Approximation Rate of the Transformer Architecture for Sequence Modeling

• URL: http://arxiv.org/abs/2305.18475v4
• Date: Thu, 02 Jan 2025 05:02:48 GMT
• Title: Approximation Rate of the Transformer Architecture for Sequence Modeling
• Authors: Haotian Jiang, Qianxiao Li,
• Abstract summary: We consider a class of non-linear relationships and identify a novel notion of complexity measures to establish an explicit Jackson-type approximation rate estimate for the Transformer. This rate reveals the structural properties of the Transformer and suggests the types of sequential relationships it is best suited for approximating.
• Score: 18.166959969957315
• License:
• Abstract: The Transformer architecture is widely applied in sequence modeling applications, yet the theoretical understanding of its working principles remains limited. In this work, we investigate the approximation rate for single-layer Transformers with one head. We consider a class of non-linear relationships and identify a novel notion of complexity measures to establish an explicit Jackson-type approximation rate estimate for the Transformer. This rate reveals the structural properties of the Transformer and suggests the types of sequential relationships it is best suited for approximating. In particular, the results on approximation rates enable us to concretely analyze the differences between the Transformer and classical sequence modeling methods, such as recurrent neural networks.

Related papers

• Dynamics of Transient Structure in In-Context Linear Regression Transformers [0.5242869847419834]
  We show that when transformers are trained on in-context linear regression tasks with intermediate task diversity, they behave like ridge regression before specializing to the tasks in their training distribution. This transition from a general solution to a specialized solution is revealed by joint trajectory principal component analysis. We empirically validate this explanation by measuring the model complexity of our transformers as defined by the local learning coefficient.
  arXiv  Detail & Related papers  (2025-01-29T16:32:14Z)
• Interpreting Affine Recurrence Learning in GPT-style Transformers [54.01174470722201]
  In-context learning allows GPT-style transformers to generalize during inference without modifying their weights. This paper focuses specifically on their ability to learn and predict affine recurrences as an ICL task. We analyze the model's internal operations using both empirical and theoretical approaches.
  arXiv  Detail & Related papers  (2024-10-22T21:30:01Z)
• What Does It Mean to Be a Transformer? Insights from a Theoretical Hessian Analysis [8.008567379796666]
  The Transformer architecture has inarguably revolutionized deep learning. At its core, the attention block differs in form and functionality from most other architectural components in deep learning. The root causes behind these outward manifestations, and the precise mechanisms that govern them, remain poorly understood.
  arXiv  Detail & Related papers  (2024-10-14T18:15:02Z)
• Can Looped Transformers Learn to Implement Multi-step Gradient Descent for In-context Learning? [69.4145579827826]
  We show a fast flow on the regression loss despite the gradient non-ity algorithms for our convergence landscape. This is the first theoretical analysis for multi-layer Transformer in this setting.
  arXiv  Detail & Related papers  (2024-10-10T18:29:05Z)
• Learning on Transformers is Provable Low-Rank and Sparse: A One-layer Analysis [63.66763657191476]
  We show that efficient numerical training and inference algorithms as low-rank computation have impressive performance for learning Transformer-based adaption. We analyze how magnitude-based models affect generalization while improving adaption. We conclude that proper magnitude-based has a slight on the testing performance.
  arXiv  Detail & Related papers  (2024-06-24T23:00:58Z)
• Understanding the Expressive Power and Mechanisms of Transformer for Sequence Modeling [10.246977481606427]
  We study the mechanisms through which different components of Transformer, such as the dot-product self-attention, affect its expressive power. Our study reveals the roles of critical parameters in the Transformer, such as the number of layers and the number of attention heads.
  arXiv  Detail & Related papers  (2024-02-01T11:43:13Z)
• Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection [88.23337313766353]
  This work first provides a comprehensive statistical theory for transformers to perform ICL. We show that transformers can implement a broad class of standard machine learning algorithms in context. A emphsingle transformer can adaptively select different base ICL algorithms.
  arXiv  Detail & Related papers  (2023-06-07T17:59:31Z)
• Forward and Inverse Approximation Theory for Linear Temporal Convolutional Networks [20.9427668489352]
  We prove an approximation rate estimate (Jackson-type result) and an inverse approximation theorem (Bernstein-type result) We provide a comprehensive characterization of the types of sequential relationships that can be efficiently captured by a temporal convolutional architecture.
  arXiv  Detail & Related papers  (2023-05-29T11:08:04Z)
• Full Stack Optimization of Transformer Inference: a Survey [58.55475772110702]
  Transformer models achieve superior accuracy across a wide range of applications. The amount of compute and bandwidth required for inference of recent Transformer models is growing at a significant rate. There has been an increased focus on making Transformer models more efficient.
  arXiv  Detail & Related papers  (2023-02-27T18:18:13Z)
• CSformer: Bridging Convolution and Transformer for Compressive Sensing [65.22377493627687]
  This paper proposes a hybrid framework that integrates the advantages of leveraging detailed spatial information from CNN and the global context provided by transformer for enhanced representation learning. The proposed approach is an end-to-end compressive image sensing method, composed of adaptive sampling and recovery. The experimental results demonstrate the effectiveness of the dedicated transformer-based architecture for compressive sensing.
  arXiv  Detail & Related papers  (2021-12-31T04:37:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.