Continuous chain-of-thought has been shown to be effective in saving reasoning tokens for large language models.By reasoning with continuous latent thought tokens, continuous CoT is able to perform implicit reasoning in a compact manner.However, the sequential dependencies between latent thought tokens spoil parallel training, leading to long training time.In this paper, we propose Parallel Continuous Chain-of-Thought (PCCoT), which performs Jacobi iteration on the latent thought tokens, updating them iteratively in parallel instead of sequentially and thus improving both training and inference efficiency of continuous CoT.Experiments demonstrate that by choosing the proper number of iterations, we are able to achieve comparable or even better performance while saving nearly 50% of the training and inference time.Moreover, PC-CoT shows better stability and robustness in the training process.Our code is available at https://github.com/whyNLP/PCCoT.

Despite the success of Transformers, handling longer contexts remains challenging due to the limited length generalization and quadratic complexity of self-attention, which often requires post-training with a larger attention window, significantly increasing computational and memory costs. In this paper, we propose a novel attention mechanism based on dynamic context, Grouped Cross Attention (GCA), which can generalize to 1000 $\times$ the pre-training context length while maintaining the ability to access distant information with a constant attention window size. For a given input sequence, we split it into chunks and use each chunk to retrieve top-$k$ relevant past chunks for subsequent text generation. Specifically, unlike most previous works that use an off-the-shelf retriever, our key innovation allows the retriever to learn how to retrieve past chunks that better minimize the auto-regressive loss of subsequent tokens in an end-to-end manner, which adapts better to causal language models. Such a mechanism accommodates retrieved chunks with a fixed-size attention window to achieve long-range information access, significantly reducing computational and memory costs during training and inference. Experiments show that GCA-based models achieve near-perfect accuracy in passkey retrieval for 16M context lengths, which is $1000 \times$ the training length.