Related papers: The Geometry of Numerical Reasoning: Language Mode…

Although behavioral studies have documented numerical reasoning errors in large language models (LLMs), the underlying representational mechanisms remain unclear. We hypothesize that numerical attributes occupy shared latent subspaces and…

Humans are believed to perceive numbers on a logarithmic mental number line, where smaller values are represented with greater resolution than larger ones. This cognitive bias, supported by neuroscience and behavioral studies, suggests that…

Large language models (LLMs) have exhibited impressive competence in various tasks, but their internal mechanisms on mathematical problems are still under-explored. In this paper, we study a fundamental question: how language models encode…

Understanding the latent space geometry of large language models (LLMs) is key to interpreting their behavior and improving alignment. Yet it remains unclear to what extent LLMs linearly organize representations related to semantic…

Large Language Models (LLMs) do not differentially represent numbers, which are pervasive in text. In contrast, neuroscience research has identified distinct neural representations for numbers and words. In this work, we investigate how…

The association between language and (non-linguistic) thinking ability in humans has long been debated, and recently, neuroscientific evidence of brain activity patterns has been considered. Such a scientific context naturally raises an…

Large language models (LLMs) frequently make errors when handling even simple numerical problems, such as comparing two small numbers. A natural hypothesis is that these errors stem from how LLMs represent numbers, and specifically, whether…

Large language models (LLMs) have demonstrated emergent abilities across diverse tasks, raising the question of whether they acquire internal world models. In this work, we investigate whether LLMs implicitly encode linear spatial world…

Although state-of-the-art LLMs can solve math problems, we find that they make errors on numerical comparisons with mixed notation: "Which is larger, $5.7 \times 10^2$ or $580$?" This raises a fundamental question: Do LLMs even know how big…

Large language models (LLMs) often benefit from intermediate steps of reasoning to generate answers to complex problems. When these intermediate steps of reasoning are used to monitor the activity of the model, it is essential that this…

Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving…

Pretrained language models (LMs) are prone to arithmetic errors. Existing work showed limited success in probing numeric values from models' representations, indicating that these errors can be attributed to the inherent unreliability of…

Prior work has shown that large language models (LLMs) often converge to accurate input embedding for numbers, based on sinusoidal representations. In this work, we quantify that these representations are in fact strikingly systematic, to…

Black-box probing models can reliably extract linguistic features like tense, number, and syntactic role from pretrained word representations. However, the manner in which these features are encoded in representations remains poorly…

Recent success of pre-trained language models (PLMs) has stimulated interest in their ability to understand and work with numbers. Yet, the numerical reasoning over measurements has not been formally studied despite their importance. In…

Human languages are full of metaphorical expressions. Metaphors help people understand the world by connecting new concepts and domains to more familiar ones. Large pre-trained language models (PLMs) are therefore assumed to encode…

Large Language Models have demonstrated the ability to generalize well at many levels across domains, modalities, and even shown in-context learning capabilities. This enables research questions regarding how they can be used to encode…

Numbers are a basic part of how humans represent and describe the world around them. As a consequence, learning effective representations of numbers is critical for the success of large language models as they become more integrated into…

Pretrained Language Models (LMs) have been shown to possess significant linguistic, common sense, and factual knowledge. One form of knowledge that has not been studied yet in this context is information about the scalar magnitudes of…

Large language models (LLMs) exhibit failures on elementary symbolic tasks such as character counting in a word, despite excelling on complex benchmarks. Although this limitation has been noted, the internal reasons remain unclear. We use…