Description
Return log1p(output/alpha), the finite negative-branch input of alpha*(exp(x)-1).
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 log1p(output/alpha), the finite negative-branch input of alpha*(exp(x)-1).
When to use this tool
Use ELU Negative Output Inverse when checking the stated ELU inverse, curvature or partial derivative convention.
How to use the tool and how it works
- Enter output, alpha. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read input. Use the output convention below.
Require alpha>0 and -alpha<output<0. Return log1p(output/alpha), the finite negative-branch input of alpha*(exp(x)-1).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 |
|---|---|---|
| output | Output | Required. Finite number; strictly below 0. |
| alpha | Positive shape parameter when required by the function convention above. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| input | Input | Required. Finite number. |
{
"input": {
"output": -1,
"alpha": 2
},
"output": {
"input": -0.6931471805599453
}
}Limitations and assumptions
- The lower asymptote -alpha and output zero are excluded; this is only the negative-output inverse branch.
- 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-negative-output-inverse — 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 Negative Curvature
Return alpha*exp(x) for x<0 and zero for x>=0 as the negative-branch curvature term.
- Activation: Elu Scalar Derivative
Return one for x>0, alpha*exp(x) for x<0 and the chosen one-sided value alpha or one at zero.