---
title: Systolic Tensor Units
url: https://www.emergentmind.com/topics/systolic-tensor-units
type: topic
---

# Systolic Tensor Units

A systolic tensor unit is a 2D or tiled array of processing elements (PEs), typically optimized for high-throughput matrix-matrix or tensor contractions, equipped with architectural features for efficient acceleration of AI workloads, including deep neural networks (DNNs), under both dense and sparse regimes. Modern systolic tensor units evolve classic systolic array designs to support complex tensor operations, multi-mode structured sparsity, on-the-fly nonlinearities, and error-checking for robust computation, and can be instantiated in both FPGA and ASIC fabrics for large-scale model deployment [2502.03763], [2507.11331].

## 1. Architectural Foundations

Systolic tensor units are fundamentally 2D arrays, typically output-stationary or weight-stationary, in which each PE receives data and partial sums in regular wavefront fashion. Recent designs organize the basic unit as "slices"—such as the Systolic Sparse Tensor (SST) slice, which is a 4×4 grid of Sparse Processing Elements (SPEs) [2502.03763]. Data enters from designated edges: weights (a_data) flow east, activations (b_data) flow south via dedicated, often hard-wired, vertical interconnects. Partial sums accumulate in situ and are egressed via local triangle buffer structures. Modular tiling of slices allows for seamless scalability into larger 2D grids.

Modern PEs implement multi-mode MAC datapaths. For structured sparsity, the PEs incorporate multiplexers, index decode logic, and local pipeline registers, supporting dynamic switching between dense and sparse compute modes with parameterizable sparsity levels (e.g., dense, 2:4, 1:3, 1:4). Control signals for enable, accumulate, and sparsity level are fanned out systolically, preserving the regularity crucial for achievable high clock frequencies (e.g., >928 MHz in FPGA SST implementations).

## 2. Dataflow and Structured Sparsity

Systolic tensor units are engineered for maximal hardware utilization under varying sparsity patterns. Modern designs, such as the SST slice, provide native support for structured N:M sparsity (e.g., 2:4, 1:3, and 1:4), with index-based compressed weight encoding, enabling compression ratios up to 3.56× for bf16 weights. The compressed weights and their indices traverse the array alongside activations; a system of pipeline registers and multiplexers routes activations to their corresponding non-zero weights, eliminating MAC idle periods and, thus, maintaining 100% utilization at all supported sparsity levels [2502.03763].

Performance in different sparsity modes is as follows:

| Sparsity Mode | Compression Ratio (int8 / bf16) | Speedup | MAC Utilization |
|---------------|----------------------------------|---------|-----------------|
| Dense         | 1× / 1×                          | 1×      | 100%            |
| 2:4           | 1.6× / 1.78×                     | 2×      | 100%            |
| 1:3           | 2.4× / 2.67×                     | 3×      | 100%            |
| 1:4           | 3.2× / 3.56×                     | 4×      | 100%            |

Key mechanisms include:
- **Index-based compression**: For every group of M weights, only N non-zeros and their respective indices are transmitted.
- **Sparse dataflow scheduling**: Pipeline staging aligns activations and non-zeros for correct temporal matching.
- **Flexible control**: On-slice sparsity_level configuration gates the relevant PE datapath, setting appropriate pipeline depth.

For unstructured sparsity, architectures such as VUSA implement "virtual upscaling," adding a third dimension of pipeline-only sparse processing elements (SPEs) per row and dynamically mapping the available MAC units to non-zero positions. This achieves area and power reductions proportional to the actual sparsity without sacrificing peak compute throughput [2506.01166].

## 3. Full-Tensor Operation Support and Nonlinearity

Beyond simple GEMMs, new systolic tensor units support generalized tensor contractions and embedded nonlinear operations. Architectures such as FSA (FlashAttention Systolic Array) and ONE-SA augment the PE microarchitecture to enable in-place, on-the-fly computation of functions like softmax, exponential, and piecewise-linear nonlinearities, essential for complete transformer and DNN forward passes [2507.11331], [2402.00395].

- **FSA (SystolicAttention)** fuses matrix multiplications and the entire FlashAttention-2/3 algorithm into a single array with embedded split units (for floating-point decomposition), comparators (row-wise argmax/rowmax), and piecewise linear approximation hardware for functions such as exp. This allows multi-phase operations—including accumulation, reduction, and nonlinearity—to execute without leaving the array context, removing the performance bottleneck of external vector units. SystolicAttention schedules all steps to preserve exact floating-point operation orders as required for numerical stability in attention mechanisms. The result is up to 4.83× higher achieved utilization (relative to Google TPUv5e) with only ~10% area overhead [2507.11331].
- **ONE-SA** enables arbitrary continuous piecewise-linear (CPWL) operations via a dual-mode datapath in each PE, with programmable tables for slope/intercept parameters, and the ability to fold general nonlinear functions—such as ReLU, GELU, or LayerNorm—directly into the systolic mesh with minimal hardware cost increase (<1.5% of BRAM/LUT/DSP resources, ~13–24% flip-flop overhead) and at negligible inference accuracy loss [2402.00395].

