Description
For a nonempty finite logWeights list take offset=max(logWeights) and return centered values logWeights-offset.
Products of small probabilities can round to zero in floating-point arithmetic. Natural logarithms turn products into sums, and centering or expm1-based expressions can reduce avoidable numerical loss. A finite log weight is different from a raw probability and cannot directly represent an exact zero probability.
For a nonempty finite logWeights list take offset=max(logWeights) and return centered values logWeights-offset.
When to use this tool
Use Log Probability Weight Centering Offset when you need the stated natural-log contribution or stable conversion between a finite log representation and an ordinary value.
How to use the tool and how it works
- Enter logWeights. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read centered, offset. Use the output convention below.
For a nonempty finite logWeights list take offset=max(logWeights) and return centered values logWeights-offset.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| logWeights | Log Weights | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| centered | Centered | Required. Array of finite number; maximum items 256. |
| offset | Offset | Required. Finite number. |
{
"input": {
"logWeights": [
1000,
998,
999
]
},
"output": {
"centered": [
0,
-2,
-1
],
"offset": 1000
}
}Limitations and assumptions
- Centering preserves relative weights but does not normalize probabilities. Inputs and differences must remain finite; negative-infinity log weights are unsupported.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Keep long products or normalizations in the log domain when feasible. Check whether exact zeros need a separate flag and whether the final ordinary-scale result is representable.
References
Similar or alternative tools
- Log Probability Logsum Two Weights
Set max=max(left,right) and return logSum=max+ln(exp(left-max)+exp(right-max)).
- Probability: Probability Product Log Under Flow Check
Multiply supplied probabilities through log space and distinguish true zero factors from floating-point underflow; logProduct zero is unused when zeroFactor=true.