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torch.Tensor.Tensor.sigmoid

Tensor.sigmoid(): Tensor<S, D, Dev>

Sigmoid activation function.

Computes σ(x) = 1 / (1 + e^(-x)). Output is bounded to (0, 1), making it ideal for probability outputs. One of the oldest and most fundamental activation functions.

Use Cases:

  • Binary classification output layer
  • Probability modeling
  • Gating mechanisms in neural networks (LSTM gates)
  • Output normalization to (0, 1) range
σ(x)=11+e−xGradient: ∂σ(x)∂x=σ(x)(1−σ(x))\begin{aligned} \sigma(x) = \frac{1}{1 + e^{-x}} \\ \text{Gradient: } \frac{\partial \sigma(x)}{\partial x} = \sigma(x)(1 - \sigma(x)) \end{aligned}σ(x)=1+e−x1​Gradient: ∂x∂σ(x)​=σ(x)(1−σ(x))​
  • Range: Output is always in (0, 1)
  • Gradient: Gradient is highest at x=0, decreases for extreme values
  • Saturation: For large |x|, gradient → 0 (can cause vanishing gradients)
  • Smooth: Continuously differentiable and smooth
  • Vanishing gradient: For |x| 5, gradient becomes very small
  • Not zero-centered: Output is centered around 0.5, not 0 (slower convergence)

Returns

Tensor<S, D, Dev>– New tensor with sigmoid applied element-wise

Examples

// Binary classification output
const logits = torch.randn(100);
const probabilities = logits.sigmoid();  // [0, 1] range

// LSTM gate (sigmoid gate)
const hidden = torch.randn(32, 128);
const forget_gate = hidden.matmul(weight).sigmoid();  // [0, 1] gate

// Probability thresholding
const scores = torch.randn(1000);
const threshold = 0.5;
const predictions = scores.sigmoid().gt(threshold).long();

See Also

  • PyTorch tensor.sigmoid()
  • tanh - Similar but zero-centered, range [-1, 1]
  • relu - Modern alternative: faster and no saturation
  • softmax - Multi-class version (sum to 1)
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