High-stakes prediction tasks (e.g., patient diagnosis) are often handled by trained

Clustering is a fundamental task in data science with wide-ranging applications.

One such filter, the partitioned learned Bloom filter (PLBF), achieves excellent memory efficiency.

In barter exchanges, participants swap goods with one another without exchanging money; these exchanges are often facilitated by a central clearinghouse, with the goal of maximizing the aggregate quality (or number) of swaps. Barter exchanges are subject to many forms of uncertainty--in participant preferences, the feasibility and quality of various swaps, and so on. Our work is motivated by kidney exchange, a real-world barter market in which patients in need of a kidney transplant swap their willing living donors, in order to find a better match. Modern exchanges include 2-and 3-way swaps, making the kidney exchange clearing problem NP-hard. Planned transplants often \emph{fail} for a variety of reasons--if the donor organ is rejected by the recipient's medical team, or if the donor and recipient are found to be medically incompatible.

This paper investigates the deep hedging framework, based on reinforcement learning (RL), for the dynamic hedging of swaptions, contrasting its performance with traditional sensitivity-based rho-hedging. We design agents under three distinct objective functions (mean squared error, downside risk, and Conditional Value-at-Risk) to capture alternative risk preferences and evaluate how these objectives shape hedging styles. Relying on a three-factor arbitrage-free dynamic Nelson-Siegel model for our simulation experiments, our findings show that near-optimal hedging effectiveness is achieved when using two swaps as hedging instruments. Deep hedging strategies dynamically adapt the hedging portfolio's exposure to risk factors across states of the market. In our experiments, their out-performance over rho-hedging strategies persists even in the presence some of model misspecification. These results highlight RL's potential to deliver more efficient and resilient swaption hedging strategies.

Large language models (LLMs) have achieved impressive results in code generation, yet struggle with program verification, especially in interactive proof frameworks such as Lean4. A central challenge is scalability: verified synthesis requires not just code, but also precise specifications and correctness proofs, and existing approaches rarely span all three domains. We present BRIDGE, the first systematic study of structured prompting for scalable verified program generation. BRIDGE decomposes verification into three interconnected domains: Code (executable implementations), Specifications (formal intent statements), and Proofs (constructive correctness arguments). Our key idea is to elicit distinct reasoning behaviors functional, specification-driven, and proof-oriented as intermediate representations that preserve semantic structure and connect these domains. Through systematic ablations, we show that this approach substantially improves both accuracy and efficiency beyond standard error feedback methods. For example, functional reasoning improves correctness of code in formal languages (Lean4) by nearly 1.5x (pass@5) over direct baselines. In inference-time compute, functional reasoning is also 2x more efficient, achieving higher pass rates with fewer generations and lower total sampling budgets. Similarly, we find that specification-driven prompting boosts Python coding pass rates by up to 17.5%. These findings suggest that structured domain alignment is a promising direction for advancing verified synthesis. BRIDGE establishes a foundation for training via expert iteration or RLVR, enabling models to internalize these reasoning strategies across code, specifications, and proofs.

Ranking methods or models based on their performance is of prime importance but is tricky because performance is fundamentally multidimensional. In the case of classification, precision and recall are scores with probabilistic interpretations that are both important to consider and complementary. The rankings induced by these two scores are often in partial contradiction. In practice, therefore, it is extremely useful to establish a compromise between the two views to obtain a single, global ranking. Over the last fifty years or so,it has been proposed to take a weighted harmonic mean, known as the F-score, F-measure, or $F_β$. Generally speaking, by averaging basic scores, we obtain a score that is intermediate in terms of values. However, there is no guarantee that these scores lead to meaningful rankings and no guarantee that the rankings are good tradeoffs between these base scores. Given the ubiquity of $F_β$ scores in the literature, some clarification is in order. Concretely: (1) We establish that $F_β$-induced rankings are meaningful and define a shortest path between precision- and recall-induced rankings. (2) We frame the problem of finding a tradeoff between two scores as an optimization problem expressed with Kendall rank correlations. We show that $F_1$ and its skew-insensitive version are far from being optimal in that regard. (3) We provide theoretical tools and a closed-form expression to find the optimal value for $β$ for any distribution or set of performances, and we illustrate their use on six case studies.

We show experimentally that the algorithm clarans of Ng and Han (1994) finds better K -medoids solutions than the V oronoi iteration algorithm of Hastie et al. (2001). This finding, along with the similarity between the V oronoi iteration algorithm and Lloyd's K -means algorithm, motivates us to use clarans as a K -means initializer. We show that clarans outperforms other algorithms on 23/23 datasets with a mean decrease over k-means-++ (Arthur and V assilvitskii, 2007) of 30% for initialization mean squared error (MSE) and 3% for final MSE. We introduce algorithmic improvements to clarans which improve its complexity and runtime, making it a viable initialization scheme for large datasets.

We approach the search for optimal element ordering in bimetallic alloy nanoparticles (NPs) as a reinforcement learning (RL) problem, and have built an RL agent that learns to perform such global optimisation using the geometric graph representation of the NPs. To demonstrate the effectiveness, we train an RL agent to perform composition-conserving atomic swap actions on the icosahedral nanoparticle structure. Trained once on randomised $Ag_{X}Au_{309-X}$ compositions and orderings, the agent discovers previously established ground state structure. We show that this optimization is robust to differently ordered initialisations of the same NP compositions. We also demonstrate that a trained policy can extrapolate effectively to NPs of unseen size. However, the efficacy is limited when multiple alloying elements are involved. Our results demonstrate that RL with pre-trained equivariant graph encodings can navigate combinatorial ordering spaces at the nanoparticle scale, and offer a transferable optimisation strategy with the potential to generalise across composition and reduce repeated individual search cost.