Fine-grained Analysis of In-context Linear Estimation: Data, Architecture, and Beyond

• URL: http://arxiv.org/abs/2407.10005v1
• Date: Sat, 13 Jul 2024 21:13:55 GMT
• Title: Fine-grained Analysis of In-context Linear Estimation: Data, Architecture, and Beyond
• Authors: Yingcong Li, Ankit Singh Rawat, Samet Oymak,
• Abstract summary: Transformers with linear attention are capable of in-context learning (ICL) by implementing a linear gradient estimator through descent steps. We develop a stronger characterization of the optimization and generalization landscape of ICL through contributions on architectures, low-rank parameterization, and correlated designs.
• Score: 44.154393889313724
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent research has shown that Transformers with linear attention are capable of in-context learning (ICL) by implementing a linear estimator through gradient descent steps. However, the existing results on the optimization landscape apply under stylized settings where task and feature vectors are assumed to be IID and the attention weights are fully parameterized. In this work, we develop a stronger characterization of the optimization and generalization landscape of ICL through contributions on architectures, low-rank parameterization, and correlated designs: (1) We study the landscape of 1-layer linear attention and 1-layer H3, a state-space model. Under a suitable correlated design assumption, we prove that both implement 1-step preconditioned gradient descent. We show that thanks to its native convolution filters, H3 also has the advantage of implementing sample weighting and outperforming linear attention in suitable settings. (2) By studying correlated designs, we provide new risk bounds for retrieval augmented generation (RAG) and task-feature alignment which reveal how ICL sample complexity benefits from distributional alignment. (3) We derive the optimal risk for low-rank parameterized attention weights in terms of covariance spectrum. Through this, we also shed light on how LoRA can adapt to a new distribution by capturing the shift between task covariances. Experimental results corroborate our theoretical findings. Overall, this work explores the optimization and risk landscape of ICL in practically meaningful settings and contributes to a more thorough understanding of its mechanics.

Related papers

• DOA: A Degeneracy Optimization Agent with Adaptive Pose Compensation Capability based on Deep Reinforcement Learning [8.895924836025666]
  Long straight corridors can cause severe degeneracy problems in 2D-SLAM.<n>In this paper, we use Proximal Policy Optimization to train an adaptive degeneracy optimization agent.
  arXiv  Detail & Related papers  (2025-07-26T02:22:54Z)
• An In-depth Investigation of Sparse Rate Reduction in Transformer-like Models [32.04194224236952]
  We propose an information-theoretic objective function called Sparse Rate Reduction (SRR) We show that SRR has a positive correlation coefficient and outperforms other baseline measures, such as path-norm and sharpness-based ones. We show that generalization can be improved using SRR as regularization on benchmark image classification datasets.
  arXiv  Detail & Related papers  (2024-11-26T07:44:57Z)
• Exploring End-to-end Differentiable Neural Charged Particle Tracking -- A Loss Landscape Perspective [0.0]
  We propose an E2E differentiable decision-focused learning scheme for particle tracking. We show that differentiable variations of discrete assignment operations allows for efficient network optimization. We argue that E2E differentiability provides, besides the general availability of gradient information, an important tool for robust particle tracking to mitigate prediction instabilities.
  arXiv  Detail & Related papers  (2024-07-18T11:42:58Z)
• Hallmarks of Optimization Trajectories in Neural Networks: Directional Exploration and Redundancy [75.15685966213832]
  We analyze the rich directional structure of optimization trajectories represented by their pointwise parameters. We show that training only scalar batchnorm parameters some while into training matches the performance of training the entire network.
  arXiv  Detail & Related papers  (2024-03-12T07:32:47Z)
• A Closer Look at the Few-Shot Adaptation of Large Vision-Language Models [19.17722702457403]
  We show that state-of-the-artETL approaches exhibit strong performance only in narrowly-defined experimental setups. We propose a CLass-Adaptive linear Probe (CLAP) objective, whose balancing term is optimized via an adaptation of the general Augmented Lagrangian method.
  arXiv  Detail & Related papers  (2023-12-20T02:58:25Z)
• PARL: A Unified Framework for Policy Alignment in Reinforcement Learning from Human Feedback [106.63518036538163]
  We present a novel unified bilevel optimization-based framework, textsfPARL, formulated to address the recently highlighted critical issue of policy alignment in reinforcement learning. Our framework addressed these concerns by explicitly parameterizing the distribution of the upper alignment objective (reward design) by the lower optimal variable. Our empirical results substantiate that the proposed textsfPARL can address the alignment concerns in RL by showing significant improvements.
  arXiv  Detail & Related papers  (2023-08-03T18:03:44Z)
• Understanding Augmentation-based Self-Supervised Representation Learning via RKHS Approximation and Regression [53.15502562048627]
  Recent work has built the connection between self-supervised learning and the approximation of the top eigenspace of a graph Laplacian operator. This work delves into a statistical analysis of augmentation-based pretraining.
  arXiv  Detail & Related papers  (2023-06-01T15:18:55Z)
• Maximize to Explore: One Objective Function Fusing Estimation, Planning, and Exploration [87.53543137162488]
  We propose an easy-to-implement online reinforcement learning (online RL) framework called textttMEX. textttMEX integrates estimation and planning components while balancing exploration exploitation automatically. It can outperform baselines by a stable margin in various MuJoCo environments with sparse rewards.
  arXiv  Detail & Related papers  (2023-05-29T17:25:26Z)
• Low-Pass Filtering SGD for Recovering Flat Optima in the Deep Learning Optimization Landscape [15.362190838843915]
  We show that LPF-SGD converges to a better optimal point with smaller generalization error than SGD. We show that our algorithm achieves superior generalization performance compared to the common DL training strategies.
  arXiv  Detail & Related papers  (2022-01-20T07:13:04Z)
• Target-Embedding Autoencoders for Supervised Representation Learning [111.07204912245841]
  This paper analyzes a framework for improving generalization in a purely supervised setting, where the target space is high-dimensional. We motivate and formalize the general framework of target-embedding autoencoders (TEA) for supervised prediction, learning intermediate latent representations jointly optimized to be both predictable from features as well as predictive of targets.
  arXiv  Detail & Related papers  (2020-01-23T02:37:10Z)

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.