CausalBind: Causal Modeling and Learning for Protein-Molecule Virtual Screening

Loka Li; Jin Tian; Kun Zhang

cs.LGOct 5, 2026

CausalBind: Causal Modeling and Learning for Protein-Molecule Virtual Screening

Authors: Loka Li, Jin Tian, Kun Zhang

Organizations: Mohamed bin Zayed University of Artificial Intelligence · Carnegie Mellon University

Abstract

Protein-molecule virtual screening is increasingly cast as a problem of representation learning in a shared embedding space. Existing methods rely on dense holistic alignment, entangling invariant binding determinants with nuisance correlations and limiting transfer to new targets. It has been noted that binding in protein-molecule systems involves sparse cross-modality interactions: binding is governed by a small contact interface and a few decisive local interactions (e.g., hydrogen bonds, hydrophobic contacts, and salt bridges) rather than the global structures of the protein and molecule. We hypothesize that uncovering and leveraging sparse interaction patterns is critical for generalization beyond the training data, as these patterns are reusable and expected to improve performance across different scenarios. In this paper, we aim to identify and leverage sparse interaction patterns, and verify our hypothesis. Since the training data contain only observed binding pairs, we formalize this prior via a V-structure causal model under Heckman-style selection, and establish three theoretical results: (i) the latent concepts of interacting proteins and molecules are not identifiable without appropriate sparsity constraints; (ii) these concepts and their sparse interactions are component-wise identifiable under structural sparsity conditions; and (iii) a low-rank relaxation of these conditions yields subspace identifiability of the concepts and interactions. Inspired by these principles, we propose CausalBind with three implementation variants. Extensive experiments on DUD-E and LIT-PCBA benchmarks show that all variants consistently outperform strong retrieval baselines, with the largest gains on LIT-PCBA early enrichment, and further generalize to target- and scaffold-level out-of-distribution splits. Code is available at https://github.com/lokali/CausalBind.

Figures & tables

Figure 1: Dense alignment versus sparse binding. (a) Holistic dense alignment. Existing retrieval-based virtual screening methods compare every protein surface feature with every molecule feature in the shared embedding space; this “full-surface” alignment entangles binding-relevant signals with nuisance correlations. (b) Biology-inspired sparse binding. Protein-molecule binding is governed by a small contact interface and a handful of key local interactions (e.g., hydrogen bonds, hydrophobic contacts, salt bridges, and $\pi$ -stacking), which together account for the majority of the binding affinity.

Panel of Figure 2 — Figure 2: Binder-selected sparse-interaction view. Observing only binders ( $B{=}1$ ) induces cross-modal dependence through the collider $B$ . Green edges denote active local interactions. Red dashed edges blocked interactions. Purple dashed curves allowed within-modality dependence.

Panel of Figure 3 — Figure 3: Implementation-level view of CausalBind . Each modality-specific encoder maps its input to atomic concepts $\{c_{v}^{k}\}$ , each with dimension $d_{c}\geq 1$ . The indicators $B_{ij}$ at the bottom visualize the branch-wise cross-modal mask $\mathcal{M}_{a,b}$ for $(a,b)\in\{(\mathrm{mol},\mathrm{poc}),(\mathrm{mol},\mathrm{seq})\}$ : $B_{ij}{=}1$ when the $(i,j)$ entry of $\mathcal{M}_{a,b}$ survives the forward threshold ( $\tau=0.5$ ) (green solid edges, active pair), and $B_{ij}{=}0$ otherwise (red dashed edges, blocked pair). Active pairs form the contrastive score, while $\mathcal{L}_{\mathrm{spa}}$ encourages the interaction sparsity.

