Attention doesn’t pick one thing — it spreads a budget of focus across everything, more onto some, less onto others, always summing to one. The knob that decides sharp-or-soft is TEMPERATURE: cold and it snaps to a single winner, hot and it smears into indifference. Slide the temperature and watch focus melt.
Softmax turns raw scores (logits) into a probability distribution: pᵢ = e^(xᵢ/T) / Σⱼ e^(xⱼ/T). It ALWAYS sums to 1 (a conserved budget of attention), and temperature T reshapes it: as T→0 it collapses onto the single largest logit (hard argmax, entropy→0), as T→∞ it flattens to uniform (maximum entropy). The instrument computes it live over five fixed logits. A fail-loud self-check throws unless the weights sum to 1, the entropy increases monotonically with T, and low T selects the argmax — the exact knob behind attention sharpness and sampling ‘creativity’.
Real attention uses T=√d_k as a fixed scale and softmaxes QKᵀ across positions; here T is a free dial over toy logits to expose the geometry. The softmax arithmetic, the sum-to-1, and the entropy monotonicity are exact.