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Jun Zhu

Publications and source records attributed to Jun Zhu.

At least 271 records · Page 15Linked to original sources
arXiv2023

Stabilizing GANs' Training with Brownian Motion Controller

The training process of generative adversarial networks (GANs) is unstable and does not converge globally. In this paper, we examine the stability of GANs from the perspective of control theory and propose a universal higher-order noise-based controller called Brownian Motion Controller (BMC). Starting with the prototypical case of Dirac-GANs, we design a BMC to retrieve precisely the same but reachable optimal equilibrium. We theoretically prove that the training process of DiracGANs-BMC is globally exponential stable and derive bounds on the rate of convergence. Then we extend our BMC to normal GANs and provide implementation instructions on GANs-BMC. Our experiments show that our GANs-BMC effectively stabilizes GANs' training under StyleGANv2-ada frameworks with a faster rate of convergence, a smaller range of oscillation, and better performance in terms of FID score.

cs.LG↗
arXiv2023

GNOT: A General Neural Operator Transformer for Operator Learning

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input functions, and complexity of the PDEs' solution. To address these challenges, we propose a general neural operator transformer (GNOT), a scalable and effective transformer-based framework for learning operators. By designing a novel heterogeneous normalized attention layer, our model is highly flexible to handle multiple input functions and irregular meshes. Besides, we introduce a geometric gating mechanism which could be viewed as a soft domain decomposition to solve the multi-scale problems. The large model capacity of the transformer architecture grants our model the possibility to scale to large datasets and practical problems. We conduct extensive experiments on multiple challenging datasets from different domains and achieve a remarkable improvement compared with alternative methods. Our code and data are publicly available at \url{https://github.com/thu-ml/GNOT}.

cs.LG↗
arXiv2023

MultiAdam: Parameter-wise Scale-invariant Optimizer for Multiscale Training of Physics-informed Neural Networks

Physics-informed Neural Networks (PINNs) have recently achieved remarkable progress in solving Partial Differential Equations (PDEs) in various fields by minimizing a weighted sum of PDE loss and boundary loss. However, there are several critical challenges in the training of PINNs, including the lack of theoretical frameworks and the imbalance between PDE loss and boundary loss. In this paper, we present an analysis of second-order non-homogeneous PDEs, which are classified into three categories and applicable to various common problems. We also characterize the connections between the training loss and actual error, guaranteeing convergence under mild conditions. The theoretical analysis inspires us to further propose MultiAdam, a scale-invariant optimizer that leverages gradient momentum to parameter-wisely balance the loss terms. Extensive experiment results on multiple problems from different physical domains demonstrate that our MultiAdam solver can improve the predictive accuracy by 1-2 orders of magnitude compared with strong baselines.

cs.LG↗
arXiv2023

A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs

We present a unified hard-constraint framework for solving geometrically complex PDEs with neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary conditions (BCs) are considered. Specifically, we first introduce the "extra fields" from the mixed finite element method to reformulate the PDEs so as to equivalently transform the three types of BCs into linear equations. Based on the reformulation, we derive the general solutions of the BCs analytically, which are employed to construct an ansatz that automatically satisfies the BCs. With such a framework, we can train the neural networks without adding extra loss terms and thus efficiently handle geometrically complex PDEs, alleviating the unbalanced competition between the loss terms corresponding to the BCs and PDEs. We theoretically demonstrate that the "extra fields" can stabilize the training process. Experimental results on real-world geometrically complex PDEs showcase the effectiveness of our method compared with state-of-the-art baselines.

cs.LG↗
arXiv2023

NUNO: A General Framework for Learning Parametric PDEs with Non-Uniform Data

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use mesh-based techniques such as the FFT. To address this, we introduce the Non-Uniform Neural Operator (NUNO), a comprehensive framework designed for efficient operator learning with non-uniform data. Leveraging a K-D tree-based domain decomposition, we transform non-uniform data into uniform grids while effectively controlling interpolation error, thereby paralleling the speed and accuracy of learning from non-uniform data. We conduct extensive experiments on 2D elasticity, (2+1)D channel flow, and a 3D multi-physics heatsink, which, to our knowledge, marks a novel exploration into 3D PDE problems with complex geometries. Our framework has reduced error rates by up to 60% and enhanced training speeds by 2x to 30x. The code is now available at https://github.com/thu-ml/NUNO.

