Systolic Array: A Dataflow Paradigm in 2D

What is a Systolic Array?

A systolic array is a type of parallel processing architecture designed to perform matrix operations efficiently. It consists of an array of processing elements (PEs) arranged in a grid, each capable of performing simple computations and communicating with its neighbors through dedicated data channels.

The key feature of a systolic array is the way it processes data: instead of moving weights or results between PEs, the input data moves through the array. This allows for efficient pipelining and reduces the need for complex inter-PE communication.

2D Weight-Stationary Systolic Array

In a 2D weight-stationary systolic array, the weights are fixed in place while data flows through the grid. This approach is particularly useful for operations like matrix multiplication, where the same set of weights is applied to multiple input vectors.

By shifting the weight matrix into the grid first and then streaming activations rightward, this 2D architecture minimizes load stalls compared to its 3D counterpart, making it more efficient in terms of computational cycles.

live demo · related simulation● LIVE

Applications and Implications

The systolic array's dataflow paradigm is crucial for applications requiring high-performance matrix operations, such as deep learning and signal processing. Its architecture can significantly reduce the time required to perform complex computations by leveraging parallelism.

Moreover, this 2D weight-stationary approach aligns well with modern hardware designs, particularly those used in specialized accelerators like Google's TPU MXU.

Real-World Examples

The systolic array has been applied in various real-world scenarios. For instance, it is used in the Tensor Processing Unit (TPU) by Google to accelerate machine learning computations.

In addition, this architecture can be found in digital signal processors and other specialized hardware designed for high-speed data processing.

Frequently asked questions

How does a systolic array differ from traditional parallel computing architectures?

Unlike traditional parallel architectures where both weights and results are moved between processing elements, in a systolic array, only the input data moves through the grid, while weights remain stationary. This reduces communication overhead and enhances efficiency.

What is the significance of load stalls in systolic arrays?

Load stalls occur when there is a delay in the availability of data or weights for processing elements to consume. In traditional 3D systolic arrays, these stalls can significantly impact performance. The 2D weight-stationary approach minimizes such stalls by pre-loading weights into the grid.

Can systolic arrays be used in any application requiring matrix operations?

Yes, systolic arrays are particularly well-suited for applications that involve large-scale matrix operations, such as those found in deep learning frameworks and signal processing systems. Their efficient data flow makes them ideal for these tasks.

What are the advantages of using a 2D weight-stationary systolic array over other architectures?

The 2D weight-stationary approach offers reduced load stalls, lower communication overhead, and higher efficiency in terms of computational cycles. It is especially advantageous for specialized hardware designs where minimizing latency and maximizing throughput are critical.

Try it live

Everything above runs in your browser — open Systolic Array: 2D Weight-Stationary Dataflow and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Systolic Array: 2D Weight-Stationary Dataflow simulation