MABLE: Masked Autoencoding with Bi-Lipschitz Decoding for Embeddings and Graph Metric Learning

Self-supervised learning on graphs is largely shaped by contrastive methods that depend on carefully designed augmentations, and by generative methods that reconstruct node attributes in the input space. Both paradigms can entangle representations with low-level input statistics rather than with relational structure. Joint-embedding predictive architectures (JEPA) instead learn by predicting latent targets rather than reconstructing inputs. Recent work has explored this idea for graph-level representation learning, but how to design JEPA-style objectives for node-level tasks, and which structural signals the predictor should condition on, remains less clear. We present NodeJEPA, a joint-embedding predictive architecture for node-level graph self-supervised learning. NodeJEPA masks structure-aware k-hop ego-subgraphs and trains a context encoder to predict the latent representations of the masked nodes. These targets come from an EMA-updated target encoder with stop-gradient. A structure-conditioned predictor integrates spectral and centrality descriptors through cross-attention. Variance, covariance, and Laplacian spectral regularizers help stabilize the embedding geometry, and an optional curriculum gradually increases masking difficulty during training. Because prediction occurs in latent space, NodeJEPA does not rely on input reconstruction or hand-crafted graph augmentations. We evaluate NodeJEPA on standard node classification benchmarks under linear probing and fine-tuning protocols, and conduct ablations on masking, prediction, and regularization design choices. Our study offers a practical recipe for node-level JEPA-style latent prediction on graphs, and clarifies when structural conditioning helps representation learning. Code, configurations, and evaluation scripts are publicly available at https://github.com/OliverZ-dot/Node-Jepa.

Representation learning is central to graph machine learning, powering tasks such as link prediction and node classification. However, most graph embeddings are hard to interpret, offering limited insight into how learned features relate to graph structure. Many networks naturally admit a role-mixture view, where nodes are best described as mixtures over latent archetypal factors. Motivated by this structure, we propose a compositional graph embedding framework grounded in Aitchison geometry, the canonical geometry for comparing mixtures. Nodes are represented as simplex-valued compositions and embedded via isometric log-ratio (ILR) coordinates, which preserve Aitchison distances while enabling unconstrained optimization in Euclidean space. This yields intrinsically interpretable embeddings whose geometry reflects relative trade-offs among archetypes and supports coherent behavior under component restriction; we consider both fixed and learnable ILR bases. Across node classification and link prediction, our method achieves competitive performance with strong baselines while providing explainability by construction rather than post-hoc. Finally, subcompositional coherence enables principled component restriction: removing and renormalizing subsets preserves a well-defined geometry, which we exploit via subcompositional dimensionality removal to probe how archetype groups influence representations and predictions.

Graph representation learning has largely focused on designing increasingly sophisticated models to transform graph topology into vector representations, or embeddings. However, the extent to which embedding quality depends on model learning, rather than on the underlying topological transformations, remains unclear. Here, we show that informative embeddings can be derived without complicated model design and gradient-based training. Propagating random features through implicit hierarchical structures induced by random walks and anonymous walks yields embeddings that capture node proximity and structural role, respectively. These two training-free embeddings preserve complementary aspects of graph organization and perform competitively with classic and recent methods across various node-, edge-, and graph-level tasks. They often require substantially less computation, resulting in a favorable quality-efficiency trade-off. Combining the two types of embeddings further improves inference quality of some tasks compared with using either embedding type alone. Our results suggest that informative graph embeddings can arise from carefully chosen topological transformations before any learning operation is applied.