cs.LG↗
arXiv2023

One Transformer Fits All Distributions in Multi-Modal Diffusion at Scale

This paper proposes a unified diffusion framework (dubbed UniDiffuser) to fit all distributions relevant to a set of multi-modal data in one model. Our key insight is -- learning diffusion models for marginal, conditional, and joint distributions can be unified as predicting the noise in the perturbed data, where the perturbation levels (i.e. timesteps) can be different for different modalities. Inspired by the unified view, UniDiffuser learns all distributions simultaneously with a minimal modification to the original diffusion model -- perturbs data in all modalities instead of a single modality, inputs individual timesteps in different modalities, and predicts the noise of all modalities instead of a single modality. UniDiffuser is parameterized by a transformer for diffusion models to handle input types of different modalities. Implemented on large-scale paired image-text data, UniDiffuser is able to perform image, text, text-to-image, image-to-text, and image-text pair generation by setting proper timesteps without additional overhead. In particular, UniDiffuser is able to produce perceptually realistic samples in all tasks and its quantitative results (e.g., the FID and CLIP score) are not only superior to existing general-purpose models but also comparable to the bespoken models (e.g., Stable Diffusion and DALL-E 2) in representative tasks (e.g., text-to-image generation).

cs.LG↗
arXiv2023

Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning

Guided sampling is a vital approach for applying diffusion models in real-world tasks that embeds human-defined guidance during the sampling procedure. This paper considers a general setting where the guidance is defined by an (unnormalized) energy function. The main challenge for this setting is that the intermediate guidance during the diffusion sampling procedure, which is jointly defined by the sampling distribution and the energy function, is unknown and is hard to estimate. To address this challenge, we propose an exact formulation of the intermediate guidance as well as a novel training objective named contrastive energy prediction (CEP) to learn the exact guidance. Our method is guaranteed to converge to the exact guidance under unlimited model capacity and data samples, while previous methods can not. We demonstrate the effectiveness of our method by applying it to offline reinforcement learning (RL). Extensive experiments on D4RL benchmarks demonstrate that our method outperforms existing state-of-the-art algorithms. We also provide some examples of applying CEP for image synthesis to demonstrate the scalability of CEP on high-dimensional data.

cs.LG↗
arXiv2023

Preserving Pre-trained Features Helps Calibrate Fine-tuned Language Models

Large pre-trained language models (PLMs) have demonstrated strong performance on natural language understanding (NLU) tasks through fine-tuning. However, fine-tuned models still suffer from overconfident predictions, especially in out-of-domain settings. In this paper, we tackle the problem of calibrating fine-tuned language models. We demonstrate that the PLMs are well-calibrated on the masked language modeling task with robust predictive confidence under domain shift, yet the fine-tuned models fail to retain such property due to catastrophic forgetting, which impacts the calibration on the downstream classification task. In light of these observations, we evaluate the calibration of several methods that preserve pre-trained features and show that preserving pre-trained features can improve the calibration of fine-tuned language models. Among these methods, our proposed method that encourages the fine-tuned model to learn generative representations with auxiliary language modeling objective achieves competitive accuracy and the lowest expected calibration error compared to several strong baselines under both in-domain and out-of-domain settings on three downstream NLU tasks.

cs.CL↗
arXiv2023

An absolutely convergent fixed-point fast sweeping WENO method on triangular meshes for steady state of hyperbolic conservation laws

High order fast sweeping methods for efficiently solving steady state solutions of hyperbolic PDEs were not available yet on unstructured meshes. In this paper, we extend high order fast sweeping methods to unstructured triangular meshes by applying fixed-point iterative sweeping techniques to a fifth-order finite volume unstructured WENO scheme, for solving steady state solutions of hyperbolic conservation laws. An advantage of fixed-point fast sweeping methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems. As in the first order fast sweeping methods on triangular meshes, we introduce multiple reference points to determine alternating sweeping directions on unstructured meshes. All the cells on the mesh are ordered according to their centroids' distances to those reference points, and the resulted orderings provide sweeping directions for iterations. To make the residue of the fast sweeping iterations converge to machine zero / round off errors, we follow the approach in our early work of developing the absolutely convergent fixed-point fast sweeping WENO methods on rectangular meshes, and adopt high order WENO scheme with unequal-sized sub-stencils for spatial discretization. Extensive numerical experiments are performed to show the accuracy, computational efficiency, and absolute convergence of the presented fifth-order fast sweeping scheme on triangular meshes. Furthermore, the proposed method is compared with the forward Euler method and the popular third order total variation diminishing Rung-Kutta method for steady state computations. Numerical examples show that the developed fixed-point fast sweeping WENO method is the most efficient scheme among them, and especially it can save up to 70% CPU time costs than TVD-RK3 to converge to steady state solutions.

