相关论文: IST is more than an algorithm to prove ZFC theorem…

Two types of approximation to the paradoxical Russell Set are presented, one approximating it from below, one from above. It is shown that any lower approximation gives rise to a better approximation containing it, and that any upper…

Lemmatization of standard languages is concerned with (i) abstracting over morphological differences and (ii) resolving token-lemma ambiguities of inflected words in order to map them to a dictionary headword. In the present paper we aim to…

A substantial amount of research has been carried out in developing machine learning algorithms that account for term dependence in text classification. These algorithms offer acceptable performance in most cases but they are associated…

Current evaluation metrics for language modeling and generation rely heavily on the accuracy of predicted (or generated) words as compared to a reference ground truth. While important, token-level accuracy only captures one aspect of a…

We show that the theory ZFC-, consisting of the usual axioms of ZFC but with the power set axiom removed-specifically axiomatized by extensionality, foundation, pairing, union, infinity, separation, replacement and the assertion that every…

An interval translation map (ITM) is a piece-wise translation $T \colon I \to I$ defined on a finite partition $I_1, \ldots, I_r$ of an interval $I$ into $r \ge 2$ subintervals. In contrast to classical interval exchange transformations…

The adaptive Iterative Soft-Thresholding Algorithm (ISTA) has been a popular algorithm for finding a desirable solution to the LASSO problem without explicitly tuning the regularization parameter $\lambda$. Despite that the adaptive ISTA is…

Statements involving metalinguistic self-reference ("This paper has six sections.") are prevalent in many domains. Can current large language models (LLMs) handle such language? In this paper, we present "I am a Strange Dataset", a new…

Cut-elimination theorems constitute one of the most important classes of theorems of proof theory. Since Gentzen's proof of the cut-elimination theorem for the system $\mathbf{LK}$, several other proofs have been proposed. Even though the…

The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…

Idioms are defined as a group of words with a figurative meaning not deducible from their individual components. Although modern machine translation systems have made remarkable progress, translating idioms remains a major challenge,…

We propose a novel discriminative model that learns embeddings from multilingual and multi-modal data, meaning that our model can take advantage of images and descriptions in multiple languages to improve embedding quality. To that end, we…

Instruction Fine-tuning~(IFT) is a critical phase in building large language models~(LLMs). Previous works mainly focus on the IFT's role in the transfer of behavioral norms and the learning of additional world knowledge. However, the…

Large language models (LLMs) have recently garnered significant interest. With in-context learning, LLMs achieve impressive results in various natural language tasks. However, the application of LLMs to sentence embeddings remains an area…

Recent reasoning LLMs (RLMs), especially those trained with verifier-based reinforcement learning, often perform worse with few-shot CoT than with direct answering. We revisit this paradox using high-quality reasoning traces from…

Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability,…

While BERT produces high-quality sentence embeddings, its pre-training computational cost is a significant drawback. In contrast, ELECTRA provides a cost-effective pre-training objective and downstream task performance improvements, but…

The main operations in Inductive Logic Programming (ILP) are generalization and specialization, which only make sense in a generality order. In ILP, the three most important generality orders are subsumption, implication and implication…

Input-to-State Stability (ISS) is fundamental in mathematically quantifying how stability degrades in the presence of bounded disturbances. If a system is ISS, its trajectories will remain bounded, and will converge to a neighborhood of an…

Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and prove program correctness. We generalize the conditions under…