Method	DUD-E ( $n{=}102$ )			LIT-PCBA ( $n{=}15$ )
Method	AUROC	BEDROC 80.5	EF 1%	AUROC	BEDROC 80.5	EF 1%
Glide-SP ( Friesner et al., 2004 )	0.767	0.407	16.18	0.532	0.040	3.41
DeepDTA ( Öztürk et al., 2018 )	0.584	0.051	2.28	0.563	0.025	1.47
Gnina ( McNutt et al., 2021 )	0.782	0.299	17.73	0.609	0.054	4.63
RTMScore ( Shen et al., 2022 )	0.753	0.434	27.10	0.525	0.039	2.94
TankBind ( Lu et al., 2022 )	0.751	0.330	13.00	0.597	0.039	2.90

Table 1: Virtual-screening comparison on two benchmarks between baselines and CausalBind SP (

K{=}128,d_{c}{=}1024

), CausalBind LR (

K{=}64,r{=}1

), and CausalBind EMB (

K{=}64,d_{c}{=}256

), and CausalBind ATOM (

K{=}128,d_{c}{=}1024

). † S 2 Drug results are paper-reported ( He et al., 2026 ) rather than reproduced in our pipeline.

Method	DUD-E ( $n{=}102$ )			LIT-PCBA ( $n{=}15$ )
Method	AUROC	BEDROC 80.5	EF 1%	AUROC	BEDROC 80.5	EF 1%
LigUnity ( Feng et al., 2025 )	0.896 $\pm$ 0.005	0.660 $\pm$ 0.018	43.14 $\pm$ 1.42	0.586 $\pm$ 0.010	0.077 $\pm$ 0.001	6.46 $\pm$ 0.18
HypSeek ( Wang et al., 2026 )	0.914 $\pm$ 0.013	0.690 $\pm$ 0.081	44.12 $\pm$ 6.14	0.603 $\pm$ 0.009	0.067 $\pm$ 0.007	5.62 $\pm$ 0.71
CausalBind SP	0.939 $\pm$ 0.004	0.746 $\pm$ 0.004	47.99 $\pm$ 0.39	0.635 $\pm$ 0.006	0.088 $\pm$ 0.007	7.55 $\pm$ 0.73
CausalBind SP $-\,L_{\mathrm{spa}}$	0.935 $\pm$ 0.004	0.732 $\pm$ 0.014	46.93 $\pm$ 1.07	0.623 $\pm$ 0.005	0.084 $\pm$ 0.004	7.17 $\pm$ 0.36
CausalBind LR	0.937 $\pm$ 0.004	0.732 $\pm$ 0.011	46.87 $\pm$ 0.91	0.630 $\pm$ 0.006	0.085 $\pm$ 0.006	7.22 $\pm$ 0.31

Table 2: Ablation and diagnostic study on DUD-E and LIT-PCBA. CausalBind SP is the sparse mask, CausalBind LR is the low-rank mask, and CausalBind EMB is the pooled embedding-space mask.

-L_{\mathrm{spa}}

removes the sparsity penalty from CausalBind SP , while

+L_{\mathrm{spa}}

tests an optional sparsity penalty on CausalBind LR without changing its rank-one parameterization.

\mathbf{M}_{\mathrm{emb}}^{r=1}

replaces the pooled embedding mask with a rank-one mask. Rows report mean

{}_{\pm\,\text{std}}

over five runs.

Figure 4: Hyperparameter sweeps for CausalBind SP on DUD-E and LIT-PCBA. Solid lines show BEDROC 80.5 and dashed lines show EF@1%; shaded bands mark the selected hyperparameters.

$\lambda_{\mathrm{spa}}$	DUD-E			LIT-PCBA			Cross-modal mask statistics
$\lambda_{\mathrm{spa}}$	AUC	BEDROC 80.5	EF@1%	AUC	BEDROC 80.5	EF@1%	$L_{1}$ avg	%zeros	$r@95\%$	$r@99\%$	Anti. viol.
$0$	0.938	0.746	48.14	0.617	0.080	6.83	0.93	0.0	1	25.0	32,512
$10^{-6}$	0.940	0.749	47.94	0.635	0.088	7.26	0.92	0.0	1	25.0	32,512
$10^{-5}$	0.938	0.735	47.09	0.607	0.078	6.29	0.88	0.0	1	26.0	32,512
$10^{-4}$	0.935	0.744	47.69	0.639	0.097	8.56	0.61	0.0	1	34.0	32,512
$10^{-3}$	0.943	0.768	49.73	0.614	0.073	5.49	0.21	20.5	45.5	79.5	0

Table 3:

\lambda_{\mathrm{spa}}

-scan for CausalBind SP with paired cross-modal mask statistics, averaged over the two branches. Small

\lambda_{\mathrm{spa}}

preserves a low-rank regime, while large

\lambda_{\mathrm{spa}}

drives hard-zero collapse. ‘Anti. viol.’ counts antichain violations, i.e., pairs of row (or column) supports in which one contains the other, over

32{,}512

pairwise tests.

