Zhichao Wang

Zhichao Wang, Andrew Engel, Anand Sarwate et al.

We investigate the spectral properties of linear-width feed-forward neural networks, where the sample size is asymptotically proportional to network width. Empirically, we show that the spectra of weight in this high dimensional regime are invariant when trained by gradient descent for small constant learning rates; we provide a theoretical justification for this observation and prove the invariance of the bulk spectra for both conjugate and neural tangent kernels. We demonstrate similar characteristics when training with stochastic gradient descent with small learning rates. When the learning rate is large, we exhibit the emergence of an outlier whose corresponding eigenvector is aligned with the training data structure. We also show that after adaptive gradient training, where a lower test error and feature learning emerge, both weight and kernel matrices exhibit heavy tail behavior. Simple examples are provided to explain when heavy tails can have better generalizations. We exhibit different spectral properties such as invariant bulk, spike, and heavy-tailed distribution from a two-layer neural network using different training strategies, and then correlate them to the feature learning. Analogous phenomena also appear when we train conventional neural networks with real-world data. We conclude that monitoring the evolution of the spectra during training is an essential step toward understanding the training dynamics and feature learning.

Lin Wang, Zhichao Wang, Ye Shi et al.

Federated Learning (FL) enables collaborative model training across distributed devices while preserving data privacy. Nonetheless, the heterogeneity of edge devices often leads to inconsistent performance of the globally trained models, resulting in unfair outcomes among users. Existing federated fairness algorithms strive to enhance fairness but often fall short in maintaining the overall performance of the global model, typically measured by the average accuracy across all clients. To address this issue, we propose a novel algorithm that leverages entropy-based aggregation combined with model and gradient alignments to simultaneously optimize fairness and global model performance. Our method employs a bi-level optimization framework, where we derive an analytic solution to the aggregation probability in the inner loop, making the optimization process computationally efficient. Additionally, we introduce an innovative alignment update and an adaptive strategy in the outer loop to further balance global model's performance and fairness. Theoretical analysis indicates that our approach guarantees convergence even in non-convex FL settings and demonstrates significant fairness improvements in generalized regression and strongly convex models. Empirically, our approach surpasses state-of-the-art federated fairness algorithms, ensuring consistent performance among clients while improving the overall performance of the global model.

Zhichao Wang, Bin Bi, Can Huang et al.

An LLM is pretrained on trillions of tokens, but the pretrained LLM may still generate undesired responses. To solve this problem, alignment techniques such as RLHF, DPO and KTO are proposed. However, these alignment techniques have limitations. For example, RLHF requires training the reward model and policy separately, which is complex, time-consuming, memory intensive and unstable during training processes. DPO proposes a mapping between an optimal policy and a reward, greatly simplifying the training process of RLHF. However, it can not take full advantages of a reward model and it is limited to pairwise preference data. In this paper, we propose \textbf{UN}ified \textbf{A}lignment (UNA) which unifies RLHF/PPO, DPO and KTO. Firstly, we mathematically prove that given the classical RLHF objective, the optimal policy is induced by a generalize implicit reward function. With this novel mapping between a reward model and an optimal policy, UNA can 1. unify RLHF/PPO, DPO and KTO into a supervised learning of minimizing the difference between an implicit reward and an explicit reward; 2. outperform RLHF/PPO while simplify, stabilize, speed up and reduce memory burden of RL fine-tuning process; 3. accommodate different feedback types including pairwise, binary and scalar feedback. Downstream experiments show UNA outperforms DPO, KTO and RLHF.

Zhichao Wang, Yizhe Zhu

We investigate the properties of random feature ridge regression (RFRR) given by a two-layer neural network with random Gaussian initialization. We study the non-asymptotic behaviors of the RFRR with nearly orthogonal deterministic unit-length input data vectors in the overparameterized regime, where the width of the first layer is much larger than the sample size. Our analysis shows high-probability non-asymptotic concentration results for the training errors, cross-validations, and generalization errors of RFRR centered around their respective values for a kernel ridge regression (KRR). This KRR is derived from an expected kernel generated by a nonlinear random feature map. We then approximate the performance of the KRR by a polynomial kernel matrix obtained from the Hermite polynomial expansion of the activation function, whose degree only depends on the orthogonality among different data points. This polynomial kernel determines the asymptotic behavior of the RFRR and the KRR. Our results hold for a wide variety of activation functions and input data sets that exhibit nearly orthogonal properties. Based on these approximations, we obtain a lower bound for the generalization error of the RFRR for a nonlinear student-teacher model.

Zhichao Wang, Xinhai Chen, Junjun Yan et al.

