- The document presents a Parallel Iterative Edit (PIE) model for local sequence transduction tasks like grammatical error correction. - The PIE model achieves accuracy competitive with encoder-decoder models by predicting edits instead of tokens, iteratively refining predictions, and factorizing logits over edits and tokens to leverage pre-trained language models. - Experiments show the PIE model provides a 5-15x speed improvement over encoder-decoder models for grammatical error correction while maintaining comparable accuracy.