Appendix figures & tables25 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 8 — Figure A1: Drug discovery pipeline funnel. Each stage progressively filters compounds, with numbers indicating typical compound counts. Our CausalBind method (green box) operates at the virtual screening stage, improving the quality of top-ranked candidates before expensive downstream validation. By identifying invariant binding determinants and suppressing spurious correlations, our method aims to increase the hit rate in subsequent experimental testing.

	Physics-based docking	Structure-aware ML scoring	Retrieval-based learning
Inference input	(protein, ligand) pair + pose search	(protein, ligand) pair, often pose-conditioned	protein and ligand encoded independently
Binding score	physics + empirical scoring on the pair	one forward pass through a joint network on the pair	dot product (or cosine) of two precomputed vectors
Pre-computable embeddings?	No (pose-coupled)	No (pair-coupled)	Yes (dual-tower)
Cost per (P, L) at inference	seconds–minutes (pose search dominates)	$\sim$ 10–100 ms (one full forward)	sub-millisecond (one dot product)
Practical library scale	$10^{4}$ – $10^{5}$	$10^{5}$ – $10^{6}$	$\mathbf{10^{8}\text{--}10^{9}}$
Where the inductive bias lives	force field + sampling protocol	complex graph / 3D-voxel architecture	shape of the shared embedding space and the similarity used on it

Appendix

Table A1: Core differences between the three virtual-screening regimes. The retrieval regime decouples encoders into two towers, enabling pre-computed library embeddings and millisecond-scale similarity scoring; the other two regimes condition on the (protein, ligand) pair at inference. CausalBind SP stays in the retrieval regime but replaces the dense holistic similarity with a sparse bipartite concept-pair interaction.

Method	Core Design	Relevance Here
Physics-based docking systems
Glide-SP [ Friesner et al., 2004 ]	Hierarchical sampling with empirical scoring function	Industry standard; accurate on small candidate sets but expensive at library scale
AutoDock Vina [ Trott and Olson, 2010 ]	Empirical scoring + iterated local search	Open-source, widely used; not designed for ultra-large libraries
Structure-aware machine-learning scoring models
DeepDTA [ Öztürk et al., 2018 ]	Sequence/graph-based affinity prediction without pairwise retrieval design	Useful DTA baseline; not optimized for target-wise early enrichment
Gnina [ McNutt et al., 2021 ]	3D CNN scoring on docking-grid voxels	Strong pose-rescoring; depends on docked poses

Appendix

Table A2: Representative methods in the three virtual-screening regimes discussed in the main text. The table highlights the main design choice of each method and the role it plays in the comparison, with CausalBind SP differing from prior retrieval baselines by imposing a sparse bipartite interaction prior rather than a dense holistic similarity.

Panel of Figure 11 — Figure A2: Three-view concept-level schematic of CausalBind . The inputs are pocket structure, molecule structure, and protein sequence. Each view is decomposed into modality-specific concepts $c_{\mathrm{poc}}$ , $c_{\mathrm{mol}}$ , and $c_{\mathrm{seq}}$ . Local binary indicators summarize whether a concept pair is active ( $1$ ) or blocked ( $0$ ). We show two interaction branches, pocket-molecule and molecule-sequence, which are then aggregated into the final pair-level binding event $B$ . Green solid arrows denote active local interactions, red dashed arrows denote blocked interactions, and gray arrows denote aggregation to the overall binding variable.

