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Sparse-GEMM (General Matrix Multiplication) Algorithms in 2025

Sparse-GEMM (General Matrix Multiplication) is a critical algorithmic advancement in the domain of edge AI and deep learning, especially when dealing with sparse neural networks. Sparse-GEMM is a specialized form of matrix multiplication that leverages sparsity in the matrices—i.e., matrices that have a large proportion of zero-valued elements. By skipping computations involving zeros, Sparse-GEMM algorithms drastically reduce the computational overhead and memory bandwidth required, enabling faster, more efficient inference on edge devices like the NVIDIA Jetson Orin Nano.

In this expanded exposition, we’ll dive into:

  1. The concept of sparse matrices and how Sparse-GEMM works.
  2. Optimizations in Sparse-GEMM for AI models on edge devices.
  3. Practical coding examples of Sparse-GEMM in Python using PyTorch and TensorRT.

1. Sparse Matrices and How Sparse-GEMM Works

Sparse Matrices

In deep learning models, especially large-scale ones like transformers or convolutional neural networks (CNNs), many of the weight matrices are sparse—meaning they have a significant number of zero-valued elements. The sparsity can be structural (e.g., deliberately removing connections between neurons) or induced through pruning techniques (where less significant weights are set to zero after training to reduce model complexity).

For example, consider a dense matrix multiplication of matrices A and B:
[ C = A \times B ]
where both (A) and (B) are large, but most elements in (A) are zeroes. Traditional GEMM algorithms would perform all multiplications, including those with zeros, wasting computation power and memory.

Sparse-GEMM

The idea behind Sparse-GEMM is simple: avoid computing multiplications with zeroes. By identifying and skipping operations involving zero elements, Sparse-GEMM significantly reduces the number of floating-point operations (FLOPs), making matrix multiplication more efficient.

The key optimizations involve:

  • Indexing non-zero elements: Representing sparse matrices using compact formats like CSR (Compressed Sparse Row) or CSC (Compressed Sparse Column), where only the non-zero elements and their positions are stored.
  • Memory efficiency: Reducing memory bandwidth usage by avoiding loading zeros into the processor’s cache or memory subsystem.
  • Parallelism: Mapping the sparse computation across available hardware resources, particularly GPUs or dedicated AI accelerators like those found in the NVIDIA Orin series, ensuring maximum throughput despite the sparsity.

Sparse-GEMM algorithms are critical in deploying sparse neural networks on hardware-constrained edge devices, where power and memory are limited.

2. Optimizations in Sparse-GEMM for Edge AI Models

Hardware Optimizations on NVIDIA Jetson Orin Nano

The NVIDIA Jetson Orin Nano is designed to handle real-time AI inference workloads on the edge, making it an ideal platform for Sparse-GEMM. NVIDIA has optimized the Sparse-GEMM operations within libraries like cuBLAS and TensorRT for high-throughput matrix multiplications.

Sparse-GEMM can exploit Orin’s parallel processing capabilities to accelerate sparse matrix operations by:

  • Using Tensor Cores: NVIDIA’s Tensor Cores are designed to accelerate GEMM operations. When integrated with sparse optimizations, they can multiply matrices faster than traditional cores, especially for 4×4 matrix multiplications.
  • Memory hierarchy optimization: Sparse matrix formats, such as CSR, are designed to optimize memory usage, ensuring that only non-zero elements are stored and processed in cache.
  • Fusing operations: Sparse-GEMM operations often fuse matrix multiplication with element-wise operations (like ReLU activations), reducing memory access and speeding up overall inference time.

Sparse Neural Networks and Pruning

Sparse-GEMM plays a key role in efficiently executing pruned neural networks. In 2025, pruning techniques such as structured pruning (removing entire filters, channels, or neurons) and unstructured pruning (setting individual weights to zero) are used widely to compress models for deployment on edge devices.

Sparse-GEMM ensures that these pruned models retain their performance while minimizing resource consumption.

