SlowGuess/NeurIPS_2023_OCR huggingface dataset:
where  $g_{j}$  is sampled from Gumbel distribution  $g_{j} = -\log (-\log U_{m})$ ,  $U_{m} \sim \mathrm{Uniform}(0,1)$ , and  $\tau_{e}$  is the controllable temperature. Then we use Huber loss [13] between the predicted pocket center  $\mathbf{x}^{p} = \frac{1}{n^{p}}\sum_{j = 1}^{n^{p}}\gamma_{j}^{p}\mathbf{x}_{j}^{p}$  and the native pocket center  $\mathbf{x}^{p*}$  as the constraint loss,
$$
\mathcal {L} _ {p} ^ {c 2 r} = l _ {H u b e r} (\mathbf {x} ^ {p}, \mathbf {x} ^ {p *}).
$$
Training Loss. The pocket prediction loss is comprised of classification loss  $\mathcal{L}_p^c$  and pocket center constraint loss  $\mathcal{L}_p^{c2r}$ , with a weight factor  $\alpha = 0.2$ ,
$$
\mathcal {L} _ {\text {p o c k e t}} = \mathcal {L} _ {p} ^ {c} + \alpha \mathcal {L} _ {p} ^ {c 2 r}.
$$
Pocket Decision. Our pocket classifier can output the classified residues in a pocket. Following previous works [31, 51], we do not directly take these predicted residues as the pocket. Instead, we calculate the center of these classified residues and take it as the predicted pocket center, and the predicted pocket is in a sphere near the predicted center under a radius  $20\mathring{\mathrm{A}}$ . However, for some proteins, our classification model may predict each residue as negative for a pocket, making it impossible to determine the pocket center. This is likely due to an imbalance between the pocket and non-pocket residues. For these rare cases, we take the Gumbel-softmax predicted center  $x^p$  as the pocket center to address this problem.
3.4 Docking
In the docking task, given a pocket substructure  $\mathcal{G}^{p*}$ , our docking module predicts the coordinate of each atom in  $\mathcal{G}^l$ . The docking task is challenging since it requires the model to preserve E(3)-equivariance for every node while capturing pocket structure and chemical bonds of ligands.
Iterative refinement. Iterative refinement [19] is adopted in docking FABind layers to refine the structures by feeding the predicted ligand pose back to the message passing layers several rounds. During refinement iterations, new graphs are generated and the edges are also constructed dynamically.
After  $k$  iterations (iterative refinement) of the  $N \times \mathrm{FABind}$  layer alternations, we obtain the final coordinates  $\mathbf{x}^L$  and node embeddings  $\mathbf{h}_i^L$  and  $\mathbf{h}_j^L$ . Besides directly optimizing the coordinate loss, we additionally add distance map constraints to refine the ligand pose better. We reconstruct distance matrices in two ways. One is to directly compute based on the predicted coordinates:  $\widetilde{D}_{ij} = \left\| \mathbf{x}_i^L - \mathbf{x}_j^L \right\|$ . The other is to predict from the pair embeddings  $\mathbf{z}_{ij}^L$  by an MLP transition:  $\widehat{D}_{ij} = \mathrm{MLP}(\mathbf{z}_{ij}^L)$ , where each vector outputs a distance scalar.
Training Loss. The docking loss is comprised of coordinate loss  $\mathcal{L}_{\text {coord }}$  and distance map loss  $\mathcal{L}_{\text {dist }}$ :
$$
\mathcal {L} _ {\text {d o c k i n g}} = \mathcal {L} _ {\text {c o o r d}} + \beta \mathcal {L} _ {\text {d i s t}}.
