AI Grounds
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AI Grounds
These interactive lessons need a larger screen. Please continue on a desktop or laptop computer.
Guided discovery
Change concentration. Keep the ranking.
Logits are raw scores, which can be negative. Softmax turns their relative sizes into positive probabilities that sum to one. Rover has a visible lead before softmax converts scores. Each preset loads its scores and Temperature 0.70.
With scores fixed, positive Temperature preserves their ranking and ties. Higher values move the distribution toward uniformity. Use arrow keys on the slider. Press Enter or leave the number field to apply an exact edit.
Raw score; it need not be a probability. Use arrow keys on the slider. Press Enter or leave the number field to apply an exact edit.
Raw score; it need not be a probability. Use arrow keys on the slider. Press Enter or leave the number field to apply an exact edit.
Raw score; it need not be a probability. Use arrow keys on the slider. Press Enter or leave the number field to apply an exact edit.
Raw score; it need not be a probability. Use arrow keys on the slider. Press Enter or leave the number field to apply an exact edit.
One shared 0–100% scale. Every class shares the same normalizing total.
Every class with the largest raw score.
Rover
Positive Temperature preserves the score ranking.
Changing a logit can change the leader.
The largest share of the normalized distribution.
88.2%
Positive weights / total weight
Concentration is not measured accuracy.
For each class, p = exp(logit / T) / sum of all four exp(logit / T). exp(x) is e raised to x and is always positive. Subtracting the largest scaled logit from every scaled logit gives the same probabilities while avoiding large exponentials.
Shifted weight = exp(scaled logit − largest scaled logit). Weight total ≈ 1.133847. Probability = shifted weight / total.
| Class | Logit | Scaled logit | Shifted weight | Probability (%) |
|---|---|---|---|---|
| Rover | 2.4 | 3.428571 | 1 | 88.2% |
| Comet | 0.8 | 1.142857 | 0.101701 | 8.97% |
| Harbor | -0.2 | -0.285714 | 0.024373 | 2.15% |
| Signal | -1 | -1.428571 | 0.007773 | 0.69% |
Entropy measures distribution spread: H = −sum(p × ln p). ln is the natural logarithm; this choice measures H in units called nats. Here H ≈ 0.443773 nats.
Four equal probabilities give the maximum H = ln(4) ≈ 1.386294 nats. Relative spread H / ln(4) ≈ 32.01%. Higher Temperature cannot decrease entropy for fixed scores. Equal scores already have maximum entropy, so changing Temperature leaves them uniform.
Entropy measures spread, not correctness. It does not reveal whether a class is actually true.
Percentages are rounded to two decimal places; positive tiny values use <0.01% and values just below one use >99.99%. These class probabilities do not establish accuracy or calibration. No actual class labels are provided.
Temperature 0.7. Rover logit 2.4, probability 88.2%; Comet logit 0.8, probability 8.97%; Harbor logit -0.2, probability 2.15%; Signal logit -1, probability 0.69%. Largest Rover; largest probability 88.2%.