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De novo protein backbone design with geometric-algebra attention, sampling designable structures whose secondary structure matches natural proteins.
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Generative models for protein backbones are judged largely on designability — the fraction of generated structures whose ProteinMPNN-designed sequences refold under ESMFold to within 2 Å of the original. The metric has a known failure mode: the easiest way to make a backbone designable is to make it an α-helical bundle. RFdiffusion reaches 0.89 designability while generating 58% helix, against 39% in the PDB, so β-strands — the structural vocabulary of most natural enzymes and binding interfaces — come out systematically under-represented.
GAFL attacks that gap at the level of the geometry rather than the loss. It comes from the Gräter and Stühmer groups at the Heidelberg Institute for Theoretical Studies, with collaborators at Heidelberg University, the Max Planck Institute for Polymer Research, Stockholm University and the Karlsruhe Institute of Technology, and was presented at NeurIPS 2024.
Its contribution is Clifford Frame Attention (CFA), a replacement for the invariant point attention block of AlphaFold 2. IPA expresses geometric node features as 3D points in each residue's local frame and combines them by weighted linear sums. CFA instead embeds both the residue frames and the node features as multivectors in the projective geometric algebra, whose basis elements are points, lines and planes rather than coordinates, and builds messages from the algebra's bilinear operations — the geometric product and the join. Since an α-helix is an axis and a β-sheet is a plane, the representation carries an inductive bias for precisely the objects the model is failing to sample. CFA is dropped into the SE(3) flow matching framework of FrameFlow with everything else held fixed, so the experiments measure the attention block itself.
The network stacks six CFA blocks with node and edge embedding sizes of 240 and 120, eight attention heads, eight query/key points and eight geometric value channels, followed by an MLP and a sequence transformer that predict frame updates. Trainable parameters total 16.7 M, matched deliberately to FrameFlow's 16.7 M. Training ran 15 days on two NVIDIA A100-80GB GPUs over FrameDiff's PDB subset — roughly 25,000 monomeric structures of up to 512 residues and at most 50% coil — with minibatch optimal transport couplings and 200 timesteps at sampling.
Across lengths of 100 to 300 residues, GAFL reaches 0.88 designability, 0.36 diversity and 0.71 novelty, generating 53% helix and 25% strand against the PDB's 39% and 23%; the Wasserstein distance between its secondary-structure distribution and the PDB's is 0.25, versus 0.35 for RFdiffusion. A length-100 backbone takes 8.8 s, about a third of RFdiffusion's 21.0 s, with no pretrained folding-model weights involved. On the curated SCOPe-128 ablation set of 3,938 proteins, designability is 90.5% against 81.2% for published FrameFlow and 88.2% for FrameFlow retrained under GAFL's procedure, the PGA features and higher-order messages contributing 1.4 and 2.3 percentage points. At lengths up to 500 residues designability is 0.74, ahead of VFN's 0.44.
GAFL is an unconditional backbone generator: it samples novel folds that are then passed to an inverse-folding and refolding pipeline to obtain sequences worth synthesizing. It suits design campaigns targeting small proteins with genuine β-content — minibinders, scaffolds for grafted motifs, compact enzyme folds — where all-helical output is a dead end. Separately, CFA is portable: any architecture already using invariant point attention can adopt it, and the released code makes that substitution concrete.
The result that matters beyond this model is that swapping IPA for a geometric-algebra block improves designability without an accompanying helix bias, isolated from training-procedure effects by a controlled ablation. The Gräter group has since built on the architecture directly — BBFlow follows the GAFL network with Clifford frame attention in place of IPA, and FliPS extends it to flexibility-conditioned design. The release is honest about its scope: the checkpoint samples unconditionally, with motif and symmetry conditioning named as future work, and helices remain over-represented for large proteins. Code and weights are public, though the LICENSE file composites terms inherited from FrameFlow, OpenFold and gatr rather than naming a single license.
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