Related papers: The Right Answer, the Wrong Direction: Why Transfo…

Large language models fail at counting repeated tokens despite strong performance on broader reasoning benchmarks. These failures are commonly attributed to limitations in internal count tracking. We show this attribution is wrong. Linear…

Language models are increasingly capable, yet still fail at a seemingly simple task of multi-digit multiplication. In this work, we study why, by reverse-engineering a model that successfully learns multiplication via \emph{implicit…

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…

Transformer-based large language models have achieved remarkable performance across various natural language processing tasks. However, they often struggle with seemingly easy tasks like arithmetic despite their vast capabilities. This…

Transformers, the backbone of modern large language models (LLMs), face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to…

The ability to perform arithmetic tasks is a remarkable trait of human intelligence and might form a critical component of more complex reasoning tasks. In this work, we investigate if the surface form of a number has any influence on how…

The poor performance of transformers on arithmetic tasks seems to stem in large part from their inability to keep track of the exact position of each digit inside of a large span of digits. We mend this problem by adding an embedding to…

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…

Despite the remarkable success of Transformer-based large language models (LLMs) across various domains, understanding and enhancing their mathematical capabilities remains a significant challenge. In this paper, we conduct a rigorous…

Large language models exhibit sophisticated capabilities, yet understanding how they work internally remains a central challenge. A fundamental obstacle is that training selects for behavior, not circuitry, so many weight configurations can…

When a tool-calling agent picks the wrong tool, the failure is invisible until execution: the email gets sent, the meeting gets missed. As agents take on consequential actions, one bad tool call can do real damage. We currently have no way…

Recent theoretical results show transformers cannot express sequential reasoning problems over long inputs, intuitively because their computational depth is bounded. However, prior work treats the depth as a constant, leaving it unclear to…

Modern AI systems have been successfully deployed to win medals at international math competitions, assist with research workflows, and prove novel technical lemmas. However, despite their progress at advanced levels of mathematics, they…

Large Language Models (LLMs) have successfully been applied to code generation tasks, raising the question of how well these models understand programming. Typical programming languages have invariances and equivariances in their semantics…

Transformers, central to the successes in modern Natural Language Processing, often falter on arithmetic tasks despite their vast capabilities --which paradoxically include remarkable coding abilities. We observe that a crucial challenge is…

Sequential fine-tuning of pretrained language encoders often overwrites previously acquired capabilities, but the forgetting behavior of parameter-efficient updates remains under-characterized. We present a controlled empirical study of…

Despite the empirical success of prompt tuning in adapting pretrained language models to new tasks, theoretical analyses of its capabilities remain limited. Existing theoretical work primarily addresses universal approximation properties,…

Vision-language models encode continuous geometry that their text pathway fails to express: a 6,000-parameter linear probe extracts hand joint angles at 6.1 degrees MAE from frozen features, while the best text output achieves only 20.0…

Though Large Language Models (LLMs) have shown remarkable abilities in mathematics reasoning, they are still struggling with performing numeric operations accurately, such as addition and multiplication. Numbers can be tokenized into tokens…

Large language models (LLMs), despite strong performance on complex mathematical problems, exhibit systematic limitations in counting tasks. This issue arises from the architectural limits of transformers, where counting is performed across…