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This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze…

Artificial Intelligence · Computer Science 2025-02-24 Johan Boye , Birger Moell

Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training…

Machine Learning · Statistics 2026-03-18 Nuri Mert Vural , Alberto Bietti , Mahdi Soltanolkotabi , Denny Wu

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…

Computation and Language · Computer Science 2026-02-18 Fengting Yuchi , Li Du , Jason Eisner

Transformers are widely used in NLP tasks. However, current approaches to leveraging transformers to understand language expose one weak spot: Number understanding. In some scenarios, numbers frequently occur, especially in semi-structured…

Computation and Language · Computer Science 2023-03-17 Hongwei Han , Jialiang Xu , Mengyu Zhou , Yijia Shao , Shi Han , Dongmei Zhang

Compressing transformer weights makes large language models cheaper to deploy. But each layer's compression introduces an error. These errors accumulate as the signal passes through later layers, and how they accumulate is not well…

Machine Learning · Computer Science 2026-05-08 Abhinaba Basu , Kumkum Basu , Koushik Deb

Transformers are widely deployed in large language models (LLMs), yet most models still fail on basic arithmetic tasks such as multidigit addition. In contrast, we show that small transformers trained from scratch can solve n-digit addition…

Machine Learning · Computer Science 2025-10-06 Philip Quirke , Clement Neo , Fazl Barez

Motivated by the Parameter-Efficient Fine-Tuning (PEFT) in large language models, we propose LoRAT, a method that unveils the power of large ViT model for tracking within laboratory-level resources. The essence of our work lies in adapting…

Computer Vision and Pattern Recognition · Computer Science 2024-07-29 Liting Lin , Heng Fan , Zhipeng Zhang , Yaowei Wang , Yong Xu , Haibin Ling

Large language models are increasingly adopted as semantic backbones for neural text-to-speech systems. However, frozen LLM representations are insufficient for modeling speaker specific acoustic and perceptual characteristics. Our…

Sound · Computer Science 2026-03-12 Anupam Purwar , Aditya Choudhary

Chain-of-thought (CoT) prompting assumes that generated reasoning reflects a model's internal computation. We show this assumption is wrong in a specific, measurable way: models internally detect their own reasoning errors but outwardly…

Computation and Language · Computer Science 2026-05-12 Aojie Yuan , Zhiyuan Julian Su , Haiyue Zhang , Yi Nian , Yue Zhao

Large language models (LLMs) achieve remarkable performance through ever-increasing parameter counts, but scaling incurs steep computational costs. To better understand LLM scaling, we study representational differences between LLMs and…

While self-correction has shown promise in improving LLM outputs in terms of style and quality (e.g. Chen et al., 2023b; Madaan et al., 2023), recent attempts to self-correct logical or reasoning errors often cause correct answers to become…

Artificial Intelligence · Computer Science 2024-06-05 Gladys Tyen , Hassan Mansoor , Victor Cărbune , Peter Chen , Tony Mak

For Large Language Models (LLMs) to be reliably deployed, models must effectively know when not to answer: abstain. Reasoning models, in particular, have gained attention for impressive performance on complex tasks. However, reasoning…

Artificial Intelligence · Computer Science 2026-04-03 Abinitha Gourabathina , Inkit Padhi , Manish Nagireddy , Subhajit Chaudhury , Prasanna Sattigeri

We present a systematic study of subtraction in large language models (LLMs). While prior benchmarks emphasize addition and multiplication, subtraction has received comparatively little attention despite being structurally distinct as a…

We present a mechanistic case study of a format-dependent reasoning failure in Llama-3.1-8B-Instruct, where the model incorrectly judges "9.11" as larger than "9.8" in chat or Q&A formats, but answers correctly in simple format. Through…

Machine Learning · Computer Science 2025-08-28 Gustavo Sandoval

Next to scaling considerations, architectural design choices profoundly shape the solution space of transformers. In this work, we analyze the solutions simple transformer blocks implement when tackling the histogram task: counting items in…

Machine Learning · Computer Science 2025-11-13 Freya Behrens , Luca Biggio , Lenka Zdeborová

Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This…

We present the surprising finding that a language model's reasoning capabilities can be improved by training on synthetic datasets of chain-of-thought (CoT) traces from more capable models, even when all of those traces lead to an incorrect…

Artificial Intelligence · Computer Science 2026-01-26 Abhranil Chandra , Ayush Agrawal , Arian Hosseini , Sebastian Fischmeister , Rishabh Agarwal , Navin Goyal , Aaron Courville

Transformers evaluated in a single, fixed-depth pass are provably limited in expressive power to the constant-depth circuit class TC0. Running a Transformer autoregressively removes that ceiling -- first in next-token prediction and, more…

Machine Learning · Computer Science 2025-07-21 Mrinal Mathur , Mike Doan , Barak Pearlmutter , Sergey Plis

Low-Rank Adaptation (LoRA) is widely used for parameter-efficient fine-tuning of large language models, but it is notably ineffective at removing backdoor behaviors from poisoned pretrained models when fine-tuning on clean dataset. Contrary…

Computation and Language · Computer Science 2026-01-13 Hoang-Chau Luong , Lingwei Chen

Vision-Language Models (VLMs) have recently gained attention due to their competitive performance on multiple downstream tasks, achieved by following user-input instructions. However, VLMs still exhibit several limitations in visual…

Computer Vision and Pattern Recognition · Computer Science 2025-10-23 Simone Alghisi , Gabriel Roccabruna , Massimo Rizzoli , Seyed Mahed Mousavi , Giuseppe Riccardi