We consider a dynamic mechanism design problem where an auctioneer sells an indivisible good to two groups of buyers in every round, for a total of T rounds. The auctioneer aims to maximize their discounted overall revenue while adhering to a fairness constraint that guarantees a minimum average allocation for each group. We begin by studying the static case ( T 1) and establish that the optimal mechanism involves two types of subsidization: one that increases the overall probability of allocation to all buyers, and another that favors the group which otherwise has a lower probability of winning the item. We then extend our results to the dynamic case by characterizing a set of recursive functions that determine the optimal allocation and payments in each round. Notably, our results establish that in the dynamic case, the seller, on one hand, commits to a participation reward to incentivize truth-telling, and, on the other hand, charges an entry fee for every round.

Generating videos with realistic and physically plausible motion is one of the main recent challenges in computer vision. While diffusion models are achieving compelling results in image generation, video diffusion models are limited by heavy training and huge models, resulting in videos that are still biased to the training dataset. In this work we propose MotionCraft, a new zero-shot video generator to craft physics-based and realistic videos. MotionCraft is able to warp the noise latent space of an image diffusion model, such as Stable Diffusion, by applying an optical flow derived from a physics simulation. We show that warping the noise latent space results in coherent application of the desired motion while allowing the model to generate missing elements consistent with the scene evolution, which would otherwise result in artefacts or missing content if the flow was applied in the pixel space.We compare our method with the state-of-the-art Text2Video-Zero reporting qualitative and quantitative improvements, demonstrating the effectiveness of our approach to generate videos with finely-prescribed complex motion dynamics.

Causal reasoning capability is critical in advancing large language models (LLMs) towards artificial general intelligence (AGI). While versatile LLMs appear to have demonstrated capabilities in understanding contextual causality and providing responses that obey the laws of causality, it remains unclear whether they perform genuine causal reasoning akin to humans. However, current evidence indicates the contrary. Specifically, LLMs are only capable of performing shallow (level-1) causal reasoning, primarily attributed to the causal knowledge embedded in their parameters, but they lack the capacity for genuine human-like (level-2) causal reasoning. To support this hypothesis, methodologically, we delve into the autoregression mechanism of transformer-based LLMs, revealing that it is not inherently causal.

Whole slide image (WSI) analysis is gaining prominence within the medical imaging field. Recent advances in pathology foundation models have shown the potential to extract powerful feature representations from WSIs for downstream tasks. However, these foundation models are usually designed for general-purpose pathology image analysis and may not be optimal for specific downstream tasks or cancer types. In this work, we present Concept Anchor-guided Task-specific Feature Enhancement (CATE), an adaptable paradigm that can boost the expressivity and discriminativeness of pathology foundation models for specific downstream tasks. Based on a set of task-specific concepts derived from the pathology vision-language model with expert-designed prompts, we introduce two interconnected modules to dynamically calibrate the generic image features extracted by foundation models for certain tasks or cancer types.

We study collaborative normal mean estimation, where m strategic agents collect i.i.d samples from a normal distribution \mathcal{N}(\mu, \sigma 2) at a cost. They all wish to estimate the mean \mu . By sharing data with each other, agents can obtain better estimates while keeping the cost of data collection small. To facilitate this collaboration, we wish to design mechanisms that encourage agents to collect a sufficient amount of data and share it truthfully, so that they are all better off than working alone. In naive mechanisms, such as simply pooling and sharing all the data, an individual agent might find it beneficial to under-collect and/or fabricate data, which can lead to poor social outcomes.

We develop a versatile new methodology for multidimensional mechanism design that incorporates side information about agent types to generate high social welfare and high revenue simultaneously. Prominent sources of side information in practice include predictions from a machine-learning model trained on historical agent data, advice from domain experts, and even the mechanism designer's own gut instinct. In this paper we adopt a prior-free perspective that makes no assumptions on the correctness, accuracy, or source of the side information. The welfare, revenue, and incentive properties of our meta-mechanism are characterized by novel constructions we introduce based on the notion of a weakest competitor, which is an agent that has the smallest impact on welfare. We show that our meta-mechanism, when carefully instantiated, simultaneously achieves strong welfare and revenue guarantees parameterized by errors in the side information.

Current approaches using sequential networks have shown promise in estimating field variables for dynamical systems, but they are often limited by high rollout errors. The unresolved issue of rollout error accumulation results in unreliable estimations as the network predicts further into the future, with each step's error compounding and leading to an increase in inaccuracy. Here, we introduce the State-Exchange Attention (SEA) module, a novel transformer-based module enabling information exchange between encoded fields through multi-head cross-attention. The cross-field multidirectional information exchange design enables all state variables in the system to exchange information with one another, capturing physical relationships and symmetries between fields. Additionally, we introduce an efficient ViT-like mesh autoencoder to generate spatially coherent mesh embeddings for a large number of meshing cells.

Accurate prediction of climate in the subseasonal-to-seasonal scale is crucial for disaster preparedness and robust decision making amidst climate change. Yet, forecasting beyond the weather timescale is challenging because it deals with problems other than initial condition, including boundary interaction, butterfly effect, and our inherent lack of physical understanding. At present, existing benchmarks tend to have shorter forecasting range of up-to 15 days, do not include a wide range of operational baselines, and lack physics-based constraints for explainability. Thus, we propose ChaosBench, a challenging benchmark to extend the predictability range of data-driven weather emulators to S2S timescale. First, ChaosBench is comprised of variables beyond the typical surface-atmospheric ERA5 to also include ocean, ice, and land reanalysis products that span over 45 years to allow for full Earth system emulation that respects boundary conditions.

Human motion capture from monocular videos has made significant progress in recent years. However, modern approaches often produce temporal artifacts, e.g. in form of jittery motion and struggle to achieve smooth and physically plausible motions. Explicitly integrating physics, in form of internal forces and exterior torques, helps alleviating these artifacts. Current state-of-the-art approaches make use of an automatic PD controller to predict torques and reaction forces in order to re-simulate the input kinematics, i.e. the joint angles of a predefined skeleton. However, due to imperfect physical models, these methods often require simplifying assumptions and extensive preprocessing of the input kinematics to achieve good performance.

Our work revisits the design of mechanisms via the learning-augmented framework. In this model, the algorithm is enhanced with imperfect (machine-learned) information concerning the input, usually referred to as prediction. The goal is to design algorithms whose performance degrades gently as a function of the prediction error and, in particular, perform well if the prediction is accurate, but also provide a worst-case guarantee under any possible error. This framework has been successfully applied recently to various mechanism design settings, where in most cases the mechanism is provided with a prediction about the types of the players.We adopt a perspective in which the mechanism is provided with an output recommendation. We make no assumptions about the quality of the suggested outcome, and the goal is to use the recommendation to design mechanisms with low approximation guarantees whenever the recommended outcome is reasonable, but at the same time to provide worst-case guarantees whenever the recommendation significantly deviates from the optimal one.