Checklist USA-NA-AIO 2026 Round 1 · Task 5
Word Embedding Similarity and Low-Rank Approximation
Build a cosine-similarity matrix of GloVe token embeddings, analyse it with the SVD and approximate it at low rank.
The task
Problem 5 (90 points) loads the 100-dimensional GloVe model glove-wiki-gigaword-100 through gensim and a text file published on Hugging Face, keeps the unique tokens present in GloVe, and studies their embeddings.
The fifteen parts ask the contestant to normalise the embeddings into a matrix W, express and compute the similarity matrix S = WW^T without loops, interpret its diagonal, build a dictionary mapping each token to its most similar other token (for example "bright": "lights"), decide whether S is invertible, compute the SVD of W and the spectral decomposition of S from it, express the Frobenius norm of S through the SVD, and construct the rank-r approximation that minimises the relative squared Frobenius error, plotting that error for r = 1, …, 100.
Abridged by SOTA from the official materials. The official statement has the exact rules, and it wins wherever this summary differs.
At a glance
- You get
- GloVe glove-wiki-gigaword-100 vectors and the text file
2026_USAAIO_Round1_NLP.txt(Hugging Face dataset usaaio-official/2026_USAAIO_Round1_public). - You submit
- Code, printed results, a plot and written answers.
- Rules
- No imports beyond the starter code; several parts forbid np.linalg, @ or loops; Part 5.11 allows np.linalg.svd.
- Format
- 2026 USA-NA-AIO Round 1, 30 January 2026 (date printed on the problem set). Individual, proctored.