Related papers: Tropical Mathematics and the Lambda Calculus I: Me…
There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
Evaluating the performance of Large Language Models (LLMs) is a critical yet challenging task, particularly when aiming to avoid subjective assessments. This paper proposes a framework for leveraging subjective metrics derived from the…
As a supplement to my talk at the workshop, this extended abstract motivates and summarizes my work with co-authors on problems in two separate areas: first, in the lambda-calculus with letrec, a universal model of computation, and second,…
Linear logic provides a framework to control the complexity of higher-order functional programs. We present an extension of this framework to programs with multithreading and side effects focusing on the case of elementary time. Our main…
We explore the integration of metaprogramming in a call-by-value linear lambda-calculus and sketch its extension to a session type system. We build on a model of contextual modal type theory with multi-level contexts, where contextual…
Optimization problems are considered in the framework of tropical algebra to minimize and maximize a nonlinear objective function defined on vectors over an idempotent semifield, and calculated using multiplicative conjugate transposition.…
This paper presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are…
Free monads (and their variants) have become a popular general-purpose tool for representing the semantics of effectful programs in proof assistants. These data structures support the compositional definition of semantics parameterized by…
In this paper, we study the tedious link between the properties of sensibility and approximability of models of untyped {\lambda}-calculus. Approximability is known to be a slightly, but strictly stronger property that sensibility. However,…
In this paper, we address program development by multiple different programmers (or programming teams), each working in different settings (programming languages or reasoning frameworks), but following a common specification; in particular,…
Recent works have proposed various explanations for the ability of modern large language models (LLMs) to perform in-context prediction. We propose an alternative conceptual viewpoint from an information-geometric and statistical…
Ensuring the reliability and verifiability of large language model (LLM)-enabled systems remains a significant challenge in software engineering. We propose a probabilistic framework for systematically analyzing and improving these systems…
Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic…
We give an adequate, concrete, categorical-based model for Lambda-S, which is a typed version of a linear-algebraic lambda calculus, extended with measurements. Lambda-S is an extension to first-order lambda calculus unifying two approaches…
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…
Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While perturbation theory is a…
Researchers working on low-resource languages face persistent challenges due to limited data availability and restricted access to computational resources. Although most large language models (LLMs) are predominantly trained in…
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for…