Variant	Mask object	Forward bottleneck	Closest theory link	Role in the paper
CausalBind SP	Dense $K\times K$ concept-pair mask with $L_{1}$ sparsity and hard thresholding.	Concept axis before pooling; each active entry selects a protein-molecule concept pair.	Direct sparse-support form of Theorem 2 ; learned masks can also enter the low-rank regime of Theorem 3 .	Primary method in the main text.
CausalBind LR	Rank- $r$ concept-basis mask $\mathbf{U}\mathbf{V}^{\top}$ with $\mathbf{U},\mathbf{V}\in\mathbb{R}^{K\times r}$ .	Concept axis before pooling; rank controls the number of interaction subspaces.	Direct implementation of the low-rank subspace-identifiability structure in Theorem 3 .	Appendix variant for explicit low-rank implementation.
CausalBind EMB	Dense $d_{c}\times d_{c}$ mask in pooled embedding space.	After mean-pooling; the mask acts on pooled features rather than concept pairs.	Compatible with a compressed interaction view, but not a direct instantiation of concept-pair sparse support.	Appendix alternative and robustness check.

Appendix

Table A3: Comparison of the three CausalBind implementations. The main paper presents CausalBind SP ; CausalBind LR and CausalBind EMB are appendix variants.

Method	Protocol	DUD-E			LIT-PCBA
		AUROC	BEDROC 80.5	EF@1%	AUROC	BEDROC 80.5	EF@1%
LigUnity	last	0.897	0.674	44.20	0.599	0.075	6.50
	best_auc	0.915	0.716	46.42	0.581	0.089	8.15
	best_bedroc	0.896	0.671	44.00	0.599	0.076	6.38
HypSeek	last	0.909	0.605	37.83	0.603	0.061	4.62
	best_auc	0.913	0.629	39.63	0.608	0.063	5.13

Appendix

Table A4: Three-protocol evaluation for main comparisons. The main text reports the fixed-endpoint last protocol; best_auc and best_bedroc are complementary validation-selected references. All rows are seed-1 results.

$K$	Protocol	DUD-E			LIT-PCBA
		AUROC	BEDROC 80.5	EF@1%	AUROC	BEDROC 80.5	EF@1%
32	last	0.938	0.749	48.41	0.620	0.081	6.90
	best_auc	0.939	0.750	48.38	0.625	0.083	6.85
	best_bedroc	0.938	0.750	48.57	0.621	0.081	6.90
64	last	0.930	0.724	46.55	0.637	0.085	6.41
	best_auc	0.933	0.715	45.90	0.638	0.088	7.88

Appendix

Table A5: CausalBind SP concept-level

K

-scan (fix

d_{c}{=}512

), seed=1, all three protocols.

K{=}256

underperforms consistently.

$d_{c}$	Protocol	DUD-E			LIT-PCBA
		AUROC	BEDROC 80.5	EF@1%	AUROC	BEDROC 80.5	EF@1%
128	last	0.919	0.589	35.75	0.615	0.062	5.25
	best_auc	0.922	0.629	39.43	0.630	0.060	4.75
	best_bedroc	0.920	0.592	36.03	0.620	0.062	5.35
256	last	0.912	0.600	36.93	0.614	0.062	5.68
	best_auc	0.922	0.683	43.07	0.620	0.067	4.73

Appendix

Table A6: CausalBind SP concept-level

d_{c}

-scan (fix

K{=}128

), seed=1, all three protocols.

d_{c}{=}1024

gives the strongest LIT-PCBA results.

$\lambda$	Protocol	DUD-E			LIT-PCBA
		AUROC	BEDROC 80.5	EF@1%	AUROC	BEDROC 80.5	EF@1%
$0$	last	0.938	0.746	48.14	0.617	0.080	6.83
	best_auc	0.943	0.744	47.68	0.629	0.073	6.26
	best_bedroc	0.934	0.732	47.03	0.613	0.075	6.10
$10^{-6}$	last	0.940	0.749	47.94	0.635	0.088	7.26
	best_auc	0.941	0.750	47.75	0.628	0.086	7.41

Appendix

Table A7: CausalBind SP concept-level

\lambda

-scan, seed=1, all three protocols.

K{=}128

d_{c}{=}1024

L{=}4

. Rows below the dotted rule show mask collapse under last and best_bedroc .

