Yuanzhang Xiao

Luca Muscarnera, Silas Ruhrberg Estévez, Yuanzhang Xiao et al.

A central problem in machine learning is that models can achieve near-perfect training performance while generalizing substantially less well to unseen examples. This gap is especially acute in high-dimensional, low-sample regimes, where many interpolating solutions exist and optimization must implicitly select among minima with different generalization properties. Following recent theoretical advances on optimization dynamics near the interpolation threshold, we note that the two-regime structure of risk minimization, with loss minimization followed by complexity minimization, motivates a biphasic optimization schedule. We thus theoretically demonstrate that GROKtimizer, a biphasic strategy that combines rapid convergence to interpolation with Critically Damped Momentum (CDM)-based post-interpolation norm minimization, offers a natural solution for selecting low-norm interpolating solutions. Under a local quadratic model of the post-interpolation basin, GROKtimizer provides a quadratic speedup over classical gradient descent, with provable optimality among first-order optimizers. To showcase the applicability of our method, we evaluate GROKtimizer on several synthetic benchmarks common in the classical grokking literature and on various real-world datasets. Finally, we reconcile our findings with the flat-minima hypothesis, highlighting the importance of post-interpolation dynamics in the construction of high-quality, generalizing models.

Mengzhe Ruan, Guangfeng Yan, Yuanzhang Xiao et al.

Distributed stochastic gradient descent (SGD) with gradient compression has become a popular communication-efficient solution for accelerating distributed learning. One commonly used method for gradient compression is Top-K sparsification, which sparsifies the gradients by a fixed degree during model training. However, there has been a lack of an adaptive approach to adjust the sparsification degree to maximize the potential of the model's performance or training speed. This paper proposes a novel adaptive Top-K in SGD framework that enables an adaptive degree of sparsification for each gradient descent step to optimize the convergence performance by balancing the trade-off between communication cost and convergence error. Firstly, an upper bound of convergence error is derived for the adaptive sparsification scheme and the loss function. Secondly, an algorithm is designed to minimize the convergence error under the communication cost constraints. Finally, numerical results on the MNIST and CIFAR-10 datasets demonstrate that the proposed adaptive Top-K algorithm in SGD achieves a significantly better convergence rate compared to state-of-the-art methods, even after considering error compensation.

Nicolás Astorga, Tennison Liu, Yuanzhang Xiao et al.

Mathematical optimization is fundamental to decision-making across diverse domains, from operations research to healthcare. Yet, translating real-world problems into optimization models remains a difficult task, often demanding specialized expertise. This paper approaches the problem of $\textit{autoformulation}$: the automated creation of solver-ready optimization models from natural language problem descriptions. We identify three core challenges of autoformulation: $\textit{(1)}$ the vast, problem-dependent hypothesis space, $\textit{(2)}$ efficient and diverse exploration of this space under uncertainty, and $\textit{(3)}$ evaluation of formulation correctness against problem description. To address these challenges, we present a novel method leveraging $\textit{Large Language Models}$ (LLMs) with $\textit{Monte-Carlo Tree Search}$, exploiting the hierarchical nature of optimization modeling to generate and systematically explore possible formulations. To enhance search efficiency, we introduce symbolic pruning to eliminate trivially equivalent search paths (branches), and employ LLM-based evaluation of partial formulations to guide search. Empirical analysis on linear and mixed-integer programming benchmarks demonstrates our method's effectiveness, with significant performance gains from both LLM-based value estimation and symbolic pruning techniques.

Guangfeng Yan, Tan Li, Yuanzhang Xiao et al.

Gradient compression has surfaced as a key technique to address the challenge of communication efficiency in distributed learning. In distributed deep learning, however, it is observed that gradient distributions are heavy-tailed, with outliers significantly influencing the design of compression strategies. Existing parameter quantization methods experience performance degradation when this heavy-tailed feature is ignored. In this paper, we introduce a novel compression scheme specifically engineered for heavy-tailed gradients, which effectively combines gradient truncation with quantization. This scheme is adeptly implemented within a communication-limited distributed Stochastic Gradient Descent (SGD) framework. We consider a general family of heavy-tail gradients that follow a power-law distribution, we aim to minimize the error resulting from quantization, thereby determining optimal values for two critical parameters: the truncation threshold and the quantization density. We provide a theoretical analysis on the convergence error bound under both uniform and non-uniform quantization scenarios. Comparative experiments with other benchmarks demonstrate the effectiveness of our proposed method in managing the heavy-tailed gradients in a distributed learning environment.

