Transformers are Provably Optimal In-context Estimators for Wireless Communications

• URL: http://arxiv.org/abs/2311.00226v3
• Date: Fri, 14 Jun 2024 18:05:14 GMT
• Title: Transformers are Provably Optimal In-context Estimators for Wireless Communications
• Authors: Vishnu Teja Kunde, Vicram Rajagopalan, Chandra Shekhara Kaushik Valmeekam, Krishna Narayanan, Srinivas Shakkottai, Dileep Kalathil, Jean-Francois Chamberland,
• Abstract summary: We show that multi-layer transformers can efficiently solve in-context estimation problems. We also prove that the optimal configuration of such transformers is indeed the minimizer of the corresponding training loss.
• Score: 12.756143424752363
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Pre-trained transformers exhibit the capability of adapting to new tasks through in-context learning (ICL), where they efficiently utilize a limited set of prompts without explicit model optimization. The canonical communication problem of estimating transmitted symbols from received observations can be modelled as an in-context learning problem: Received observations are essentially a noisy function of transmitted symbols, and this function can be represented by an unknown parameter whose statistics depend on an (also unknown) latent context. This problem, which we term in-context estimation (ICE), has significantly greater complexity than the extensively studied linear regression problem. The optimal solution to the ICE problem is a non-linear function of the underlying context. In this paper, we prove that, for a subclass of such problems, a single layer softmax attention transformer (SAT) computes the optimal solution of the above estimation problem in the limit of large prompt length. We also prove that the optimal configuration of such transformer is indeed the minimizer of the corresponding training loss. Further, we empirically demonstrate the proficiency of multi-layer transformers in efficiently solving broader in-context estimation problems. Through extensive simulations, we show that solving ICE problems using transformers significantly outperforms standard approaches. Moreover, just with a few context examples, it achieves the same performance as an estimator with perfect knowledge of the latent context.

