Related papers: Proofs that Modify Proofs, 1/2
We study two ways (levels) of finding free-probability analogues of classical infinitely divisible measures. More precisely, we identify their Voiculescu transforms. For free-selfdecomposable measures we found the formula (a differential…
This note discusses proofs for convergence of first-order methods based on simple potential-function arguments. We cover methods like gradient descent (for both smooth and non-smooth settings), mirror descent, and some accelerated variants.
This paper explores the idea of using defunctionalization as a proof technique for higher-order programs. Defunctionalization builds on substituting functional values by a first-order representation. Thus, its interest is that one can use…
This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three components: a powerful type system for size analysis and a sound type inference procedure for it, a ticking…
Proofs are traditionally syntactic, inductively generated objects. This paper reformulates first-order logic (predicate calculus) with proofs which are graph-theoretic rather than syntactic. It defines a combinatorial proof of a formula…
This paper deals with the revision of partially ordered beliefs. It proposes a semantic representation of epistemic states by partial pre-orders on interpretations and a syntactic representation by partially ordered belief bases. Two…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
The main observation of this paper is that some sequential weak compactness arguments in Hilbert space theory can be replaced by Heine/Borel compactness arguments (for the strong topology). Even though the latter form of compactness fails…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
We improve and refine a method for certifying that the values' sizes computed by an imperative program will be bounded by polynomials in the program's inputs' sizes. Our work ''tames'' the non-determinism of the original analysis, and…
Parameterization extends higher-order processes with the capability of abstraction (akin to that in lambda-calculus), and is known to be able to enhance the expressiveness. This paper focuses on the parameterization of names, i.e. a…
Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…
We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…
Probing experiments investigate the extent to which neural representations make properties -- like part-of-speech -- predictable. One suggests that a representation encodes a property if probing that representation produces higher accuracy…
This paper introduces the \textit{weighted partial copula} function for testing conditional independence. The proposed test procedure results from these two ingredients: (i) the test statistic is an explicit Cramer-von Mises transformation…
The lambda-Pi-calculus modulo theory is a logical framework in which many type systems can be expressed as theories. We present such a theory, the theory U, where proofs of several logical systems can be expressed. Moreover, we identify a…
Based on the order parameter expansion, we present an approximate method which allows us to reduce large systems of coupled differential equations with diverse parameters to three equations: one for the global, mean field, variable and two…
The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate $n^{-1/2}$, $n$ being the sample…
This paper presents a logical approach to the translation of functional calculi into concurrent process calculi. The starting point is a type system for the {\pi}-calculus closely related to linear logic. Decompositions of intuitionistic…
The functional interpretation is a systematic, syntactic method for transforming certain non-constructive proofs into constructive proofs with explicit bounds. We illustrate the interpretation by working through a concrete, fairly simple…