Description
Return one for x>0, alpha*exp(x) for x<0 and the chosen one-sided value alpha or one at zero.
ELU uses x on the nonnegative branch and alpha*(exp(x)-1) on the negative branch. Its negative asymptote is -alpha for positive alpha. Input derivatives, alpha partial derivatives and one-sided join conventions answer different mathematical questions.
Return one for x>0, alpha*exp(x) for x<0 and the chosen one-sided value alpha or one at zero.
When to use this tool
Use Activation: Elu Scalar Derivative when checking the stated ELU inverse, curvature or partial derivative convention.
How to use the tool and how it works
- Enter x, alpha, zeroSide. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Require alpha>0 and zeroSide left or right. Return one for x>0, alpha*exp(x) for x<0 and the chosen one-sided value alpha or one at zero.1
ELU has a linear positive branch and an alpha-scaled exponential negative branch. The local derivative, inverse and join conventions above do not imply a particular network’s behavior.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | Finite scalar input coordinate; use the mathematical scale specified above. | Required. Finite number. |
| alpha | Positive shape parameter when required by the function convention above. | Required. Finite number. |
| zeroSide | One-sided input-derivative choice at zero, left=alpha and right=1. | Required. Text; one of "left", "right". Implementation limit: 8192 Unicode code points and 16384 UTF-16 code units. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the operation-specific returned members listed below. | Required. Object. |
| result.derivative | Scalar derivative with respect to the variable and at the fixed coordinates specified above; not a tensor/model gradient. | Calculated result member: number. |
{
"input": {
"x": 0,
"alpha": 2,
"zeroSide": "left"
},
"output": {
"result": {
"derivative": 2
}
}
}Limitations and assumptions
- The two-sided derivative at zero exists only when alpha=1; selecting a side does not remove a mathematical kink.
- Outputs are nested inside result. 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/elu-scalar-derivative — tool.io
-
Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs) — Djork-Arné Clevert, Thomas Unterthiner and Sepp Hochreiter
Similar or alternative tools
- ELU Alpha Partial Derivative
Return expm1(x) for x<0 and zero otherwise, the partial derivative of ELU with respect to alpha at fixed x.
- ELU Negative Output Inverse
Return log1p(output/alpha), the finite negative-branch input of alpha*(exp(x)-1).