Towards Theoretical Understanding of Transformer Test-Time Computing: Investigation on In-Context Linear Regression

Using more test-time computation during language model inference, such as generating more intermediate thoughts or sampling multiple candidate answers, has proven effective in significantly improving model performance. This paper takes an initial step toward bridging the gap between practical language model inference and theoretical transformer analysis by incorporating randomness and sampling. We focus on in-context linear regression with continuous/binary coefficients, where our framework simulates language model decoding through noise injection and binary coefficient sampling. Through this framework, we provide detailed analyses of widely adopted inference techniques. Supported by empirical results, our theoretical framework and analysis demonstrate the potential for offering new insights into understanding inference behaviors in real-world language models.

Enhancing Vehicular Platooning with Wireless Federated Learning: A Resource-Aware Control Framework

This paper aims to enhance the performance of Vehicular Platooning (VP) systems integrated with Wireless Federated Learning (WFL). In highly dynamic environments, vehicular platoons experience frequent communication changes and resource constraints, which significantly affect information exchange and learning model synchronization. To address these challenges, we first formulate WFL in VP as a joint optimization problem that simultaneously considers Age of Information (AoI) and Federated Learning Model Drift (FLMD) to ensure timely and accurate control. Through theoretical analysis, we examine the impact of FLMD on convergence performance and develop a two-stage Resource-Aware Control framework (RACE). The first stage employs a Lagrangian dual decomposition method for resource configuration, while the second stage implements a multi-agent deep reinforcement learning approach for vehicle selection. The approach integrates Multi-Head Self-Attention and Long Short-Term Memory networks to capture spatiotemporal correlations in communication states. Experimental results demonstrate that, compared to baseline methods, the proposed framework improves AoI optimization by up to 45%, accelerates learning convergence, and adapts more effectively to dynamic VP environments on the AI4MARS dataset.

Benign Oscillation of Stochastic Gradient Descent with Large Learning Rates

In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) algorithm with large learning rates. Under such a training regime, our finding is that, the oscillation of the NN weights caused by the large learning rate SGD training turns out to be beneficial to the generalization of the NN, which potentially improves over the same NN trained by SGD with small learning rates that converges more smoothly. In view of this finding, we call such a phenomenon "benign oscillation". Our theory towards demystifying such a phenomenon builds upon the feature learning perspective of deep learning. Specifically, we consider a feature-noise data generation model that consists of (i) weak features which have a small $\ell_2$-norm and appear in each data point; (ii) strong features which have a larger $\ell_2$-norm but only appear in a certain fraction of all data points; and (iii) noise. We prove that NNs trained by oscillating SGD with a large learning rate can effectively learn the weak features in the presence of those strong features. In contrast, NNs trained by SGD with a small learning rate can only learn the strong features but makes little progress in learning the weak features. Consequently, when it comes to the new testing data which consist of only weak features, the NN trained by oscillating SGD with a large learning rate could still make correct predictions consistently, while the NN trained by small learning rate SGD fails. Our theory sheds light on how large learning rate training benefits the generalization of NNs. Experimental results demonstrate our finding on "benign oscillation".