Embedding-based code retrieval is a core component of coding agents and retrieval-augmented code generation, where retrieving *correct* code matters more than retrieving lexically similar code. Existing code-retrieval benchmarks do not plant controlled, execution-verified single-edit variants of each query’s canonical implementation in the search pool, leaving the question of whether embeddings can functionally discriminate correct from near-clone-but-incorrect code unanswered in a retrieval setting. Resolving this requires a benchmark whose search pool itself contains the relevant counterfactuals — execution-verified buggy variants near-identical to each canonical — so that a retriever’s rank ordering can be directly tested for functional discrimination rather than topical or identity overlap. We introduce ExecRetrieval, 939 Python tasks each paired with one execution-verified canonical implementation and up to four execution-verified buggy distractors, each generated by a mechanical mutation making a single targeted edit, and evaluate 23 dense embedding configurations plus BM25 under provider-native invocation with paired McNemar tests and query-level bootstrap intervals. With near-clone counterfactuals in the pool, the top hosted system reaches exec@10 = 1.00 but only exec@1 = 0.331; rank-1 misses are paired buggy variants 91.5–99.4% of the time across the four leading systems, and the canonical scores below at least one of its four paired distractors in 67–78% of queries on the leading systems. The full dataset, execution oracle, embedding matrices, environment snapshot, and pairwise statistical tests are released at the URL in Appendix D.

Federated learning with heterogeneous client architectures cannot rely on parameter aggregation. Prototype-based methods address architectural heterogeneity by exchanging class-level representations, but naively averaging prototypes across non-IID clients leads to semantic drift and poor inter-class separation. We propose FedPAGR, a framework where heterogeneous clients project their features into a shared consensus space and exchange class prototypes with a central server. The server refines aggregated prototypes through a geometric regularization objective that enforces agreement with client submissions and inter-class angular separation. Clients anchor their classifiers to the refined prototypes and train with a composite objective combining classification, prototype alignment, and entropy regularization. We evaluate FedPAGR across multiple domains, including four image benchmarks and a clinical NLP task using heterogeneous ClinicalBERT variants, with five architectures per federation under severe label heterogeneity (𝛼=0.1). FedPAGR achieves the highest ensemble accuracy across all four image datasets and the highest local test accuracy on low-class and clinical tasks, including a 4.99-point improvement over the strongest baseline on MIMIC-IV, while remaining competitive on high-class benchmarks.