Description
Return slope one for positive x, zero for negative x and the supplied slope at zero; flag x=0 as nondifferentiable.
ReLU clips negative input to zero; ReLU6 also clips above six. Saturated outputs have entire input rays as preimages, unlike interior values with single inverses. At a ReLU kink a selected subgradient is not an ordinary two-sided derivative.
Return slope one for positive x, zero for negative x and the supplied slope at zero; flag x=0 as nondifferentiable.
When to use this tool
Use ReLU Zero Subgradient Choice when checking the stated rectifier value, inverse region or subgradient convention.
How to use the tool and how it works
- Enter x, suppliedZeroSlope. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read slope, atNondifferentiablePoint. Inspect atNondifferentiablePoint before interpreting the associated values.
Require suppliedZeroSlope in [0,1]. Return slope one for positive x, zero for negative x and the supplied slope at zero; flag x=0 as nondifferentiable.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | Finite scalar input coordinate; use the mathematical scale specified above. | Required. Finite number. |
| suppliedZeroSlope | Chosen subgradient in [0,1] at the ReLU kink, not an ordinary derivative there. | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| slope | Slope | Required. Finite number. |
| atNondifferentiablePoint | At Nondifferentiable Point | Required. Boolean. |
{
"input": {
"x": 0,
"suppliedZeroSlope": 0.25
},
"output": {
"slope": 0.25,
"atNondifferentiablePoint": true
}
}Limitations and assumptions
- A chosen ReLU subgradient at zero is not an ordinary two-sided derivative there or a complete autodifferentiation policy.
- 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
- ReLU Squared Inverse Branch
Return sqrt(output) as positiveInput and zeroRay when output=0.
- ReLU6 Output Preimage Interval
Return lower=upper=output with unbounded flags at zero/six; interior outputs have singleton=true.