DeepSeek-R1 has successfully enhanced Large Language Models (LLMs) reasoning capabilities through its rule-based reward system. While it's a "perfect" reward system that effectively mitigates reward hacking, such reward functions are often discrete. Our experimental observations suggest that discrete rewards can lead to gradient anomaly, unstable optimization, and slow convergence. To address this issue, we propose ReDit (Reward Dithering), a method that dithers the discrete reward signal by adding simple random noise. With this perturbed reward, exploratory gradients are continuously provided throughout the learning process, enabling smoother gradient updates and accelerating convergence.

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When agents trade in a Duality-based Cost Function prediction market, they collectively implement the learning algorithm Follow-The-Regularized-Leader [Abernethy et al., 2013]. We ask whether other learning algorithms could be used to inspire the design of prediction markets. By decomposing and modifying the Duality-based Cost Function Market Maker's (DCFMM) pricing mechanism, we propose a new prediction market, called the Smooth Quadratic Prediction Market, the incentivizes agents to collectively implement general steepest gradient descent. Relative to the DCFMM, the Smooth Quadratic Prediction Market has a better worst-case monetary loss for AD securities while preserving axiom guarantees such as the existence of instantaneous price, information incorporation, expressiveness, no arbitrage, and a form of incentive compatibility. To motivate the application of the Smooth Quadratic Prediction Market, we independently examine agents' trading behavior under two realistic constraints: bounded budgets and buy-only securities. Finally, we provide an introductory analysis of an approach to facilitate adaptive liquidity using the Smooth Quadratic Prediction Market. Our results suggest future designs where the price update rule is separate from the fee structure, yet guarantees are preserved.

Snapchat's parent company has announced it is releasing new smart glasses, a decade after its original pair lost the company tens of millions of dollars . The new augmented reality (AR) glasses, called Specs, will allow users to see digital elements overlaid onto the world. They will cost £1,995 in the UK and $2,195 in the US when shipping begins this autumn. That makes them cheaper than Apple's Vision Pro mixed-reality headset and its $3,499 starting price, but far more than Meta's smart glasses, which start at $224. Evan Spiegel, co-founder and chief executive of Snap Inc, said the glasses marked the beginning of a new era in computing.

Graph Neural Networks (GNNs) have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult--especially under distributional shifts. Unlike traditional uncertainty estimation, graph-based uncertainty must account for randomness arising from both the graph's structure and its label distribution, which adds complexity. In this paper, making an analogy between the evolution of a stochastic partial differential equation (SPDE) driven by Mat\'ern Gaussian Process and message passing using GNN layers, we present a principled way to design a novel message passing scheme that incorporates spatial-temporal noises motivated by the Gaussian Process approach to SPDE. Our method simultaneously captures uncertainty across space and time and allows explicit control over the covariance kernel's smoothness, thereby enhancing uncertainty estimates on graphs with both low and high label informativeness. Our extensive experiments on Out-of-Distribution (OOD) detection on graph datasets with varying label informativeness demonstrate the soundness and superiority of our model to existing approaches.

Earth observation foundation models have shown strong generalization across multiple Earth observation tasks, but their robustness under real-world perturbations remains underexplored. To bridge this gap, we introduce REOBench, the first comprehensive benchmark for evaluating the robustness of Earth observation foundation models across six tasks and twelve types of image corruptions, including both appearance-based and geometric perturbations. To ensure realistic and fine-grained evaluation, our benchmark focuses on high-resolution optical remote sensing images, which are widely used in critical applications such as urban planning and disaster response. We conduct a systematic evaluation of a broad range of models trained using masked image modeling, contrastive learning, and vision-language pre-training paradigms. Our results reveal that existing Earth observation foundation models experience significant performance degradation when exposed to input corruptions. The severity of degradation varies across tasks, model architectures, backbone sizes, and types of corruption, with performance drop varying from less than 1% to over 25%. Vision-language models show enhanced robustness, particularly in multimodal tasks. REOBench underscores the vulnerability of current Earth observation foundation models to real-world corruptions and provides actionable insights for developing more robust and reliable models. Code and data are publicly available at https://github.com/lx709/REOBench.

In the aftermath of a devastating earthquake, unpiloted aerial vehicles (UAVs) could fly through a collapsed building to map the scene, giving rescuers information they need to quickly reach survivors. But this remains an extremely challenging problem for an autonomous robot, which would need to swiftly adjust its trajectory to avoid sudden obstacles while staying on course. Researchers from MIT and the University of Pennsylvania developed a new trajectory-planning system that tackles both challenges at once. Their technique enables a UAV to react to obstacles in milliseconds while staying on a smooth flight path that minimizes travel time. Their system uses a new mathematical formulation that ensures the robot travels safely to its destination along a feasible path, and that is less computationally intensive than other techniques.

Craig interpolation plays a central role in formal verification tasks such as model checking, invariant generation, and abstraction refinement. In the domain of linear integer arithmetic (LIA), interpolants are crucial for deriving inductive invariants that characterize unreachable or safe program states, enabling scalable and precise reasoning about software and hardware correctness. Despite progress in interpolation algorithms, generating concise and interpretable interpolants remains a key challenge. We propose a lightweight learning-based approach to generating simple interpolants for LIA. Our model learns to lazily sample input problems directly and is complementary to existing logical methods. We show that when Z3 is guided by our learned model, the complexity of the interpolants it produces can be reduced by up to 47.3%. For older solvers, the reduction rate can reach up to 69.1%.

While latent diffusion models (LDMs), such as Stable Diffusion, are designed for high-resolution (HR) image generation, they often struggle with significant structural one. Instead distortions of relying when generating on extensiv images e retraining, at resolutions a more resource-ef higher than ficient their approach training is to reprogram the pretrained model for HR image generation; however, existing methods often result in poor image quality and long inference time. We introduce RepLDM, high-quality a, no high-ef vel reprogramming ficiency, high-r frame esolution work image for pretrained generation; LDMs see that Fig. enables 1. RepLDM consists of two stages: (i) an attention guidance stage, which generates a latent training-free representa self-attention tion of a higher mechanism -quality to training-resolution enhance the structural image consistenc using a y; no and vel (ii) a progressive upsampling stage, which progressively performs upsampling in pixel space to mitigate the severe artifacts caused by latent space upsampling.

We introduce Aeolus, a large-scale Multi-modal Flight Delay Dataset designed to advance research on flight delay prediction and support the development of foundation models for tabular data. Existing datasets in this domain are typically limited to flat tabular structures and fail to capture the spatiotemporal dynamics inherent in delay propagation. Aeolus addresses this limitation by providing three aligned modalities: (i) a tabular dataset with rich operational, meteorological, and airportlevel features for over 50 million flights; (ii) a flight chain module that models delay propagation along sequential flight legs, capturing upstream and downstream dependencies; and (iii) a flight network graph that encodes shared aircraft, crew, and airport resource connections, enabling cross-flight relational reasoning. The dataset is carefully constructed with temporal splits, comprehensive features, and strict leakage prevention to support realistic and reproducible machine learning evaluation. Aeolus supports a broad range of tasks, including regression, classification, temporal structure modeling, and graph learning, serving as a unified benchmark across tabular, sequential, and graph modalities. We release baseline experiments and preprocessing tools to facilitate adoption.