimizing the data processing and pre-training of a set of 5 encoder-decoder LLMs. We performed a fine-grained study to quantify the relationships between three ML methods, specifically exploring Microsoft DeepSpeed Zero Redundancy stages.
  arXiv  Detail & Related papers  (2023-10-09T02:22:00Z)
• An Efficient Algorithm for Clustered Multi-Task Compressive Sensing [60.70532293880842]
  Clustered multi-task compressive sensing is a hierarchical model that solves multiple compressive sensing tasks. The existing inference algorithm for this model is computationally expensive and does not scale well in high dimensions. We propose a new algorithm that substantially accelerates model inference by avoiding the need to explicitly compute these covariance matrices.
  arXiv  Detail & Related papers  (2023-09-30T15:57:14Z)
• ADC/DAC-Free Analog Acceleration of Deep Neural Networks with Frequency Transformation [2.7488316163114823]
  This paper proposes a novel approach to an energy-efficient acceleration of frequency-domain neural networks by utilizing analog-domain frequency-based tensor transformations. Our approach achieves more compact cells by eliminating the need for trainable parameters in the transformation matrix. On a 16$times$16 crossbars, for 8-bit input processing, the proposed approach achieves the energy efficiency of 1602 tera operations per second per Watt.
  arXiv  Detail & Related papers  (2023-09-04T19:19:39Z)
• Geometry-Informed Neural Operator for Large-Scale 3D PDEs [76.06115572844882]
  We propose the geometry-informed neural operator (GINO) to learn the solution operator of large-scale partial differential equations. We successfully trained GINO to predict the pressure on car surfaces using only five hundred data points.
  arXiv  Detail & Related papers  (2023-09-01T16:59:21Z)
• RWKV: Reinventing RNNs for the Transformer Era [54.716108899349614]
  We propose a novel model architecture that combines the efficient parallelizable training of transformers with the efficient inference of RNNs. We scale our models as large as 14 billion parameters, by far the largest dense RNN ever trained, and find RWKV performs on par with similarly sized Transformers.
  arXiv  Detail & Related papers  (2023-05-22T13:57:41Z)
• UNETR++: Delving into Efficient and Accurate 3D Medical Image Segmentation [93.88170217725805]
  We propose a 3D medical image segmentation approach, named UNETR++, that offers both high-quality segmentation masks as well as efficiency in terms of parameters, compute cost, and inference speed. The core of our design is the introduction of a novel efficient paired attention (EPA) block that efficiently learns spatial and channel-wise discriminative features. Our evaluations on five benchmarks, Synapse, BTCV, ACDC, BRaTs, and Decathlon-Lung, reveal the effectiveness of our contributions in terms of both efficiency and accuracy.
  arXiv  Detail & Related papers  (2022-12-08T18:59:57Z)
• Batch-efficient EigenDecomposition for Small and Medium Matrices [65.67315418971688]
  EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. We propose a QR-based ED method dedicated to the application scenarios of computer vision.
  arXiv  Detail & Related papers  (2022-07-09T09:14:12Z)
• Large Scale Distributed Linear Algebra With Tensor Processing Units [0.0]
  We have curated Google Processing Units (TPUs), application-specific chips developed for machine learning, into large-scale dense linear algebra supercomputers. The matrix-multiply units (MXU)s dominate the runtime, yielding impressive scaling, performance, and raw size.
  arXiv  Detail & Related papers  (2021-12-16T16:55:22Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.