Xiaojun Lin

Hao Wang, Jianwei Huang, Xiaojun Lin et al.

In order to reduce the energy cost of data centers, recent studies suggest distributing computation workload among multiple geographically dispersed data centers, by exploiting the electricity price difference. However, the impact of data center load redistribution on the power grid is not well understood yet. This paper takes the first step towards tackling this important issue, by studying how the power grid can take advantage of the data centers' load distribution proactively for the purpose of power load balancing. We model the interactions between power grid and data centers as a two-stage problem, where the utility company chooses proper pricing mechanisms to balance the electric power load in the first stage, and the data centers seek to minimize their total energy cost by responding to the prices in the second stage. We show that the two-stage problem is a bilevel quadratic program, which is NP-hard and cannot be solved using standard convex optimization techniques. We introduce benchmark problems to derive upper and lower bounds for the solution of the two-stage problem. We further propose a branch and bound algorithm to attain the globally optimal solution, and propose a heuristic algorithm with low computational complexity to obtain an alternative close-to-optimal solution. We also study the impact of background load prediction error using the theoretical framework of robust optimization. The simulation results demonstrate that our proposed scheme can not only improve the power grid reliability but also reduce the energy cost of data centers.

Peizhong Ju, Xiaojun Lin, Ness B. Shroff

In this paper, we study the generalization performance of overparameterized 3-layer NTK models. We show that, for a specific set of ground-truth functions (which we refer to as the "learnable set"), the test error of the overfitted 3-layer NTK is upper bounded by an expression that decreases with the number of neurons of the two hidden layers. Different from 2-layer NTK where there exists only one hidden-layer, the 3-layer NTK involves interactions between two hidden-layers. Our upper bound reveals that, between the two hidden-layers, the test error descends faster with respect to the number of neurons in the second hidden-layer (the one closer to the output) than with respect to that in the first hidden-layer (the one closer to the input). We also show that the learnable set of 3-layer NTK without bias is no smaller than that of 2-layer NTK models with various choices of bias in the neurons. However, in terms of the actual generalization performance, our results suggest that 3-layer NTK is much less sensitive to the choices of bias than 2-layer NTK, especially when the input dimension is large.

Ruiqi Kong, He Chen, Xiaojun Lin

To make cross-band channel prediction practical for AI-native RAN, algorithms must generalize across diverse environments and support real-time inference. Existing approaches achieve one but not both. To bridge this gap, we introduce GUIDE, a physics-guided deep unfolding framework that embeds wireless channel physics into differentiable layers. Without retraining in unseen environments, GUIDE achieves 2.75x beamforming gain than the deep learning-based baseline FIRE with only a slight increase in inference time, and 1.39x beamforming gain than the strongest model-based baseline R2F2 while running over 1610x faster.

Liren Yu, Jiaming Xu, Xiaojun Lin

There is a growing interest in designing Graph Neural Networks (GNNs) for seeded graph matching, which aims to match two unlabeled graphs using only topological information and a small set of seed nodes. However, most previous GNNs for this task use a semi-supervised approach, which requires a large number of seeds and cannot learn knowledge that is transferable to unseen graphs. In contrast, this paper proposes a new supervised approach that can learn from a training set how to match unseen graphs with only a few seeds. Our SeedGNN architecture incorporates several novel designs, inspired by theoretical studies of seeded graph matching: 1) it can learn to compute and use witness-like information from different hops, in a way that can be generalized to graphs of different sizes; 2) it can use easily-matched node-pairs as new seeds to improve the matching in subsequent layers. We evaluate SeedGNN on synthetic and real-world graphs and demonstrate significant performance improvements over both non-learning and learning algorithms in the existing literature. Furthermore, our experiments confirm that the knowledge learned by SeedGNN from training graphs can be generalized to test graphs of different sizes and categories.

Ting Yu, Xiaojun Lin, Shuhui Wang et al.

Three-Dimensional (3D) dense captioning is an emerging vision-language bridging task that aims to generate multiple detailed and accurate descriptions for 3D scenes. It presents significant potential and challenges due to its closer representation of the real world compared to 2D visual captioning, as well as complexities in data collection and processing of 3D point cloud sources. Despite the popularity and success of existing methods, there is a lack of comprehensive surveys summarizing the advancements in this field, which hinders its progress. In this paper, we provide a comprehensive review of 3D dense captioning, covering task definition, architecture classification, dataset analysis, evaluation metrics, and in-depth prosperity discussions. Based on a synthesis of previous literature, we refine a standard pipeline that serves as a common paradigm for existing methods. We also introduce a clear taxonomy of existing models, summarize technologies involved in different modules, and conduct detailed experiment analysis. Instead of a chronological order introduction, we categorize the methods into different classes to facilitate exploration and analysis of the differences and connections among existing techniques. We also provide a reading guideline to assist readers with different backgrounds and purposes in reading efficiently. Furthermore, we propose a series of promising future directions for 3D dense captioning by identifying challenges and aligning them with the development of related tasks, offering valuable insights and inspiring future research in this field. Our aim is to provide a comprehensive understanding of 3D dense captioning, foster further investigations, and contribute to the development of novel applications in multimedia and related domains.

