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We propose a synthetic reasoning task, LEGO (Learning Equality and Group Operations), that encapsulates the problem of following a chain of reasoning, and we study how the Transformer architectures learn this task. We pay special attention…

Machine Learning · Computer Science 2023-02-21 Yi Zhang , Arturs Backurs , Sébastien Bubeck , Ronen Eldan , Suriya Gunasekar , Tal Wagner

Trained on vast corpora of human language, language models demonstrate emergent human-like reasoning abilities. Yet they are still far from true intelligence, which opens up intriguing opportunities to explore the parallels of humans and…

Computation and Language · Computer Science 2024-11-05 Tengxiao Liu , Qipeng Guo , Xiangkun Hu , Cheng Jiayang , Yue Zhang , Xipeng Qiu , Zheng Zhang

In cognition theory, human thinking is governed by two systems: the fast and intuitive System 1 and the slower but more deliberative System 2. Analogously, Large Language Models (LLMs) can operate in two reasoning modes: outputting only the…

Artificial Intelligence · Computer Science 2025-07-14 DiJia Su , Sainbayar Sukhbaatar , Michael Rabbat , Yuandong Tian , Qinqing Zheng

We advance the recently proposed neuro-symbolic Differentiable Tree Machine, which learns tree operations using a combination of transformers and Tensor Product Representations. We investigate the architecture and propose two key…

Chain-of-Thought reasoning has emerged as a pivotal methodology for enhancing model inference capabilities. Despite growing interest in Chain-of-Thought reasoning, its underlying mechanisms remain unclear. This paper explores the working…

Computation and Language · Computer Science 2025-09-03 Hao Yang , Zhiyu Yang , Yunjie Zhang , Shanyi Zhu , Lin Yang

Humans have a powerful and mysterious capacity to reason. Working through a set of mental steps enables us to make inferences we would not be capable of making directly even though we get no additional data from the world. Similarly, when…

Artificial Intelligence · Computer Science 2023-11-06 Ben Prystawski , Michael Y. Li , Noah D. Goodman

Latent reasoning has been recently proposed as a reasoning paradigm and performs multi-step reasoning through generating steps in the latent space instead of the textual space. This paradigm enables reasoning beyond discrete language tokens…

Artificial Intelligence · Computer Science 2026-02-27 Yingqian Cui , Zhenwei Dai , Bing He , Zhan Shi , Hui Liu , Rui Sun , Zhiji Liu , Yue Xing , Jiliang Tang , Benoit Dumoulin

Humans learn to solve tasks of increasing complexity by building on top of previously acquired knowledge. Typically, there exists a natural progression in the tasks that we learn - most do not require completely independent solutions, but…

Computer Vision and Pattern Recognition · Computer Science 2018-10-01 Seung Wook Kim , Makarand Tapaswi , Sanja Fidler

Chain-of-thought (CoT) prompting enables reasoning in language models but requires explicit verbalization of intermediate steps. Looped transformers offer an alternative by iteratively refining representations within hidden states. This…

Computation and Language · Computer Science 2026-03-12 Markus Frey , Behzad Shomali , Ali Hamza Bashir , David Berghaus , Joachim Koehler , Mehdi Ali

Transformers have demonstrated remarkable performance in natural language processing and related domains, as they largely focus on sequential, autoregressive next-token prediction tasks. Yet, they struggle in logical reasoning, not…

Artificial Intelligence · Computer Science 2025-10-08 Renee Ge , Qianli Liao , Tomaso Poggio

When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…

Computation and Language · Computer Science 2022-11-07 Shikhar Murty , Pratyusha Sharma , Jacob Andreas , Christopher D. Manning

Learning vector representations for programs is a critical step in applying deep learning techniques for program understanding tasks. Various neural network models are proposed to learn from tree-structured program representations, e.g.,…

Software Engineering · Computer Science 2023-01-10 Wenhan Wang , Kechi Zhang , Ge Li , Shangqing Liu , Anran Li , Zhi Jin , Yang Liu

We present a general framework for training deep neural networks without backpropagation. This substantially decreases training time and also allows for construction of deep networks with many sorts of learners, including networks whose…

Machine Learning · Statistics 2017-06-09 Chris Hettinger , Tanner Christensen , Ben Ehlert , Jeffrey Humpherys , Tyler Jarvis , Sean Wade

Chain-of-Thought (CoT) is an efficient prompting method that enables the reasoning ability of large language models by augmenting the query using multiple examples with multiple intermediate steps. Despite the empirical success, the…

Machine Learning · Computer Science 2025-05-27 Hongkang Li , Songtao Lu , Pin-Yu Chen , Xiaodong Cui , Meng Wang

Instructing the model to generate a sequence of intermediate steps, a.k.a., a chain of thought (CoT), is a highly effective method to improve the accuracy of large language models (LLMs) on arithmetics and symbolic reasoning tasks. However,…

Machine Learning · Computer Science 2024-09-24 Zhiyuan Li , Hong Liu , Denny Zhou , Tengyu Ma

While Pre-trained Language Models (PLMs) internalize a great amount of world knowledge, they have been shown incapable of recalling these knowledge to solve tasks requiring complex & multi-step reasoning. Similar to how humans develop a…

Computation and Language · Computer Science 2022-10-25 Boshi Wang , Xiang Deng , Huan Sun

In open-ended continuous environments, robots need to learn multiple parameterised control tasks in hierarchical reinforcement learning. We hypothesise that the most complex tasks can be learned more easily by transferring knowledge from…

Artificial Intelligence · Computer Science 2021-02-22 Nicolas Duminy , Sao Mai Nguyen , Junshuai Zhu , Dominique Duhaut , Jerome Kerdreux

Large language models (LLMs) solve complex problems by generating multi-step reasoning traces. Yet these traces are typically analyzed from only one of two perspectives: the sequence of tokens across different reasoning steps in the…

Computation and Language · Computer Science 2026-03-25 Ruidi Chang , Jiawei Zhou , Hanjie Chen

Large Language Models (LLMs) employing Chain-of-Thought (CoT) prompting have broadened the scope for improving multi-step reasoning capabilities. We generally divide multi-step reasoning into two phases: path generation to generate the…

Computation and Language · Computer Science 2024-08-20 Shumin Deng , Ningyu Zhang , Nay Oo , Bryan Hooi

Evaluation of multimodal reasoning models is typically reduced to a single accuracy score, implicitly treating reasoning as a unitary capability. We introduce MathLens, a benchmark of textbook-style geometry problems that exposes this…

Computation and Language · Computer Science 2026-05-08 Jiwan Chung , Neel Joshi , Pratyusha Sharma , Youngjae Yu , Vibhav Vineet