Related papers: B\"uchi Automata can have Smaller Quotients

This paper deals with the convergence time analysis of a class of fixed-time stable systems with the aim to provide a new non-conservative upper bound for its settling time. Our contribution is fourfold. First, we revisit the well-known…

To generate coherent responses, language models infer unobserved meaning from their input text sequence. One potential explanation for this capability arises from theories of delay embeddings in dynamical systems, which prove that…

We introduce annotated grammars, an extension of context-free grammars which allows annotations on terminals. Our model extends the standard notion of regular spanners, and is more expressive than the extraction grammars recently introduced…

We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…

This paper addresses, for the first time in the literature, optimal control problems for dynamic systems governed by a novel class of sweeping processes with time delay. We establish well-posedness of such processes, in the sense of the…

Simulations play a key role for inference in collider physics. We explore various approaches for enhancing the precision of simulations using machine learning, including interventions at the end of the simulation chain (reweighting), at the…

Modal automata are a classic formal model for component-based systems that comes equipped with a rich specification theory supporting abstraction, refinement and compositional reasoning. In recent years, quantitative variants of modal…

We introduce a novel framework for simulating finite automata using representation-theoretic semidirect products and Fourier modules, achieving more efficient Transformer-based implementations.

We define formally decohered quantum computers (using density matrices), and present a simulation of them by a probabalistic classical Turing Machine. We study the slowdown of the simulation for two cases: (1) sequential quantum computers,…

Simulation and refinement are variations of the bisimulation relation, where in the former we keep only atoms and forth, and in the latter only atoms and back. Quantifying over simulations and refinements captures the effects of information…

It has been shown for English that discrete and soft prompting perform strongly in few-shot learning with pretrained language models (PLMs). In this paper, we show that discrete and soft prompting perform better than finetuning in…

Subword tokenization introduces a computational layer in language models where many distinct token sequences decode to the same surface form and preserve meaning, yet induce different internal computations. Despite this non-uniqueness,…

Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way…

Structured prompts require integrating components according to task-relevant relations. How a network implements this integration is often hard to judge in language or vision, where those relations are rarely specified precisely enough to…

We define a quantum computational model over infinite words, called Measure-Many Quantum B\"uchi Automata (MMQBA), which extends Measure-many Quantum Finite automata (MMQFA) to the infinite word setting with B\"uchi acceptance condition. In…

Looped Transformers have emerged as an efficient and powerful class of models for reasoning in the language domain. Recent studies show that these models achieve strong performance on algorithmic and reasoning tasks, suggesting that looped…

Pretrained language models can be effectively stimulated by textual prompts or demonstrations, especially in low-data scenarios. Recent works have focused on automatically searching discrete or continuous prompts or optimized verbalizers,…

The fast growth of renewable energies increases the power congestion risk. To address this issue, the French Transmission System Operator (RTE) has developed closed-loop controllers to handle congestion. RTE wishes to estimate the…

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

We investigate the effectiveness of ensembles of pretrained transformer-based language models on short answer questions using the Kaggle Automated Short Answer Scoring dataset. We fine-tune a collection of popular small, base, and large…