Description
Return zero before squaring when s rounds to zero or one.
Swish multiplies its input by sigmoid(beta*x). Differentiating input x and differentiating the shape parameter beta produce different sensitivities. At beta zero the value becomes a linear half-input, without requiring a neural-network evaluation.
Return zero before squaring when s rounds to zero or one.
When to use this tool
Use Swish Beta Partial Derivative when checking the stated Swish limit or scalar partial derivative convention.
How to use the tool and how it works
- Enter x, beta. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivative. Use the output convention below.
Require beta*x finite, set s=sigmoid(beta*x), and return x²*s*(1-s) as the beta partial derivative. Return zero before squaring when s rounds to zero or one.1
Swish combines its input with a beta-scaled sigmoid gate. This scalar helper evaluates the stated limit or derivative, rather than establishing training performance or a preferred beta.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | Finite scalar input coordinate; use the mathematical scale specified above. | Required. Finite number. |
| beta | Supplied scalar shape parameter under the explicitly stated function convention. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Scalar derivative with respect to the variable and at the fixed coordinates specified above; not a tensor/model gradient. | Required. Finite number. |
{
"input": {
"x": 2,
"beta": 0
},
"output": {
"derivative": 1
}
}Limitations and assumptions
- This differentiates beta at fixed x; numerical saturation is handled explicitly and is not a mathematical claim of an exactly zero tail.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete explicit function and the intended parameter, branch and numerical conventions for symbolic, tensor or model-level differentiation; assess training behavior independently.
References
-
Calculation and input contract: activation/swish-beta-partial-derivative — tool.io
-
Searching for Activation Functions — Prajit Ramachandran, Barret Zoph and Quoc V. Le
Similar or alternative tools
- Activation: Swish Scalar Derivative Beta
For f(x)=x*sigmoid(beta*x), require abs(beta*x)<=10^300.
- Swish Beta Zero Limit
For x*sigmoid(beta*x), return the beta→0 limit x/2 and the beta partial derivative at zero, x²/4.