Guangfeng Yan, Tan Li, Yuanzhang Xiao et al.

To address the communication bottleneck challenge in distributed learning, our work introduces a novel two-stage quantization strategy designed to enhance the communication efficiency of distributed Stochastic Gradient Descent (SGD). The proposed method initially employs truncation to mitigate the impact of long-tail noise, followed by a non-uniform quantization of the post-truncation gradients based on their statistical characteristics. We provide a comprehensive convergence analysis of the quantized distributed SGD, establishing theoretical guarantees for its performance. Furthermore, by minimizing the convergence error, we derive optimal closed-form solutions for the truncation threshold and non-uniform quantization levels under given communication constraints. Both theoretical insights and extensive experimental evaluations demonstrate that our proposed algorithm outperforms existing quantization schemes, striking a superior balance between communication efficiency and convergence performance.

Jie Xu, Yiannis Andrepoulos, Yuanzhang Xiao et al.

Due to the high bandwidth requirements and stringent delay constraints of multi-user wireless video transmission applications, ensuring that all video senders have sufficient transmission opportunities to use before their delay deadlines expire is a longstanding research problem. We propose a novel solution that addresses this problem without assuming detailed packet-level knowledge, which is unavailable at resource allocation time. Instead, we translate the transmission delay deadlines of each sender's video packets into a monotonically-decreasing weight distribution within the considered time horizon. Higher weights are assigned to the slots that have higher probability for deadline-abiding delivery. Given the sets of weights of the senders' video streams, we propose the low-complexity Delay-Aware Resource Allocation (DARA) approach to compute the optimal slot allocation policy that maximizes the deadline-abiding delivery of all senders. A unique characteristic of the DARA approach is that it yields a non-stationary slot allocation policy that depends on the allocation of previous slots. We prove that the DARA approach is optimal for weight distributions that are exponentially decreasing in time. We further implement our framework for real-time video streaming in wireless personal area networks that are gaining significant traction within the new Internet-of-Things (IoT) paradigm. For multiple surveillance videos encoded with H.264/AVC and streamed via the 6tisch framework that simulates the IoT-oriented IEEE 802.15.4e TSCH medium access control, our solution is shown to be the only one that ensures all video bitstreams are delivered with acceptable quality in a deadline-abiding manner.

Yuanzhang Xiao, Mihaela van der Schaar

Recent years have seen an explosion in wireless video communication systems. Optimization in such systems is crucial - but most existing methods intended to optimize the performance of multi-user wireless video transmission are inefficient. Some works (e.g. Network Utility Maximization (NUM)) are myopic: they choose actions to maximize instantaneous video quality while ignoring the future impact of these actions. Such myopic solutions are known to be inferior to foresighted solutions that optimize the long-term video quality. Alternatively, foresighted solutions such as rate-distortion optimized packet scheduling focus on single-user wireless video transmission, while ignoring the resource allocation among the users. In this paper, we propose an optimal solution for performing joint foresighted resource allocation and packet scheduling among multiple users transmitting video over a shared wireless network. A key challenge in developing foresighted solutions for multiple video users is that the users' decisions are coupled. To decouple the users' decisions, we adopt a novel dual decomposition approach, which differs from the conventional optimization solutions such as NUM, and determines foresighted policies. Specifically, we propose an informationally-decentralized algorithm in which the network manager updates resource "prices" (i.e. the dual variables associated with the resource constraints), and the users make individual video packet scheduling decisions based on these prices. Because a priori knowledge of the system dynamics is almost never available at run-time, the proposed solution can learn online, concurrently with performing the foresighted optimization. Simulation results show 7 dB and 3 dB improvements in Peak Signal-to-Noise Ratio (PSNR) over myopic solutions and existing foresighted solutions, respectively.