Related papers: Contextual Equivalence for a Probabilistic Languag…
Language models can learn sophisticated language understanding skills from fitting raw text. They also unselectively learn useless corpus statistics and biases, especially during finetuning on domain-specific corpora. In this paper, we…
Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of…
Rational decision-making under uncertainty requires coherent degrees of belief in events. However, event probabilities generated by Large Language Models (LLMs) have been shown to exhibit incoherence, violating the axioms of probability…
We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages…
Within the framework of generalized noncontextuality, we introduce a general technique for systematically deriving noncontextuality inequalities for any experiment involving finitely many preparations and finitely many measurements, each of…
One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Reading a document and extracting an answer to a question about its content has attracted substantial attention recently. While most work has focused on the interaction between the question and the document, in this work we evaluate the…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
Conditional acceptability refers to how plausible a conditional statement is perceived to be. It plays an important role in communication and reasoning, as it influences how individuals interpret implications, assess arguments, and make…
We consider the contextual bandit problem on general action and context spaces, where the learner's rewards depend on their selected actions and an observable context. This generalizes the standard multi-armed bandit to the case where side…
The object of contextuality analysis is a set of random variables each of which is uniquely labeled by a content and a context. In the measurement terminology, the content is that which the random variable measures, whereas the context…
We study a formalization of the grammar induction problem that models sentences as being generated by a compound probabilistic context-free grammar. In contrast to traditional formulations which learn a single stochastic grammar, our…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…
The paper investigates behavioural equivalence between programs in a call-by-value functional language extended with a signature of (algebraic) effect-triggering operations. Two programs are considered as being behaviourally equivalent if…
In this chapter, we explore how (Type-2) computable distributions can be used to give both (algorithmic) sampling and distributional semantics to probabilistic programs with continuous distributions. Towards this end, we sketch an encoding…
Anthropic reasoning is a critical tool to understand probabilities, especially in a large universe or multiverse. According to anthropic reasoning, we should consider ourselves typical among members of a reference class that must include…
A long-standing open problem in the semantics of programming languages supporting probabilistic choice is to find a commutative monad for probability on the category DCPO. In this paper we present three such monads and a general…