Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2603.07962

GOMA: Geometrically Optimal Mapping via Analytical Modeling for Spatial Accelerators

Wulve Yang·Hailong Zou·Rui Zhou·Jionghao Zhang·Qiang Li·Gang Li·Yi Zhan·Shushan Qiao
View original source ↗Read source document ↗Export metadata ↓

Abstract

General matrix multiplication (GEMM) on spatial accelerators is highly sensitive to mapping choices in both execution efficiency and energy consumption. However, the mapping space exhibits combinatorial explosion, which makes it extremely challenging to obtain optimal mappings within an acceptable time budget. Existing approaches typically face challenges: They often lack global-optimality guarantees and become prohibitively slow as the mapping space grows. To address these limitations, we propose \textsc{GOMA}, a geometric-abstraction-based, globally optimal GEMM mapping framework via analytical modeling, which achieves efficient solving while guaranteeing optimality. \textsc{GOMA} introduces, from first principles, a geometric abstraction for GEMM mapping, yielding an exact analytical energy objective with $O(1)$ evaluation for any given mapping. The objective is highly accurate. \textsc{GOMA} then formulates mapping selection as an integer optimization problem under hardware and mapping constraints, using the analytical energy model as the objective to automate mapping search. \textsc{GOMA} can quickly compute a global-optimal mapping for any (GEMM workload, target hardware) pair, achieving this for the first time in mapping space exploration. Experiments confirm that across representative accelerators and large language model prefill workloads, \textsc{GOMA} improves the energy--delay product (EDP) by $2.24$--$4.24\times$ over SOTA mappers, while accelerating time-to-solution by $3.83$--$73.6\times$.

Explore related subjects

cs.AR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Wulve Yang, Hailong Zou, Rui Zhou, Jionghao Zhang, Qiang Li, Gang Li, Yi Zhan, Shushan Qiao. 2026-03-23. GOMA: Geometrically Optimal Mapping via Analytical Modeling for Spatial Accelerators. https://arxiv.org/abs/2603.07962

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

HLSmith: An Expert-Guided Agentic Framework for C/C++-to-HLS Translation

Application-specific FPGA accelerators offer substantial performance and energy-efficiency gains across many application domains, but developing them is costly, often requiring months of specialized effort. Even with high-level synthesis (HLS), designers still need extensive hardware expertise to build high-performance accelerators. Although large language models (LLMs) have demonstrated strong software-generation capabilities, even frontier models lack the hardware intuition and procedural knowledge needed to reliably translate baseline C/C++ programs into high-performance HLS designs: they struggle to identify effective architectures, follow the optimization processes used by HLS experts, and apply hardware transformations consistently across diverse kernels. We present HLSmith, an expert-guided framework for translating C/C++ programs into optimized HLS accelerators. HLSmith combines three components: an HLS optimization expertise library that encodes guarded transformation recipes, their applicability and prerequisite conditions, and unsafe cases to avoid; a staged, feedback-driven orchestration flow modeled on expert HLS development practice that guides agents through synthesis, bottleneck analysis, and optimization; and a tool-grounded model-adaptation pipeline that converts optimization trajectories from commercial frontier models into training data for fine-tuning open-weight LLMs. We evaluate HLSmith on PolyBench against ChatHLS, a leading prior agent-orchestration framework for HLS accelerator development. HLSmith achieves a geometric mean speedup of 4.24x over ChatHLS while producing functionally correct designs, in both software and RTL simulation, for every benchmark, compared with ChatHLS's 57% valid-design rate. It further reaches speedups of up to 252x and 138x with commercial frontier models and open-weight models, respectively.

cs.AR↗
arXiv2026

Accelerating the Mitigation of LLM Inference Nondeterminism Across GPU Architectures

Large language model (LLM) outputs are expected to be reproducible under greedy decoding, yet in practice the same model, prompt, and software stack produce different outputs on different GPUs. The root cause is floating-point non-associativity combined with hardware-dependent kernel selection. Inference frameworks select different matrix-multiplication kernels on each architecture, with different parallel reduction orders and unspecified tensor-core arithmetic, and the resulting rounding differences can flip output tokens. Existing solutions have imperfect cross-architecture reproducibility and incur a significant performance penalty. We present a solution employing a set of fixed-configuration fused-upcast GEMM kernels that load 16-bit weights from memory, upcast them to FP32 in registers, and accumulate with IEEE-754 arithmetic in a reduction order that is a pure function of the problem shape and is therefore independent of the device, its SM count, or kernel scheduling. By fixing the floating-point reduction order as a function of problem shape alone, every GPU runs the same operation sequence, so cross-architecture reproducibility of the linear layers reduces to correct IEEE-754 arithmetic rather than to rounding differences staying below a tie-flip threshold. We confirm our solution's linear-layer outputs are bitwise identical across NVIDIA Ampere, Ada, and Hopper GPUs, while running $1.17$ to $3.1\times$ faster end-to-end than the state-of-the-art solution and cutting weight-memory traffic in half.

cs.AR↗
arXiv2026

Decoupling Logical Masks from GPU Execution for Dynamic Block-Sparse Attention

Attention computation makes inference expensive in video diffusion transformers (vDiTs), which generate videos through iterative denoising. Block-sparse attention (BSA) reduces this cost by computing only blocks selected by a logical mask, which specifies attention interactions to compute. However, coupling logical block geometry to execution choices limits adaptation to varying masks and graphics processing units (GPUs), while runtime kernel specialization can incur preparation overhead that outweighs execution time savings. We present Tessera, a specialized runtime for dynamic BSA that decouples logical masks from GPU execution while preserving specified attention interactions. Its physical mapping layer retains, combines, or subdivides logical attention blocks into physical tiles suited to different attention mask shapes and GPU architectures. Its task organization layer groups and schedules tiles within GPU tasks to reuse data, expose parallelism, and overlap data movement with computation. Finally, profile-guided regime selection enables low- overhead execution plan selection through a lookup table constructed from offline profiling. We implement Tessera with specialized CUDA kernels supporting four NVIDIA GPU generations. Evaluated on 2,315 real attention masks and industrial video diffusion models, Tessera achieves up to 6.79x BSA request speedup over baseline systems in the evaluated video diffusion models.

cs.AR↗