Description
Return temperature-scaled logistic probability and its logit derivative.
Training losses compare predicted probabilities with target mass, and temperature rescales logits before a probability transformation. Label smoothing and focal weighting alter particular loss terms; evaluating one term or transformation does not train a model, select its hyperparameters or establish calibrated confidence.
Return temperature-scaled logistic probability and its logit derivative.
When to use this tool
Use Binary Logit Temperature Slope when evaluating the stated loss contribution, smoothed target or temperature transformation.
How to use the tool and how it works
- Enter logit, temperature. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read probability, logitSlope. Use the output convention below.
Return temperature-scaled logistic probability and its logit derivative. Require temperature > 0; evaluate sigmoid(logit/temperature) using a sign-stable expression and logitSlope = p*(1-p)/temperature via an equivalent exponential form.1
Temperature scaling is a calibration method when its parameter is fitted and evaluated appropriately; an arbitrary supplied temperature alone does not establish calibration.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| logit | Logit | Required. Finite number. |
| temperature | Temperature | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| probability | Probability | Required. Finite number. |
| logitSlope | Derivative of the returned probability with respect to logit: p*(1-p)/temperature. | Required. Finite number. |
{
"input": {
"logit": 0,
"temperature": 2
},
"output": {
"probability": 0.5,
"logitSlope": 0.125
}
}Limitations and assumptions
- Temperature is dimensionless; this local transformation does not fit a calibration temperature or establish calibrated predictions.
- 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
Sum the appropriate contributions for a complete loss, and use a validated training/calibration procedure and held-out evaluation to select hyperparameters and assess predictions.
References
-
Calculation and input contract: classification/binary-logit-temperature-slope — tool.io
-
On Calibration of Modern Neural Networks — Chuan Guo and coauthors
Similar or alternative tools
- Classification: Binary Label Smoothing Target Pair
Return a uniformly smoothed binary target pair.
- Focal Loss One Probability Term
Return one focal-loss term for a true class.