$$
Methods	Ligand RMSD	Centroid Distance	Average
Percentiles ↓	% Below ↑	Percentiles ↓	% Below ↑
25%	50%	75%	Mean	2Å	5Å	25%	50%	75%	Mean	2Å	5Å	Runtime (s)
QVINA-W	2.5	7.7	23.7	13.6	20.9	40.2	0.9	3.7	22.9	11.9	41.0	54.6	49*
GNINA	2.8	8.7	22.1	13.3	21.2	37.1	1.0	4.5	21.2	11.5	36.0	52.0	146
SMINA	3.8	8.1	17.9	12.1	13.5	33.9	1.3	3.7	16.2	9.8	38.0	55.9	146*
GLIDE	2.6	9.3	28.1	16.2	21.8	33.6	0.8	5.6	26.9	14.4	36.1	48.7	1405*
VINA	5.7	10.7	21.4	14.7	5.5	21.2	1.9	6.2	20.1	12.1	26.5	47.1	205*
EQUIBIND	3.8	6.2	10.3	8.2	5.5	39.1	1.3	2.6	7.4	5.6	40.0	67.5	0.03
TANKBIND	2.6	4.2	7.6	7.8	17.6	57.8	0.8	1.7	4.3	5.9	55.0	77.8	0.87
E3BIND	2.1	3.8	7.8	7.2	23.4	60.0	0.8	1.5	4.0	5.1	60.0	78.8	0.44
DIFFDOCK (1)	2.4	4.9	8.9	8.3	20.4	51.0	0.7	1.8	4.5	5.8	54.1	76.8	2.72
DIFFDOCK (10)	1.6	3.8	7.9	7.4	32.4	59.7	0.6	1.4	3.6	5.2	60.7	79.8	20.81
DIFFDOCK (40)	1.5	3.5	7.4	7.4	36.0	61.7	0.5	1.2	3.3	5.4	62.9	80.2	82.83
FABIND	1.7	3.1	6.7	6.4	33.1	64.2	0.7	1.3	3.6	4.7	60.3	80.2	0.12
Table 1: Flexible blind self-docking performance. The top half contains results from traditional docking software; the bottom half contains results from recent deep learning based docking methods. The last line shows the results of our FABind. The number of poses that DiffDock samples is specified in parentheses. We run the experiments of DiffDock three times with different random seeds and report the mean result for robust comparison. The symbol " * " means that the method operates exclusively on the CPU. The superior results are emphasized by bold formatting, while those of the second-best are denoted by an underline.
$\mathcal{L}_{coord}$  is computed as the Huber distance between the predicted coordinates and ground truth coordinates of the ligand atoms.  $\mathcal{L}_{dist}$  is comprised of three terms, each of which is  $\mathcal{L}_2$  loss between different components of the ground truth and the two reconstructed distance maps. Formally,
$$
\mathcal {L} _ {d i s t} = \frac {1}{n ^ {l} n ^ {p *}} [ \sum_ {i = 1} ^ {n ^ {l}} \sum_ {j = 1} ^ {n ^ {p *}} (D _ {i j} - \widetilde {D} _ {i j}) ^ {2} + \sum_ {i = 1} ^ {n ^ {l}} \sum_ {j = 1} ^ {n ^ {p *}} (D _ {i j} - \widehat {D} _ {i j}) ^ {2} + \gamma \sum_ {i = 1} ^ {n ^ {l}} \sum_ {j = 1} ^ {n ^ {p *}} (\widetilde {D} _ {i j} - \widehat {D} _ {i j}) ^ {2} ],
$$
where  $D_{ij}$  is ground truth distance matrix. In practice, we set  $\beta = \gamma = 1.0$ .
3.5 Pipeline
We first predict the protein pocket and then predict the docked ligand coordinates in a hierarchical unified framework. However, the common approach is to only use the native pocket for docking in the training phase, which is known as teacher-forcing [24] training. Therefore, there is a mismatch in that the training phase takes the native pocket while the inference phase can only take the predicted pocket since we do not know the native pocket in inference. To reduce this gap, we incorporate a scheduled training strategy to gradually involve the predicted pocket in the training stage instead of using the native pocket only. Specifically, our training pipeline consists of two stages, (1) in the initial stage, since the performance of pocket prediction is poor, we only use the native pocket to perform the docking training; (2) In the second stage, with the improved pocket prediction ability, we then involve the predicted pocket into docking, where the native pocket is still kept in docking. The ratio between the predicted pocket and the native pocket is  $1:3$ .
