Knowledge Graphs as Structured Memory for Embedding Spaces: From Training Clusters to Explainable Inference

We introduce Graph Memory (GM), a structured non-parametric framework that augments embedding-based inference with a compact, relational memory over region-level prototypes. Rather than treating each training instance in isolation, GM summarizes the embedding space into prototype nodes annotated with reliability indicators and connected by edges that encode geometric and contextual relations. This design unifies instance retrieval, prototype-based reasoning, and graph-based label propagation within a single inductive model that supports both efficient inference and faithful explanation. Experiments on synthetic and real datasets including breast histopathology (IDC) show that GM achieves accuracy competitive with $k$NN and Label Spreading while offering substantially better calibration and smoother decision boundaries, all with an order of magnitude fewer samples. By explicitly modeling reliability and relational structure, GM provides a principled bridge between local evidence and global consistency in non-parametric learning.

Concave losses for robust dictionary learning

Traditional dictionary learning methods are based on quadratic convex loss function and thus are sensitive to outliers. In this paper, we propose a generic framework for robust dictionary learning based on concave losses. We provide results on composition of concave functions, notably regarding super-gradient computations, that are key for developing generic dictionary learning algorithms applicable to smooth and non-smooth losses. In order to improve identification of outliers, we introduce an initialization heuristic based on undercomplete dictionary learning. Experimental results using synthetic and real data demonstrate that our method is able to better detect outliers, is capable of generating better dictionaries, outperforming state-of-the-art methods such as K-SVD and LC-KSVD.