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From the modern perspective of causal inference, Bell's theorem -- a fundamental signature of quantum theory -- is a particular case where quantum correlations are incompatible with the classical theory of causality, and the generalization…
Incorporation of a new knowledge into neural networks with simultaneous preservation of the previous one is known to be a nontrivial problem. This problem becomes even more complex when new knowledge is contained not in new training…
The immensely fruitful concept of Grothendieck topology or covering issued from the efforts of algebraic geometers to study "sheaf-like" objects defined on categories more general than the lattice of open sets on a topological space. In the…
We introduce a new two-sided type system for verifying the correctness and incorrectness of functional programs with atoms and pattern matching. A key idea in the work is that types should range over sets of normal forms, rather than sets…
Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the…
We apply the recently developed technology of cofinality spectrum problems to prove a range of theorems in model theory. First, we prove that any model of Peano arithmetic is $\lambda$-saturated iff it has cofinality $\geq \lambda$ and the…
The notion of graph covers is a discretization of covering spaces introduced and deeply studied in topology. In discrete mathematics and theoretical computer science, they have attained a lot of attention from both the structural and…
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
We introduce layers to modal type theories, which subsequently enables type theories for pattern matching on code in meta-programming and clean and straightforward semantics.
In general a universal covering of a non connected topological group need not admit a topological group structure such that the covering map is a morphism of topological groups. This result is due to R.L. Taylor (1953). We generalise this…
We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than…
We introduce a framework for coverings of noncommutative spaces. Moreover, we study noncommutative coverings of irrational quantum tori and characterize all such coverings that are connected in a reasonable sense.
We propose a new framework for integrating quantifiers with other logical connectives in a higher-categorical setting. Our method systematically incorporates key coherence conditions-including those akin to the Beck-Chevalley property-and…
In studies of bundled modalities, we encode a complex conceptual notion into the semantics of a single modal operator and study its logic. Although there is already a substantial body of work on various concrete bundled operators, we still…
Round-based models are very common message-passing models; combinatorial topology applied to distributed computing provides sweeping results like general lower bounds. We combine both to study the computability of k-set agreement. Among all…
Graph transformation theory relies upon the composition of rules to express the effects of sequences of rules. In practice, graphs are often subject to constraints, ruling out many candidates for composed rules. Focusing on the case of…
Embedding models trained separately on similar data often produce representations that encode stable information but are not directly interchangeable. This lack of interoperability raises challenges in several practical applications, such…
Conformal prediction is a distribution-free uncertainty quantification method that has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use. Its most common variant, dubbed split conformal…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
Diffusion models have recently shown strong progress in generative tasks, offering a more stable alternative to GAN-based approaches for makeup transfer. Existing methods often suffer from limited datasets, poor disentanglement between…