Researchers asked whether generative tools could produce sequence variants that beat the best examples in a training set. Two approaches were compared: an attention‑based variational auto‑encoder (AVA) that learns from data, and a purely information‑theoretic Biased Typewriter (BT) that needs no training. Both were tested on a complete Dihydrofolate Reductase (DHFR) fitness landscape. The BT model generated more unique, high‑fitness sequences than AVA, even with few training examples, and reached a search efficiency up to 4.75 times that of random search when 512 examples were used. In contrast, AVA produced many duplicate sequences and lower‑fitness variants, indicating overfitting when data were limited. These results show that a simple, fast, training‑free method can find rare, highly functional proteins more effectively than a state‑of‑the‑art neural model.