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Tabular foundational models are pre-trained models designed for a wide range of tabular data tasks. They have shown strong performance across domains, yet their internal representations and learned concepts remain poorly understood. This…

To foster usefulness and accountability of machine learning (ML), it is essential to explain a model's decisions in addition to evaluating its performance. Accordingly, the field of explainable artificial intelligence (XAI) has resurfaced…

Theory of Mind (ToM) is the ability to understand and reflect on the mental states of others. Although this capability is crucial for human interaction, testing on Large Language Models (LLMs) reveals that they possess only a rudimentary…

Counterfactual explanation is an important Explainable AI technique to explain machine learning predictions. Despite being studied actively, existing optimization-based methods often assume that the underlying machine-learning model is…

In this paper, we demonstrate how to do automated theorem proving in the presence of a large knowledge base of potential premises without learning from human proofs. We suggest an exploration mechanism that mixes in additional premises…

In this note we introduce a new family of non-commutative spaces that we call non-commutative toric varieties and we describe some of their main properties. The main technical tool in this investigation is a natural extension of LVM-theory…

Let $R$ be the class of regular cardinals which are not hyperinaccessible. We show that $L[R]$, and similar inner models in the $\alpha$-inaccessible hierarchy, can be generated by iterating a small "machete" mouse up through all the…

Suppose that $T^*$ is an $\omega_1$-Aronszajn tree with no stationary antichain. We introduce a forcing axiom PFA($T^*$) for proper forcings which preserve these properties of $T^*$. We prove that PFA($T^*$) implies many of the strong…

Recent interest has surged in eigenvalue's nonlinearity-based topological transport governed by the equation of auxiliary eigenvalues $H\Psi=\omega S(\omega)\Psi$ [T. Isobe et al., Phys. Rev. Lett. 132, 126601 (2024); C. Bai and Z. Liang,…

Building on the seminal work of Gromov on endomorphisms of symbolic algebraic varieties [10], we introduce a notion of cellular automata over schemes which generalize affine algebraic cellular automata in [7]. We extend known results to…

We compare tame actions in the category of schemes with torsors in the category of log schemes endowed with the log flat topology. We prove that actions underlying log flat torsors are tame. Conversely, starting from a tame cover of a…

We combine two approaches to the study of classification theory of AECs: 1. that of Shelah: studying non-forking frames without assuming the amalgamation property but assuming the existence of uniqueness triples and 2. that of Grossberg and…

Language models can be persuaded to abandon factual knowledge. This vulnerability is central to AI safety, but its internal mechanism remains poorly understood. We uncover a compact causal mechanism for persuasion-induced factual errors. A…

We establish the conjugacy of Cartan subalgebras for extended affine Lie algebras whose centreless core is "of type A", i.e., matrices over a quantum torus Q whose trace lies in the commutator space of Q. This settles the last outstanding…

Large Language Models (LLMs) have developed rapidly and are widely applied to both general-purpose and professional tasks to assist human users. However, they still struggle to comprehend and respond to the true user needs when intentions…

Recent advances in large language models (LLMs) have highlighted the effectiveness of chain-of-thought reasoning in symbolic domains such as mathematics and programming. However, our study shows that directly transferring such text-based…

With the wide-scale adoption of conversational AI systems, AI are now able to exert unprecedented influence on human opinion and beliefs. Recent work has shown that many Large Language Models (LLMs) comply with requests to persuade users…

We give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type…

We prove Los conjecture = Morley theorem in ZF, with the same characterization (of first order countable theories categorical in aleph_alpha for some (equivalently for every) ordinal alpha>0. Another central result here is, in this context:…

Let $R$ be a ring (associative, with 1), and let $R<< a,b>>$ denote the power-series $R$-ring in two non-commuting, $R$-centralizing variables, $a$ and $b$. Let $A$ be an $R$-subring of $R<< a>>$ and $B$ be an $R$-subring of $R<< b>>$, and…