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Generating Highly Designable Proteins with Geometric Algebra Flow Matching
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Proposes GAFL, a FrameFlow-based flow matching model for protein backbone generation whose IPA block is replaced by Clifford Frame Attention using projective geometric algebra features, bilinear messages and higher-order message passing.
Problem
Protein backbone generation with flow matching on SE(3)^N needs geometric features that capture secondary structure and designability, while IPA-based models often over-represent alpha-helices.
Approach
Replace AlphaFold2's invariant point attention with Clifford Frame Attention, representing frames and features as PGA multivectors and building messages via geometric product and join bilinears, including higher-order messages formed by multiplying aggregated two-body messages.
Key results
- GAFL achieves designability 0.88 vs RFdiffusion 0.89 and FrameFlow 0.85 on PDB-trained generation at lengths 100-300, with diversity 0.36 and novelty 0.71.
- On SCOPe-128, GAFL reaches 90.5% designability vs 81.2% for published FrameFlow-SCOPe; retrained FrameFlow with IPA reaches 88.2%.
- For lengths up to 500, GAFL designability is 0.74 vs FrameFlow 0.64, RFdiffusion 0.71 and VFN 0.44.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace FrameFlow's IPA with CFA | FrameFlow · PDB, lengths 100–300 | designability: 0.85 (0.01) -> 0.88 (0.01) | Helped |
| replace FrameFlow's IPA with CFA | FrameFlow · PDB, lengths 100–300 | helix content: 0.56 (0.01) -> 0.53 (0.01) | Helped |
| replace FrameFlow's IPA with CFA | FrameFlow · PDB, lengths 100–300 | strand content: 0.20 (0.00) -> 0.25 (0.01) | Helped |
| replace FrameFlow's IPA with CFA | FrameFlow · PDB, lengths 100–300 | diversity: 0.35 (0.00) -> 0.36 (0.00) | Hurt |
| replace FrameFlow's IPA with CFA | FrameFlow · PDB, lengths 100–300 | novelty: 0.70 (0.00) -> 0.71 (0.00) | Hurt |
| replace FrameFlow's IPA with CFA | FrameFlow · PDB, length 100 | generation time: 6.6 -> 8.8 | Hurt |
| add PGA-valued features (ablation) | CFA on SCOPe-128 · SCOPe-128 | designability: +1.4 percentage points | Helped |
| add higher-order message passing (ablation) | CFA on SCOPe-128 · SCOPe-128 | designability: +2.3 percentage points | Helped |
| replace original IPA with CFA (ablation) | FrameFlow on SCOPe-128 · SCOPe-128 | designability: 88.2% -> 90.5% | Helped |
| use GAFL training procedure instead of the published FrameFlow training setup | FrameFlow on SCOPe · SCOPe | designability: 81.2% -> 88.2% | Helped |
| replace published FrameFlow model with GAFL | protein backbone generation · lengths 100–500 | designability: 0.64 -> 0.74 | Helped |
| replace RFdiffusion with GAFL | protein backbone generation · lengths under 150 | Wasserstein distance of secondary-structure distributions: 0.35 -> 0.25 | Helped |
Surprising findings
- RFdiffusion over-represents alpha-helices for short proteins, with a Wasserstein distance of 0.35 vs 0.25 for GAFL.
- Higher designability correlates with alpha-helix over-representation across checkpoints for IPA-based models, which GAFL partially breaks.
Limitations
- Does not perfectly capture secondary structure distribution, especially for large proteins which are helix-overrepresented.
- Evaluated only on unconditional generation; conditional sampling not tested.
- Achieving high designability without compromising secondary structure diversity remains challenging.
Experimental setup
Datasets: PDB monomeric subset (FrameDiff filtered) SCOPe-128
Benchmarks: PDB-trained generation at lengths 100-300 SCOPe-128 ablation lengths 100-500 vs VFN
Metrics: designability (scRMSD < 2 Å) diversity (TM-score) novelty (TM-score to PDB) helix content strand content inference time
Baselines: RFdiffusion FrameDiff FoldFlow-SFM FoldFlow-OT FrameFlow VFN
Builds on: FrameFlow FrameDiff invariant point attention Geometric Algebra Transformer flow matching
Closest papers by meaning
- Proteina: Scaling Flow-based Protein Structure Generative Models (ICLR 2025 · similarity 0.89)
- ReQFlow: Rectified Quaternion Flow for Efficient and High-Quality Protein Backbone Generation (ICML 2025 · similarity 0.89)
- Learning conformational ensembles of proteins based on backbone geometry (NeurIPS 2025 · similarity 0.88)
- Full-Atom Peptide Design based on Multi-modal Flow Matching (ICML 2024 · similarity 0.88)
- SE(3)-Stochastic Flow Matching for Protein Backbone Generation (ICLR 2024 · similarity 0.87)
- Sequence-Augmented SE(3)-Flow Matching For Conditional Protein Generation (NeurIPS 2024 · similarity 0.87)
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