# Transitive Array: An Efficient GEMM Accelerator with Result Reuse

arXiv: https://arxiv.org/abs/2504.16339 · HTML: https://mlsanity.com/paper/2504.16339/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2025.

## Built on by (most cited first, 7 of 7)

- [Phi: Leveraging Pattern-based Hierarchical Sparsity for High-Efficiency Spiking Neural Networks](https://mlsanity.com/paper/2505.10909/) (2025)
- [Focus: A Streaming Concentration Architecture for Efficient Vision-Language Models](https://mlsanity.com/paper/2512.14661/) (2025)
- [Platinum: Path-Adaptable LUT-Based Accelerator Tailored for Low-Bit Weight Matrix Multiplication](https://mlsanity.com/paper/2511.21910/) (2025)
- [EVA: Accelerating LLM Decoding via an Efficient Vector Quantization Architecture](https://mlsanity.com/paper/2605.24144/) (2026)
- [FaRAccel: FPGA-Accelerated Defense Architecture for Efficient Bit-Flip Attack Resilience in Transformer Models](https://mlsanity.com/paper/2510.24985/) (2025)
- [BitStopper: An Efficient Transformer Attention Accelerator via Stage-fusion and Early Termination](https://mlsanity.com/paper/2512.06457/) (2025)
- [Vortex: Bridging Extreme Compression and Efficient LLM Inference](https://mlsanity.com/paper/2609.12208/) (2026)

## Abstract (arXiv)

Deep Neural Networks (DNNs) and Large Language Models (LLMs) have revolutionized artificial intelligence, yet their deployment faces significant memory and computational challenges, especially in resource-constrained environments. Quantization techniques have mitigated some of these issues by reducing data precision, primarily focusing on General Matrix Multiplication (GEMM). This study introduces a novel sparsity paradigm, transitive sparsity, which leverages the reuse of previously computed results to substantially minimize computational overhead in GEMM operations. By representing transitive relations using a directed acyclic graph, we develop an efficient strategy for determining optimal execution orders, thereby overcoming inherent challenges related to execution dependencies and parallelism. Building on this foundation, we present the Transitive Array, a multiplication-free accelerator designed to exploit transitive sparsity in GEMM. Our architecture effectively balances computational workloads across multiple parallel lanes, ensuring high efficiency and optimal resource utilization. Comprehensive evaluations demonstrate that the Transitive Array achieves approximately 7.46× and 3.97× speedup and 2.31× and 1.65× energy reduction compared to state-of-the-art accelerators such as Olive and BitVert while maintaining comparable model accuracy on LLaMA models.