Related papers: Normalization for multimodal type theory
The capability to jointly process multi-modal information is becoming an essential task. However, the limited number of paired multi-modal data and the large computational requirements in multi-modal learning hinder the development. We…
It is well known that general recursion cannot be expressed within Martin-Loef's type theory and various approaches have been proposed to overcome this problem still maintaining the termination of the computation of the typable terms. In…
Variational Neural Machine Translation (VNMT) is an attractive framework for modeling the generation of target translations, conditioned not only on the source sentence but also on some latent random variables. The latent variable modeling…
We prove the Sato-Tate conjecture for Hilbert modular forms. More precisely, we prove the natural generalisation of the Sato-Tate conjecture for regular algebraic cuspidal automorphic representations of $\GL_2(\A_F)$, $F$ a totally real…
SMT-based model checkers, especially IC3-style ones, are currently the most effective techniques for verification of infinite state systems. They infer global inductive invariants via local reasoning about a single step of the transition…
We consider the extensions of modal transition systems (MTS), namely Boolean MTS and parametric MTS and we investigate the refinement problems over both classes. Firstly, we reduce the problem of modal refinement over both classes to a…
We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and…
In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…
This paper studies normalisation by evaluation for typed lambda calculus from a categorical and algebraic viewpoint. The first part of the paper analyses the lambda definability result of Jung and Tiuryn via Kripke logical relations and…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory as well as number theory and…
The modal logic S4 can be used via a Curry-Howard style correspondence to obtain a lambda-calculus. Modal (boxed) types are intuitively interpreted as `closed syntax of the calculus'. This lambda-calculus is called modal type theory ---…
The renormalization of the Minimal Supersymmetric Standard Model (MSSM) is presented. We describe symmetry identities that constitute a framework in which the MSSM is completely characterized and renormalizability can be proven.…
Monotonic abstraction is a technique introduced in model checking parameterized distributed systems in order to cope with transitions containing global conditions within guards. The technique has been re-interpreted in a declarative setting…
Current multi-view factorization methods make assumptions that are not acceptable for many kinds of data, and in particular, for graphical data with hierarchical structure. At the same time, current hierarchical methods work only in the…
We define and develop two-level type theory (2LTT), a version of Martin-L\"of type theory which combines two different type theories. We refer to them as the inner and the outer type theory. In our case of interest, the inner theory is…
The formalization of process knowledge using ontologies enables consistent modeling of parameter interdependencies in manufacturing. These interdependencies are typically represented as mathematical expressions that define relations between…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
A modified realisability interpretation of infinitary logic is formalised and proved sound in constructive type theory (CTT). The logic considered subsumes first order logic. The interpretation makes it possible to extract programs with…
We define typical forcings encompassing many informal forcing arguments in bounded arithmetic and give general conditions for such forcings to produce models of the universal variant of relativized $T^1_2$. We apply this result to study the…
In this paper we describe how to leverage higher-order unification to type check a dependently typed language with meta-variables. The literature usually presents the unification algorithm as a standalone component, however the need to…