# BAT3R: Robust Online 3D Reconstruction with Bayesian Adaptive State Updates

arXiv: https://arxiv.org/abs/2610.16330 · HTML: https://mlsanity.com/paper/2610.16330/

## Key facts

- No citing papers in the map yet (data through 19 Oct 2026).
- Placed in Sparse-input reconstruction, one of 15 directions in 3D reconstruction and neural rendering.
- Builds on 24 of its 64 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Placed in

- 3D reconstruction and neural rendering / [Sparse-input reconstruction](https://mlsanity.com/recon3d/sparse-input-reconstruction/)

## Builds on (most cited first, 24 of 24)

- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [MonST3R: A Simple Approach for Estimating Geometry in the Presence of Motion](https://mlsanity.com/paper/2410.03825/) (2024)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [π3: Permutation-Equivariant Visual Geometry Learning](https://mlsanity.com/paper/2507.13347/) (2025)
- [Repeat After Me: Transformers are Better than State Space Models at Copying](https://mlsanity.com/paper/2402.01032/) (2024)
- [Streaming 4D Visual Geometry Transformer](https://mlsanity.com/paper/2507.11539/) (2025)
- [Frame Context Packing and Drift Prevention in Next-Frame-Prediction Video Diffusion Models](https://mlsanity.com/paper/2504.12626/) (2025)
- [Test-Time Training Done Right](https://mlsanity.com/paper/2505.23884/) (2025)
- [TTT3R: 3D Reconstruction as Test-Time Training](https://mlsanity.com/paper/2509.26645/) (2025)
- [FastVGGT: Training-Free Acceleration of Visual Geometry Transformer](https://mlsanity.com/paper/2509.02560/) (2025)
- [Point3R: Streaming 3D Reconstruction with Explicit Spatial Pointer Memory](https://mlsanity.com/paper/2507.02863/) (2025)
- [Test-time regression: a unifying framework for designing sequence models with associative memory](https://mlsanity.com/paper/2501.12352/) (2025)
- [Longhorn: State Space Models are Amortized Online Learners](https://mlsanity.com/paper/2407.14207/) (2024)
- [Learning without training: The implicit dynamics of in-context learning](https://mlsanity.com/paper/2507.16003/) (2025)
- [Human3R: Everyone Everywhere All at Once](https://mlsanity.com/paper/2510.06219/) (2025)
- [Advances in Feed-Forward 3D Reconstruction and View Synthesis: A Survey](https://mlsanity.com/paper/2507.14501/) (2025)
- [ZipMap: Linear-Time Stateful 3D Reconstruction via Test-Time Training](https://mlsanity.com/paper/2603.04385/) (2026)
- [Test3R: Learning to Reconstruct 3D at Test Time](https://mlsanity.com/paper/2506.13750/) (2025)
- [Stuffed Mamba: Oversized States Lead to the Inability to Forget](https://mlsanity.com/paper/2410.07145/) (2024)
- [TTSA3R: Training-Free Temporal-Spatial Adaptive Persistent State for Streaming 3D Reconstruction](https://mlsanity.com/paper/2601.22615/) (2026)
- [ConfCtrl: Enabling Precise Camera Control in Video Diffusion via Confidence-Aware Interpolation](https://mlsanity.com/paper/2603.09819/) (2026)

## Abstract (arXiv)

Feed-forward transformer models have driven remarkable progress in 3D vision,yet their quadratic complexity renders them impractical for long video sequences. Streaming 3D reconstruction addresses this bottleneck by processing frames sequen?tially with constant memory. However, existing recurrent architectures inevitably suffer from progressive degradation over long sequences, as they fail to account for the intrinsic reliability of observations and the accumulated confidence of the historical state, leading to severe error accumulation. To address these issues, we introduce BAT3R, a training-free Bayesian adaptation framework comprising two synergistic modules: State Innovation Gating (SIG) and Bayesian-guided Adaptive State Updating (BASU). SIG acts as a distributional regularizer that anchors state evolution to its geometric initialization, effectively arresting representational drift during long-term inference. Building on this, BASU reformulates state update as a recursive Bayesian inference process within a Kalman filtering framework. By jointly modeling the temporal reliability of observations via information-theoretic gain and spatial relevance via cross-attention maps, BASU achieves an asymmetric spatio-temporal state fusion: well-consolidated historical regions are protected from redundant updates, while genuinely novel scene content is aggressively incor?porated. Extensive experiments on standard benchmarks (7-Scenes, TUM, ScanNet, KITTI, etc.) demonstrate that BAT3R consistently outperforms state-of-the-art online 3D reconstruction methods, with the most significant gains observed on long sequences and complex scenes.