In CFD, mesh smoothing methods are commonly utilized to refine the mesh quality to achieve high-precision numerical simulations. Specifically, optimization-based smoothing is used for high-quality mesh smoothing, but it incurs significant computational overhead. Pioneer works improve its smoothing efficiency by adopting supervised learning to learn smoothing methods from high-quality meshes. However, they pose difficulty in smoothing the mesh nodes with varying degrees and also need data augmentation to address the node input sequence problem. Additionally, the required labeled high-quality meshes further limit the applicability of the proposed method. In this paper, we present GMSNet, a lightweight neural network model for intelligent mesh smoothing. GMSNet adopts graph neural networks to extract features of the node's neighbors and output the optimal node position. During smoothing, we also introduce a fault-tolerance mechanism to prevent GMSNet from generating negative volume elements. With a lightweight model, GMSNet can effectively smoothing mesh nodes with varying degrees and remain unaffected by the order of input data. A novel loss function, MetricLoss, is also developed to eliminate the need for high-quality meshes, which provides a stable and rapid convergence during training. We compare GMSNet with commonly used mesh smoothing methods on two-dimensional triangle meshes. The experimental results show that GMSNet achieves outstanding mesh smoothing performances with 5% model parameters of the previous model, and attains 13.56 times faster than optimization-based smoothing.

Lin Wang, Zhichao Wang, Xi Leng et al.

Preserving privacy and reducing communication costs for edge users pose significant challenges in recommendation systems. Although federated learning has proven effective in protecting privacy by avoiding data exchange between clients and servers, it has been shown that the server can infer user ratings based on updated non-zero gradients obtained from two consecutive rounds of user-uploaded gradients. Moreover, federated recommendation systems (FRS) face the challenge of heterogeneity, leading to decreased recommendation performance. In this paper, we propose FedRec+, an ensemble framework for FRS that enhances privacy while addressing the heterogeneity challenge. FedRec+ employs optimal subset selection based on feature similarity to generate near-optimal virtual ratings for pseudo items, utilizing only the user's local information. This approach reduces noise without incurring additional communication costs. Furthermore, we utilize the Wasserstein distance to estimate the heterogeneity and contribution of each client, and derive optimal aggregation weights by solving a defined optimization problem. Experimental results demonstrate the state-of-the-art performance of FedRec+ across various reference datasets.

Andrew Engel, Zhichao Wang, Natalie S. Frank et al.

A recent trend in explainable AI research has focused on surrogate modeling, where neural networks are approximated as simpler ML algorithms such as kernel machines. A second trend has been to utilize kernel functions in various explain-by-example or data attribution tasks. In this work, we combine these two trends to analyze approximate empirical neural tangent kernels (eNTK) for data attribution. Approximation is critical for eNTK analysis due to the high computational cost to compute the eNTK. We define new approximate eNTK and perform novel analysis on how well the resulting kernel machine surrogate models correlate with the underlying neural network. We introduce two new random projection variants of approximate eNTK which allow users to tune the time and memory complexity of their calculation. We conclude that kernel machines using approximate neural tangent kernel as the kernel function are effective surrogate models, with the introduced trace NTK the most consistent performer. Open source software allowing users to efficiently calculate kernel functions in the PyTorch framework is available (https://github.com/pnnl/projection\_ntk).

Zhichao Wang, Denny Wu, Zhou Fan

Many recent works have studied the eigenvalue spectrum of the Conjugate Kernel (CK) defined by the nonlinear feature map of a feedforward neural network. However, existing results only establish weak convergence of the empirical eigenvalue distribution, and fall short of providing precise quantitative characterizations of the ''spike'' eigenvalues and eigenvectors that often capture the low-dimensional signal structure of the learning problem. In this work, we characterize these signal eigenvalues and eigenvectors for a nonlinear version of the spiked covariance model, including the CK as a special case. Using this general result, we give a quantitative description of how spiked eigenstructure in the input data propagates through the hidden layers of a neural network with random weights. As a second application, we study a simple regime of representation learning where the weight matrix develops a rank-one signal component over training and characterize the alignment of the target function with the spike eigenvector of the CK on test data.

Zhichao Wang, Bin Bi, Zixu Zhu et al.

By pretraining on trillions of tokens, an LLM gains the capability of text generation. However, to enhance its utility and reduce potential harm, SFT and alignment are applied sequentially to the pretrained model. Due to the differing nature and objective functions of SFT and alignment, catastrophic forgetting has become a significant issue. To address this, we introduce Unified Fine-Tuning (UFT), which integrates SFT and alignment into a single training stage using the same objective and loss functions through an implicit reward function. Our experimental results demonstrate that UFT outperforms SFT on instruction-tuning data alone. Moreover, when combining instruction-tuning data with alignment data, UFT effectively prevents catastrophic forgetting across these two stages and shows a clear advantage over sequentially applying SFT and alignment. This is evident in the significant improvements observed in the \textbf{ifeval} task for instruction-following and the \textbf{truthful-qa} task for factuality. The proposed general fine-tuning framework UFT establishes an effective and efficient pretraining-UFT paradigm for LLM training.

Qian Li, Zhichao Wang, Shaowu Liu et al.

Causal inference is capable of estimating the treatment effect (i.e., the causal effect of treatment on the outcome) to benefit the decision making in various domains. One fundamental challenge in this research is that the treatment assignment bias in observational data. To increase the validity of observational studies on causal inference, representation based methods as the state-of-the-art have demonstrated the superior performance of treatment effect estimation. Most representation based methods assume all observed covariates are pre-treatment (i.e., not affected by the treatment), and learn a balanced representation from these observed covariates for estimating treatment effect. Unfortunately, this assumption is often too strict a requirement in practice, as some covariates are changed by doing an intervention on treatment (i.e., post-treatment). By contrast, the balanced representation learned from unchanged covariates thus biases the treatment effect estimation.