math.NA↗
arXiv2023

Revisiting Discriminative vs. Generative Classifiers: Theory and Implications

A large-scale deep model pre-trained on massive labeled or unlabeled data transfers well to downstream tasks. Linear evaluation freezes parameters in the pre-trained model and trains a linear classifier separately, which is efficient and attractive for transfer. However, little work has investigated the classifier in linear evaluation except for the default logistic regression. Inspired by the statistical efficiency of naive Bayes, the paper revisits the classical topic on discriminative vs. generative classifiers. Theoretically, the paper considers the surrogate loss instead of the zero-one loss in analyses and generalizes the classical results from binary cases to multiclass ones. We show that, under mild assumptions, multiclass naive Bayes requires $O(\log n)$ samples to approach its asymptotic error while the corresponding multiclass logistic regression requires $O(n)$ samples, where $n$ is the feature dimension. To establish it, we present a multiclass $\mathcal{H}$-consistency bound framework and an explicit bound for logistic loss, which are of independent interests. Simulation results on a mixture of Gaussian validate our theoretical findings. Experiments on various pre-trained deep vision models show that naive Bayes consistently converges faster as the number of data increases. Besides, naive Bayes shows promise in few-shot cases and we observe the "two regimes" phenomenon in pre-trained supervised models. Our code is available at https://github.com/ML-GSAI/Revisiting-Dis-vs-Gen-Classifiers.

cs.LG↗
arXiv2023

Amplification trojan network: Attack deep neural networks by amplifying their inherent weakness

Recent works found that deep neural networks (DNNs) can be fooled by adversarial examples, which are crafted by adding adversarial noise on clean inputs. The accuracy of DNNs on adversarial examples will decrease as the magnitude of the adversarial noise increase. In this study, we show that DNNs can be also fooled when the noise is very small under certain circumstances. This new type of attack is called Amplification Trojan Attack (ATAttack). Specifically, we use a trojan network to transform the inputs before sending them to the target DNN. This trojan network serves as an amplifier to amplify the inherent weakness of the target DNN. The target DNN, which is infected by the trojan network, performs normally on clean data while being more vulnerable to adversarial examples. Since it only transforms the inputs, the trojan network can hide in DNN-based pipelines, e.g. by infecting the pre-processing procedure of the inputs before sending them to the DNNs. This new type of threat should be considered in developing safe DNNs.

cs.CR↗
arXiv2023

Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations

Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from scientific data thrives as a new attempt to model complex phenomena in nature, but the effectiveness of current practice is typically limited by the scarcity of data and the complexity of phenomena. Especially, the discovery of PDEs with highly nonlinear coefficients from low-quality data remains largely under-addressed. To deal with this challenge, we propose a novel physics-guided learning method, which can not only encode observation knowledge such as initial and boundary conditions but also incorporate the basic physical principles and laws to guide the model optimization. We theoretically show that our proposed method strictly reduces the coefficient estimation error of existing baselines, and is also robust against noise. Extensive experiments show that the proposed method is more robust against data noise, and can reduce the estimation error by a large margin. Moreover, all the PDEs in the experiments are correctly discovered, and for the first time we are able to discover three-dimensional PDEs with highly nonlinear coefficients.

cs.LG↗
arXiv2023

Preferential bond formation and interstitial/vacancy annihilation rate drive atomic clustering in gallium ion sputtered compound materials

The investigation of chemical reactions during the ion irradiation is a frontier for the study of the ion-material interaction. In order to derive the contribution of bond formation to chemistry of ion produced nanoclusters, the valence electron energy loss spectroscopy (VEELS) was exploited to investigate the Ga$^+$ ion damage in Al$_2$O$_3$, InP and InGaAs, where each target material has been shown to yield different process for altering the clustering of recoil atoms: metallic Ga, metallic In and InGaP clusters in Al$_2$O$_3$, InP and InGaAs respectively. Supporting simulations based on Monte Carlo and crystal orbital Hamiltonianindicate that the chemical constitution of cascade induced nano-precipitates is a result of a competition between interstitial/vacancy consumption rate and preferential bond formation.

cond-mat.mtrl-sci↗
arXiv2023

On the Reuse Bias in Off-Policy Reinforcement Learning

Importance sampling (IS) is a popular technique in off-policy evaluation, which re-weights the return of trajectories in the replay buffer to boost sample efficiency. However, training with IS can be unstable and previous attempts to address this issue mainly focus on analyzing the variance of IS. In this paper, we reveal that the instability is also related to a new notion of Reuse Bias of IS -- the bias in off-policy evaluation caused by the reuse of the replay buffer for evaluation and optimization. We theoretically show that the off-policy evaluation and optimization of the current policy with the data from the replay buffer result in an overestimation of the objective, which may cause an erroneous gradient update and degenerate the performance. We further provide a high-probability upper bound of the Reuse Bias, and show that controlling one term of the upper bound can control the Reuse Bias by introducing the concept of stability for off-policy algorithms. Based on these analyses, we finally present a novel Bias-Regularized Importance Sampling (BIRIS) framework along with practical algorithms, which can alleviate the negative impact of the Reuse Bias. Experimental results show that our BIRIS-based methods can significantly improve the sample efficiency on a series of continuous control tasks in MuJoCo.

