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In quantum mechanics events can happen in no definite causal order: in practice this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement. Indefinite causal order can be observed…

Quantum Physics · Physics 2018-11-05 K. Goswami , C. Giarmatzi , M. Kewming , F. Costa , C. Branciard , J. Romero , A. G. White

Time series forecasting with limited data is a challenging yet critical task. While transformers have achieved outstanding performances in time series forecasting, they often require many training samples due to the large number of…

Machine Learning · Computer Science 2019-10-23 Yunkai Zhang , Qiao Jiang , Shurui Li , Xiaoyong Jin , Xueying Ma , Xifeng Yan

Transformers generalize to novel compositions of structures and entities after being trained on a complex dataset, but easily overfit on datasets of insufficient complexity. We observe that when the training set is sufficiently complex, the…

Computation and Language · Computer Science 2024-02-12 Yichen Jiang , Xiang Zhou , Mohit Bansal

In decoder-only (causal) transformers, the computation graph created by causal masking routes information through both direct-path attention and indirect paths formed by intermediate tokens. We denote these indirect paths between token…

Machine Learning · Computer Science 2026-01-22 Hunjae Lee , Corey Clark

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…

Machine Learning · Computer Science 2026-02-27 Joshua S. Schiffman

While attention has been empirically shown to improve model performance, it lacks a rigorous mathematical justification. This short paper establishes a novel connection between attention mechanisms and multinomial regression. Specifically,…

Machine Learning · Computer Science 2025-10-28 Jonas A. Actor , Anthony Gruber , Eric C. Cyr

Transformers require positional encodings to represent sequence order, yet most prior work focuses on designing new positional encodings rather than examining how positional information is fused with token embeddings. In this paper, we…

Machine Learning · Computer Science 2026-01-12 Mohamed Amine Hallam , Kuo-Kun Tseng

The self-attention mechanism, a cornerstone of Transformer-based state-of-the-art deep learning architectures, is largely heuristic-driven and fundamentally challenging to interpret. Establishing a robust theoretical foundation to explain…

Computer Vision and Pattern Recognition · Computer Science 2026-02-10 Laziz U. Abdullaev , Maksim Tkachenko , Tan M. Nguyen

The attention mechanisms are playing a boosting role in advancements in sequence-to-sequence problems. Transformer architecture achieved new state of the art results in machine translation, and it's variants are since being introduced in…

Machine Learning · Computer Science 2020-05-12 Abhishek Niranjan , M Ali Basha Shaik , Kushal Verma

Deep learning models have been widely applied in various aspects of daily life. Many variant models based on deep learning structures have achieved even better performances. Attention-based architectures have become almost ubiquitous in…

Machine Learning · Computer Science 2022-02-25 Zhiying Fang , Yidong Ouyang , Ding-Xuan Zhou , Guang Cheng

Transformer architecture has become ubiquitous in the natural language processing field. To interpret the Transformer-based models, their attention patterns have been extensively analyzed. However, the Transformer architecture is not only…

Computation and Language · Computer Science 2021-09-16 Goro Kobayashi , Tatsuki Kuribayashi , Sho Yokoi , Kentaro Inui

Continual learning aims to sequentially learn new tasks without forgetting previous tasks' knowledge (catastrophic forgetting). One factor that can cause forgetting is the interference between the gradients on losses from different tasks.…

Computation and Language · Computer Science 2025-12-01 Xueying Bai , Jinghuan Shang , Yifan Sun , Niranjan Balasubramanian

The causal structure of a unitary transformation is the set of relations of possible influence between any input subsystem and any output subsystem. We study whether such causal structure can be understood in terms of compositional…

Quantum Physics · Physics 2021-07-28 Robin Lorenz , Jonathan Barrett

We investigate how embedding dimension affects the emergence of an internal "world model" in a transformer trained with reinforcement learning to perform bubble-sort-style adjacent swaps. Models achieve high accuracy even with very small…

Machine Learning · Computer Science 2025-10-22 Brady Bhalla , Honglu Fan , Nancy Chen , Tony Yue YU

Large-scale foundation models for scientific machine learning adapt to physical settings unseen during training, such as zero-shot transfer between turbulent scales. This phenomenon, in-context learning, challenges conventional…

Machine Learning · Computer Science 2026-04-14 Anthony Bao , Jeffrey Lai , William Gilpin

To capture user preference, transformer models have been widely applied to model sequential user behavior data. The core of transformer architecture lies in the self-attention mechanism, which computes the pairwise attention scores in a…

Information Retrieval · Computer Science 2024-04-05 Zhen Tian , Wayne Xin Zhao , Changwang Zhang , Xin Zhao , Zhongrui Ma , Ji-Rong Wen

Understanding Transformer-based models has attracted significant attention, as they lie at the heart of recent technological advances across machine learning. While most interpretability methods rely on running models over inputs, recent…

Computation and Language · Computer Science 2023-12-27 Guy Dar , Mor Geva , Ankit Gupta , Jonathan Berant

Music relies heavily on repetition to build structure and meaning. Self-reference occurs on multiple timescales, from motifs to phrases to reusing of entire sections of music, such as in pieces with ABA structure. The Transformer (Vaswani…

Temporal causal discovery is a crucial task aimed at uncovering the causal relations within time series data. The latest temporal causal discovery methods usually train deep learning models on prediction tasks to uncover the causality…

Machine Learning · Computer Science 2024-06-25 Lingbai Kong , Wengen Li , Hanchen Yang , Yichao Zhang , Jihong Guan , Shuigeng Zhou

Transformers have the capacity to act as supervised learning algorithms: by properly encoding a set of labeled training ("in-context") examples and an unlabeled test example into an input sequence of vectors of the same dimension, the…

Machine Learning · Computer Science 2024-12-16 Spencer Frei , Gal Vardi