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Langevin Quasi-Monte Carlo

Neural Information Processing Systems

Sampling from probability distributions is a crucial task in both statistics and machine learning. However, when the target distribution does not permit exact sampling, researchers often rely on Markov chain Monte Carlo (MCMC) methods.






In-ContextSymmetries: Self-Supervised LearningthroughContextualWorldModels

Neural Information Processing Systems

In this work, drawing insights from world models, we propose to instead learn a general representation that can adapt to be invariant or equivariant to different transformations by paying attention tocontext-- a memory module that tracks task-specificstates,actions,andfuturestates.



Logical Characterizations of Recurrent Graph Neural Networks with Reals and Floats

Neural Information Processing Systems

In pioneering work from 2019, Barceló and coauthors identified logics that precisely match the expressive power of constant iteration-depth graph neural networks (GNNs) relative to properties definable in first-order logic. In this article, we give exact logical characterizations of recurrent GNNs in two scenarios: (1) in the setting with floating-point numbers and (2) with reals. For floats, the formalism matching recurrent GNNs is a rule-based modal logic with counting, while for reals we use a suitable infinitary modal logic, also with counting. These results give exact matches between logics and GNNs in the recurrent setting without rel-ativising to a background logic in either case, but using some natural assumptions about floating-point arithmetic. Applying our characterizations, we also prove that, relative to graph properties definable in monadic second-order logic (MSO), our infinitary and rule-based logics are equally expressive. This implies that recurrent GNNs with reals and floats have the same expressive power over MSO-definable properties and shows that, for such properties, also recurrent GNNs with reals are characterized by a (finitary!)