Unfortunately, if cross-task knowledge transfer is impossible, then we will overfit each task due to limited amount of labeled data. One way to circumvent this dilemma is to use an external data source, e.g.

We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It is therefore critical to account for kernel uncertainty in our predictive distributions. We propose a distribution over kernels formed by modelling a spectral mixture density with a L evy process. The resulting distribution has support for all stationary covariances--including the popular RBF, periodic, and Mat ern kernels-- combined with inductive biases which enable automatic and data efficient learning, long-range extrapolation, and state of the art predictive performance. The proposed model also presents an approach to spectral regularization, as the L evy process introduces a sparsity-inducing prior over mixture components, allowing automatic selection over model order and pruning of extraneous components. We exploit the algebraic structure of the proposed process for O (n) training and O (1) predictions. We perform extrapolations having reasonable uncertainty estimates on several benchmarks, show that the proposed model can recover flexible ground truth covariances and that it is robust to errors in initialization.

"thermostat" variables to control the effect of this noise on the momentum terms [

Many graphical models, such as Markov Logic Networks (MLNs) with evidence, possess highly symmetric substructures but no exact symmetries. Unfortunately, there are few principled methods that exploit these symmetric substructures to perform efficient approximate inference. In this paper, we present a lifted variant of the Weighted Mini-Bucket elimination algorithm which provides a principled way to (i) exploit the highly symmetric substructure of MLN models, and (ii) incorporate high-order inference terms which are necessary for high quality approximate inference. Our method has significant control over the accuracy-time trade-off of the approximation, allowing us to generate any-time approximations. Experimental results demonstrate the utility of this class of approximations, especially in models with strong repulsive potentials.

We introduce a principled approach for unsupervised structure learning of deep neural networks. We propose a new interpretation for depth and inter-layer connectivity where conditional independencies in the input distribution are encoded hierarchically in the network structure. Thus, the depth of the network is determined inherently. The proposed method casts the problem of neural network structure learning as a problem of Bayesian network structure learning. Then, instead of directly learning the discriminative structure, it learns a generative graph, constructs its stochastic inverse, and then constructs a discriminative graph. We prove that conditional-dependency relations among the latent variables in the generative graph are preserved in the class-conditional discriminative graph. We demonstrate on image classification benchmarks that the deepest layers (convolutional and dense) of common networks can be replaced by significantly smaller learned structures, while maintaining classification accuracy---state-of-the-art on tested benchmarks. Our structure learning algorithm requires a small computational cost and runs efficiently on a standard desktop CPU.

The player's goal is to accumulate the

These mechanisms typically retrieve items in a single step and are fixed after training.

Global optimization of expensive, potentially gradient-free functions has long been a critical component of many complex problems in science and engineering.

We introduce SkyRL-Agent, a framework for efficient, multi-turn, long-horizon agent training and evaluation. It provides efficient asynchronous dispatching, lightweight tool integration, and flexible backend interoperability, enabling seamless use with existing RL frameworks such as SkyRL-train, VeRL, and Tinker. Using SkyRL-Agent, we train SA-SWE-32B, a software engineering agent trained from Qwen3-32B (24.4% Pass@1) purely with reinforcement learning. We introduce two key components: an optimized asynchronous pipeline dispatcher that achieves a 1.55x speedup over naive asynchronous batching, and a tool-enhanced training recipe leveraging an AST-based search tool to facilitate code navigation, boost rollout Pass@K, and improve training efficiency. Together, these optimizations enable SA-SWE-32B to reach 39.4% Pass@1 on SWE-Bench Verified with more than 2x cost reduction compared to prior models reaching similar performance. Despite being trained solely on SWE tasks, SA-SWE-32B generalizes effectively to other agentic tasks, including Terminal-Bench, BrowseComp-Plus, and WebArena. We further demonstrate SkyRL-Agent's extensibility through case studies on deep research, computer use, and memory agents, each trained using a different training backend.