116 research outputs found
New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances
We propose an improved stability condition for a class of discrete-time genetic regulatory networks (GRNs) with interval time-varying delays and stochastic disturbances. By choosing an augmented novel Lyapunov-Krasovskii functional which contains some triple summation terms, a less conservative sufficient condition is obtained in terms of linear matrix inequalities (LMIs) by using the combination of the lower bound lemma, the discrete-time Jensen inequality, and the free-weighting matrix method. It is shown that the proposed results can be readily solved by using the Matlab software. Finally, two numerical examples are provided to illustrate the effectiveness and advantages of the theoretical results
Language Models can be Logical Solvers
Logical reasoning is a fundamental aspect of human intelligence and a key
component of tasks like problem-solving and decision-making. Recent
advancements have enabled Large Language Models (LLMs) to potentially exhibit
reasoning capabilities, but complex logical reasoning remains a challenge. The
state-of-the-art, solver-augmented language models, use LLMs to parse natural
language logical questions into symbolic representations first and then adopt
external logical solvers to take in the symbolic representations and output the
answers. Despite their impressive performance, any parsing errors will
inevitably result in the failure of the execution of the external logical
solver and no answer to the logical questions. In this paper, we introduce
LoGiPT, a novel language model that directly emulates the reasoning processes
of logical solvers and bypasses the parsing errors by learning to strict
adherence to solver syntax and grammar. LoGiPT is fine-tuned on a newly
constructed instruction-tuning dataset derived from revealing and refining the
invisible reasoning process of deductive solvers. Experimental results on two
public deductive reasoning datasets demonstrate that LoGiPT outperforms
state-of-the-art solver-augmented LMs and few-shot prompting methods on
competitive LLMs like ChatGPT or GPT-4.Comment: Preprin
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