Description
Return -output/slope², the slope sensitivity of negative-branch inverse output/slope.
Leaky ReLU uses x on its nonnegative branch and slope*x on its negative branch. A positive nonzero slope gives a single inverse, while a negative slope maps both branches to nonnegative outputs and can give two preimages. Input and slope derivatives differ.
Return -output/slope², the slope sensitivity of negative-branch inverse output/slope.
When to use this tool
Use Leaky ReLU Negative Inverse Slope Sensitivity when checking the stated leaky-rectifier inverse or slope sensitivity convention.
How to use the tool and how it works
- Enter output, slope. 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 output<0 and slope>0. Return -output/slope², the slope sensitivity of negative-branch inverse output/slope.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| output | Output | Required. Finite number; strictly below 0. |
| slope | Slope | Required. Finite number; strictly above 0. |
| 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": {
"output": -2,
"slope": 0.5
},
"output": {
"derivative": 8
}
}Limitations and assumptions
- This holds the negative output fixed and does not differentiate the forward activation with respect to its input.
- 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
Similar or alternative tools
- Activation: Leaky ReLU Scalar Inverse
For positive slope return one inverse, y when y>=0 otherwise y/slope.
- Leaky ReLU Slope Partial Derivative
For leaky ReLU, return x when x<0 and zero otherwise as the partial derivative with respect to the negative-branch slope.