fastText

1) Each word w is expanded to a subword representation: boundary markers are added (e.g. <where> → <wh, whe, her, ere, re>), and a bag of character n-grams G_w is formed for lengths minn to maxn (typically 3–6), plus the word itself. 2) Each n-gram g is assigned a vector z_g; the word vector is v_w = Σ_{g∈G_w} z_g. 3) Training proceeds as in word2vec — skip-gram or CBOW with negative sampling — but gradients are propagated to all n-grams composing the word. 4) To bound parameter count, n-grams are hashed into a fixed number of buckets via the hashing trick (Fowler-Noll-Vo, typically 2M buckets). 5) For OOV words at inference time, a vector is computed from the word's n-grams even if the word never appeared in training. 6) In text-classification mode (a separate model), sentences are represented as the mean of word+n-gram vectors, and a linear classifier with hierarchical softmax computes class probabilities — enabling training on millions of examples in minutes.