Description
For x*sigmoid(beta*x), return the beta→0 limit x/2 and the beta partial derivative at zero, x²/4.
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.
For x*sigmoid(beta*x), return the beta→0 limit x/2 and the beta partial derivative at zero, x²/4.
When to use this tool
Use Swish Beta Zero Limit when checking the stated Swish limit or scalar partial derivative convention.
How to use the tool and how it works
- Enter x. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read limit, betaDerivative. Use the output convention below.
For x*sigmoid(beta*x), return the beta→0 limit x/2 and the beta partial derivative at zero, x²/4.1
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. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| limit | Limit | Required. Finite number. |
| betaDerivative | Beta Derivative | Required. Finite number. |
{
"input": {
"x": 4
},
"output": {
"limit": 2,
"betaDerivative": 4
}
}Limitations and assumptions
- The input x is held fixed; very large finite inputs can overflow the squared sensitivity and be rejected.
- 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-zero-limit — 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 Partial Derivative
Return zero before squaring when s rounds to zero or one.