## 4. Error Detection and Reliability

As the deployment of systolic tensor units expands to safety-critical domains, robust online error checking becomes essential. Sparse systolic tensor array designs incorporate algorithm-based fault tolerance (ABFT) schemes wherein dedicated accumulator modules compute row- and column-wise checksums of both the input and output tensors. A predicted checksum is generated by replaying the input checksums through the array using the same compressed weights; a mismatch with the actual output checksum flags an error. Digit-serial checksum feeding accommodates wide accumulators at modest area (<5%) and power (<9%) cost, while maintaining high detection coverage (above 90% for typical CNN workloads) [2402.10850].

## 5. Area, Frequency, and Energy Efficiency Trade-offs

Systolic tensor units introduce sparsity handling, dedicated interconnects, and additional control logic with minimal overhead relative to their efficiency gains:
- **SST slice (FPGA):** +20% area increase over dense blocks, <1% frequency penalty, area reduction of up to 10.9× and frequency improvement up to 5× compared to traditional (CLB+DSP) solutions.
- **VUSA:** Area reduction up to 37%, power reduction up to 68% at the same peak performance when fully leveraging sparsity [2506.01166].
- **Structured-sparse STA (ASIC):** 2–3× improvements in area and power efficiency at iso-throughput versus classical SAs [2005.08098], [2009.02381].
- **Energy per operation**: Reductions of 2–3× are reported due to localized routing, dedicated wires, and avoidance of "zero-multiplies."

## 6. Model Performance, Accuracy, and Domain Integration

Systolic tensor units achieve substantial practical speedups for DNN inference under realistic conditions:
- **Transformer models (ViT, ConvNeXt, FlashAttention):** Multi-mode structured sparsity (e.g., 2:4, 1:4) enables up to 3.52× speedup with <1% accuracy degradation for large ViT models on representative hardware [2502.03763].
- **Full attention kernels:** Fused systolic FlashAttention achieves mean utilization of 58% of MAC resources (vs 21–33% for prior commercial SAs), with end-to-end speedups of 1.77–4.83× over leading ASIC units [2507.11331].
- **Compression and low-rank structure**: Tensor-train decomposition (TTD) mapped to "group vector" systolic accelerators yields blockwise compression (>10× on LLM layers) and throughput improvements of 2–4× on the most compute-bound kernels, with up to 59% overall throughput improvement over high-end GPUs [2501.19135].

## 7. Limitations and Future Directions

Despite these advantages, current systolic tensor units have certain constraints:
- **Support is limited to fixed blockwise structured sparsity (e.g., 2:4, 1:4, 1:3), not arbitrary unstructured patterns**, except in architectures like VUSA which dynamically assign MACs to nonzero weights [2506.01166].
- **Activation (input) sparsity is not fully exploited**—most designs focus on weight sparsity.
- **Dynamic kernel adaptation and further fusion of tensor contractions with arbitrary nonlinearities** are active research directions. ONE-SA and FSA suggest methods for fusing more general nonlinear transformations into the systolic dataflow without major hardware cost [2507.11331], [2402.00395].
- **Sparse-aware software toolchains** and compiler support for mapping arbitrary model graph operations onto multi-mode tensor units remain a significant area for advancement.

## References

- Systolic Sparse Tensor Slices: FPGA Building Blocks for Sparse and Dense AI Acceleration [2502.03763]
- Error Checking for Sparse Systolic Tensor Arrays [2402.10850]
- SystolicAttention: Fusing FlashAttention within a Single Systolic Array [2507.11331]
- VUSA: Virtually Upscaled Systolic Array Architecture to Exploit Unstructured Sparsity in AI Acceleration [2506.01166]
- A Tensor-Train Decomposition based Compression of LLMs on Group Vector Systolic Accelerator [2501.19135]
- Sparse Systolic Tensor Array for Efficient CNN Hardware Acceleration [2009.02381]
- Systolic Tensor Array: An Efficient Structured-Sparse GEMM Accelerator for Mobile CNN Inference [2005.08098]
- ONE-SA: Enabling Nonlinear Operations in Systolic Arrays for Efficient and Flexible Neural Network Inference [2402.00395]
- Low-Cost Multi-Precision Systolic Arrays for Accelerating FHE NTTs on AI ASICs [2606.19866]

Source: https://www.emergentmind.com/topics/systolic-tensor-units