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Sinusoidal Positional Encoding is a hard coding interview question covering deep learning, math, nlp — the kind asked at FAANG (Facebook/Meta, Apple, Amazon, Netflix, Google) and AI-first companies like Anthropic, OpenAI, and Nvidia.
Implement sinusoidal positional encodings from "Attention Is All You Need" (Vaswani et al., 2017).
PE(pos, 2i) = sin(pos / 10000^(2i / d_model)) PE(pos, 2i+1) = cos(pos / 10000^(2i / d_model))
Given max_seq_len and d_model, return a (max_seq_len, d_model) matrix.
Explain: (1) why this works for positions the model has not seen during training, (2) how PE(pos+k) can be expressed as a linear transform of PE(pos).
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