Bayesian causal discovery aims to infer the posterior distribution over causal models from observed data, quantifying epistemic uncertainty and benefiting downstream tasks. However, computational challenges arise due to joint inference over combinatorial space of Directed Acyclic Graphs (DAGs) and nonlinear functions. Despite recent progress towards efficient posterior inference over DAGs, existing methods are either limited to variational inference on node permutation matrices for linear causal models, leading to compromised inference accuracy, or continuous relaxation of adjacency matrices constrained by a DAG regularizer, which cannot ensure resulting graphs are DAGs. In this work, we introduce a scalable Bayesian causal discovery framework based on a combination of stochastic gradient Markov Chain Monte Carlo (SG-MCMC) and Variational Inference (VI) that overcomes these limitations. Our approach directly samples DAGs from the posterior without requiring any DAG regularization, simultaneously draws function parameter samples and is applicable to both linear and nonlinear causal models. To enable our approach, we derive a novel equivalence to the permutation-based DAG learning, which opens up possibilities of using any relaxed gradient estimator defined over permutations. To our knowledge, this is the first framework applying gradient-based MCMC sampling for causal discovery. Empirical evaluation on synthetic and real-world datasets demonstrate our approach's effectiveness compared to state-of-the-art baselines.

Security experts have urged people to be cautious with the viral agentic AI tool, known for being highly capable but also wildly unpredictable. Last month, Jason Grad issued a late-night warning to the 20 employees at his tech startup. "You've likely seen Clawdbot trending on X/LinkedIn. While cool, it is currently unvetted and high-risk for our environment, he wrote in a Slack message with a red siren emoji. "Please keep Clawdbot off all company hardware and away from work-linked accounts." Grad isn't the only tech executive who has raised concerns to staff about the experimental agentic AI tool, which was briefly known as MoltBot and is now named OpenClaw. A Meta executive says he recently told his team to keep OpenClaw off their regular work laptops or risk losing their jobs. The executive told reporters he believes the software is unpredictable and could lead to a privacy breach if used in otherwise secure environments. He spoke on the condition of anonymity to speak frankly.

RBF kernel to increase pretraining data diversity. Architectural details In all experiments, we use the same ExPT architecture. This section details how we constructed new objectives from the original D'Kitty and Ant that we In Ant-Energy, the reward at each time step is: R =1+ Survival reward Control cost Contact cost, (6) which means we incentivize the robot to conserve energy instead of running fast. D'Kitty tasks In D'Kitty, the goal is to design a morphology that allows the D'Kitty robot to reach We found the approximate oracle provided by Design-Bench not accurate enough to provide a reliable comparison of optimization methods on this task. C.1 Effects of GP hyperparameters We empirically examine the impact of two GP hyperparameters, the variance and the length scale ` Specifically, we evaluate the performance of ExPT on D'Kitty We average the performance across 3 seeds.

Consider An n= grad (r)+ A grad (r)+ C| 0 B @ 01 10 ... 1 C

For the synthetic regression task, it suffices to use only0.25% of the training samples to extract the symmetry as precisely as when utilizing all available training data. Symmetries are extracted from the models with the highest validation accuracyover300training epochs.

A.21 SocietalImpact Our proposed SALKG approach for learning from KG explanations can be applied to any KGaugmented model and can be adapted from any off-the-shelf saliency method. This enables KGaugmented models to improve generalization ability and learn more efficiently from data, thus yielding better performance while requiring less labeled data.

Different inner loss and outer loss other than what we used can be instantiated in the subclass.

During testing, we set the posterior sampling steps to 300 forDogs and Cars,and2.5K,5Kand5Kfor

In this work, we introduce a scalable Bayesian causal discovery framework based on a combination of stochastic gradient Markov Chain Monte Carlo (SG-MCMC) and V ariational Inference (VI) that overcomes these limitations.

Modern auto-bidding systems are required to balance overall performance with diverse advertiser goals and real-world constraints, reflecting the dynamic and evolving needs of the industry. Recent advances in conditional generative models, such as transformers and diffusers, have enabled direct trajectory generation tailored to advertiser preferences, offering a promising alternative to traditional Markov Decision Process-based methods. However, these generative methods face significant challenges, such as the distribution shift between offline and online environments, limited exploration of the action space, and the necessity to meet constraints like marginal Cost-per-Mille (CPM) and Return on Investment (ROI). To tackle these challenges, we propose GRAD (Generative Reward-driven Ad-bidding with Mixture-of-Experts), a scalable foundation model for auto-bidding that combines an Action-Mixture-of-Experts module for diverse bidding action exploration with the Value Estimator of Causal Transformer for constraint-aware optimization. Extensive offline and online experiments demonstrate that GRAD significantly enhances platform revenue, highlighting its effectiveness in addressing the evolving and diverse requirements of modern advertisers. Furthermore, GRAD has been implemented in multiple marketing scenarios at Meituan, one of the world's largest online food delivery platforms, leading to a 2.18% increase in Gross Merchandise Value (GMV) and 10.68% increase in ROI.