Description
Return -x/(scale+abs(x))², differentiating scale at fixed x.
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.
Return -x/(scale+abs(x))², differentiating scale at fixed x.
When to use this tool
Use Softsign Scale Parameter Sensitivity when checking the stated softsign inverse, saturation or derivative convention.
How to use the tool and how it works
- Enter x, scale. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivative. Use the output convention below.
Require scale>0 in x/(scale+abs(x)). Return -x/(scale+abs(x))², differentiating scale at fixed x.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | Finite scalar input coordinate; use the mathematical scale specified above. | Required. Finite number. |
| scale | Supplied scale parameter with its operation-specific meaning stated above. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Partial derivative of x/(scale+abs(x)) with respect to its positive denominator scale. | Required. Finite number. |
{
"input": {
"x": 2,
"scale": 2
},
"output": {
"derivative": -0.125
}
}Limitations and assumptions
- This uses an additive positive denominator scale, not the alternative convention softsign(scale*x).
- 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
- Softsign Scalar Second Derivative
For x!=0, return -2*sign(x)/(1+abs(x))³.
- Activation: Softsign Scalar Inverse
Invert softsign x/(1+abs(x)) as x=y/(1-abs(y)).