Saptarshi Mandal, Xiaojun Lin, R. Srikant

Knowledge distillation, where a small student model learns from a pre-trained large teacher model, has achieved substantial empirical success since the seminal work of \citep{hinton2015distilling}. Despite prior theoretical studies exploring the benefits of knowledge distillation, an important question remains unanswered: why does soft-label training from the teacher require significantly fewer neurons than directly training a small neural network with hard labels? To address this, we first present motivating experimental results using simple neural network models on a binary classification problem. These results demonstrate that soft-label training consistently outperforms hard-label training in accuracy, with the performance gap becoming more pronounced as the dataset becomes increasingly difficult to classify. We then substantiate these observations with a theoretical contribution based on two-layer neural network models. Specifically, we show that soft-label training using gradient descent requires only $O\left(\frac{1}{γ^2 ε}\right)$ neurons to achieve a classification loss averaged over epochs smaller than some $ε> 0$, where $γ$ is the separation margin of the limiting kernel. In contrast, hard-label training requires $O\left(\frac{1}{γ^4} \cdot \ln\left(\frac{1}ε\right)\right)$ neurons, as derived from an adapted version of the gradient descent analysis in \citep{ji2020polylogarithmic}. This implies that when $γ\leq ε$, i.e., when the dataset is challenging to classify, the neuron requirement for soft-label training can be significantly lower than that for hard-label training. Finally, we present experimental results on deep neural networks, further validating these theoretical findings.

Ajinkya Kiran Mulay, Xiaojun Lin

Sparse basis recovery is a classical and important statistical learning problem when the number of model dimensions $p$ is much larger than the number of samples $n$. However, there has been little work that studies sparse basis recovery in the Federated Learning (FL) setting, where the client data's differential privacy (DP) must also be simultaneously protected. In particular, the performance guarantees of existing DP-FL algorithms (such as DP-SGD) will degrade significantly when $p \gg n$, and thus, they will fail to learn the true underlying sparse model accurately. In this work, we develop a new differentially private sparse basis recovery algorithm for the FL setting, called SPriFed-OMP. SPriFed-OMP converts OMP (Orthogonal Matching Pursuit) to the FL setting. Further, it combines SMPC (secure multi-party computation) and DP to ensure that only a small amount of noise needs to be added in order to achieve differential privacy. As a result, SPriFed-OMP can efficiently recover the true sparse basis for a linear model with only $n = O(\sqrt{p})$ samples. We further present an enhanced version of our approach, SPriFed-OMP-GRAD based on gradient privatization, that improves the performance of SPriFed-OMP. Our theoretical analysis and empirical results demonstrate that both SPriFed-OMP and SPriFed-OMP-GRAD terminate in a small number of steps, and they significantly outperform the previous state-of-the-art DP-FL solutions in terms of the accuracy-privacy trade-off.

Linghan Zheng, Hui Liu, Xiaojun Lin et al.

In previous studies, code-based models have consistently outperformed text-based models in reasoning-intensive scenarios. When generating our knowledge base for Retrieval-Augmented Generation (RAG), we observed that code-based models also perform exceptionally well in Chinese QA Pair Extraction task. Further, our experiments and the metrics we designed discovered that code-based models containing a certain amount of Chinese data achieve even better performance. Additionally, the capabilities of code-based English models in specified Chinese tasks offer a distinct perspective for discussion on the philosophical "Chinese Room" thought experiment.

Guanzhe Hong, Zhiyuan Mao, Xiaojun Lin et al.

Feature-based student-teacher learning, a training method that encourages the student's hidden features to mimic those of the teacher network, is empirically successful in transferring the knowledge from a pre-trained teacher network to the student network. Furthermore, recent empirical results demonstrate that, the teacher's features can boost the student network's generalization even when the student's input sample is corrupted by noise. However, there is a lack of theoretical insights into why and when this method of transferring knowledge can be successful between such heterogeneous tasks. We analyze this method theoretically using deep linear networks, and experimentally using nonlinear networks. We identify three vital factors to the success of the method: (1) whether the student is trained to zero training loss; (2) how knowledgeable the teacher is on the clean-input problem; (3) how the teacher decomposes its knowledge in its hidden features. Lack of proper control in any of the three factors leads to failure of the student-teacher learning method.

