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We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…

The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…

Causal inference is a science with multi-disciplinary evolution and applications. On the one hand, it measures effects of treatments in observational data based on experimental designs and rigorous statistical inference to draw causal…

When dealing with control systems, it is useful and even necessary to assess the performance of underlying transfer functions. The functions may or may not be linear, may or may not be even monotonic. In addition, they may have structural…

Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…

The study of modal logic has witnessed tremendous development following the introduction of Kripke semantics. However, recent developments in programming languages and type theory have led to a second way of studying modalities, namely…

Recent work in model-agnostic explanations of black-box machine learning has demonstrated that interpretability of complex models does not have to come at the cost of accuracy or model flexibility. However, it is not clear what kind of…

We describe a design-based framework for drawing causal inference in general randomized experiments. Causal effects are defined as linear functionals evaluated at unit-level potential outcome functions. Assumptions about the potential…

Constructive type theory combines logic and programming in one language. This is useful both for reasoning about programs written in type theory, as well as for reasoning about other programming languages inside type theory. It is…

The ability to compose code in a modular fashion is important to the construction of large programs. In the logic programming setting, it is desirable that such capabilities be realized through logic-based devices. We describe an approach…

Recent advances in large language models (LLMs) have shown that test-time scaling can substantially improve model performance on complex tasks, particularly in the coding domain. Under this paradigm, models use a larger token budget during…

Systems whose variable are constrained to be positive allow computationally efficient control design. We generalize these results to linear systems which leave a cone invariant. This is a wider class of systems than positive systems. We…

We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by…

We propose some new method of constructing configurations, which consists in consecutive inscribing copies of one underlying configuration. A uniform characterization of the obtained class and the one introduced in our paper untitled…

In formation control, an ensemble of autonomous agents is required to stabilize at a given configuration in the plane, doing so while agents are allowed to observe only a subset of the ensemble. As such, formation control provides a rich…

Controlling the syntactic structure of text generated by language models is valuable for applications requiring clarity, stylistic consistency, or interpretability, yet it remains a challenging task. In this paper, we argue that sampling…

This paper deals with strong structural controllability of linear structured systems in which the system matrices are given by zero/nonzero/arbitrary pattern matrices. Instead of assuming that the nonzero and arbitrary entries of the system…

How to generate summaries of different styles without requiring corpora in the target styles, or training separate models? We present two novel methods that can be deployed during summary decoding on any pre-trained Transformer-based…

Transformers have demonstrated impressive capabilities across various tasks, yet their performance on compositional problems remains a subject of debate. In this study, we investigate the internal mechanisms underlying Transformers'…

Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…