Description
Return -1/(probability × ln(logBase)).
Information units depend on the logarithm base: base two gives bits and the natural logarithm gives nats. A derivative or conversion factor must preserve its stated variable and base.
Return -1/(probability × ln(logBase)).
When to use this tool
Use Symbol Self Information Gradient when you need an explicit information-unit conversion or surprisal component.
How to use the tool and how it works
- Enter probability, logBase. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read gradient. Use the output convention below.
Require probability in (0, 1] and positive logBase different from one. Return -1/(probability × ln(logBase)).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| probability | Probability in the stated interval; zero handling follows the calculation above. | Required. Finite number; maximum 1; strictly above 0. |
| logBase | Logarithm base; base 2 gives bits and base e gives nats under conventional bases greater than one. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| gradient | Surprisal derivative with respect to probability, in log-base units per probability unit. | Required. Finite number. |
{
"input": {
"probability": 0.5,
"logBase": 2.718281828459045
},
"output": {
"gradient": -2
}
}Limitations and assumptions
- This derivative is with respect to probability; bases below one reverse the usual information orientation and are accepted explicitly.
- 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
Check the probability domain and logarithm convention of the complete measure before combining values.
References
Similar or alternative tools
- Information: Surprisal Log Base Crosswalk
Multiply nonnegative surprisal by ln(sourceBase)/ln(targetBase), requiring both bases greater than one.
- Binary Entropy Local Slope
For mass strictly inside (0, 1), return log2((1 - mass)/mass).