Description
Return -ln(probability)/ln(logBase) and multiply it by nonnegative weight for weightedTerm.
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 -ln(probability)/ln(logBase) and multiply it by nonnegative weight for weightedTerm.
When to use this tool
Use Surprisal Concentration Weight Term when you need an explicit information-unit conversion or surprisal component.
How to use the tool and how it works
- Enter probability, weight, logBase. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read surprisal, weightedTerm. Use the output convention below.
Return -ln(probability)/ln(logBase) and multiply it by nonnegative weight for weightedTerm. Require probability in (0, 1] and logBase > 1.1
| 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. |
| weight | Weight | Required. Finite number; minimum 0. |
| logBase | Logarithm base; base 2 gives bits and base e gives nats under conventional bases greater than one. | Required. Finite number; strictly above 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| surprisal | Information value in the specified logarithm-base units. | Required. Finite number. |
| weightedTerm | Weighted Term | Required. Finite number. |
{
"input": {
"probability": 0.25,
"weight": 0.5,
"logBase": 2
},
"output": {
"surprisal": 2,
"weightedTerm": 1
}
}Limitations and assumptions
- Weight is an explicit multiplier rather than automatically a probability mass; this is one term without aggregate normalization.
- 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
- Symbol Self Information Gradient
Return -1/(probability × ln(logBase)).
- Information: Conditional Surprisal Cell
Return [ln(condition) - ln(joint)]/ln(base).