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# χ₀
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# χ₀: Resource-Aware Robust Manipulation viaTaming Distributional Inconsistencies
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χ₀ (**kai0**) is a resource-efficient framework for achieving production-level robustness in robotic manipulation by taming distributional inconsistencies. This repository is built on top of [openpi](https://github.com/Physical-Intelligence/openpi), the open-source models and packages for robotics published by the [Physical Intelligence team](https://www.physicalintelligence.company/).
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χ₀ (**kai0**) is a resource-efficient framework for achieving production-level robustness in robotic manipulation by taming distributional inconsistencies.
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χ₀ addresses the systematic distributional shift among the human demonstration distribution ($P_\text{train}$), the inductive bias learned by the policy ($Q_\text{model}$), and the test-time execution distribution ($P_\text{test}$) through three technical modules:
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- **[Model Arithmetic](#model-arithmetic)**: A weight-space merging strategy that combines models trained on different data subsets, efficiently capturing diverse knowledge without architectural complexity. **[Released]**
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- **[Stage Advantage](#stage-advantage-coming-soon)**: A stage-aware advantage estimator that provides stable, dense progress signals for policy training. **[Coming Soon]**
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- **[Train-Deploy Alignment](#train-deploy-alignment-coming-soon)**: Bridges the distribution gap via spatio-temporal augmentation, heuristic DAgger corrections, and temporal chunk-wise smoothing. **[Coming Soon]**
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χ₀ enables two sets of dual-arm robots to collaboratively orchestrate long-horizon garment manipulation — flattening, folding, and hanging — surpassing the state-of-the-art $\pi_{0.5}$ baseline by approximately 250% in success rate, with only 20 hours of data and 8 A100 GPUs.
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χ₀ enables two sets of dual-arm robots to collaboratively orchestrate long-horizon garment manipulation — flattening, folding, and hanging — surpassing the state-of-the-art $\pi_{0.5}$ baseline by approximately 250% in success rate, with `only 20 hours of data and 8 A100 GPUs`.
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<!-- [[Paper]](https://github.com/OpenDriveLab/kai0) [[Blog]](https://mmlab.hk/research/kai0) -->
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- [Troubleshooting](#troubleshooting)
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- [Links and Community](#links-and-community)
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## Updates
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## Update
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- [Feb 10 2026] Initial release of the **Model Arithmetic** module with support for both JAX and PyTorch checkpoints (not tested thoroughly).
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- [Feb 10 2025] χ₀ paper released.

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