z_i / T

Temperature

Read "z i over T". Each logit is divided by the temperature T before softmax. T below 1 makes the distribution sharper; T above 1 makes it flatter.

Dividing by $T < 1$ makes the gaps between logits bigger, so softmax puts more probability on the top tokens: safer, more repetitive text. $T > 1$ makes the gaps smaller, pushing toward equal probabilities: more varied text, and eventually nonsense.

The division happens before the exponential. So the ratio between any two probabilities, $p_i / p_j = e^{(z_i - z_j)/T}$ , gets raised to the power $1/T$ . The effect is a power on probability ratios, not a simple shift of the probabilities.

Example

\frac{[2, 1, 0]}{0.5} = [4, 2, 0] \;\xrightarrow{\text{softmax}}\; [0.867,\, 0.117,\, 0.016]

At T = 1 the same logits give [0.665, 0.245, 0.090]. Halving T sharpens the distribution.

Where the course uses it

4.3 Logits, Softmax, and Cross-Entropy · Module 4, How a Model Learns From Datafirst use

Related terms

SoftmaxRead "softmax of z". It turns any list of numbers into probabilities: every output is positive and they add up to 1. Bigger inputs get bigger shares.
lim — limitRead "the limit as T goes to 0". It is the value a quantity gets closer and closer to as something is pushed toward an extreme, even if that extreme can't be plugged in directly.
argmax — position of the largestRead "arg max". It gives the position (index) of the largest value, not the largest value itself.