Softmax Probability Plot Calculator

Transform multiclass logits into clear probabilities, explore temperature effects, compare samples, measure confidence, and export interactive softmax charts with detailed results instantly for analysis.

Calculated results

Waiting for input
Choose a preset or enter logits, then select Calculate probabilities.

Softmax probability plot

Temperature comparison

This view shows sharpening, smoothing, entropy changes, and possible class-rank movement.

Probability results table

Select a numeric cell to copy it.

Sample Index Class Logit Shifted Exponential Probability Percentage Rank Predicted Threshold

Sample comparison

SamplePredictionConfidenceMarginEntropyTop-k share

Average class probabilities

ClassAverage probabilityPrediction frequency

Calculation steps

Confidence statistics

Input and calculation controls

Use commas or new lines.
First column is the sample label. Remaining headers are class names.
Use one sample per line. Separate labels with a pipe, comma, or tab.

Softmax settings

Chart controls

Formula used

Numerically stable softmax
Pi = exp((zi − max(z)) / T) ÷ Σ exp((zj − max(z)) / T)

Each logit is shifted before exponentiation. This prevents avoidable overflow. Temperature controls the final distribution.

A lower temperature sharpens the probabilities. A higher temperature smooths them. Every probability should sum to one.

How to use

  1. Choose a preset or enter class names.
  2. Add sample labels and logits.
  3. Set temperature, precision, threshold, and top-k.
  4. Select the required chart style.
  5. Calculate and inspect every result section.
  6. Copy, print, or export the report.

Example data format

sampleCatDogBird
Image 12.41.2-0.3
Image 20.52.10.8

Understanding softmax probabilities

What softmax does

Softmax converts unrestricted logits into comparable class probabilities. Larger logits receive larger shares. The total remains one.

Softmax and sigmoid

Softmax models mutually exclusive classes. Sigmoid scores classes independently. Multilabel problems usually use sigmoid outputs.

Confidence and correctness

High confidence does not guarantee a correct prediction. Models can become overconfident. Calibration should be checked separately.

Temperature scaling

Temperature changes probability sharpness without changing logits. It often supports calibration. Class rankings usually remain unchanged.

Softmax limitations

Softmax only compares supplied classes. Unknown classes remain unrepresented. Distribution shifts can reduce reliability.

Frequently asked questions

Why use stable softmax?

Stable softmax subtracts the maximum logit. This avoids numerical overflow. The final probabilities remain mathematically equivalent.

What does temperature equal to one mean?

A temperature of one uses ordinary softmax. No extra sharpening occurs. No extra smoothing occurs.

Can logits be negative?

Yes, logits may be negative. Softmax accepts unrestricted real values. Their relative differences determine probabilities.

Why do probabilities sum to one?

Every exponential value uses the same denominator. Each value becomes a share. All shares therefore total one.

Does softmax change class ranking?

Ordinary positive temperature scaling preserves ranking. Larger logits remain more probable. Ties may remain tied.

What is entropy?

Entropy measures uncertainty across classes. Higher entropy means a flatter distribution. Lower entropy indicates stronger concentration.

What is the confidence margin?

The margin is the top probability minus second place. Larger margins suggest separation. They do not prove correctness.

What does top-k cumulative probability show?

It sums the largest k probabilities. This shows concentrated probability mass. It helps review broader candidate sets.

Can CSV data contain multiple samples?

Yes, each CSV row becomes one sample. The first column supplies labels. Remaining columns supply class logits.

Related Calculators

Cost Function CurveGradient Descent Path PlotContour Plot3D Loss SurfaceLearning-Rate Comparison PlotRegularisation CurveSigmoid Function GraphEntropy CurveGini Impurity CurveCross-Entropy Loss Curve

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.