We present a new algorithmic approach for the task of finding a chordal Markov network structure that maximizes a given scoring function. The algorithm is based on branch and bound and integrates dynamic programming for both domain pruning and for obtaining strong bounds for search-space pruning. Empirically, we show that the approach dominates in terms of running times a recent integer programming approach (and thereby also a recent constraint optimization approach) for the problem.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, state-of-the-art embedding methods typically do not account for latent hierarchical structures which are characteristic for many complex symbolic datasets. In this work, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincaré ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We present an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincaré embeddings can outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Your Out-of-Distribution Detection Method is Not Robust!

Plus: AI fakes of the Iran war are flooding X--and Grok is failing to flag them. Pokémon Go was the world's first augmented-reality megahit. Released in 2016 by Niantic, the AR twist on the juggernaut Pokémon franchise fast became a global phenomenon. "500 million people installed that app in 60 days," says Brian McClendon, CTO at Niantic Spatial, an AI company that Niantic spun out last year. Now Niantic Spatial is using that vast trove of crowdsourced data to build a kind of world model--a buzzy new technology that grounds the smarts of LLMs in real environments. The firm wants to use it to help robots navigate more precisely.

Reasoning with LLMs increasingly unfolds inside a broader verification loop. Internally, systems use cheap checks, such as self-consistency or proxy rewards, which we call weak verification. Externally, users inspect outputs and steer the model through feedback until results are trustworthy, which we call strong verification. These signals differ sharply in cost and reliability: strong verification can establish trust but is resource-intensive, while weak verification is fast and scalable but noisy and imperfect. We formalize this tension through weak--strong verification policies, which decide when to accept or reject based on weak verification and when to defer to strong verification. We introduce metrics capturing incorrect acceptance, incorrect rejection, and strong-verification frequency. Over population, we show that optimal policies admit a two-threshold structure and that calibration and sharpness govern the value of weak verifiers. Building on this, we develop an online algorithm that provably controls acceptance and rejection errors without assumptions on the query stream, the language model, or the weak verifier.

Mixture-of-Experts (MoE) has emerged as a prominent architecture for scaling model size while maintaining computational efficiency.

However, there's a lack of insight into how these models perform in terms

Full BBH results are in Appendix C Table 3.