VANGUARD: Vehicle-Anchored Ground Sample Distance Estimation for UAVs in GPS-Denied Environments

Autonomous aerial robots operating in GPS-denied or communication-degraded environments frequently lose access to camera metadata and telemetry, leaving onboard perception systems unable to recover the absolute metric scale of the scene. As LLM/VLM-based planners are increasingly adopted as high-level agents for embodied systems, their ability to reason about physical dimensions becomes safety-critical -- yet our experiments show that five state-of-the-art VLMs suffer from spatial scale hallucinations, with median area estimation errors exceeding 50%. We propose VANGUARD, a lightweight, deterministic Geometric Perception Skill designed as a callable tool that any LLM-based agent can invoke to recover Ground Sample Distance (GSD) from ubiquitous environmental anchors: small vehicles detected via oriented bounding boxes, whose modal pixel length is robustly estimated through kernel density estimation and converted to GSD using a pre-calibrated reference length. The tool returns both a GSD estimate and a composite confidence score, enabling the calling agent to autonomously decide whether to trust the measurement or fall back to alternative strategies. On the DOTA~v1.5 benchmark, VANGUARD achieves 6.87% median GSD error on 306~images. Integrated with SAM-based segmentation for downstream area measurement, the pipeline yields 19.7% median error on a 100-entry benchmark -- with 2.6x lower category dependence and 4x fewer catastrophic failures than the best VLM baseline -- demonstrating that equipping agents with deterministic geometric tools is essential for safe autonomous spatial reasoning.

Deep Learning for Double Auction

Auctions are important mechanisms extensively implemented in various markets, e.g., search engines' keyword auctions, antique auctions, etc. Finding an optimal auction mechanism is extremely difficult due to the constraints of imperfect information, incentive compatibility (IC), and individual rationality (IR). In addition to the traditional economic methods, some recently attempted to find the optimal (single) auction using deep learning methods. Unlike those attempts focusing on single auctions, we develop deep learning methods for double auctions, where imperfect information exists on both the demand and supply sides. The previous attempts on single auction cannot directly apply to our contexts and those attempts additionally suffer from limited generalizability, inefficiency in ensuring the constraints, and learning fluctuations. We innovate in designing deep learning models for solving the more complex problem and additionally addressing the previous models' three limitations. Specifically, we achieve generalizability by leveraging a transformer-based architecture to model market participants as sequences for varying market sizes; we utilize the numerical features of the constraints and pre-treat them for a higher learning efficiency; we develop a gradient-conflict-elimination scheme to address the problem of learning fluctuation. Extensive experimental evaluations demonstrate the superiority of our approach to classical and machine learning baselines.

Mean Parity Fair Regression in RKHS

We study the fair regression problem under the notion of Mean Parity (MP) fairness, which requires the conditional mean of the learned function output to be constant with respect to the sensitive attributes. We address this problem by leveraging reproducing kernel Hilbert space (RKHS) to construct the functional space whose members are guaranteed to satisfy the fairness constraints. The proposed functional space suggests a closed-form solution for the fair regression problem that is naturally compatible with multiple sensitive attributes. Furthermore, by formulating the fairness-accuracy tradeoff as a relaxed fair regression problem, we derive a corresponding regression function that can be implemented efficiently and provides interpretable tradeoffs. More importantly, under some mild assumptions, the proposed method can be applied to regression problems with a covariance-based notion of fairness. Experimental results on benchmark datasets show the proposed methods achieve competitive and even superior performance compared with several state-of-the-art methods.