Year: 2025
Type: article
Abstract: This paper introduces the continuous tensor abstraction, allowing indices to take real-number values (e.g., A[3.14]). It also presents continuous tensor algebra expressions, such as C x,y = A x,y * B x,y , where indices are defined over a continuous domain. This work expands the traditional tensor model to include continuous tensors. Our implementation supports piecewise-constant tensors, on which infinite domains can be processed in finite time. We also introduce a new tensor format for efficient storage and a code generation technique for automatic kernel generation. For the first time, our abstraction expresses domains like computational geometry and computer graphics in the language of tensor programming. Our approach demonstrates competitive or better performance to hand-optimized kernels in leading libraries across diverse applications. Compared to hand-implemented libraries on a CPU, our compiler-based implementation achieves an average speedup of 9.20× on 2D radius search with ∼60× fewer lines of code (LoC), 1.22× on genomic interval overlapping queries (with ∼18× LoC saving), and 1.69× on trilinear interpolation in Neural Radiance Field (with ∼6× LoC saving).
DOI: 10.1145/3763146
Language: English
Subfield: Hardware and Architecture
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Awards: G2515541506, Collaborative Research: SHF: Medium: Spatial Multi-Tenant Neural Acceleration for Next Generation Datacenters, G5664986334, G7578581503, PPoSS: LARGE: Intel: Combining Learning and Formal Verification for Scalable Machine Programming (ScaMP), Collaborative Research: PPoSS: LARGE: A Full-Stack Architecture for Sparse Computation, WE PROPOSE THE CREATION OF A SINGLE-DISCIPLINE CENTER (SDC) FOR THE EXASCALE SIMULATION OF MATERIALS IN
HYPERSONIC FLOW ENVIRONMENTS. OUR OBJECTIVES ARE AS FOLLOWS. FIRST, WE TARGET A SIGNIFICANT ADVANCE IN THE
ABILITY TO PREDICT THE DEGRADATION (OXIDATION AND MELTING) OF COMPLEX (DISORDERED AND MULTI-COMPONENT) MATERIALS
UNDER EXTREME LOADING, INACCESSIBLE TO DIRECT EXPERIMENTAL OBSERVATION. THIS APPLICATION REPRESENTS A
TECHNOLOGY DOMAIN OF INTENSE CURRENT INTEREST, AND HAS CLEAR EXTENSIONS TO A MUCH WIDER CLASS OF PROBLEMS—
I.E., THOSE INVOLVING MATERIAL INTERFACES IN EXTREME ENVIRONMENTS. INDEED, INTERFACES ARE CRUCIAL TO OUR ABILITY
TO UNDERSTAND, ENGINEER, AND CONTROL MATERIAL BEHAVIOR. YET THE PREDICTIVE SIMULATION OF INTERFACE PROPERTIES
AND THEIR IMPACT REMAINS EXTREMELY CHALLENGING. CAPTURING THE IMPACT OF INTERFACES REQUIRES RESOLVING INTERFACIAL
ATOMIC STRUCTURE AND THUS APPEALING TO FIRST PRINCIPLES (I.E., QUANTUM MECHANICAL) SIMULATIONS; AT THE
SAME TIME, INTERFACIAL STRUCTURES ARE AFFECTED BY CONDITIONS (E.G., THERMAL, MECHANICAL, AND CHEMICAL LOADING)
AT THE ENGINEERING SCALE. THIS PROBLEM THUS PRESENTS AN ENORMOUS AND FUNDAMENTAL MULTISCALE SIMULATION
CHALLENGE, WITH MYRIAD APPLICATIONS—TO HYPERSONICS AND FAR BEYOND.
OpenAlex ID: W4415007445