Description
Compute y=x/(1+abs(x)); return positiveGap=1-y and negativeGap=1+y.
Softsign uses x/(1+abs(x)); its finite-input range is between -1 and 1. It has a first derivative at zero but different one-sided second derivatives there. Changing an additive denominator scale is distinct from multiplying the function’s input by a scale.
Compute y=x/(1+abs(x)); return positiveGap=1-y and negativeGap=1+y.
When to use this tool
Use Softsign Output Distance To Saturation when checking the stated softsign inverse, saturation or derivative convention.
How to use the tool and how it works
- Enter x. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read positiveGap, negativeGap. Use the output convention below.
Compute y=x/(1+abs(x)); return positiveGap=1-y and negativeGap=1+y.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | Finite scalar input coordinate; use the mathematical scale specified above. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| positiveGap | Positive Gap | Required. Finite number. |
| negativeGap | Negative Gap | Required. Finite number. |
{
"input": {
"x": 3
},
"output": {
"positiveGap": 0.25,
"negativeGap": 1.75
}
}Limitations and assumptions
- These are distances in output coordinates to saturation values, not input distances; numerical rounding can produce a zero gap.
- 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: Softsign Scalar Derivative
Return 1/(1+abs(x))² as the first scalar derivative of x/(1+abs(x)), including derivative one at zero.
- Softsign Curvature Magnitude
For x!=0, return magnitude=2/(1+abs(x))³ with defined=true.