`scale`¶

Multiply a tensor by a fixed scalar.

Category: arithmetic · Identity: scale@1

Shape¶

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

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

Arguments¶

Name	Type	Default	Constraints	Description
`factor` (positional)	float	required	—	Constant every element is multiplied by; it is not learned.

Description¶

out = factor * x: a shape-, rank-, and dtype-preserving constant gain with no parameters and no buffers. factor is a plan constant, not a learned value, so the gradient is factor * grad_out and the behavior is identical in train and eval mode. The multiplication happens in the input dtype; a large factor can overflow float16, so keep the product inside the representable range for the plan's compute dtype.

Examples¶

Example 1¶

A residual whose branch is damped by 0.5 before the sum.

saved = x
linear(8, name="branch")
relu()
h = linear(4)
s = scale(h, 0.5)
add(s, saved)

Input ['B', 4] → output ['B', 4].

Network: [B, 4] -> [B, 4]  dtype=float32
index  name    operation  input shapes        output shapes
0      branch  linear     x=[B, 4]            out=[B, 8]
1      n1      relu       x=[B, 8]            out=[B, 8]
2      n2      linear     x=[B, 8]            out=[B, 4]
3      n3      scale      x=[B, 4]            out=[B, 4]
4      n4      add        a=[B, 4], b=[B, 4]  out=[B, 4]

Parameters: 76

Example 2¶

Sequences: the factor applies to every position and feature.

linear(8)
scale(2.0)
tanh()

Input ['B', 5, 4] → output ['B', 5, 8].

Network: [B, 5, 4] -> [B, 5, 8]  dtype=float32
index  name  operation  input shapes  output shapes
0      n0    linear     x=[B, 5, 4]   out=[B, 5, 8]
1      n1    scale      x=[B, 5, 8]   out=[B, 5, 8]
2      n2    tanh       x=[B, 5, 8]   out=[B, 5, 8]

Parameters: 40

Example 3¶

Images: a constant gain on the convolution output.

conv(4, kernel_size=3, padding=1)
scale(0.1)
relu()

Input ['B', 3, 8, 8] → output ['B', 4, 8, 8].

Network: [B, 3, 8, 8] -> [B, 4, 8, 8]  dtype=float32
index  name  operation  input shapes    output shapes
0      n0    conv       x=[B, 3, 8, 8]  out=[B, 4, 8, 8]
1      n1    scale      x=[B, 4, 8, 8]  out=[B, 4, 8, 8]
2      n2    relu       x=[B, 4, 8, 8]  out=[B, 4, 8, 8]

Parameters: 112

scale¶