$L$	Protocol	DUD-E			LIT-PCBA
		AUROC	BEDROC 80.5	EF@1%	AUROC	BEDROC 80.5	EF@1%
$\mathbf{2}$	last	0.940	0.763	49.20	0.625	0.087	6.98
	best_auc	0.946	0.776	49.99	0.616	0.082	6.53
	best_bedroc	0.942	0.757	48.48	0.622	0.085	7.95
$\mathbf{4}$ (default)	last	0.935	0.744	47.69	0.639	0.097	8.56
	best_auc	0.934	0.722	46.41	0.628	0.074	5.84

Appendix

Table A8: CausalBind SP concept-level Perceiver-depth (

L

) scan, seed=1, all three protocols.

K{=}128

d_{c}{=}1024

\lambda{=}10^{-4}

$\lambda$	branch	$\overline{\sigma(\mathcal{M})}$	max $\sigma(\mathcal{M})$	$L_{1}$ (sum)	$r@95\%$	$r@99\%$
$0$	mol	0.920	1.311	15068	1	5
	poc	0.993	1.398	16267	1	1
	seq	1.023	1.374	16758	1	1
$10^{-6}$	mol	0.910	1.301	14914	1	5
	poc	0.991	1.395	16228	1	1
	seq	1.023	1.374	16755	1	1

Appendix

Table A9: Mask structural analysis across

\lambda

for the concept-level model. Per-stream numbers are reported at

K{=}128

under the last protocol, seed=1.

L_{1}

and rank statistics use the continuous pre-gate masks; zeros use the hard-gated forward masks.

\lambda{=}10^{-4}

remains element-wise dense but has a richer spectral tail, while

\lambda{\geq}10^{-3}

produces hard zeros and rank-1 masks.

Configuration	Primary metrics			ROC-enrichment (RE)
Configuration	AUROC	BEDROC 80.5	EF@1%	@0.5%	@1%	@2%	@5%
DrugCLIP [ Gao et al., 2023 ]	0.809	0.505	31.89	73.97	41.79	23.68	11.16
LigUnity [ Feng et al., 2025 ]	0.897	0.674	44.20	104.69	57.47	33.76	13.88
HypSeek [ Wang et al., 2026 ]	0.909	0.605	37.83	95.20	54.49	30.74	14.01
CausalBind SP ( $K{=}128,d_{c}{=}512,L{=}4$ )	0.943	0.752	47.93	127.56	69.94	37.83	16.39
CausalBind SP ( $K{=}128,d_{c}{=}1024,L{=}4$ )	0.935	0.744	47.69	128.06	69.26	37.07	15.99

Appendix

Table A10: ROC-enrichment (RE) on DUD-E under the last checkpoint protocol. Values are

102

-target means. AUROC / BEDROC 80.5 / EF@1% are reproduced from the main DUD-E comparison for context.

Method	Pearson $r$	Spearman $\rho$
LigUnity	0.532	0.499
HypSeek	0.423	0.390
CausalBind SP	0.598	0.548

Appendix

Table A11: Merck-FEP-8 affinity-ranking correlations. Higher Pearson

r

and Spearman

\rho

are better. CausalBind SP uses the main

K{=}128,d_{c}{=}1024

configuration under seed 1 and the last checkpoint.

Method	EF@0.5%	EF@1%
S 2 Drug (paper-reported)	11.44	7.38
CausalBind SP	10.88	8.56
CausalBind LR	11.59	8.84
CausalBind EMB	12.20	9.60

Appendix

Table A12: LIT-PCBA EF@0.5% comparison with the paper-reported S 2 Drug result.

Method	Target-level OOD (9 targets)			Scaffold-level OOD (6 targets)
Method	AUROC	BEDROC 80.5	EF@1%	AUROC	BEDROC 80.5	EF@1%
HypSeek [ Wang et al., 2026 ]	0.819	0.593	20.06	0.880	0.630	44.47
LigUnity [ Feng et al., 2025 ]	0.859	0.570	19.82	0.915	0.612	43.11
CausalBind SP	0.860	0.658	23.00	0.945	0.712	43.66
CausalBind LR	0.867	0.653	22.71	0.949	0.716	44.70
CausalBind ATOM	0.837	0.666	22.94	0.941	0.744	50.77

Appendix

Table A13: Zero-shot out-of-distribution evaluation on DEKOIS 2.0. CausalBind ATOM is the atom-attentive version of CausalBind SP (Section 4 ).

