SubQuad: Near-Quadratic-Free Structure Inference with Distribution-Balanced Objectives in Adaptive Receptor framework

Foundation models are increasingly adapted for downstream medical imaging tasks, yet the influence of the chosen adaptation strategy on subgroup fairness remains poorly understood. We investigate how three parameter-efficient adaptation techniques, including linear heads on the raw CLS token, an MLP, and an attention-pooling module over multi-layer patch features, affect both pathology classification performance and subgroup disparities when applied to the frozen Rad-DINO chest X-ray encoder. Using MIMIC-CXR, we evaluate eight pathologies across race, sex, and imaging-view subgroups on a prevalence-preserving, demographically balanced test set, and additionally probe how strongly each adapter encodes protected attributes. We find that attention pooling achieves the strongest overall discriminative performance and encodes attributes, particularly race, most strongly, but that improved overall performance does not consistently reduce subgroup disparities. Notably, stronger attribute encoding did not correspond to larger disparities: early network layers encoded race most weakly yet produced the largest subgroup performance gaps. Exploring different attention-pooling layer combinations further revealed no consistent relationship between the layers pooled, attribute encoding strength, and subgroup fairness. Our results indicate that richer, more expressive representations can improve accuracy while leaving fairness implications task-dependent and unpredictable, which must be assessed directly and per-task rather than inferred from encoding strength or overall performance alone.

Recovering the underlying $k$-clustering of a set $U$ of $n$ points by asking pair-wise same-cluster queries has garnered significant interest in the past few years. Given a query $S \subset U$, $|S|=2$, the oracle returns "yes" if the points are in the same cluster and "no" otherwise. For adaptive algorithms, the query complexity is known to be $Θ(nk)$, while non-adaptive algorithms are extremely limited: even for $k=3$, such algorithms require $Ω(n^2)$ queries, matching the trivial upper bound. However, non-adaptivity is highly desirable since it allows queries to be asked in parallel. To break the quadratic barrier for non-adaptive queries, we study a natural generalization of this problem to subset queries for $|S|>2$, where the oracle returns the number of clusters intersecting $S$. Previous work obtained an $O(n)$ query adaptive algorithm, but the realm of non-adaptive algorithms remained completely unknown. In this paper, we give the first non-adaptive algorithms for clustering with subset queries. Our main result is a non-adaptive algorithm making $O(n \log k \cdot (\log k + \log\log n)^2)$ queries, improving to $O(n \log \log n)$ when $k$ is constant. In addition to non-adaptivity, we make other practical considerations, such as enforcing a bound, $s$, on the query size. We show $Ω(\max(n^2/s^2,n))$ queries are necessary and obtain algorithms making $\smash{\widetilde{O}(n^2k/s^2)}$ queries for any $s \leq \sqrt{n}$ and $\smash{\widetilde{O}(n^2/s)}$ queries for any $s \leq n$. Finally, we obtain improved upper bounds when the clusters are roughly balanced, and when the algorithm is allowed two rounds of adaptivity.

Accurate prediction of antibody-antigen binding affinity is fundamental to therapeutic design, yet remains constrained by severe label sparsity and the complexity of antigenic variations. In this paper, we propose AbLWR (Antibody-antigen binding affinity List-Wise Ranking), a novel framework that reformulates the conventional affinity regression task as a listwise ranking problem. To mitigate label sparsity, AbLWR incorporates a PU (Positive-Unlabeled) learning mechanism leveraging a dual-level contrastive objective and meta-optimized label refinement to learn robust representations. Furthermore, we address antigenic variation by employing a homologous antigen sampling strategy where Multi-Head Self-Attention (MHSA) explicitly models inter-sample relationships within training lists to capture subtle affinity nuances. Extensive experiments demonstrate that AbLWR significantly outperforms state-of-the-art baselines, improving the Precision@1 (P@1) by over 10$\%$ in randomized cross-validation experiments. Notably, case studies on Influenza and IL-33 validate its practical utility, demonstrating robust ranking consistency in distinguishing subtle viral mutations and efficiently prioritizing top-tier candidates for wet-lab screening.