Comprehensive Training Loss. Our comprehensive training loss comprises two components: the pocket prediction loss and the docking loss,
$$
\mathcal {L} = \mathcal {L} _ {\text {p o c k e t}} + \mathcal {L} _ {\text {d o c k i n g}}. \tag {1}
$$
4.1 Setting
Dataset. We conduct experiments on the PDBbind v2020 dataset [29], which is from Protein Data Bank (PDB) [5] and contains 19,443 protein-ligand complex structures. To maintain consistency with prior works [41, 31], we follow similar preprocessing steps (see Appendix Section A.1 for more details). After the filtration, we used 17, 299 complexes that were recorded before 2019 for training purposes, and an additional 968 complexes from the same period for validation. For our testing phase, we utilized 363 complexes recorded after 2019.
Methods	Ligand RMSD	Centroid Distance	AverageRuntime (s)
Percentiles ↓	% Below ↑	Percentiles ↓	% Below ↑
25%	50%	75%	Mean	2Å	5Å	25%	50%	75%	Mean	2Å	5Å
QVINA-W	3.4	10.3	28.1	16.9	15.3	31.9	1.3	6.5	26.8	15.2	35.4	47.9	49*
GNINA	4.5	13.4	27.8	16.7	13.9	27.8	2.0	10.1	27.0	15.1	25.7	39.5	146
SMINA	4.8	10.9	26.0	15.7	9.0	25.7	1.6	6.5	25.7	13.6	29.9	41.7	146*
GLIDE	3.4	18.0	31.4	19.6	19.6	28.7	1.1	17.6	29.1	18.1	29.4	40.6	1405*
VINA	7.9	16.6	27.1	18.7	1.4	12.0	2.4	15.7	26.2	16.1	20.4	37.3	205*
EQUIBIND	5.9	9.1	14.3	11.3	0.7	18.8	2.6	6.3	12.9	8.9	16.7	43.8	0.03
TANKBIND	3.4	5.7	10.8	10.5	3.5	43.7	1.2	2.6	8.4	8.2	40.9	70.8	0.87
E3BIND	3.0	6.1	10.2	10.1	6.3	38.9	1.2	2.3	7.0	7.6	43.8	66.0	0.44
DIFFDOCK (1)	4.1	7.2	18.2	12.5	8.1	33.1	1.4	3.7	16.7	10.0	33.6	58.3	2.72
DIFFDOCK (10)	3.2	6.4	16.5	11.8	14.2	38.7	1.1	2.8	13.3	9.3	39.7	62.6	20.81
DIFFDOCK (40)	2.8	6.4	16.3	12.0	17.2	42.3	1.0	2.7	14.2	9.8	43.3	62.6	82.83
FABIND	2.2	3.4	8.3	7.7	19.4	60.4	0.9	1.5	4.7	5.9	57.6	75.7	0.12
Table 2: Flexible blind self-docking performance on unseen receptors.
Model Configuration. For pocket prediction, we use  $M = 1$  FABind layer with 128 hidden dimensions. The pocket radius is set to  $20\mathring{\mathrm{A}}$ . As for docking, we use  $N = 4$  FABind layers with 512 hidden dimensions. Each layer comprises three-step message passing modules (refer to Fig. 1). We perform a total of  $k = 8$  iterations for structure refinement during the docking process. Additional training details can be found in the Appendix Section A.2.
Evaluation. Following EquiBind [41], the evaluation metrics are (1) Ligand RMSD, which calculates the root-mean-square deviation between predicted and true ligand atomic Cartesian coordinates, indicating the model capability of finding the right ligand conformation at atom level; (2) Centroid Distance, which calculates the Euclidean distance between predicted and true averaged ligand coordinates, reflecting the model capacity to identify the right binding site. To generate an initial ligand conformation, we employed the ETKDG algorithm [37] using RDKit [25], which randomly produces a low-energy ligand conformation.
4.2 Performance in Flexible Self-docking
In the context of flexible blind self-docking, where the bound ligand conformation is unknown and the model is tasked with predicting both the bound ligand conformation and its translation and orientation, we observe the notable performance of our FABind. Across most metrics, FABind ranking either as the best or second best, as presented in Table 1. Our FABind exceeds the DiffDock with 10 sampled poses. Although FABind may not achieve the best performance in terms of the  $<2\AA$  metric, it demonstrates exceptional proficiency with a mean RMSD score of  $6.4\AA$ . The comparatively lower performance in the  $<2\AA$  metric can be attributed to the optimization objective of DiffDock, which primarily focuses on optimizing ligand poses towards achieving  $<2\AA$  accuracy. FABind also gets comparative performance on Centroid Distance metrics. Overall, the experimental results showcase the remarkable efficacy of FABind.