Stage	Evidence	Observation	Purpose
Local structure	Heavy-atom contacts ( $\leq 4$ Å)	98 contacts involving 27 ligand and 47 pocket atoms	Identify the local binding interface
Learned concept	Contact concentration in the most contact-aligned concept pair	0.0505 vs. 0.00881 uniform baseline (5.73 $\times$ enrichment)	Test whether contacts concentrate in concepts
Predicted score	Mask the associated 4 ligand and 8 pocket atoms (encoder fixed)	Score decreases $1.878\to 0.851$ ( $-54.7\%$ )	Test contribution to the prediction
Random control	Mask 64 matched random sets of 4 ligand and 8 pocket atoms	Mean decrease $0.026\pm 0.073$ ; guided decrease $1.027$ (99.2nd percentile)	Exclude an arbitrary masking effect

Appendix

Table A14: Local-to-global attribution on the DUD-E THRB complex.

Figure A3: Local-to-global attribution on the DUD-E THRB complex. (A) Ligand–pocket heavy-atom contacts within 4 Å in a 2D projection; highlighted atoms are those occluded at the concept bottleneck. (B) Attention-weighted contact probability over ligand–pocket concept pairs, with the contact-selected concepts and the top pair marked. (C) Decrease in the final binding score after masking the local contact atoms, matched random atoms, or the contact-selected concepts.

$r$	Params/branch	Protocol	DUD-E			LIT-PCBA
			AUROC	BEDROC 80.5	EF@1%	AUROC	BEDROC 80.5	EF@1%
1	256	last	0.935	0.720	45.86	0.630	0.087	8.41
		best_auc	0.946	0.756	48.78	0.636	0.079	6.53
		best_bedroc	0.935	0.724	46.28	0.632	0.089	8.56
4	1,024	last	0.934	0.731	47.14	0.632	0.085	7.45
		best_auc	0.933	0.710	45.14	0.633	0.080	7.67

Appendix

Table A15: CausalBind LR rank scan, seed=1, all three checkpoint protocols. All rows use

K{=}128

d_{c}{=}1024

L{=}4

, and

\lambda{=}10^{-4}

Method	$n$	DUD-E			LIT-PCBA
		AUROC	BEDROC 80.5	EF@1%	AUROC	BEDROC 80.5	EF@1%
CausalBind LR ( $r{=}1$ )	3	$0.937{\pm}0.004$	$0.732{\pm}0.011$	$46.87{\pm}0.91$	$0.630{\pm}0.006$	$0.085{\pm}0.006$	$7.22{\pm}0.31$
CausalBind LR ( $r{=}1$ ) $+L_{\mathrm{spa}}$	3	$0.935{\pm}0.003$	$0.727{\pm}0.007$	$46.39{\pm}0.58$	$0.623{\pm}0.007$	$0.083{\pm}0.005$	$7.51{\pm}0.94$
CausalBind LR ( $r{=}8$ ) $+L_{\mathrm{spa}}$	3	$0.940{\pm}0.001$	$0.750{\pm}0.011$	$48.30{\pm}0.97$	$0.621{\pm}0.005$	$0.087{\pm}0.003$	$7.73{\pm}0.40$
CausalBind SP main	4	$0.938{\pm}0.004$	$0.746{\pm}0.004$	$47.99{\pm}0.39$	$0.631{\pm}0.006$	$0.088{\pm}0.007$	$7.55{\pm}0.73$

Appendix

Table A16: Multi-seed last -checkpoint comparison for CausalBind LR and the main CausalBind SP reference.

