Description
Return leftLimit=0, rightLimit=threshold and their jump size threshold for the thresholded ReLU boundary.
Thresholded ReLU returns the input only on a chosen side of a threshold and zero otherwise. Boundary inclusion, continuity and differentiability are separate questions: a jump can persist even if a value is assigned at the threshold.
Return leftLimit=0, rightLimit=threshold and their jump size threshold for the thresholded ReLU boundary.
When to use this tool
Use Thresholded ReLU Jump Size when checking the stated threshold and zero-input policy convention.
How to use the tool and how it works
- Enter threshold. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read leftLimit, rightLimit, jump. Use the output convention below.
Require threshold>=0. Return leftLimit=0, rightLimit=threshold and their jump size threshold for the thresholded ReLU boundary.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| threshold | Supplied symmetric or one-sided activation threshold as defined above. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| leftLimit | Left Limit | Required. Finite number. |
| rightLimit | Right Limit | Required. Finite number. |
| jump | Jump | Required. Finite number. |
{
"input": {
"threshold": 2
},
"output": {
"leftLimit": 0,
"rightLimit": 2,
"jump": 2
}
}Limitations and assumptions
- These are one-sided limits, not the function value at the boundary or a derivative; zero jump does not imply differentiability.
- 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
- Thresholded ReLU Zero Input Policy
For thresholded ReLU, compare zero to threshold using >= or > according to passAtThreshold; zeroOutput stays zero.
- ReLU
Apply the rectified linear activation, flooring negatives at zero.