Related papers: Linear Additives
We present the PML 2 language, which provides a uniform environment for programming, and for proving properties of programs in an ML-like setting. The language is Curry-style and call-by-value, it provides a control operator (interpreted in…
The set of points of a one-dimensional cut-and-project quasicrystal or model set, while not additive, is shown to be multiplicative for appropriate choices of acceptance windows. This leads to the definition of an associative additive…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…
System I is a simply-typed lambda calculus with pairs, extended with an equational theory obtained from considering the type isomorphisms as equalities. In this work we propose an extension of System I to polymorphic types, adding the…
Retrieval-Augmented Large Language Models (LLMs), which incorporate the non-parametric knowledge from external knowledge bases into LLMs, have emerged as a promising approach to enhancing response accuracy in several tasks, such as…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits…
While deep learning is a powerful tool for natural language processing (NLP) problems, successful solutions to these problems rely heavily on large amounts of annotated samples. However, manually annotating data is expensive and…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…
While deep learning is a powerful tool for natural language processing (NLP) problems, successful solutions to these problems rely heavily on large amounts of annotated samples. However, manually annotating data is expensive and…
Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…
Multi-label classification (MLC) is a supervised learning problem in which, contrary to standard multiclass classification, an instance can be associated with several class labels simultaneously. In this chapter, we advocate a rule-based…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Ensuring factuality is essential for the safe use of Large Language Models (LLMs) in high-stakes domains such as medicine and law. Conformal inference provides distribution-free guarantees, but existing approaches are either overly…
Multi-AI collaboration, such as ensembling or debating large language models (LLMs), is a promising paradigm for aggregating information and boosting performance. A foundational step in these pipelines is to feed the responses of several…
Large language models (LLMs) excel at rapid generation of text and multimodal content, yet they falter on transaction-style planning that demands ACID-like guarantees and real-time disruption recovery. We present Adaptive LLM Agent System…
In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…
The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear…
In communication complexity the Arthur-Merlin (AM) model is the most natural one that allows both randomness and non-determinism. Presently we do not have any super-logarithmic lower bound for the AM-complexity of an explicit function.…