$K$	Params/branch	Protocol	DUD-E			LIT-PCBA
			AUROC	BEDROC 80.5	EF@1%	AUROC	BEDROC 80.5	EF@1%
64	128	last	0.935	0.704	44.87	0.632	0.103	8.84
		best_auc	0.934	0.702	44.63	0.638	0.099	9.03
		best_bedroc	0.936	0.716	45.92	0.631	0.095	6.54
128	256	last	0.935	0.720	45.86	0.630	0.087	8.41
		best_auc	0.946	0.756	48.78	0.636	0.079	6.53

Appendix

Table A17: CausalBind LR

K

-scan with

r{=}1

, seed=1, all three protocols. All rows use

d_{c}{=}1024

L{=}4

, and

\lambda{=}10^{-4}

$r$ capacity	$\overline{\sigma(\mathcal{M})}$	%zeros	$r@95\%$	$r@99\%$	Interpretation
1	0.86	0.0%	1	1	rank-one by construction
4	0.63	0.0%	1	1	trained solution collapses to rank one
8	0.54	8.9%	1	1	some thresholded zeros, still rank one
16	0.51	23.3%	1	1	more zeros, same effective rank
32	0.51	34.3%	1	1	unused rank capacity
64	0.50	39.7%	1	1	unused rank capacity

Appendix

Table A18: Mask diagnostics for the CausalBind LR rank scan. The reported branch uses the same protocol as Table A9 .

$K$	Protocol	DUD-E			LIT-PCBA
		AUROC	BEDROC 80.5	EF@1%	AUROC	BEDROC 80.5	EF@1%
32	last	0.942	0.743	47.35	0.638	0.090	7.48
	best_auc	0.942	0.747	47.84	0.640	0.085	6.86
	best_bedroc	0.937	0.716	45.79	0.643	0.066	4.38
64	last	0.939	0.754	48.56	0.636	0.102	9.60
	best_auc	0.941	0.765	49.47	0.635	0.097	8.18

Appendix

Table A19: CausalBind EMB

K

-scan (fix

d_{c}{=}256

), seed=1, all three protocols.

$d_{c}$	Protocol	DUD-E			LIT-PCBA
		AUROC	BEDROC 80.5	EF@1%	AUROC	BEDROC 80.5	EF@1%
128	last	0.943	0.732	47.09	0.606	0.074	5.88
	best_auc	0.944	0.726	46.59	0.617	0.075	6.97
	best_bedroc	0.943	0.738	47.49	0.602	0.071	6.03
256	last	0.939	0.754	48.56	0.636	0.102	9.60
	best_auc	0.941	0.765	49.47	0.635	0.097	8.18

Appendix

Table A20: CausalBind EMB

d_{c}

-scan (fix

K{=}64

), seed=1, all three protocols.

d_{c}{=}256

is strongest on LIT-PCBA early enrichment.

Model	Protocol	DUD-E			LIT-PCBA
Model	Protocol	AUROC	BEDROC 80.5	EF@1%	AUROC	BEDROC 80.5	EF@1%
HypSeek [ Wang et al., 2026 ]	last	0.909	0.605	37.83	0.603	0.061	4.62
	best_auc	0.913	0.629	39.63	0.608	0.063	5.13
	best_bedroc	0.923	0.676	42.71	0.607	0.063	4.56
CausalBind SP	last	0.935	0.744	47.69	0.639	0.097	8.56
	best_auc	0.934	0.722	46.41	0.628	0.074	5.84

Appendix

Table A21: Three-protocol comparison among HypSeek, CausalBind SP , and CausalBind EMB . CausalBind SP uses

K{=}128

d_{c}{=}1024

\lambda{=}10^{-4}

L{=}4

, which is the main operating point analyzed in the paper. CausalBind EMB uses

K{=}64

d_{c}{=}256

\lambda{=}10^{-2}

, selected as the strongest setting in the embedding-level sweep. All rows are seed-1 results.

Branch	%zeros	$r@95\%$	$r@99\%$
mol–pocket	0.0%	1	46
mol–sequence	0.0%	1	46

Appendix

Table A22: Spectral diagnostics for the embedding-level mask (

K{=}64

d_{c}{=}256

\lambda{=}10^{-2}

, seed 1). We report the two branchwise product masks used in the paper’s interaction view, evaluated under the last checkpoint.

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