Related papers

• Provable In-Context Learning of Nonlinear Regression with Transformers [58.018629320233174]
  In-context learning (ICL) is the ability to perform unseen tasks using task-specific prompts without updating parameters.<n>Recent research has actively explored the training dynamics behind ICL.<n>This paper investigates more complex nonlinear regression tasks, aiming to uncover how transformers acquire in-context learning capabilities.
  arXiv  Detail & Related papers  (2025-07-28T00:09:28Z)
• Transformers Meet In-Context Learning: A Universal Approximation Theory [25.109347875620436]
  We develop a universal approximation theory to better understand how transformers enable in-context learning.<n>Our work sheds light on how transformers can simultaneously learn general-purpose representations and adapt dynamically to in-context examples.
  arXiv  Detail & Related papers  (2025-06-05T16:12:51Z)
• Accelerated zero-order SGD under high-order smoothness and overparameterized regime [79.85163929026146]
  We present a novel gradient-free algorithm to solve convex optimization problems. Such problems are encountered in medicine, physics, and machine learning. We provide convergence guarantees for the proposed algorithm under both types of noise.
  arXiv  Detail & Related papers  (2024-11-21T10:26:17Z)
• Training Nonlinear Transformers for Chain-of-Thought Inference: A Theoretical Generalization Analysis [82.51626700527837]
  Chain-of-shift (CoT) is an efficient method that enables the reasoning ability of large language models by augmenting the query using examples with multiple intermediate steps. We show that despite the theoretical success of CoT, it fails to provide an accurate generalization when CoT does.
  arXiv  Detail & Related papers  (2024-10-03T03:12:51Z)
• Unveiling the Statistical Foundations of Chain-of-Thought Prompting Methods [59.779795063072655]
  Chain-of-Thought (CoT) prompting and its variants have gained popularity as effective methods for solving multi-step reasoning problems. We analyze CoT prompting from a statistical estimation perspective, providing a comprehensive characterization of its sample complexity.
  arXiv  Detail & Related papers  (2024-08-25T04:07:18Z)
• Transformers are Minimax Optimal Nonparametric In-Context Learners [36.291980654891496]
  In-context learning of large language models has proven to be a surprisingly effective method of learning a new task from only a few demonstrative examples. We develop approximation and generalization error bounds for a transformer composed of a deep neural network and one linear attention layer. We show that sufficiently trained transformers can achieve -- and even improve upon -- the minimax optimal estimation risk in context.
  arXiv  Detail & Related papers  (2024-08-22T08:02:10Z)
• Does learning the right latent variables necessarily improve in-context learning? [13.828665019247444]
  Large autoregressive models like Transformers can solve tasks through in-context learning (ICL) without learning new weights. In this paper, we investigate the effect of explicitly inferring task latents. We find little discernible difference between the two; biasing towards task-relevant latent variables does not lead to better out-of-distribution performance.
  arXiv  Detail & Related papers  (2024-05-29T15:06:10Z)
• Few-Shot Class Incremental Learning via Robust Transformer Approach [16.590193619691416]
  Few-Shot Class-Incremental Learning presents an extension of the Class Incremental Learning problem where a model is faced with the problem of data scarcity. This problem remains an open problem because all recent works are built upon the convolutional neural networks performing sub-optimally. Our paper presents Robust Transformer Approach built upon the Compact Convolution Transformer.
  arXiv  Detail & Related papers  (2024-05-08T03:35:52Z)
• Linear Transformers are Versatile In-Context Learners [19.988368693379087]
  We prove that each layer of a linear transformer maintains a weight vector for an implicit linear regression problem. We also investigate the use of linear transformers in a challenging scenario where the training data is corrupted with different levels of noise. Remarkably, we demonstrate that for this problem linear transformers discover an intricate and highly effective optimization algorithm.
  arXiv  Detail & Related papers  (2024-02-21T23:45:57Z)
• Learning Optimal Power Flow Value Functions with Input-Convex Neural Networks [15.791200937436837]
  The Optimal Power Flow (OPF) problem is integral to power systems, aiming to optimize generation while adhering to dispatch constraints. This research explores machine learning (ML) to learn for faster analysis in the online setting while still allowing for coupling into other convex dependent decision problems.
  arXiv  Detail & Related papers  (2023-10-06T21:48:39Z)
• 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)
• What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization [111.55277952086155]
  We study In-Context Learning (ICL) by addressing several open questions. We show that, without updating the neural network parameters, ICL implicitly implements the Bayesian model averaging algorithm. We prove that the error of pretrained model is bounded by a sum of an approximation error and a generalization error.
  arXiv  Detail & Related papers  (2023-05-30T21:23:47Z)
• Offline Model-Based Optimization via Normalized Maximum Likelihood Estimation [101.22379613810881]
  We consider data-driven optimization problems where one must maximize a function given only queries at a fixed set of points. This problem setting emerges in many domains where function evaluation is a complex and expensive process. We propose a tractable approximation that allows us to scale our method to high-capacity neural network models.
  arXiv  Detail & Related papers  (2021-02-16T06:04:27Z)
• Consistency analysis of bilevel data-driven learning in inverse problems [1.0705399532413618]
  We consider the adaptive learning of the regularization parameter from data by means of optimization. We demonstrate how to implement our framework on linear inverse problems. Online numerical schemes are derived using the gradient descent method.
  arXiv  Detail & Related papers  (2020-07-06T12:23:29Z)
• Automatically Learning Compact Quality-aware Surrogates for Optimization Problems [55.94450542785096]
  Solving optimization problems with unknown parameters requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the optimization problem as a layer in a complex training model pipeline results in predictions of iteration of unobserved decision making. We show that we can improve solution quality by learning a low-dimensional surrogate model of a large optimization problem.
  arXiv  Detail & Related papers  (2020-06-18T19:11:54Z)
• Unsupervised Deep Learning for Optimizing Wireless Systems with Instantaneous and Statistic Constraints [29.823814915538463]
  We establish a unified framework of using unsupervised deep learning to solve both kinds of problems with both instantaneous and statistic constraints. We show that unsupervised learning outperforms supervised learning in terms of violation probability and approximation accuracy of the optimal policy.
  arXiv  Detail & Related papers  (2020-05-30T13:37:14Z)

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.