Related papers: Evolving the Incremental {\lambda} Calculus into a…
This article focuses on making discrete-time Adaptive Iterative Learning Control (ILC) more effective using multiple estimation models. Existing strategies use the tracking error to adjust the parametric estimates. Our strategy uses the…
Iterative Learning Control (ILC) can achieve perfect tracking performance for mechatronic systems. The aim of this paper is to present an ILC design tutorial for industrial mechatronic systems. First, a preliminary analysis reveals the…
Derivative computation is a key component of optimization, sensitivity analysis, uncertainty quantification, and nonlinear solvers. Automatic differentiation (AD) is a powerful technique for evaluating such derivatives, and in recent years,…
The Algebraic lambda-calculus and the Linear-Algebraic lambda-calculus extend the lambda-calculus with the possibility of making arbitrary linear combinations of terms. In this paper we provide a fine-grained, System F-like type system for…
We add to intuitionistic logic infinitely many classical disjunctive tautologies and use the Curry--Howard correspondence to obtain typed concurrent $\lambda$-calculi; each of them features a specific communication mechanism, including…
We describe Imandra, a modern computational logic theorem prover designed to bridge the gap between decision procedures such as SMT, semi-automatic inductive provers of the Boyer-Moore family like ACL2, and interactive proof assistants for…
Interpreting the internal process of neural models has long been a challenge. This challenge remains relevant in the era of large language models (LLMs) and in-context learning (ICL); for example, ICL poses a new issue of interpreting which…
Transformer-based models demonstrate a remarkable ability for in-context learning (ICL), where they can adapt to unseen tasks from a few prompt examples without parameter updates. Recent research has illuminated how Transformers perform…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
In 2005, Abramsky introduced various linear/affine combinatory algebras of partial involutions over a suitable formal language, to discuss reversible computation in a game-theoretic setting. These algebras arise as instances of the general…
The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
We introduce a proof language for Intuitionistic Multiplicative Additive Linear Logic (IMALL), extended with a modality B to capture mixed-state quantum computation. The language supports algebraic constructs such as linear combinations,…
Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We…
Investment decisions can benefit from incorporating an accumulated knowledge of the past to drive future decision making. We introduce Continual Learning Augmentation (CLA) which is based on an explicit memory structure and a feed forward…
In-context learning (ICL) allows Transformers to adapt to novel tasks without weight updates, yet the underlying algorithms remain poorly understood. We adopt a statistical decision-theoretic perspective by investigating simple binary…
In this paper, we present an extension of $\lambda\mu$-calculus called $\lambda\mu^{++}$-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on…
Logical reasoning is essential for large language models (LLMs) to ensure accurate and coherent inference. However, LLMs struggle with reasoning order variations and fail to generalize across logically equivalent transformations. LLMs often…
Analogical reasoning is a hallmark of human intelligence, enabling us to solve new problems by transferring knowledge from one situation to another. Yet, developing artificial intelligence systems capable of robust human-like analogical…
In-context learning (ICL) refers to a remarkable capability of pretrained large language models, which can learn a new task given a few examples during inference. However, theoretical understanding of ICL is largely under-explored,…