Event Embedding of Protein Networks : Compositional Learning of Biological Function

Antonin Sulc

cs.LGApr 1, 2026

Event Embedding of Protein Networks : Compositional Learning of Biological Function

Authors: Antonin Sulc

Organizations: Lawrence Berkeley National Lab

Abstract

In this work, we study whether enforcing strict compositional structure in sequence embeddings yields meaningful geometric organization when applied to protein-protein interaction networks. Using Event2Vec, an additive sequence embedding model, we train 64-dimensional representations on random walks from the human STRING interactome, and compare against a DeepWalk baseline based on Word2Vec, trained on the same walks. We find that compositional structure substantially improves pathway coherence (30.2 $\times$ vs 2.9 $\times$ above random), functional analogy accuracy (mean similarity 0.966 vs 0.650), and hierarchical pathway organization, while geometric properties such as norm--degree anticorrelation are shared with or exceeded by the non-compositional baseline. These results indicate that enforced compositionality specifically benefits relational and compositional reasoning tasks in biological networks.

Figures & tables

Figure 1: Pathway coherence comparison. Event2Vec (left) shows higher coherence and much lower random baseline than DeepWalk (right) across all 10 pathways.

Figure 2: Protein arithmetic comparison. Event2Vec (left column) recovers biologically specific targets with high similarity. DeepWalk (right column) returns less specific predictions with lower similarity.

Figure 3: Norm–degree anticorrelation. Both methods show that high-degree proteins (hubs) receive smaller embedding norms, but DeepWalk exhibits stronger anticorrelation ( $r=-0.801$ ) than Event2Vec ( $r=-0.627$ ). This suggests the pattern arises from skip-gram frequency effects rather than compositional structure. Red points highlight canonical hubs (TP53, MYC, AKT1, EGFR, SRC, JUN, BRCA1, TNF). Note the different norm scales: Event2Vec’s additive constraint produces smaller, more tightly distributed norms.

Figure 4: Hierarchical pathway organization. Cosine similarity between pathway centroids, reordered by Ward clustering. Event2Vec (left) reveals three biologically coherent super-clusters: housekeeping (Ribosome, OxPhos), nuclear/genome (DNA Repair, p53, Cell Cycle), and signaling (PI3K-AKT, MAPK/ERK, NF- $\kappa$ B, Apoptosis). Negative correlations (blue) sharply delineate housekeeping pathways from signaling cascades. DeepWalk (right) shows uniformly positive similarities without clear cluster boundaries, indicating weaker functional discrimination.

Figure 5: Embedding drift along signaling cascades. Cumulative sums of protein embeddings (

h_{t}=\sum_{i=1}^{t}e_{i}

) are computed along three canonical pathways (EGFR signaling, PI3K-AKT-mTOR, p53 DNA damage) and projected via PCA. Event2Vec (top row) produces smooth, directional trajectories where PC1 captures 96–98% of variance, indicating that sequential addition follows a coherent linear path. DeepWalk (bottom row) shows noisier trajectories with greater PC2 spread (PC1 explains only 89–94% of variance), reflecting the absence of an additive constraint. This directly validates Event2Vec’s compositional structure: the embedding of a signaling history approximates the sum of its constituent proteins.

Compositional advantages (Event2Vec wins)
Metric	Event2Vec	DeepWalk
Pathway coherence (mean)	0.870	0.648
Coherence / random baseline	30.2 $\times$	2.9 $\times$
Relationship transfer (mean sim)	0.966	0.650
Top-1 analogy (EGFR:AKT1::INSR:?)	KRAS	AKT3
Pathway cluster structure	Sharp	Diffuse

Table 1: Comparison of Event2Vec and DeepWalk across all evaluation axes. Event2Vec shows large advantages in compositional tasks (arithmetic, transfer, clustering), while norm-based geometric properties are shared with or exceeded by the non-compositional baseline.

Research Activity	Human	AI
Study design & implementation	Complete	None
Evaluation strategy development	Complete	None
Statistical analysis & validation	Complete	None
Baseline comparison design	Joint	Joint
Example & test case selection	Verification	Complete
Biological pattern identification	Verification	Proposal

Table 2: Division of labor between human researchers and AI assistant.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Pathway	Event2Vec	DeepWalk	$\Delta$
Ribosome	0.993	0.784	+0.209
DNA Repair	0.966	0.683	+0.283
MAPK/ERK	0.952	0.641	+0.311
NF- $\kappa$ B	0.950	0.638	+0.312
OxPhos	0.938	0.718	+0.220
Cell Cycle	0.886	0.687	+0.199

Appendix

Table 3: Per-pathway coherence for Event2Vec vs DeepWalk. Event2Vec exceeds DeepWalk on all 10 pathways.

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Abstract

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