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In this paper, I introduce the retrieval problem, a simple yet common reasoning task that can be solved only by transformers with a minimum number of layers, which grows logarithmically with the input size. I empirically show that large…

Machine Learning · Computer Science 2025-10-29 Tiberiu Musat

Retrosynthesis prediction is one of the fundamental challenges in organic synthesis. The task is to predict the reactants given a core product. With the advancement of machine learning, computer-aided synthesis planning has gained…

Chemical Physics · Physics 2022-02-01 Yue Wan , Benben Liao , Chang-Yu Hsieh , Shengyu Zhang

The Transformer architecture has revolutionized artificial intelligence, yet a principled theoretical understanding of its internal mechanisms remains elusive. This paper introduces a novel analytical framework that reconceptualizes the…

Machine Learning · Computer Science 2025-09-30 Yukun Zhang , Xueqing Zhou

Contemporary autoregressive transformers operate in open loop: each hidden state is computed in a single forward pass and never revised, causing errors to propagate uncorrected through the sequence. We identify this open-loop bottleneck as…

Machine Learning · Computer Science 2025-12-01 Akbar Anbar Jafari , Gholamreza Anbarjafari

A new generation of language models reasons entirely in continuous hidden states, producing no tokens and leaving no audit trail. We show that this silence creates a fundamentally new attack surface. ThoughtSteer perturbs a single embedding…

Machine Learning · Computer Science 2026-04-02 Swapnil Parekh

We present the discriminative recurrent sparse auto-encoder model, comprising a recurrent encoder of rectified linear units, unrolled for a fixed number of iterations, and connected to two linear decoders that reconstruct the input and…

Machine Learning · Computer Science 2013-03-20 Jason Tyler Rolfe , Yann LeCun

The Transformer is an extremely powerful and prominent deep learning architecture. In this work, we challenge the commonly held belief in deep learning that going deeper is better, and show an alternative design approach that is building…

Machine Learning · Computer Science 2022-11-10 Jason Ross Brown , Yiren Zhao , Ilia Shumailov , Robert D Mullins

Deep learning employs multi-layer neural networks trained via the backpropagation algorithm. This approach has achieved success across many domains and relies on adaptive gradient methods such as the Adam optimizer. Sequence modeling…

Machine Learning · Computer Science 2025-07-16 Esmail Gumaan

Latent or continuous chain-of-thought methods replace explicit textual rationales with a number of internal latent steps, but these intermediate computations are difficult to evaluate beyond correlation-based probes. In this paper, we view…

Artificial Intelligence · Computer Science 2026-05-29 Zirui Li , Xuefeng Bai , Kehai Chen , Yizhi Li , Jian Yang , Chenghua Lin , Min Zhang

Autoregressive language models trained with next-token prediction generate text by sampling one discrete token at a time. Although very scalable, this objective forces the model to commit at every step, preventing it from exploring or…

Computation and Language · Computer Science 2026-03-24 Lorenzo Noci , Gregor Bachmann , Seyed-Mohsen Moosavi-Dezfooli , Moin Nabi

In this paper, we advocate for two stages in a neural network's decision making process. The first is the existing feed-forward inference framework where patterns in given data are sensed and associated with previously learned patterns. The…

Machine Learning · Computer Science 2022-09-20 Mohit Prabhushankar , Ghassan AlRegib

Chain-of-thought traces from large reasoning models can span tens of thousands of tokens, yet we lack a vocabulary for describing their internal structure. Previous methods developed to analyze chain-of-thought traces are either too rigid…

Artificial Intelligence · Computer Science 2026-05-29 Daniel Lee , Owen Queen , James Zou

Chain-of-Thought (CoT) and Looped Transformers have been shown to empirically improve performance on reasoning tasks and to theoretically enhance expressivity by recursively increasing the number of computational steps. However, their…

Machine Learning · Computer Science 2025-10-27 Kevin Xu , Issei Sato

Depth in the real world is rarely singular. Transmissive materials create layered ambiguities that confound conventional perception systems. Existing models remain passive; conventional approaches typically estimate static depth maps…

Computer Vision and Pattern Recognition · Computer Science 2026-03-26 Junhong Min , Jimin Kim , Minwook Kim , Cheol-Hui Min , Youngpil Jeon , Minyong Choi

Our goal is to combine the rich multistep inference of symbolic logical reasoning with the generalization capabilities of neural networks. We are particularly interested in complex reasoning about entities and relations in text and…

Computation and Language · Computer Science 2017-05-02 Rajarshi Das , Arvind Neelakantan , David Belanger , Andrew McCallum

We conduct a systematic study of the approximation properties of Transformer for sequence modeling with long, sparse and complicated memory. We investigate the mechanisms through which different components of Transformer, such as the…

Machine Learning · Computer Science 2024-10-31 Mingze Wang , Weinan E

The ability to reason with multiple hierarchical structures is an attractive and desirable property of sequential inductive biases for natural language processing. Do the state-of-the-art Transformers and LSTM architectures implicitly…

Computation and Language · Computer Science 2021-11-30 Bill Tuck Weng Pung , Alvin Chan

The computational overhead of Vision Transformers in practice stems fundamentally from their deep architectures, yet existing acceleration strategies have primarily targeted algorithmic-level optimizations such as token pruning and…

Computer Vision and Pattern Recognition · Computer Science 2025-11-26 Chengwei Zhou , Vipin Chaudhary , Gourav Datta

While biological vision systems rely heavily on feedback connections to iteratively refine perception, most artificial neural networks remain purely feedforward, processing input in a single static pass. In this work, we propose a…

Computer Vision and Pattern Recognition · Computer Science 2025-07-15 David Calhas , Arlindo L. Oliveira

Large language models have consistently struggled with complex reasoning tasks, such as mathematical problem-solving. Investigating the internal reasoning mechanisms of these models can help us design better model architectures and training…

Artificial Intelligence · Computer Science 2025-09-10 Zhiwei Wang , Yunji Wang , Zhongwang Zhang , Zhangchen Zhou , Hui Jin , Tianyang Hu , Jiacheng Sun , Zhenguo Li , Yaoyu Zhang , Zhi-Qin John Xu