E(n)-Equivariant Transformer

Implementation of E(n)-Equivariant Transformer, which extends the ideas from Welling's E(n)-Equivariant Graph Neural Network with attention mechanisms and ideas from transformer architecture.

Update: Used for designing of CDR loops in antibodies!

Install

bash $ pip install En-transformer

Usage

```python import torch from en_transformer import EnTransformer

model = EnTransformer( dim = 512, depth = 4, # depth dimhead = 64, # dimension per head heads = 8, # number of heads edgedim = 4, # dimension of edge feature neighbors = 64, # only do attention between coordinates N nearest neighbors - set to 0 to turn off talkingheads = True, # use Shazeer's talking heads https://arxiv.org/abs/2003.02436 checkpoint = True, # use checkpointing so one can increase depth at little memory cost (and increase neighbors attended to) usecrossproduct = True, # use cross product vectors (idea by @MattMcPartlon) numgloballinearattn_heads = 4 # if your number of neighbors above is low, you can assign a certain number of attention heads to weakly attend globally to all other nodes through linear attention (https://arxiv.org/abs/1812.01243) )

feats = torch.randn(1, 1024, 512) coors = torch.randn(1, 1024, 3) edges = torch.randn(1, 1024, 1024, 4)

mask = torch.ones(1, 1024).bool()

feats, coors = model(feats, coors, edges, mask = mask) # (1, 1024, 512), (1, 1024, 3) ```

Letting the network take care of both atomic and bond type embeddings

```python import torch from en_transformer import EnTransformer

model = EnTransformer( numtokens = 10, # number of unique nodes, say atoms relposemb = True, # set this to true if your sequence is not an unordered set. it will accelerate convergence numedgetokens = 5, # number of unique edges, say bond types dim = 128, edgedim = 16, depth = 3, heads = 4, dim_head = 32, neighbors = 8 )

atoms = torch.randint(0, 10, (1, 16)) # 10 different types of atoms bonds = torch.randint(0, 5, (1, 16, 16)) # 5 different types of bonds (n x n) coors = torch.randn(1, 16, 3) # atomic spatial coordinates

featsout, coorsout = model(atoms, coors, edges = bonds) # (1, 16, 512), (1, 16, 3) ```

If you would like to only attend to sparse neighbors, as defined by an adjacency matrix (say for atoms), you have to set one more flag and then pass in the N x N adjacency matrix.

```python import torch from en_transformer import EnTransformer

model = EnTransformer( numtokens = 10, dim = 512, depth = 1, heads = 4, dimhead = 32, neighbors = 0, onlysparseneighbors = True, # must be set to true numadjdegrees = 2, # the number of degrees to derive from 1st degree neighbors passed in adj_dim = 8 # whether to pass the adjacency degree information as an edge embedding )

atoms = torch.randint(0, 10, (1, 16)) coors = torch.randn(1, 16, 3)

naively assume a single chain of atoms

i = torch.arange(atoms.shape[1]) adj_mat = (i[:, None] <= (i[None, :] + 1)) & (i[:, None] >= (i[None, :] - 1))

adjacency matrix must be passed in

featsout, coorsout = model(atoms, coors, adjmat = adjmat) # (1, 16, 512), (1, 16, 3) ```

Edges

If you need to pass in continuous edges

```python import torch from entransformer import EnTransformer from entransformer.utils import rot

model = EnTransformer( dim = 512, depth = 1, heads = 4, dimhead = 32, edgedim = 4, numnearestneighbors = 0, onlysparseneighbors = True )

feats = torch.randn(1, 16, 512) coors = torch.randn(1, 16, 3) edges = torch.randn(1, 16, 16, 4)

i = torch.arange(feats.shape[1]) adj_mat = (i[:, None] <= (i[None, :] + 1)) & (i[:, None] >= (i[None, :] - 1))

feats1, coors1 = model(feats, coors, adjmat = adjmat, edges = edges) ```

Example

To run a protein backbone coordinate denoising toy task, first install sidechainnet

bash $ pip install sidechainnet

Then

bash $ python denoise.py

Todo

• [ ] add https://arxiv.org/abs/2112.05682 for researchers to stretch to even bigger molecules

Citations

bibtex @misc{satorras2021en, title = {E(n) Equivariant Graph Neural Networks}, author = {Victor Garcia Satorras and Emiel Hoogeboom and Max Welling}, year = {2021}, eprint = {2102.09844}, archivePrefix = {arXiv}, primaryClass = {cs.LG} }

bibtex @misc{shazeer2020talkingheads, title = {Talking-Heads Attention}, author = {Noam Shazeer and Zhenzhong Lan and Youlong Cheng and Nan Ding and Le Hou}, year = {2020}, eprint = {2003.02436}, archivePrefix = {arXiv}, primaryClass = {cs.LG} }

bibtex @misc{liu2021swin, title = {Swin Transformer V2: Scaling Up Capacity and Resolution}, author = {Ze Liu and Han Hu and Yutong Lin and Zhuliang Yao and Zhenda Xie and Yixuan Wei and Jia Ning and Yue Cao and Zheng Zhang and Li Dong and Furu Wei and Baining Guo}, year = {2021}, eprint = {2111.09883}, archivePrefix = {arXiv}, primaryClass = {cs.CV} }

bibtex @inproceedings{Kim2020TheLC, title = {The Lipschitz Constant of Self-Attention}, author = {Hyunjik Kim and George Papamakarios and Andriy Mnih}, booktitle = {International Conference on Machine Learning}, year = {2020}, url = {https://api.semanticscholar.org/CorpusID:219530837} }

bibtex @article {Mahajan2023.07.15.549154, author = {Sai Pooja Mahajan and Jeffrey A. Ruffolo and Jeffrey J. Gray}, title = {Contextual protein and antibody encodings from equivariant graph transformers}, elocation-id = {2023.07.15.549154}, year = {2023}, doi = {10.1101/2023.07.15.549154}, publisher = {Cold Spring Harbor Laboratory}, URL = {https://www.biorxiv.org/content/early/2023/07/29/2023.07.15.549154}, eprint = {https://www.biorxiv.org/content/early/2023/07/29/2023.07.15.549154.full.pdf}, journal = {bioRxiv} }

bibtex @article{Bondarenko2023QuantizableTR, title = {Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothing}, author = {Yelysei Bondarenko and Markus Nagel and Tijmen Blankevoort}, journal = {ArXiv}, year = {2023}, volume = {abs/2306.12929}, url = {https://api.semanticscholar.org/CorpusID:259224568} }

bibtex @inproceedings{Arora2023ZoologyMA, title = {Zoology: Measuring and Improving Recall in Efficient Language Models}, author = {Simran Arora and Sabri Eyuboglu and Aman Timalsina and Isys Johnson and Michael Poli and James Zou and Atri Rudra and Christopher R'e}, year = {2023}, url = {https://api.semanticscholar.org/CorpusID:266149332} }