Numeral systems and units of measurement are two conjoined topics in activities of human beings and have mutual effects with the languages expressing them. Currently, the evaluation of Large Language Models (LLMs) often involves mathematical reasoning, yet little attention is given to how minor changes in numbers or units can drastically alter the complexity of problems and the performance of LLMs. In this paper, we scrutinize existing LLMs on processing of numerals and units of measurement by constructing datasets with perturbations. We first anatomize the reasoning of math word problems to different sub-procedures like numeral conversions from language to numbers and measurement conversions based on units. Then we further annotate math word problems from ancient Chinese arithmetic works which are challenging in numerals and units of measurement. Experiments on perturbed datasets demonstrate that LLMs still encounter difficulties in handling numeral and measurement conversions.

Prompt engineering is effective for controlling the output of text-to-image (T2I) generative models, but it is also laborious due to the need for manually crafted prompts. This challenge has spurred the development of algorithms for automated prompt generation. However, these methods often struggle with transferability across T2I models, require white-box access to the underlying model, and produce non-intuitive prompts. In this work, we introduce PRISM, an algorithm that automatically identifies human-interpretable and transferable prompts that can effectively generate desired concepts given only black-box access to T2I models. Inspired by large language model (LLM) jailbreaking, PRISM leverages the in-context learning ability of LLMs to iteratively refine the candidate prompts distribution for given reference images. Our experiments demonstrate the versatility and effectiveness of PRISM in generating accurate prompts for objects, styles, and images across multiple T2I models, including Stable Diffusion, DALL-E, and Midjourney.

Unsupervised learning algorithms have been derived for several sta(cid:173) tistical models of English grammar, but their computational com(cid:173) plexity makes applying them to large data sets intractable. This paper presents a probabilistic model of English grammar that is much simpler than conventional models, but which admits an effi(cid:173) cient EM training algorithm. The model is based upon grammat(cid:173) ical bigrams, i.e., syntactic relationships between pairs of words. We present the results of experiments that quantify the represen(cid:173) tational adequacy of the grammatical bigram model, its ability to generalize from labelled data, and its ability to induce syntactic structure from large amounts of raw text.

DisCoCirc is a newly proposed framework for representing the grammar and semantics of texts using compositional, generative circuits. While it constitutes a development of the Categorical Distributional Compositional (DisCoCat) framework, it exposes radically new features. In particular, [14] suggested that DisCoCirc goes some way toward eliminating grammatical differences between languages. In this paper we provide a sketch that this is indeed the case for restricted fragments of English and Urdu. We first develop DisCoCirc for a fragment of Urdu, as it was done for English in [14]. There is a simple translation from English grammar to Urdu grammar, and vice versa. We then show that differences in grammatical structure between English and Urdu - primarily relating to the ordering of words and phrases - vanish when passing to DisCoCirc circuits.

Eida is an English language coach that helps you practise English grammar, English vocabulary, English pronunciation, English listening, English writing, reading in order for you to improve your English vocabulary, your English grammar, your English pronunciation and speak English fluently. Chatbot to learn English: it a language assistant that acts like an English chatbot to help you study English and speak English perfectly and fluently. With Eida English Coach, you have the opportunity to listen to native voices and speak exactly like them. English listening and speaking: Eida English coach gives you the possibility to tap and listen to a native speaker and to record your own voice and test it to know if it is right or wrong. Learn English grammar: Eida presents various grammatical rules on conjugations of verbs, English phrasal verbs, English pronouns, English conjunctions, English prepositions and many other English grammatical rules to improve your English grammar.