Related papers: IST is more than an algorithm to prove ZFC theorem…
Parameter-Efficient Fine-Tuning (PEFT) methods have gained significant popularity for adapting pre-trained Large Language Models (LLMs) to downstream tasks, primarily due to their potential to significantly reduce memory and computational…
Word and sentence embeddings are useful feature representations in natural language processing. However, intrinsic evaluation for embeddings lags far behind, and there has been no significant update since the past decade. Word and sentence…
There have been many attempts to solve the P versus NP problem. However, with a new proof method, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit…
After highlighting the cases in which the semantics of a language cannot be mechanically reproduced (in which case it is called inherent), the main epistemological consequences of the first incompleteness Theorem for the two fundamental…
Set theory is widely believed to provide a secure foundation for deductive mathematics, but current set theories do not quite do this. The mainstream essentially uses na\"\i ve set theory. After Russell's paradox showed this to be…
Mathematical Theory of Evidence called also Dempster-Shafer Theory (DST) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its…
In this paper, we introduce the Instruction Following Score (IFS), a metric that detects language models' ability to follow instructions. The metric has a dual purpose. First, IFS can be used to distinguish between base and instruct models.…
Semantic textual similarity (STS), a cornerstone task in NLP, measures the degree of similarity between a pair of sentences, and has broad application in fields such as information retrieval and natural language understanding. However,…
This paper continues the study of the integral input-to-state stability (IISS) property. It is shown that the IISS property is equivalent to one which arises from the consideration of mixed norms on states and inputs, as well as to the…
Rewriting Induction (RI) is a method to prove inductive theorems, originating from equational reasoning. By using Logically Constrained Simply-typed Term Rewriting Systems (LCSTRSs) as an intermediate language, rewriting induction becomes a…
The concepts used in IFOL have associated to them a list of sorted attributes, and the sorts are the intensional concepts as well. The requirement to extend the unsorted IFOL (Intensional FOL) to many-sorted IFOL is mainly based on the fact…
Generalization to unseen instances is our eternal pursuit for all data-driven models. However, for realistic task like machine translation, the traditional approach measuring generalization in an average sense provides poor understanding…
Measuring Sentence Textual Similarity (STS) is a classic task that can be applied to many downstream NLP applications such as text generation and retrieval. In this paper, we focus on unsupervised STS that works on various domains but only…
Recent years have seen the rise of large language models (LLMs), where practitioners use task-specific prompts; this was shown to be effective for a variety of tasks. However, when applied to semantic textual similarity (STS) and natural…
A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the…
We survey and compare, mainly in the two-dimensional case, various results obtained by IST and PDE techniques for integrable equations. We also comment on what can be predicted from integrable equations on non integrable ones.
Assessing the trustworthiness of artificial intelligence systems requires knowledge from many different disciplines. These disciplines do not necessarily share concepts between them and might use words with different meanings, or even use…
One generalizes the intuitionistic fuzzy logic (IFL) and other logics to neutrosophic logic (NL). The distinctions between IFL and NL {and the corresponding intuitionistic fuzzy set (IFS) and neutrosophic set (NS) respectively} are…
In the present article, we identified the qualitative differences between Statistical Machine Translation (SMT) and Neural Machine Translation (NMT) outputs. We have tried to answer two important questions: 1. Does NMT perform equivalently…
A test set for a formal language (set of strings) L is a subset T of L such that for any two string homomorphisms f and g defined on L, if the restrictions of f and g on T are identical functions, then f and g are identical on the entire L.…