A Joint Finite-Sample Certificate for Adaptive Selective Conformal Risk Control

Selective predictors answer on confident inputs and abstain elsewhere; deploying one safely needs a single finite-sample certificate that simultaneously upper-bounds the selected risk, lower-bounds the acceptance probability $\pacc$ above a floor $\pmin$, and lower-bounds the deployment utility. This certificate must be valid under adaptive threshold selection from a finite grid of $m$ pairs on $\ncert$ samples. We give such a certificate for bounded, possibly non-monotone losses by treating the selected risk directly as a ratio rather than through a Hoeffding-style range bound. The construction couples three confidence bounds: a variance-adaptive empirical-Bernstein bound on the ratio risk, a Clopper--Pearson bound on acceptance, and a two-sided closeness bound on utility. Together they lower-bound the certified policy's utility absolutely and to within $2\gammau$ of the best over the \emph{certified set}, both non-vacuous whenever feasible; a regime-scoped third leg matches an external oracle, informative only where the risk margin $\gammar < α$ and vacuous at the headline operating points. Relative to the range-only Hoeffding-ratio construction this sharpens the acceptance-floor dependence from $1/\pmin$ to $1/\sqrt{\pmin}$, and a closed-form corollary identifies a per-pair regime in which our risk bound dominates a Hoeffding conformal risk control (Hoeffding--CRC) selective bound. Empirically, on ImageNet (three ResNets) and COCO val 2017 panoptic, the certificate opens a $+22$ pp certified-acceptance frontier over Hoeffding--CRC and is ${\approx}10{\times}$ tighter than a non-vacuous matched-valid baseline; these gains are regime-scoped, not universal, and absent on ADE20K. The certifier runs in $O(\ncert m)$ time.

UrbanMoE: A Sparse Multi-Modal Mixture-of-Experts Framework for Multi-Task Urban Region Profiling

Urban region profiling, the task of characterizing geographical areas, is crucial for urban planning and resource allocation. However, existing research in this domain faces two significant limitations. First, most methods are confined to single-task prediction, failing to capture the interconnected, multi-faceted nature of urban environments where numerous indicators are deeply correlated. Second, the field lacks a standardized experimental benchmark, which severely impedes fair comparison and reproducible progress. To address these challenges, we first establish a comprehensive benchmark for multi-task urban region profiling, featuring multi-modal features and a diverse set of strong baselines to ensure a fair and rigorous evaluation environment. Concurrently, we propose UrbanMoE, the first sparse multi-modal, multi-expert framework specifically architected to solve the multi-task challenge. Leveraging a sparse Mixture-of-Experts architecture, it dynamically routes multi-modal features to specialized sub-networks, enabling the simultaneous prediction of diverse urban indicators. We conduct extensive experiments on three real-world datasets within our benchmark, where UrbanMoE consistently demonstrates superior performance over all baselines. Further in-depth analysis validates the efficacy and efficiency of our approach, setting a new state-of-the-art and providing the community with a valuable tool for future research in urban analytics