4.3 Performance in Self-docking for Unseen Protein
To perform a more rigorous evaluation, we apply an additional filtering step to exclude samples whose UniProt IDs of the proteins are not contained in the data that is seen during training and validation. The resulting subset, consisting of 144 complexes, was then used to evaluate the performance of FABind. The results of this evaluation are presented in Table 2, demonstrating that FABind surpasses other deep learning and traditional methods by a significant margin across all evaluation metrics. These findings strongly indicate the robust generalization capability of FABind.
4.4 Inference Efficiency
We conducted an inference study to demonstrate the efficiency of FABind. The statistics regarding the average time cost per sample are presented in Table 1. Comparing our method to others, we observe that the inference time cost of FABind ranks second lowest. Notably, when compared to DiffDock with 10 sampled poses, our FABind achieves better docking performance while being over 170 times faster. The efficiency of our method can be attributed to eliminating the need for an external
pocket selection module, and the sampling and scoring steps used by other methods. By doing so, our FABind produces significantly faster docking. While EquiBind exhibits superior inference speed, it performs poorly in the docking task. These compelling findings strongly support the claim that our FABind is not only highly fast but also accurate.
5 Further Analysis
5.1 Pocket Prediction Analysis
In this study, We conduct an independent analysis of our pocket prediction module. To evaluate its performance, we compared it with two existing methods, TankBind and E3Bind, both of which use P2Rank to first segment the protein to multiple pocket blocks, and then apply a confidence module for ranking and selection. The selected pockets are used to compare with our predicted pockets. The pocket prediction performance is measured by the distance between the predicted pocket center and the center of the native binding site (DCC) metric, which is a widely-used metric in pocket pre
diction task [1]. We use thresholds of  $3\mathring{\mathrm{A}}$ ,  $4\mathring{\mathrm{A}}$ , and  $5\mathring{\mathrm{A}}$ , to determine successful predictions. From Table 3, we can see that: (1) removing the center constraint (classification only) significantly hurts the prediction performance. (2) The integration of ligand information into the pocket prediction task also enhances performance and efficiency. Previous two-stage methods involve initial docking for multiple pocket candidates, followed by the selection of the optimal candidate. Nevertheless, the majority of potential binding sites are irrelevant to the particular ligand [51]. Our FABind further improves the inference efficiency as our pocket prediction is essentially designed for predicting the most probable pocket for the specific ligand. (3) Combined with center constraint, even without incorporating ligand information, our pocket prediction performance outperforms TankBind and E3Bind, which shows our rational design of the pocket prediction module is effective.
Methods	DCC % Below ↑
3Å	4Å	5Å
TANKBIND	18.2	32.0	39.9
E3BIND	26.7	35.8	50.1
P2RANK	36.4	50.1	57.0
FABIND	42.7	56.5	62.8
- LIGAND INFORMATION	36.9	51.5	59.0
- CENTER CONSTRAINT	8.8	22.9	31.7
In this subsection, we perform several ablation studies to analyze the contribution of different components, the results for selected metrics are reported in Table 4. We examine four specific settings: removal of the scheduled training strategy (teacher forcing); removal of the distance map related losses; removal of the iterative refinement; and removal of the cross-attention update. From the table, we can see that: (1) each
of the components contributes to the good performance of our FABind. (2) The combination of distance map losses impacts most of the docking performance. (3) The remaining components primarily contribute to improvements in fine-grained scales  $(< 2\AA)$ . A full ablation study can be found in Appendix Section C.1.
Table 3: Results of pocket prediction.
Methods	RMSD Mean (Å)↓	RMSD % Below 2Å↑
FABIND	6.4	33.1
NO SCHEDULED SAMPLING	6.4	28.7
COORD LOSS ONLY	6.9	16.3
NO ITERATIVE REFINEMENT	6.6	22.5
NO CROSS-ATTENTION	6.4	21.4
Table 4: Results of ablation study.
