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CUDA Sparse Matrix Operations Guide

December 25, 202513 minBy RightNow AI Team

Introduction

Sparse matrices appear in graph neural networks, recommender systems, and pruned neural networks. When matrices are sufficiently sparse (>90%), sparse formats save memory and computation. NVIDIA's cuSPARSE and Tensor Core sparse support make GPU sparse operations practical. This guide covers sparse formats, cuSPARSE operations, and when sparsity helps vs. hurts performance.

Common Performance Issues

Sparse overhead exceeds benefits for low sparsity (<80%)
Irregular memory access patterns limit GPU efficiency
Format conversion overhead when switching between dense/sparse
Poor load balancing for power-law degree distributions

Optimization Techniques

1. Choose Right Format

CSR for SpMV, COO for construction, BSR for block-sparse.

2. Tensor Core Sparsity

2:4 structured sparsity gets 2x speedup on Ampere+.

3. Merge-based SpMM

Better load balancing for power-law graphs.

Implementation Comparison

Before (Naive Implementation)

Basic CSR SpMV has poor parallelism for rows with many non-zeros.

cuda

// CSR format: row_ptr, col_idx, values
__global__ void spmv_csr_naive(int* row_ptr, int* col_idx, float* values,
                               float* x, float* y, int num_rows) {
    int row = blockIdx.x * blockDim.x + threadIdx.x;
    if (row >= num_rows) return;

    float sum = 0.0f;
    int row_start = row_ptr[row];
    int row_end = row_ptr[row + 1];

    for (int j = row_start; j < row_end; j++) {
        sum += values[j] * x[col_idx[j]];
    }
    y[row] = sum;
}

After (Optimized Implementation)

cuSPARSE provides optimized SpMM with multiple algorithms.

cuda

#include <cusparse.h>

void sparse_matmul(cusparseHandle_t handle,
                   cusparseSpMatDescr_t A,   // Sparse matrix
                   cusparseDnMatDescr_t B,   // Dense matrix
                   cusparseDnMatDescr_t C) { // Output

    float alpha = 1.0f, beta = 0.0f;
    size_t bufferSize;

    // Get buffer size
    cusparseSpMM_bufferSize(handle, CUSPARSE_OPERATION_NON_TRANSPOSE,
                            CUSPARSE_OPERATION_NON_TRANSPOSE,
                            &alpha, A, B, &beta, C,
                            CUDA_R_32F, CUSPARSE_SPMM_ALG_DEFAULT,
                            &bufferSize);

    void* buffer;
    cudaMalloc(&buffer, bufferSize);

    // Execute SpMM
    cusparseSpMM(handle, CUSPARSE_OPERATION_NON_TRANSPOSE,
                 CUSPARSE_OPERATION_NON_TRANSPOSE,
                 &alpha, A, B, &beta, C,
                 CUDA_R_32F, CUSPARSE_SPMM_ALG_DEFAULT, buffer);
}

// For 2:4 structured sparsity (Ampere+ Tensor Cores):
// Use cusparseLtMatmul for 2x speedup with 50% sparsity

Performance Results

Metric	Naive	Optimized	Improvement
SpMV throughput	50 GB/s	300 GB/s	6x with cuSPARSE
2:4 Sparse TC	1x (dense)	2x	With structured sparsity

Frequently Asked Questions

When is sparse faster than dense?

Generally when sparsity > 90% for SpMV, > 80% for SpMM. Structured 2:4 sparsity is always 2x at 50% sparsity on Tensor Cores.

Matrix Multiplication

Dense alternative

→

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CUDA sparsecuSPARSEsparse matrix GPUCSR CUDASpMMsparse neural networks

Introduction

Implementation Comparison

Before (Naive Implementation)

Basic CSR SpMV has poor parallelism for rows with many non-zeros.

cuda

// CSR format: row_ptr, col_idx, values
__global__ void spmv_csr_naive(int* row_ptr, int* col_idx, float* values,
                               float* x, float* y, int num_rows) {
    int row = blockIdx.x * blockDim.x + threadIdx.x;
    if (row >= num_rows) return;

    float sum = 0.0f;
    int row_start = row_ptr[row];
    int row_end = row_ptr[row + 1];

    for (int j = row_start; j < row_end; j++) {
        sum += values[j] * x[col_idx[j]];
    }
    y[row] = sum;
}

After (Optimized Implementation)

cuSPARSE provides optimized SpMM with multiple algorithms.

cuda

#include <cusparse.h>

void sparse_matmul(cusparseHandle_t handle,
                   cusparseSpMatDescr_t A,   // Sparse matrix
                   cusparseDnMatDescr_t B,   // Dense matrix
                   cusparseDnMatDescr_t C) { // Output

    float alpha = 1.0f, beta = 0.0f;
    size_t bufferSize;

    // Get buffer size
    cusparseSpMM_bufferSize(handle, CUSPARSE_OPERATION_NON_TRANSPOSE,
                            CUSPARSE_OPERATION_NON_TRANSPOSE,
                            &alpha, A, B, &beta, C,
                            CUDA_R_32F, CUSPARSE_SPMM_ALG_DEFAULT,
                            &bufferSize);

    void* buffer;
    cudaMalloc(&buffer, bufferSize);

    // Execute SpMM
    cusparseSpMM(handle, CUSPARSE_OPERATION_NON_TRANSPOSE,
                 CUSPARSE_OPERATION_NON_TRANSPOSE,
                 &alpha, A, B, &beta, C,
                 CUDA_R_32F, CUSPARSE_SPMM_ALG_DEFAULT, buffer);
}

// For 2:4 structured sparsity (Ampere+ Tensor Cores):
// Use cusparseLtMatmul for 2x speedup with 50% sparsity

Metric

Naive

Optimized

Improvement

SpMV throughput

50 GB/s

300 GB/s

6x with cuSPARSE

2:4 Sparse TC

1x (dense)

With structured sparsity

CUDA Sparse Matrix Operations Guide

Introduction

Common Performance Issues

Optimization Techniques

1. Choose Right Format

2. Tensor Core Sparsity

3. Merge-based SpMM

Implementation Comparison

Before (Naive Implementation)

After (Optimized Implementation)

Performance Results

Frequently Asked Questions

When is sparse faster than dense?

Related Guides

CUDA Sparse Matrix Operations Guide

Introduction

Common Performance Issues

Optimization Techniques

1. Choose Right Format

2. Tensor Core Sparsity

3. Merge-based SpMM

Implementation Comparison

Before (Naive Implementation)

After (Optimized Implementation)

Performance Results

Frequently Asked Questions

When is sparse faster than dense?

Related Guides