Attention sink (AS) is a consistent pattern in transformer attention maps where certain tokens (often special tokens or positional anchors) disproportionately attract attention from other tokens. We show that in transformers, AS is not an architectural artifact, but it is the manifestation of a fundamental geometric principle: the establishment of reference frames that anchor representational spaces. We analyze several architectures and identify three distinct reference frame types, centralized, distributed, and bidirectional, that correlate with the attention sink phenomenon. We show that they emerge during the earliest stages of training as optimal solutions to the problem of establishing stable coordinate systems in high-dimensional spaces. We show the influence of architecture components, particularly position encoding implementations, on the specific type of reference frame. This perspective transforms our understanding of transformer attention mechanisms and provides insights for both architecture design and the relationship with AS.

The explosive growth in sequence length has intensified the demand for effective and efficient long sequence modeling. Benefiting from intrinsic oscillatory membrane dynamics, Resonate-and-Fire (RF) neurons can efficiently extract frequency components from input signals and encode them into spatiotemporal spike trains, making them well-suited for long sequence modeling.

Best Arm Identification (BAI) algorithms are deployed in data-sensitive applications, such as adaptive clinical trials or user studies. Driven by the privacy concerns of these applications, we study the problem of fixed-confidence BAI under global Differential Privacy (DP) for Bernoulli distributions. While numerous asymptotically optimal BAI algorithms exist in the non-private setting, a significant gap remains between the best lower and upper bounds in the global DP setting. This work reduces this gap to a small multiplicative constant, for any privacy budget ϵ. First, we provide a tighter lower bound on the expected sample complexity of any δ-correct and ϵ-global DP strategy.

The detection of ligand binding sites for proteins is a fundamental step in StructureBased Drug Design. Despite notable advances in recent years, existing methods, datasets, and evaluation metrics are confronted with several key challenges: (1) current datasets and methods are centered on individual protein-ligand complexes and neglect that diverse binding sites may exist across multiple complexes of the same protein, introducing significant statistical bias; (2) ligand binding site detection is typically modeled as a discontinuous workflow, employing binary segmentation and subsequent clustering algorithms; (3) traditional evaluation metrics do not adequately reflect the actual performance of different binding site prediction methods. To address these issues, we first introduce UniSite-DS, the first UniProt (Unique Protein)-centric ligand binding site dataset, which contains 4.81 times more multi-site data and 2.08 times more overall data compared to the previously most widely used datasets. We then propose UniSite, the first end-to-end ligand binding site detection framework supervised by set prediction loss with bijective matching. In addition, we introduce Average Precision based on Intersection over Union (IoU) as a more accurate evaluation metric for ligand binding site prediction. Extensive experiments on UniSite-DS and several representative benchmark datasets demonstrate that IoU-based Average Precision provides a more accurate reflection of prediction quality, and that UniSite outperforms current state-of-theart methods in ligand binding site detection.

In real-world decision-making problems, one needs to pick among multiple policies the one that performs best while respecting economic constraints. This motivates the problem of constrained best-arm identification for bandit problems where every arm is a joint distribution of reward and cost. We investigate the general case where reward and cost are dependent. The goal is to accurately identify the arm with the highest mean reward among all arms whose mean cost is below a given threshold. We prove information-theoretic lower bounds on the sample complexity for three models: Gaussian with fixed covariance, Gaussian with unknown covariance, and non-parametric distributions of rectangular support. We propose a combination of a sampling and a stopping rule that correctly identifies the constrained best arm and matches the optimal sample complexities for each of the three models. Simulations demonstrate the performance of our algorithms.

Meritocratic systems, from admissions to hiring, aim to impartially reward skill and effort.

Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by performing a fixed number of a single type of these operations. Although we discover that the corresponding problems are NP-complete in general, we provide a comprehensive parameterized-complexity analysis with the aim of determining those properties of the problems that explain the hardness and those that make the problems tractable. For instance, we show that the problems remain hard for a small number d of features or small domain size D but the combination of both yields fixed-parameter tractability. That is, the problems are solvable in (D+1)2d |I|O(1) time, where |I|is the size of the input. We also provide a proof-of-concept implementation of this algorithm and report on empirical results.

Ensuring fairness in machine learning models is a critical challenge. Existing debiasing methods often compromise performance, rely on static correction strategies, and struggle with data sparsity, particularly within minority groups. Furthermore, their utilization of sensitive attributes is often suboptimal, either depending excessively on complete attribute labeling or disregarding these attributes entirely. To overcome these limitations, we propose FairNet, a novel framework for dynamic, instance-level fairness correction. FairNet integrates a bias detector with conditional low-rank adaptation (LoRA), which enables selective activation of the fairness correction mechanism exclusively for instances identified as biased, and thereby preserve performance on unbiased instances. A key contribution is a new contrastive loss function for training the LoRA module, specifically designed to minimize intra-class representation disparities across different sensitive groups and effectively address underfitting in minority groups. The FairNet framework can flexibly handle scenarios with complete, partial, or entirely absent sensitive attribute labels. Theoretical analysis confirms that, under moderate TPR/FPR for the bias detector, FairNet can enhance the performance of the worst group without diminishing overall model performance, and potentially yield slight performance improvements.

We study the high-dimensional asymptotics of empirical risk minimization (ERM) in over-parametrized two-layer neural networks with quadratic activations trained on synthetic data. We derive sharp asymptotics for both training and test errors by mapping the ℓ2-regularized learning problem to a convex matrix sensing task with nuclear norm penalization. This reveals that capacity control in such networks emerges from a low-rank structure in the learned feature maps. Our results characterize the global minima of the loss and yield precise generalization thresholds, showing how the width of the target function governs learnability. This analysis bridges and extends ideas from spin-glass methods, matrix factorization, and convex optimization and emphasizes the deep link between low-rank matrix sensing and learning in quadratic neural networks.