3. Sparse-GEMM in Practice: Code Example

Let’s walk through an example of how to implement Sparse-GEMM using PyTorch’s support for sparse tensors, along with CUDA optimizations for edge AI.

Sparse Linear Layer in PyTorch with Sparse Matrix Multiplication

import torch
import torch.nn as nn

# Custom Sparse Linear Layer using PyTorch
class SparseLinear(nn.Module):
    def __init__(self, input_size, output_size, sparsity=0.8):
        super(SparseLinear, self).__init__()
        self.input_size = input_size
        self.output_size = output_size
        self.sparsity = sparsity

        # Initialize the weight matrix
        dense_weight = torch.randn(output_size, input_size)

        # Create a mask for sparsity (set weights to zero based on the given sparsity ratio)
        self.mask = torch.rand(dense_weight.shape) > self.sparsity
        sparse_weight = dense_weight * self.mask.float()

        # Convert dense weight matrix to sparse format
        self.sparse_weight = sparse_weight.to_sparse()
        self.bias = nn.Parameter(torch.randn(output_size))

    def forward(self, x):
        # Sparse matrix multiplication using torch.sparse.mm
        return torch.sparse.mm(self.sparse_weight, x.T).T + self.bias

# Example usage
input_tensor = torch.randn(1, 1024)  # Example input

# Instantiate a sparse linear layer (85% sparsity)
sparse_layer = SparseLinear(1024, 512, sparsity=0.85)
output = sparse_layer(input_tensor)
print(output)

In this example, we define a custom sparse linear layer in PyTorch that:

  • Generates a sparse weight matrix with a specified sparsity level (85% in this case).
  • Uses torch.sparse.mm() to perform sparse matrix multiplication, which ensures that only non-zero elements are involved in the computation.

By applying Sparse-GEMM algorithms, we reduce the memory and compute requirements on the edge device, which is crucial for real-time inference workloads.

Running Sparse-GEMM with TensorRT on Jetson Orin Nano

TensorRT, NVIDIA’s inference optimization engine, has built-in support for sparse tensor operations. When deploying a sparse model on a Jetson Orin Nano, TensorRT can automatically optimize the model by identifying sparsity patterns and utilizing specialized hardware (Tensor Cores) for sparse matrix multiplication.

Below is a sample workflow for optimizing a sparse model with TensorRT on a Jetson device:

# Install TensorRT on Jetson Orin Nano
sudo apt-get install python3-libnvinfer-dev

# Convert model to ONNX format (if not already done)
# For instance, using a sparse model from PyTorch:
torch.onnx.export(sparse_layer, input_tensor, "sparse_model.onnx")

# Optimize the ONNX model with TensorRT for sparse inference
trtexec --onnx=sparse_model.onnx --sparsity=enable --saveEngine=sparse_model.trt

Here’s what happens:

  1. ONNX export: We export the PyTorch model (which includes sparse layers) to the ONNX format.
  2. TensorRT optimization: TensorRT’s trtexec tool is used to optimize the ONNX model for sparse inference. By specifying the --sparsity=enable flag, TensorRT identifies and exploits sparsity in the model.

TensorRT’s optimization of sparse models allows for faster inference times and reduced memory usage on the edge, particularly in scenarios like object detection or real-time video analytics.

Conclusion

Sparse-GEMM algorithms represent a fundamental shift in how matrix multiplication is executed in deep learning models, particularly for edge AI. By skipping computations involving zero elements and using efficient memory representations, Sparse-GEMM dramatically improves the speed and efficiency of inference, making it ideal for deployment on edge devices like the NVIDIA Jetson Orin Nano.

In 2025, sparse neural networks, along with hardware accelerators and TensorRT optimizations, allow AI systems to deliver high-performance, real-time intelligence at the edge, enabling applications ranging from autonomous drones to smart city infrastructure. As Sparse-GEMM continues to evolve, it will remain a cornerstone technology in the era of efficient and scalable AI deployment.