Peizhong Ju, Xiaojun Lin, Ness B. Shroff

In this paper, we study the generalization performance of min $\ell_2$-norm overfitting solutions for the neural tangent kernel (NTK) model of a two-layer neural network with ReLU activation that has no bias term. We show that, depending on the ground-truth function, the test error of overfitted NTK models exhibits characteristics that are different from the "double-descent" of other overparameterized linear models with simple Fourier or Gaussian features. Specifically, for a class of learnable functions, we provide a new upper bound of the generalization error that approaches a small limiting value, even when the number of neurons $p$ approaches infinity. This limiting value further decreases with the number of training samples $n$. For functions outside of this class, we provide a lower bound on the generalization error that does not diminish to zero even when $n$ and $p$ are both large.

Liren Yu, Jiaming Xu, Xiaojun Lin

This paper studies seeded graph matching for power-law graphs. Assume that two edge-correlated graphs are independently edge-sampled from a common parent graph with a power-law degree distribution. A set of correctly matched vertex-pairs is chosen at random and revealed as initial seeds. Our goal is to use the seeds to recover the remaining latent vertex correspondence between the two graphs. Departing from the existing approaches that focus on the use of high-degree seeds in $1$-hop neighborhoods, we develop an efficient algorithm that exploits the low-degree seeds in suitably-defined $D$-hop neighborhoods. Specifically, we first match a set of vertex-pairs with appropriate degrees (which we refer to as the first slice) based on the number of low-degree seeds in their $D$-hop neighborhoods. This significantly reduces the number of initial seeds needed to trigger a cascading process to match the rest of the graphs. Under the Chung-Lu random graph model with $n$ vertices, max degree $Θ(\sqrt{n})$, and the power-law exponent $2<β<3$, we show that as soon as $D> \frac{4-β}{3-β}$, by optimally choosing the first slice, with high probability our algorithm can correctly match a constant fraction of the true pairs without any error, provided with only $Ω((\log n)^{4-β})$ initial seeds. Our result achieves an exponential reduction in the seed size requirement, as the best previously known result requires $n^{1/2+ε}$ seeds (for any small constant $ε>0$). Performance evaluation with synthetic and real data further corroborates the improved performance of our algorithm.

Liren Yu, Jiaming Xu, Xiaojun Lin

Graph matching aims to find the latent vertex correspondence between two edge-correlated graphs and has found numerous applications across different fields. In this paper, we study a seeded graph matching problem, which assumes that a set of seeds, i.e., pre-mapped vertex-pairs, is given in advance. While most previous work requires all seeds to be correct, we focus on the setting where the seeds are partially correct. Specifically, consider two correlated graphs whose edges are sampled independently from a parent \ER graph $\mathcal{G}(n,p)$. A mapping between the vertices of the two graphs is provided as seeds, of which an unknown $β$ fraction is correct. We first analyze a simple algorithm that matches vertices based on the number of common seeds in the $1$-hop neighborhoods, and then further propose a new algorithm that uses seeds in the $2$-hop neighborhoods. We establish non-asymptotic performance guarantees of perfect matching for both $1$-hop and $2$-hop algorithms, showing that our new $2$-hop algorithm requires substantially fewer correct seeds than the $1$-hop algorithm when graphs are sparse. Moreover, by combining our new performance guarantees for the $1$-hop and $2$-hop algorithms, we attain the best-known results (in terms of the required fraction of correct seeds) across the entire range of graph sparsity and significantly improve the previous results in \cite{10.14778/2794367.2794371,lubars2018correcting} when $p\ge n^{-5/6}$. For instance, when $p$ is a constant or $p=n^{-3/4}$, we show that only $Ω(\sqrt{n\log n})$ correct seeds suffice for perfect matching, while the previously best-known results demand $Ω(n)$ and $Ω(n^{3/4}\log n)$ correct seeds, respectively. Numerical experiments corroborate our theoretical findings, demonstrating the superiority of our $2$-hop algorithm on a variety of synthetic and real graphs.

Peizhong Ju, Xiaojun Lin, Jia Liu

Recently, there have been significant interests in studying the so-called "double-descent" of the generalization error of linear regression models under the overparameterized and overfitting regime, with the hope that such analysis may provide the first step towards understanding why overparameterized deep neural networks (DNN) still generalize well. However, to date most of these studies focused on the min $\ell_2$-norm solution that overfits the data. In contrast, in this paper we study the overfitting solution that minimizes the $\ell_1$-norm, which is known as Basis Pursuit (BP) in the compressed sensing literature. Under a sparse true linear regression model with $p$ i.i.d. Gaussian features, we show that for a large range of $p$ up to a limit that grows exponentially with the number of samples $n$, with high probability the model error of BP is upper bounded by a value that decreases with $p$. To the best of our knowledge, this is the first analytical result in the literature establishing the double-descent of overfitting BP for finite $n$ and $p$. Further, our results reveal significant differences between the double-descent of BP and min $\ell_2$-norm solutions. Specifically, the double-descent upper-bound of BP is independent of the signal strength, and for high SNR and sparse models the descent-floor of BP can be much lower and wider than that of min $\ell_2$-norm solutions.