Description
Return sqrt(output) as positiveInput and zeroRay when output=0.
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 sqrt(output) as positiveInput and zeroRay when output=0.
When to use this tool
Use ReLU Squared Inverse Branch when checking the stated rectifier value, inverse region or subgradient convention.
How to use the tool and how it works
- Enter output. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read positiveInput, zeroRay. Inspect zeroRay before interpreting the associated values.
Require output>=0 for squared ReLU max(0,x)². Return sqrt(output) as positiveInput and zeroRay when output=0.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| output | Output | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| positiveInput | Positive Input | Required. Finite number. |
| zeroRay | True at output zero, whose full inverse is all input values<=0. | Required. Boolean. |
{
"input": {
"output": 9
},
"output": {
"positiveInput": 3,
"zeroRay": false
}
}Limitations and assumptions
- At zero all inputs<=0 are preimages; the returned zero is a boundary marker, not a unique inverse.
- 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 Zero Subgradient Choice
Return slope one for positive x, zero for negative x and the supplied slope at zero; flag x=0 as nondifferentiable.
- ReLU6 Output Preimage Interval
Return lower=upper=output with unbounded flags at zero/six; interior outputs have singleton=true.