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Rotary Position Embedding (RoPE) encodes token positions by rotating each two-dimensional channel of the query and key vectors at a channel-specific frequency, making the attention logits invariant to a common shift of positions. However, this rotation is periodic, and it leads to position aliasing where relative posit...
Language model pretraining has become almost synonymous with prohibitive cost, placing it out of reach for much of the academic and open-source communities. Although strong open-source efforts already exist, including open-weight models and open-source training recipes, a cost-efficient, hardware-accessible, and open-s...
This report presents an open pretraining recipe that trains a collection of Puro-2B models from scratch on up to 1.4 trillion tokens with FP8 precision on consumer-grade RTX 5090 GPUs, and derives a Puro Cost Scaling Law that relates training cost to average model performance.
2D-RoPE is introduced, which organizes text into a 2D grid rather than a 1D sequence and assigns each token a row ID and a column ID, and suggests that viewing text in 2D can benefit language modeling.
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