CUDA Sigmoid Activation Optimization Guide

Introduction

Sigmoid squashes values to (0,1), essential for binary classification outputs and attention gates. Naive exp(-x) overflows for large positive x; stable implementation handles all float32 values.

Common Performance Issues

• Overflow for large positive x
• Underflow precision loss
• Slow exp() computation
• Not fused with BCE loss

Optimization Techniques

__device__ float sigmoid_stable(float x) {
    if (x >= 0) {
        float z = expf(-x);
        return 1.0f / (1.0f + z);
    } else {
        float z = expf(x);
        return z / (1.0f + z);
    }
}

Implementation Comparison

Before (Naive Implementation)

Overflows for x > 88.

__global__ void sigmoid_naive(float* x, float* y, int n) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < n) y[idx] = 1.0f / (1.0f + expf(-x[idx]));  // Overflows!
}

After (Optimized Implementation)

Uses fast intrinsics and stable formulation.

// Fast approximation (< 0.3% error)
__device__ float sigmoid_fast(float x) {
    return 0.5f + 0.5f * tanhf(0.5f * x);  // tanh is well-optimized
}

// Or use CUDA intrinsics
__global__ void sigmoid_opt(float* x, float* y, int n) {
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < n) {
        float v = x[idx];
        y[idx] = (v >= 0) ? 1.0f / (1.0f + __expf(-v))
                          : __expf(v) / (1.0f + __expf(v));
    }
}

Performance Results

Frequently Asked Questions

Related Guides

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