Description
For x!=0, return -2*sign(x)/(1+abs(x))³.
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.
For x!=0, return -2*sign(x)/(1+abs(x))³.
When to use this tool
Use Softsign Scalar Second Derivative when checking the stated softsign inverse, saturation or derivative convention.
How to use the tool and how it works
- Enter x, zeroSide. 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.
For x!=0, return -2*sign(x)/(1+abs(x))³. At zero, zeroSide=left returns the one-sided second derivative +2, right returns -2, and reject causes an input error.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | Finite scalar input coordinate; use the mathematical scale specified above. | Required. Finite number. |
| zeroSide | left returns one-sided +2, right returns -2, reject errors at x=0; no two-sided second derivative exists there. | Required. Text; one of "left", "right", "reject"; maximum UTF-16 length 8192. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Scalar derivative with respect to the variable and at the fixed coordinates specified above; not a tensor/model gradient. | Required. Finite number. |
{
"input": {
"x": 1,
"zeroSide": "reject"
},
"output": {
"derivative": -0.25
}
}Limitations and assumptions
- Softsign has no two-sided second derivative at zero; selecting a side does not make that derivative defined.
- 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.
- Activation: Softsign Scalar Inverse
Invert softsign x/(1+abs(x)) as x=y/(1-abs(y)).