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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) 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…
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…
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…
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…
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…
Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writing software and solving quantitative problems. We provide a…
Large language models (LLMs) are increasingly deployed on complex reasoning tasks, yet little is known about their ability to internally evaluate problem difficulty, which is an essential capability for adaptive reasoning and efficient…
Counting is one of the fundamental abilities of large language models (LLMs) and large vision-language models (LVLMs). This paper examines how these foundation models represent and compute numerical information in counting tasks. We use…
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…
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…
This paper investigates whether large language models (LLMs) utilize numerical attributes encoded in a low-dimensional subspace of the embedding space when answering questions involving numeric comparisons, e.g., Was Cristiano born before…
Large language models (LLMs) have led to breakthroughs in language tasks, yet the internal mechanisms that enable their remarkable generalization and reasoning abilities remain opaque. This lack of transparency presents challenges such as…
Transformer-based language models often achieve strong results on mathematical reasoning benchmarks while remaining fragile on basic numerical understanding and arithmetic operations. A central limitation is that numbers are processed as…
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…
Despite the effectiveness of large language models (LLMs) for code generation, they often output incorrect code. One reason is that model output probabilities are often not well-correlated with correctness, and reflect only the final output…
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…
From extracting features to generating text, the outputs of large language models (LLMs) typically rely on the final layers, following the conventional wisdom that earlier layers capture only low-level cues. However, our analysis shows that…
Previous work has showcased the intriguing capability of large language models (LLMs) in retrieving facts and processing context knowledge. However, only limited research exists on the layer-wise capability of LLMs to encode knowledge,…