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Full-stack recurrence

PonderLM

PonderLM: Pretraining Language Models to Ponder in Continuous Space

Boyi Zeng, Shixiang Song, Siyuan Huang, Yixuan Wang, He Li, Ziwei He, Xinbing Wang, Zhiyu Li, Zhouhan Lin

Teaches language models to ponder in continuous space: within one token step, the model feeds back the probability-weighted sum of token embeddings and runs another forward pass, learned through ordinary self-supervised pretraining.

Inside the method

Forward → expected embedding Σ pᵢ eᵢ → Forward … → token

Simplified conceptual schematic. Consult the paper for the complete architecture.

Recurrence family
Full-stack recurrence
Depth control
Fixed pondering steps per token
KV / state strategy
See paper

Reading note

Works on GPT-2, Pythia and LLaMA architectures; PonderPythia-2.8B surpasses Pythia-6.9B and rivals Pythia-12B on nine benchmarks.

Sources checked 2026-10-28. This catalog does not imply independent reproduction.

Related works

Cite this work

@misc{ponderlm2025,
  title = {PonderLM: Pretraining Language Models to Ponder in Continuous Space},
  author = {Boyi Zeng and Shixiang Song and Siyuan Huang and Yixuan Wang and He Li and Ziwei He and Xinbing Wang and Zhiyu Li and Zhouhan Lin},
  year = {2025},
  eprint = {2505.20674},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2505.20674}
}

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