Related papers: Oracle modalities
We proved in a previous work that Cattani-Sassone's higher dimensional transition systems can be interpreted as a small-orthogonality class of a topological locally finitely presentable category of weak higher dimensional transition…
We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…
In this article we revisit the theory of homotopic Hopf-Galois extensions introduced in arXiv:0902.3393v2 [math.AT], in light of the homotopical Morita theory of comodules established in arXiv:1411.6517 [math.AT]. We generalize the theory…
Computational paths treat propositional equality as explicit paths built from labelled deduction steps and rewrite rules. This view originates in work by de Queiroz and collaborators [1] and yields a weak groupoid structure for equality,…
It is shown that a singular equivalence induced by tensoring with a suitable complex of bimodules defines a singular equivalence of Morita type with level, in the sense of Wang. This result is applied to homological ideals and idempotents…
Brouwer's constructivist foundations of mathematics is based on an intuitively meaningful notion of computation shared by all mathematicians. Martin-L\"of's meaning explanations for constructive type theory define the concept of a type in…
Deep learning methods have demonstrated outstanding performances on classification and regression tasks on homogeneous data types (e.g., image, audio, and text data). However, tabular data still pose a challenge, with classic machine…
We introduce a framework for universal algebra in categories of relational structures given by finitary relational signatures and finitary or infinitary Horn theories, with the arity $\lambda$ of a Horn theory understood as a strict upper…
There is a recent interest for the verification of monadic programs using proof assistants. This line of research raises the question of the integration of monad transformers, a standard technique to combine monads. In this paper, we extend…
We investigate the scaling properties of implicit deductive reasoning over Horn clauses in depth-bounded Transformers. By systematically decorrelating provability from spurious features and enforcing algorithmic alignment, we find that in…
Invertibility is an important concept in category theory. In higher category theory, it becomes less obvious what the correct notion of invertibility is, as extra coherence conditions can become necessary for invertible structures to have…
Judgment aggregation studies how to combine individual judgments on logically related propositions into a collective judgment. Classical impossibility results show that sufficiently strong logical interconnections force dictatorship under…
Modularity is appealing for solving many problems in optimization. It brings the benefits of manufacturability and reconfigurability to structural optimization, and enables a trade-off between the computational performance of a Periodic…
A hybrid model involves the cooperation of an interpretable model and a complex black box. At inference, any input of the hybrid model is assigned to either its interpretable or complex component based on a gating mechanism. The advantages…
Multimodal representation learning produces high-dimensional embeddings that align diverse modalities in a shared latent space. While this enables strong generalization, it also introduces scalability challenges, both in terms of storage…
Homotopy type theory is a logical setting based on Martin-L\"of type theory in which geometric constructions and proofs can be carried out synthetically. Here, types can be interpreted as spaces up to homotopy, and proofs as…
Our main objective is to demonstrate how homological perturbation theory (HPT) results over the last 40 years immediately or with little extra work give some of the Koszul duality results that have appeared in the last decade. Higher…
The aim of this paper is to introduce tau-tilting theory, which completes (classical) tilting theory from the viewpoint of mutation. It is well-known in tilting theory that an almost complete tilting module for any finite dimensional…
Higher theta series on moduli spaces of Hermitian shtukas were constructed by Feng--Yun--Zhang and conjectured to be modular, parallel to classical conjectures in the Kudla program. In this paper we prove the modularity of higher theta…
We study Abramsky's applicative bisimilarity abstractly, in the context of call-by-value $\lambda$-calculi with algebraic effects. We first of all endow a computational $\lambda$-calculus with a monadic operational semantics. We then show…