Description
Return lower=upper=output with unbounded flags at zero/six; interior outputs have singleton=true.
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 lower=upper=output with unbounded flags at zero/six; interior outputs have singleton=true.
When to use this tool
Use ReLU6 Output Preimage Interval 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 lower, upper, lowerUnbounded, upperUnbounded, singleton. Inspect lowerUnbounded, upperUnbounded, singleton before interpreting the associated values.
Require output in [0,6]. Return lower=upper=output with unbounded flags at zero/six; interior outputs have singleton=true.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| output | Output | Required. Finite number; minimum 0; maximum 6. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| lower | Finite output boundary marker; lowerUnbounded=true replaces it by -∞ as an interval end. | Required. Finite number. |
| upper | Finite output boundary marker; upperUnbounded=true replaces it by +∞ as an interval end. | Required. Finite number. |
| lowerUnbounded | Lower Unbounded | Required. Boolean. |
| upperUnbounded | Upper Unbounded | Required. Boolean. |
| singleton | Singleton | Required. Boolean. |
{
"input": {
"output": 0
},
"output": {
"lower": 0,
"upper": 0,
"lowerUnbounded": true,
"upperUnbounded": false,
"singleton": false
}
}Limitations and assumptions
- At zero the preimage is (-∞,0], and at six it is [6,∞). Numeric endpoints are finite boundary markers, not a full singleton when an unbounded flag is true.
- 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: ReLU6 Scalar Value
Return min(6,max(0,x)), clipping the scalar input into the closed interval [0,6].
- 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.