Related papers: Optimistic Higher-Order Superposition
Let $\bx_j = \btheta +\bep_j, j=1,...,n$, be observations of an unknown parameter $\btheta$ in a Euclidean or separable Hilbert space $\scrH$, where $\bep_j$ are noises as random elements in $\scrH$ from a general distribution. We study the…
We give a domination condition implying good-$\lambda$ and exponential inequalities for couples of measurable functions. Those inequalities recover several classical and new estimations involving some operators in Harminic Analysis. Among…
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…
Safety is a syntactic condition of higher-order grammars that constrains occurrences of variables in the production rules according to their type-theoretic order. In this paper, we introduce the safe lambda calculus, which is obtained by…
We discuss the relative merits of optimistic and randomized approaches to exploration in reinforcement learning. Optimistic approaches presented in the literature apply an optimistic boost to the value estimate at each state-action pair and…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
Algebraic effects & handlers have become a standard approach for side-effects in functional programming. Their modular composition with other effects and clean separation of syntax and semantics make them attractive to a wide audience.…
The exploration-exploitation dilemma has been an intriguing and unsolved problem within the framework of reinforcement learning. "Optimism in the face of uncertainty" and model building play central roles in advanced exploration methods.…
We present an algorithm for a class of statistical inference problems. The main idea is to reformulate the inference problem as an optimization procedure, based on the generation of surrogate (auxiliary) functions. This approach is…
In this paper we present a semantics for a linear algebraic lambda-calculus based on realizability. This semantics characterizes a notion of unitarity in the system, answering a long standing issue. We derive from the semantics a set of…
Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which…
We combine the fixed-order evaluation of the $b\bar{b}$ sum rules with a non-relativistic effective-theory approach. The combined result for the $n$-th moment includes all terms suppressed with respect to the leading-order result by ${\cal…
We describe a mathematical structure that can give extensional denotational semantics to higher-order probabilistic programs. It is not limited to discrete probabilities, and it is compatible with integration in a way the models that have…
Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…
We study bisimulation and context equivalence in a probabilistic $\lambda$-calculus. The contributions of this paper are threefold. Firstly we show a technique for proving congruence of probabilistic applicative bisimilarity. While the…
Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus…
We derive the general analytical expressions for the statistical uncertainties of cumulants up to fourth order including an efficiency correction. The analytical expressions have been tested with a toy Monte Carlo model analysis. An…