Description
Return (firstLogit-secondLogit)/temperature as the natural-log ratio of their softmax probabilities.
Softmax normalizes exponentiated logits into probabilities. At temperature T it applies logits/T, so Jacobian entries contain a 1/T factor. Log-softmax derivatives and pairwise log probability ratios differ from the softmax derivative and from ordinary odds.
Return (firstLogit-secondLogit)/temperature as the natural-log ratio of their softmax probabilities.
When to use this tool
Use Activation: Softmax Pairwise Logit Odds when checking the stated softmax/log-softmax coordinate or log-ratio convention.
How to use the tool and how it works
- Enter firstLogit, secondLogit, temperature. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Require temperature>0. Return (firstLogit-secondLogit)/temperature as the natural-log ratio of their softmax probabilities.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstLogit | First Logit | Required. Finite number. |
| secondLogit | Second Logit | Required. Finite number. |
| temperature | Positive dimensionless logit/input temperature multiplier under the stated convention. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the operation-specific returned members listed below. | Required. Object. |
| result.logOdds | Natural logarithm of first/second softmax probability ratio; not exponentiated odds. | Calculated result member: number. |
{
"input": {
"firstLogit": 4,
"secondLogit": 2,
"temperature": 2
},
"output": {
"result": {
"logOdds": 1
}
}
}Limitations and assumptions
- Other logits cancel in this ratio; the tool does not return odds themselves, construct probabilities or validate a full logit vector.
- Outputs are nested inside result. 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
- Softmax One Logit Coordinate Derivative
Return p[row]*(indicator(row=column)-p[column])/temperature.
- LogSoftmax One Logit Coordinate Derivative
Return (indicator(row=column)-p[column])/temperature, the log-softmax coordinate derivative.