FABind can identify the right binding pocket for a new large protein. In Fig. 2(a), the large protein target (PDB 6NPI) is not seen during training, thus posing a significant challenge to accurately locate the binding pocket. Though predicted poses of other deep learning models (DiffDock, E3Bind, TankBind, and EquiBind) are all off-site, FABind can successfully identify the native binding site and predict the binding pose (in green) with low RMSD  $(3.9\AA)$ , showing the strong generalization ability.
FABind generates ligand pose with better performance and validity. Fig. 2(b) shows the docked results of another protein (PDB 6G3C). All methods find the right pocket, but our FABind aligns best RMSD  $(0.8\AA)$  with the ground truth ligand pose. In comparison, E3Bind produces a knotted pose where rings are knotted together which is not valid. DiffDock also produces the same accurate ligand
(a) PDB: 6NPI
Figure 2: Case studies. Pose prediction by FABind (green), DiffDock (wheat), E3Bind (magenta), TankBind (cyan), and EquiBind (orange) are placed together with protein target, and RMSDs to ground truth (red) are reported. (a) For large unseen protein (PDB 6NPI), FABind successfully identifies the pocket, while the others are all off-site. (b) For the other protein (PDB 6G3C), all models find the right pocket, among which FABind predicts the most precise and valid binding pose as the DiffDock but with faster speed.
pose but is much slower. These show that FABind can not only find good pose with high speed but also maintain structural rationality.
In this paper, we propose an end-to-end framework, FABind, with several rational strategies. We propose a pocket prediction mechanism to be jointly trained with the docking module and bridge the gap between pocket training and inference with a scheduled training strategy. We also introduce a novel equivariant layer for both pocket prediction and docking. For ligand pose prediction, we incorporate both direct coordinate optimization and the protein-ligand distance map-based refinement. Empirical experiments show that FABind outperforms most existing methods with higher efficiency. In future work, we aim to better align the pocket prediction and docking modules and develop more efficient and effective tools.
We would like to thank the reviewers for their insightful comments. This work was partially supported by National Natural Science Foundation of China (NSFC Grant No. 62122089), Beijing Outstanding Young Scientist Program NO. BJWZYJH012019100020098, and Intelligent Social Governance Platform, Major Innovation & Planning Interdisciplinary Platform for the "Double-First Class" Initiative, Renmin University of China.
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A More Detailed Descriptions
A.1 Dataset Preprocessing
As we stated in paper Section 4.1, PDBBind v2020 dataset [29] contains 19,443 ligand-protein complex structures, and we pre-process the structures as follows. First, we only keep complex structures whose ligand structure file (in sdf or mol2 format) can be processed by RDKit [25] or TorchDrug [52], leaving 19,126 complexes. Then, to address the multiple equally valid binding ligand pose issue for symmetric receptor structures, we only keep the protein chains that have an atom within  $10\AA$  radius of any atom of the ligand. We further filter out complexes in which the contact (distance is within  $10\AA$ ) number between ligand atom and protein amino acid  $C_{\alpha}$  are less than or equal to 5, or the number of ligand atom is more than or equal to 100. After applying these filters, 18,630 complexes are left. Finally, we process the remaining complexes with the time split as described in EquiBind [41].
A.2 Experiment Settings
Baseline. We compare our model with traditional score-based docking methods and recent geometry-based deep learning methods. For traditional docking methods, QVina-W, GNINA [33], SMINA [21], GLIDE [8] and AutoDock Vina [43] are included. For deep learning methods, EquiBind [41], TankBind [31], E3Bind [51] and DiffDock [7] are included.
We report corrected results for the deep learning baselines including EquiBind, TankBind, and E3Bind. The corrected results adopt post-optimization methods on model outputs, including fast point cloud fitting (used in EquiBind) and gradient descent (used in TankBind and E3Bind), which can further enforce geometry constraints within the ligand. For TankBind, the post-optimization method is used to get final ligand coordinates through the predicted distance matrix, which is essential for distance to coordinate transformation. However, for a fair comparison, the reported average runtime of EquiBind, TankBind, E3Bind, and FABind is the uncorrected version without post-optimization. The reported baseline results are mainly derived from the original paper of E3Bind [51]. For the DiffDock results, as the results of the sample-based method are unstable, we reproduce the results using its pre-trained checkpoint<sup>4</sup>. Specifically, we run the DiffDock inference codes with three random seeds and report the average results.