Related papers: Fagin's Theorem for Semiring Turing Machines
Large Language Models (LLMs) can significantly improve their reasoning capabilities by interacting with external tools, a paradigm known as Tool-Integrated Reasoning (TIR). However, extending TIR to multi-turn scenarios using Reinforcement…
Natural Language Processing (NLP) faces challenges in the ability to quickly model polysemous words. The Grover's Algorithm (GA) is expected to solve this problem but lacks adaptability. To address the above dilemma, a Quantum Text…
We characterize group representations that factor through monomial representations, respectively, block-triangular representations with monomial diagonal blocks, by arithmetic properties. Similar results are obtained for semigroup…
Computability theory is a discipline in the intersection of computer science and mathematical logic where the fundamental question is: given two mathematical objects X and Y, does X compute Y in principle? In case X and Y are real numbers,…
Accurate financial volatility forecasting is crucial but challenged by the non-linear, highly correlated nature of market data. Recently, quantum computing has emerged as a promising paradigm for solving complex high-dimensional sampling…
Bearing fault diagnosis is of great importance to decrease the damage risk of rotating machines and further improve economic profits. Recently, machine learning, represented by deep learning, has made great progress in bearing fault…
Computational modelling offers a powerful tool for formalising psychological theories, making them more transparent, testable, and applicable in digital contexts. Yet, the question often remains: how should one computationally model a…
We present new results on the landscape of problems that can be solved by quantum Turing machines (QTM's) employing severely limited amounts of memory. In this context, we demonstrate two infinite time hierarchies of complexity classes…
Pretraining deep language models has led to large performance gains in NLP. Despite this success, Schick and Sch\"utze (2020) recently showed that these models struggle to understand rare words. For static word embeddings, this problem has…
In this paper, we consider Turing machines based on unsharp quantum logic. For a lattice-ordered quantum multiple-valued (MV) algebra E, we introduce E-valued non-deterministic Turing machines (ENTMs) and E-valued deterministic Turing…
Quantizing large language models has become a standard way to reduce their memory and computational costs. Typically, existing methods focus on breaking down the problem into individual layer-wise sub-problems, and minimizing per-layer…
Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner…
Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational…
Chain-of-thought (CoT) reasoning improves large language models (LLMs) on difficult tasks, but it also makes inference expensive because every intermediate step must be generated as a discrete token. Latent reasoning reduces visible token…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
We present Federated QT-LSTM, a novel framework that combines the Quantum-Train (QT) methodology with Long Short-Term Memory (LSTM) networks in a federated learning setup. By leveraging quantum neural networks (QNNs) to generate classical…
The potential of neural networks (NN) in engineering is rooted in their capacity to understand intricate patterns and complex systems, leveraging their universal nonlinear approximation capabilities and high expressivity. Meanwhile,…
Reasoning with knowledge expressed in natural language and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. General neural architectures that…
This paper demonstrates the relativity of Computability and Nondeterministic; the nondeterministic is just Turing's undecidable Decision rather than the Nondeterministic Polynomial time. Based on analysis about TM, UM, DTM, NTM, Turing…
We study a generalized version of reversal bounded Turing machines where, apart from several tapes on which the number of head reversals is bounded by r(n), there are several further tapes on which head reversals remain unrestricted, but…