cs.LG↗
arXiv2023

Phase diagram of the $ν= 2$ quantum Hall state in bilayer graphene

Bilayer graphene exhibits a rich phase diagram in the quantum Hall regime, arising from a multitude of internal degrees of freedom, including spin, valley, and orbital indices. The variety of fractional quantum Hall states between filling factors $1 < ν\leq 2$ suggests, among other things, a quantum phase transition between valley-unpolarized and polarized states at a perpendicular electric field $D^{*}$. We find the behavior of $D^{*}$ with $ν$ changes markedly as $B$ is reduced. At $ν= 2$, $D^{*}$ may even vanish when $B$ is sufficiently small. We present a theoretical model for lattice-scale interactions which explains these observations; surprisingly, both repulsive and attractive components in the interactions are required. Within this model we analyze the nature of the $ν= 2$ state as a function of the magnetic and electric fields, and predict that valley-coherence may emerge for $D \sim D^{*}$ in the high $B$ regime. This suggests the system supports Kekule bond-ordering, which could in principle be verified via STM measurements.

cond-mat.mes-hall↗
arXiv2023

Learning CLIP Guided Visual-Text Fusion Transformer for Video-based Pedestrian Attribute Recognition

Existing pedestrian attribute recognition (PAR) algorithms are mainly developed based on a static image. However, the performance is not reliable for images with challenging factors, such as heavy occlusion, motion blur, etc. In this work, we propose to understand human attributes using video frames that can make full use of temporal information. Specifically, we formulate the video-based PAR as a vision-language fusion problem and adopt pre-trained big models CLIP to extract the feature embeddings of given video frames. To better utilize the semantic information, we take the attribute list as another input and transform the attribute words/phrase into the corresponding sentence via split, expand, and prompt. Then, the text encoder of CLIP is utilized for language embedding. The averaged visual tokens and text tokens are concatenated and fed into a fusion Transformer for multi-modal interactive learning. The enhanced tokens will be fed into a classification head for pedestrian attribute prediction. Extensive experiments on a large-scale video-based PAR dataset fully validated the effectiveness of our proposed framework.

cs.CV↗
arXiv2023

PREIM3D: 3D Consistent Precise Image Attribute Editing from a Single Image

We study the 3D-aware image attribute editing problem in this paper, which has wide applications in practice. Recent methods solved the problem by training a shared encoder to map images into a 3D generator's latent space or by per-image latent code optimization and then edited images in the latent space. Despite their promising results near the input view, they still suffer from the 3D inconsistency of produced images at large camera poses and imprecise image attribute editing, like affecting unspecified attributes during editing. For more efficient image inversion, we train a shared encoder for all images. To alleviate 3D inconsistency at large camera poses, we propose two novel methods, an alternating training scheme and a multi-view identity loss, to maintain 3D consistency and subject identity. As for imprecise image editing, we attribute the problem to the gap between the latent space of real images and that of generated images. We compare the latent space and inversion manifold of GAN models and demonstrate that editing in the inversion manifold can achieve better results in both quantitative and qualitative evaluations. Extensive experiments show that our method produces more 3D consistent images and achieves more precise image editing than previous work. Source code and pretrained models can be found on our project page: https://mybabyyh.github.io/Preim3D/

cs.CV↗
arXiv2023

A compact simple HWENO scheme with ADER time discretization for hyperbolic conservation laws I: structured meshes

In this paper, a compact and high order ADER (Arbitrary high order using DERivatives) scheme using the simple HWENO method (ADER-SHWENO) is proposed for hyperbolic conservation laws. The newly-developed method employs the Lax-Wendroff procedure to convert time derivatives to spatial derivatives, which provides the time evolution of the variables at the cell interfaces. This information is required for the simple HWENO reconstructions, which take advantages of the simple WENO and the classic HWENO. Compared with the original Runge-Kutta HWENO method (RK-HWENO), the new method has two advantages. Firstly, RK-HWENO method must solve the additional equations for reconstructions, which is avoided for the new method. Secondly, the SHWENO reconstruction is performed once with one stencil and is different from the classic HWENO methods, in which both the function and its derivative values are reconstructed with two different stencils, respectively. Thus the new method is more efficient than the RK-HWENO method. Moreover, the new method is more compact than the existing ADER-WENO method. Besides, the new method makes the best use of the information in the ADER method. Thus, the time evolution of the cell averages of the derivatives is simpler than that developed in the work [Li et. al., 447 (2021), 110661.]. Numerical tests indicate that the new method can achieve high order for smooth solutions both in space and time, keep non-oscillatory at discontinuities.

math.NA↗