INT8 Matrix Engines

• INT8 matrix engines are hardware subsystems that perform GEMMs using 8‐bit arithmetic with INT32 accumulation, optimizing computational density and energy efficiency.
• They employ techniques like deep pipelining, block-tiling, and on-chip memory management to maximize throughput in neural network inference and training.
• Advanced methods such as CRT reconstruction and split-integer decomposition enable these engines to emulate high-precision arithmetic for scientific and signal processing applications.

An INT8 matrix engine is a class of hardware or algorithmic subsystem optimized for performing general matrix-matrix multiplications (GEMMs) using 8-bit signed integer (INT8) arithmetic in the multiply stage, with accumulation into higher-precision registers (typically INT32). These engines are the core computational primitives in modern neural network accelerators, high-throughput Deep Learning inference and training hardware (e.g., NVIDIA Tensor Cores, AMD AI Engines), and are increasingly leveraged as the computational substrate for both native low-precision workloads and high-precision emulation via modular arithmetic schemes. INT8 matrix engines exploit the low memory and energy footprints of 8-bit operations to maximize computational density, power efficiency, and memory bandwidth use, while driving innovations in quantization, error management, and hardware design for large-scale data-parallel computation.

1. Hardware and Microarchitectural Principles

Modern INT8 matrix engines are deeply pipelined arrays of multiply–accumulate (MAC) or fused multiply–add (FMA) functional units, orchestrated to perform block-tiled matrix multiplications at extremely high throughput. The canonical design instantiates hundreds to thousands of small MAC units in a SIMD or systolic configuration, operating on INT8 operands and accumulating into INT32 registers to avoid overflow (Mhatre et al., 13 Apr 2025, Taka et al., 2023, Liu et al., 2020).

Key microarchitectural primitives include:

• Block-tiling and register fragment orchestration: Workloads are partitioned into tiles (e.g., 8×8, 16×16), which are mapped to register-resident "fragments" for efficient MAC scheduling (Chen et al., 25 Sep 2024, Ichimura et al., 21 Apr 2024).
• Shared-memory and local-data orchestration: Tiles are staged in on-chip scratchpads (shared memory/L1), enabling high operand reuse and minimizing DRAM bandwidth (Chen et al., 25 Sep 2024, Mhatre et al., 13 Apr 2025).
• Hierarchical accumulation: MAC results are accumulated in INT32, with further post-processing (post-scaling, CRT reconstruction, etc.) as needed by the higher-level algorithm (Taka et al., 2023, Ozaki et al., 10 Apr 2025).
• Sparse and structured formats: Recent variants incorporate block-sparse, density-bound, or fine-grained structured representations (e.g., DBB in mobile CNNs (Liu et al., 2020)) and associated scheduler logic, enabling further area and power savings.

Typical performance characteristics for state-of-the-art matrix engines are as follows:

Architecture	INT8 Peak Throughput	Power Efficiency (TOPS/W)	Block Size/Tiling
NVIDIA Blackwell B200 (Uchino et al., 9 Dec 2025)	4500 TOPS	>10 (device-level)	8×8 or 16×16 tiles
AMD AIE2 (Versal ML) (Mhatre et al., 13 Apr 2025)	194 TOPS	0.46–1.16	Custom, e.g., 64×224×64
AMC Versal AIE (VCK1902) (Taka et al., 2023)	128 TOPS	1.16	32×128×32 etc.
Mobile Systolic STA (Liu et al., 2020)	Device-specific	1.36× over baseline	Tensor-PE fused

Designs optimize for compute-to-communication ratios, SIMD lane utilization, register file pressure, area, and energy per MAC.

2. Quantization and Data Representation

INT8 matrix engines rely on robust quantization schemes to map floating-point or higher-precision tensors to 8-bit integer domains. Two canonical strategies are employed:

• Range-preserving per-tensor scaling: Each weight or activation tensor is mapped to INT8 via a scale $s_\mathcal{X}$ such that $$\mathcal{X}\approx s_\mathcal{X}\,\mathcal{X}_{\text{int},8}$$, with $s_W$ covering the full dynamic range of weights to avoid clipping (Wu, 2020, Chen et al., 25 Sep 2024).
• Learned or automatic activation scales: Activation scales are learned or adaptively estimated (optionally, $s_\mathcal{X}=2^{z}$ with $z\in\mathbb{R}$) to optimize a downstream loss function and balance range against quantization error (Wu, 2020).

Quantization may occur at:

• Token/row-level granularity (per-token scales, as in INT-FlashAttention (Chen et al., 25 Sep 2024))
• Block-level/tile-level granularity (as in block-quantized transformer training (Zhang et al., 11 Mar 2025))
• Tensor-level/global scales (e.g., for small/flat matrices or global softmax scaling)

Dequantization is performed with a single scaling multiply following the INT32 accumulation.

Advanced engines handle outlier blocks via dynamic fallback (mixed-precision quantization), constructing higher-precision code paths for blocks that would otherwise suffer from catastrophic underflow or overload (Zhang et al., 11 Mar 2025).

