Description
Return sigmoidDerivative=p*(1-p), inverse-logit derivative=1/(p*(1-p)) and sign=1.
The logistic sigmoid is 1/(1+exp(-x)) and its inverse logit is log(p/(1-p)) on 0<p<1. Temperature and input sensitivities use different derivatives. The logarithm of a derivative is distinct from the derivative of a logarithm, especially when numerical tails underflow.
Return sigmoidDerivative=p*(1-p), inverse-logit derivative=1/(p*(1-p)) and sign=1.
When to use this tool
Use Sigmoid Logit Jacobian Sign when checking the stated sigmoid/logit scalar derivative or stable product convention.
How to use the tool and how it works
- Enter probability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read sigmoidDerivative, logitDerivative, sign. Use the output convention below.
Require 0<probability<1. Return sigmoidDerivative=p*(1-p), inverse-logit derivative=1/(p*(1-p)) and sign=1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| probability | Probability Unit: 1. | Required. Finite number; strictly above 0; strictly below 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| sigmoidDerivative | Sigmoid Derivative | Required. Finite number. |
| logitDerivative | Logit Derivative | Required. Finite number. |
| sign | Sign | Required. Safe integer. |
{
"input": {
"probability": 0.5
},
"output": {
"sigmoidDerivative": 0.25,
"logitDerivative": 4,
"sign": 1
}
}Limitations and assumptions
- These are forward and inverse derivatives at corresponding coordinates; probabilities zero/one are excluded and no probability calibration is verified.
- 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
- Sigmoid Scalar Third Derivative
With s=sigmoid(x), return s*(1-s)*(1-6*s+6*s²), the third scalar input derivative.
- Sigmoid Log Derivative
Return -abs(x)-2*log1p(exp(-abs(x))), the natural logarithm of sigmoid's first derivative.