`sigmoid`¶

Logistic sigmoid, squashing values into (0, 1).

Category: activation · Identity: sigmoid@1

Shape¶

x[B, ...] -> out[B, ...]

Port	Direction	Pattern	dtype
`x`	input	`x[B, ...]`	compute
`out`	output	`out[B, ...]`	compute

Arguments¶

This operator takes no scalar arguments.

Description¶

Elementwise out = 1 / (1 + exp(-x)).

The output lies strictly in (0, 1), which makes the operator a natural final activation for probabilities and for images normalized to the unit interval. Gradients vanish for inputs far from zero, so it is a poor choice for hidden layers; prefer silu or gelu there. When the loss is a binary cross entropy, keep the logits and use a fused loss rather than stacking sigmoid in front of it.

The operator is elementwise and shape preserving on [B, F], [B, T, D] and [B, C, H, W] tensors, has no parameters, behaves identically in train and eval mode, and is computed out of place in the plan's compute dtype.

Examples¶

Example 1¶

A binary classification head emitting a probability.

linear(1)
sigmoid()

Input ['B', 32] → output ['B', 1].

Network: [B, 32] -> [B, 1]  dtype=float32
index  name  operation  input shapes  output shapes
0      n0    linear     x=[B, 32]     out=[B, 1]
1      n1    sigmoid    x=[B, 1]      out=[B, 1]

Parameters: 33

Example 2¶

On a [B, T, D] sequence the activation applies elementwise at every position.

linear(32)
sigmoid()
linear()

Input ['B', 6, 16] → output ['B', 6, 8].

Network: [B, 6, 16] -> [B, 6, 8]  dtype=float32
index  name  operation  input shapes  output shapes
0      n0    linear     x=[B, 6, 16]  out=[B, 6, 32]
1      n1    sigmoid    x=[B, 6, 32]  out=[B, 6, 32]
2      n2    linear     x=[B, 6, 32]  out=[B, 6, 8]

Parameters: 808

Example 3¶

A final activation for image generators that emit values in [0, 1].

conv(3, kernel_size=3, padding=1)
sigmoid()

Input ['B', 8, 16, 16] → output ['B', 3, 16, 16].

Network: [B, 8, 16, 16] -> [B, 3, 16, 16]  dtype=float32
index  name  operation  input shapes      output shapes
0      n0    conv       x=[B, 8, 16, 16]  out=[B, 3, 16, 16]
1      n1    sigmoid    x=[B, 3, 16, 16]  out=[B, 3, 16, 16]

Parameters: 219

sigmoid¶