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BOE-ViT: Boosting Orientation Estimation with Equivariance in Self-Supervised 3D Subtomogram Alignment
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Proposes BOE-ViT, a self-supervised Vision Transformer for 3D subtomogram alignment that adds shift-equivariant Polyshift and rotation-equivariant MARE modules to estimate rotation and translation under low SNR.
Problem
Subtomogram alignment in cryo-ET requires estimating 3D rotation and translation from very noisy (SNR 0.01–0.1) volumes with few labels, and standard ViTs lack shift and rotation equivariance needed for accurate orientation estimation.
Approach
Self-supervised training that predicts synthetic rigid transformations applied to subtomograms, with a ViT augmented by Polyshift (polyphase anchoring plus circularly padded depthwise-conv positional encoding) for shift equivariance and MARE (axis-wise learnable skew-symmetric rotations applied to queries and keys) for rotation equivariance.
Key results
- At SNR 0.01, BOE-ViT reduces rotation error by 77.3% and translation error by 62.5% relative to state-of-the-art methods.
- BOE-ViT achieves rotation error around 0.33-0.34 across all SNR levels versus 1.50 for Gum-Net and 1.58 for Jim-Net at SNR 0.01 on the 5LQW-style table.
- Ablation shows removing Polyshift raises translation error to about 6.14 (self-attention), while removing MARE increases translation error to about 2.62 versus 2.32 for full BOE-ViT at SNR 0.01.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BOE-ViT rather than Gum-Net | Subtomogram alignment · Subtomogram alignment (all datasets), SNR 0.01 | rotation error: 1.50±0.78 -> 0.34±0.15 | Helped |
| Use BOE-ViT rather than Gum-Net | Subtomogram alignment · Subtomogram alignment (all datasets), SNR 0.01 | translation error: 6.78±4.22 -> 2.54±0.91 | Helped |
| Add Polyshift (ablation) | BOE-ViT · Subtomogram alignment, SNR 0.01 | translation error: 6.20±1.78 -> 2.32±0.80 | Helped |
| Add MARE (ablation) | BOE-ViT · Subtomogram alignment, SNR 0.01 | rotation error: 0.35±0.15 -> 0.33±0.15 | Helped |
| Add MARE (ablation) | BOE-ViT · Subtomogram alignment, SNR 0.01 | translation error: 2.62±0.91 -> 2.32±0.80 | Helped |
| Use self-attention rather than cross-attention (ablation) | BOE-ViT · Subtomogram alignment, SNR 0.01 | translation error: 3.63±1.78 -> 2.32±0.80 | Helped |
Surprising findings
- Vanilla ViTs (SelfViT, CrossViT) show much higher translation error than CNN baselines despite comparable or better rotation error in low-SNR settings.
Limitations
- Polyshift increases memory usage and training time (over two days on a single V100)
- Evaluated only on simulated grayscale subtomograms of five complexes
- Rotation improvements are larger than translation improvements
Experimental setup
Datasets: simulated cryo-ET subtomograms for 5LQW, 1I6V, 6A5L, 5T2C, 5MPA
Benchmarks: simulated subtomogram alignment datasets at SNR 0.1, 0.05, 0.03, 0.01 for five macromolecular complexes
Metrics: rotation error translation error
Baselines: H-T align F&A align Gum-Net Jim-Net CrossViT SelfViT
Builds on: Vision Transformer rotary position encoding adaptive polyphase sampling Gum-Net Jim-Net
Closest papers by meaning
- At FullTilt: Real-Time Open-Set 3D Macromolecule Detection Directly from Tilted 2D Projections (NeurIPS 2026 · similarity 0.88)
- Vox-UDA: Voxel-wise Unsupervised Domain Adaptation for Cryo-Electron Subtomogram Segmentation with Denoised Pseudo-Labeling (AAAI 2025 · similarity 0.87)
- cryoSPHERE: Single-Particle HEterogeneous REconstruction from cryo EM (ICLR 2025 · similarity 0.86)
- CryoBench: Diverse and challenging datasets for the heterogeneity problem in cryo-EM (NeurIPS 2024 · similarity 0.85)
- CryoSPIN: Improving Ab-Initio Cryo-EM Reconstruction with Semi-Amortized Pose Inference (NeurIPS 2024 · similarity 0.85)
- Reconstructing Heterogeneous Biomolecules via Hierarchical Gaussian Mixtures and Part Discovery (NeurIPS 2025 · similarity 0.84)
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