3. Algorithmic Extensions: High-Precision Emulation

INT8 engines are now routinely used for emulating higher-precision arithmetic (FP32, FP64, complex types) using splitting or modular reconstruction:

• Ozaki Scheme II + Chinese Remainder Theorem (CRT): Matrices are scaled and truncated to integer form, then mapped to N coprime moduli $p_\ell$, with each residue product $C'_\ell$ computed via a fast INT8 GEMM. CRT reconstruction aggregates these back into a full-precision result, with precision controlled by the number of moduli (Ozaki et al., 10 Apr 2025, Uchino et al., 6 Aug 2025, Uchino et al., 9 Dec 2025). This method enables FP64-accuracy GEMM and even double-complex GEMM at up to 6× the throughput of native implementations (Uchino et al., 9 Dec 2025).
• Split-integer mantissa decomposition: Each high-precision number is decomposed into several base-256 (or comparable radix) INT8 "digits," with matrix products performed as convolutions across these digit layers, then reassembled and normalized (Luszczek et al., 28 Sep 2025).
• Mixed low/high-precision fallback: Kernels fall back (blockwise or tokenwise) to 16-bit or FP16/FP32 in the presence of outliers, auto-tuning the fallback ratio to bound accuracy loss and maximize engine usage (Zhang et al., 11 Mar 2025).

Emulation modes can achieve 1.4×–6.5× speedups for high-precision GEMM over standard BLAS routines on modern GPUs, with end-to-end accuracy controlled to within 1–2 ULPs for practical scientific problems (Ozaki et al., 10 Apr 2025, Uchino et al., 6 Aug 2025, Uchino et al., 9 Dec 2025, Luszczek et al., 28 Sep 2025).

4. Architectures and Performance Optimization Strategies

Engine microarchitecture and scheduling optimizations are central to exploiting INT8 matrix engines’ potential:

• Tile sizing and register/accumulator mapping: Block sizes must be tuned to maximize local (on-core or on-SM) memory and fill vector/SIMD lanes. Double-buffering and careful bank placement eliminate memory stalls and routing bottlenecks (Mhatre et al., 13 Apr 2025, Taka et al., 2023).
• Broadcast/reduce and cascade: Inputs are broadcast statically across compute tiles, with partial results reduced on-core or via nearest-neighbor communication to avoid global memory traffic (Taka et al., 2023, Liu et al., 2020).
• Software pipelining and bubble avoidance: Explicit schedule optimization ensures all vector lanes and VLIW slots are filled, using exhaustive search for register/buffer placement where necessary (Mhatre et al., 13 Apr 2025).
• Hybrid and sparsity-aware datapaths: Fusing adjacent MACs into "tensor-PEs" enables intra-PE operand reuse and aggressive register sharing, yielding >2× area and power efficiency increases (Liu et al., 2020).

Performance figures demonstrate up to 165 TOPS aggregate throughput (85% of device peak) and energy efficiency improvements >6× over prior-generation FPGA matrix engines (Mhatre et al., 13 Apr 2025, Taka et al., 2023, Zhuang et al., 2023).

5. Applications: Neural Networks, Scientific Computing, Signal Processing

INT8 matrix engines are foundational for:

• Transformer models and LLMs: All dense and attention multiplications can be mapped to INT8 with negligible accuracy loss after scale-tuning, enabling 2–3× inference speedups and memory throughput gains (Wu, 2020, Chen et al., 25 Sep 2024, Zhang et al., 11 Mar 2025).
• CNN inference (particularly mobile): Systolic Tensor Arrays (STA) and density-bound block (DBB) sparsity extensions enable area/power savings for edge inference in vision models (Liu et al., 2020).
• Scientific computing and high-precision numerics: CRT-based and split-integer GEMM emulations make INT8 engines viable for dense linear solvers, QR/LU factorizations, complex matrix arithmetic, and time-domain wave propagation with FP64-level error bounds when well-conditioned (Ozaki et al., 10 Apr 2025, Luszczek et al., 28 Sep 2025, Uchino et al., 9 Dec 2025, Ichimura et al., 21 Apr 2024).
• Explicit PDE solvers (FEM, FDM): Quantization and tile mapping for elementwise GEMM enables explicit time-stepping methods to exploit INT8 Tensor Cores for 10–30× speedup at high accuracy (Ichimura et al., 21 Apr 2024).

6. Trade-offs, Limitations, and Future Prospects

While INT8 matrix engines offer exceptional computational density, several trade-offs and constraints govern their applicability:

• Numerical accuracy vs. speed: Precision can be arbitrarily tuned in modular emulation (via number of moduli or digits), but at increased cost in redundant compute. Well-conditioned problems (e.g., κ(A) ≲ 10⁸) permit INT8 emulation with minimal error inflation; ill-conditioned systems require fallback to true FP64 (Luszczek et al., 28 Sep 2025, Ozaki et al., 10 Apr 2025).
• Outlier management: Sparse activation or weight outliers degrade quantization quality and may necessitate dynamic fallback or mixed-precision handling (Zhang et al., 11 Mar 2025).
• LUT-based algorithmic acceleration: Custom engines implementing table-lookup MAC replacement (e.g., msGeMM) can reduce arithmetic by 2–2.5× but require additional on-chip SRAM per tile (Maleki, 2023).
• Programmability and system-level bottlenecks: High-throughput engines achieve their architectural potential only when data movement is orchestrated to match computation rates; bottlenecks in memory bandwidth, routing congestion, or pipeline stalls can undercut theoretical gains (Mhatre et al., 13 Apr 2025, Taka et al., 2023).
• Generalization to arbitrary precisions and formats: Token-, block-, or row-wise quantization, as well as engineered support for INT4, INT6, FP8, and other data formats, are active areas of extension, with design choices affecting software complexity, hardware reusability, and deployment flexibility (Chen et al., 25 Sep 2024, Wu, 2020).

INT8 matrix engine developments intersect with the broader movement toward precision-optimized, hardware-conscious algorithm design across machine learning, scientific computing, and edge inference, with ongoing research refining the balance between hardware efficiency, algorithmic transparency, and numerical rigor.