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Machine learning systems perform well on pattern matching tasks, but their ability to perform algorithmic or logical reasoning is not well understood. One important reasoning capability is algorithmic extrapolation, in which models trained…

A hallmark of human intelligence is the ability to construct self-contained chunks of knowledge and adequately reuse them in novel combinations for solving different yet structurally related problems. Learning such compositional structures…

A fundamental challenge in developing general learning algorithms is their tendency to forget past knowledge when adapting to new data. Addressing this problem requires a principled understanding of forgetting; yet, despite decades of…

Construct recursively a long string of words w1. .. wn, such that at each step k, w k+1 is a new word with a fixed probability p $\in$ (0, 1), and repeats some preceding word with complementary probability 1 -- p. More precisely, given a…

Hierarchical reasoning model (HRM) achieves extraordinary performance on various reasoning tasks, significantly outperforming large language model-based reasoners. To understand the strengths and potential failure modes of HRM, we conduct a…

Verbal omissions are complex syntactic phenomena in VP coordination structures. They occur when verbs and (some of) their arguments are omitted from subsequent clauses after being explicitly stated in an initial clause. Recovering these…

The regular languages with a neutral letter expressible in first-order logic with one alternation are characterized. Specifically, it is shown that if an arbitrary $\Sigma_2$ formula defines a regular language with a neutral letter, then…

Reasoning models enhance problem-solving by scaling test-time compute, yet they face a critical paradox: excessive thinking tokens often degrade performance rather than improve it. We attribute this to a fundamental architectural flaw:…

In this paper, we introduce a concept of non-dependence of variables in formulas. A formula in first-order logic is non-dependent of a variable if the truth value of this formula does not depend on the value of that variable. This variable…

The ability of humans to quickly identify general concepts from a handful of images has proven difficult to emulate with robots. Recently, a computer architecture was developed that allows robots to mimic some aspects of this human ability…

Despite the remarkable progress in neural models, their ability to generalize, a cornerstone for applications such as logical reasoning, remains a critical challenge. We delineate two fundamental aspects of this ability: compositionality,…

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer…

Answering multi-hop reasoning questions requires retrieving and synthesizing information from diverse sources. Large Language Models (LLMs) struggle to perform such reasoning consistently. Here we propose an approach to pinpoint and rectify…

Robin Hood hashing is a variation on open addressing hashing designed to reduce the maximum search time as well as the variance in the search time for elements in the hash table. While the case of insertions only using Robin Hood hashing is…

We present an algorithm for active learning of deterministic timed automata with a single clock. The algorithm is within the framework of Angluin's $L^*$ algorithm and inspired by existing work on the active learning of symbolic automata.…

Machine unlearning aims to remove specific content from trained models while preserving overall performance. However, the phenomenon of benign relearning, in which forgotten information reemerges even from benign fine-tuning data, reveals…

Even though every mathematician knows intuitively what it means to "simplify" a mathematical expression, there is still no universally accepted rigorous mathematical definition of "simplify". In this paper, we shall give a simple and…

Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…

A growing body of research in continual learning focuses on the catastrophic forgetting problem. While many attempts have been made to alleviate this problem, the majority of the methods assume a single model in the continual learning…

Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…