What does AI pay attention to?

The whole answer to how its finds Law fits in one line of math. Attention of Q, K, and V equals softmax of Q times K transposed, divided by the square root of d k, all multiplied by V. Today we read that line out loud, piece by piece. Every word in the sentence gets three vectors, which are just lists of numbers. The first is the query. A query is what a word is actively looking for. When the model processes its, the query works like a search for a singular noun. The second is the key. A key is the label on a file folder. The word Law projects a key that advertises what it is: a singular noun, something a pronoun could point to. The third is the value. The value is what is inside the folder, the actual information the word carries. Query, key, value. Search, label, contents. Now the scoring. The model takes the query from its and compares it against the key of every word in the sentence, including its own. The comparison is a dot product, which multiplies the two lists of numbers and adds them up. Keys that match the query give a big number. Keys that don't give a small one. Law's key matches, so Law scores high. Then comes the part that looks like a fussy detail. The paper divides every score by the square root of d k. Here d k is the length of the key vectors, 64 in the paper, so each score gets divided by 8. Why? With long vectors the dot products grow large, and the authors suspect that pushes the next step into a zone where learning nearly stalls. Dividing by the square root of d k keeps the scores in a sensible range. That is the scaled in Scaled Dot-Product Attention. The next step is softmax, which turns the scores into weights that add up to one. Think of it as dividing a single pie among all the words. Law gets the biggest slice. Remember that sharp attention in the paper's Figure 4? This is where the sharpness comes from. Finally, the model uses those weights to take a weighted sum of the values. Mostly the value of Law, with slivers from everything else, gets mixed into the new representation of its. So the output for its now carries the meaning of Law inside it. In self-attention, the queries, keys, and values all come from the same sentence, and the paper packs them into three matrices, Q, K, and V. One matrix multiplication scores every word against every other word at the same moment. That is why this runs in parallel, and why it is so fast on a GPU. Nothing in there understands grammar. It is multiplication, tuned by training until the right keys match the right queries. But a single attention pass averages everything into one view, and it also has no idea which word came first. Next time we fix both: eight heads attending in parallel, and the sine and cosine trick the paper uses to tell the model where each word sits.

Shuffle the words of a sentence, and a bare self-attention layer would score every pair exactly as before. It has no idea who came first. Last time I promised two fixes, so let's take them in order. The first fix is multi-head attention. Multi-head attention means the model runs several attention passes side by side instead of one. A single pass blends everything into one averaged view, and the paper says that with a single head, averaging inhibits the model from looking at different things at once. Here is the setup. The model projects the queries, keys, and values h times, and the paper sets h equal to 8. Eight heads. Each head has its own learned projection and works in 64 dimensions, because the full width of 512 divided by 8 is 64. Since every head is small, the total cost stays close to one big head. Each head can pick up a different job. In Figure 4, heads 5 and 6 in layer 5 send its straight to Law. In Figure 3, other heads connect making to more difficult across a long sentence. The paper says of Figure 5 that the heads clearly learned to perform different tasks. Then the eight outputs get concatenated, which means glued end to end, and projected once more, leaving one richer map of the sentence. Does the count matter? Table 3 says yes. Eight heads scored 25.8 BLEU. One head scored 24.9, the 0.9 drop the authors mention. And more is not always better, because thirty-two heads slipped back to 25.4. Now the catch. Self-attention compares all words at once, so nothing in its arithmetic records order, and The Law will never be perfect looks the same as any scrambled version of those words. The second fix is positional encoding. Positional encoding means adding a signal to each word's embedding that says where in the sentence the word sits. The paper builds that signal from sine and cosine functions of different frequencies. Each dimension is a wave, and the wavelengths stretch from 2 pi all the way up to 10000 times 2 pi. Picture a short wave and a long wave sampled at the same word. The short wave changes sharply from one word to the next. The long wave barely moves. Put hundreds of waves together, and every position gets a pattern no other position shares, a mathematical timestamp. The encoding has the same 512 dimensions as the embedding, so the two simply add. The authors had a reason for sines and cosines. For any fixed offset k, the encoding at position pos plus k is a linear function of the encoding at pos. That should make it easy for the model to attend by relative distance, like three words back. They also tried learned position embeddings and got nearly identical results, 25.7 against 25.8 BLEU. They kept the sinusoids because those might extend to sentences longer than any seen in training. So here is the full picture of its finding Law. Positional encoding stamps every word with its place. Multi-head attention then lets eight heads, each working in 64 dimensions, look at that stamped sentence from eight angles at once. Eight heads at 25.8 BLEU, one head at 24.9. That gap is the case for multiple perspectives.