Tianyang Hu

Yan Wang, Tianyang Hu

Topological Data Analysis (TDA) offers a principled, intrinsic lens for comparing neural representations. However, existing paired topological divergences (e.g., RTD) are limited by heuristic asymmetry and, more critically, unbounded scores that depend on sample size, hindering reliable cross-scenario benchmarking. To address these challenges, we develop a unified topological toolkit serving two complementary needs: fine-grained structural diagnosis and robust, standardized evaluation. First, we complete the RTD framework by introducing Symmetric Representation Topology Divergence (SRTD) and its efficient variant SRTD-lite. Beyond resolving the theoretical asymmetry of prior variants, SRTD consolidates diagnostic information into a single, comprehensive cross-barcode signature. This allows for precise localization of structural discrepancies and serves as an effective optimization objective without the overhead of dual directional computations. Second, to enable reliable benchmarking across heterogeneous settings, we propose Normalized Topological Similarity (NTS). By measuring the rank correlation of hierarchical merge orders, NTS yields a scale-invariant metric bounded between -1 and 1, effectively overcoming the scale and sample-dependence of unnormalized divergences. Experiments across synthetic and real-world deep learning settings demonstrate that our toolkit captures functional shifts in CNNs missed by geometric measures and robustly maps LLM genealogy even under distance saturation, offering a rigorous, topology-aware perspective that complements measures like CKA.

Longhui Yu, Tianyang Hu, Lanqing Hong et al. · cambridge

It has been observed that neural networks perform poorly when the data or tasks are presented sequentially. Unlike humans, neural networks suffer greatly from catastrophic forgetting, making it impossible to perform life-long learning. To address this issue, memory-based continual learning has been actively studied and stands out as one of the best-performing methods. We examine memory-based continual learning and identify that large variation in the representation space is crucial for avoiding catastrophic forgetting. Motivated by this, we propose to diversify representations by using two types of perturbations: model-agnostic variation (i.e., the variation is generated without the knowledge of the learned neural network) and model-based variation (i.e., the variation is conditioned on the learned neural network). We demonstrate that enlarging representational variation serves as a general principle to improve continual learning. Finally, we perform empirical studies which demonstrate that our method, as a simple plug-and-play component, can consistently improve a number of memory-based continual learning methods by a large margin.

Jiajun Ma, Tianyang Hu, Wenjia Wang et al.

Guidance in conditional diffusion generation is of great importance for sample quality and controllability. However, existing guidance schemes are to be desired. On one hand, mainstream methods such as classifier guidance and classifier-free guidance both require extra training with labeled data, which is time-consuming and unable to adapt to new conditions. On the other hand, training-free methods such as universal guidance, though more flexible, have yet to demonstrate comparable performance. In this work, through a comprehensive investigation into the design space, we show that it is possible to achieve significant performance improvements over existing guidance schemes by leveraging off-the-shelf classifiers in a training-free fashion, enjoying the best of both worlds. Employing calibration as a general guideline, we propose several pre-conditioning techniques to better exploit pretrained off-the-shelf classifiers for guiding diffusion generation. Extensive experiments on ImageNet validate our proposed method, showing that state-of-the-art diffusion models (DDPM, EDM, DiT) can be further improved (up to 20%) using off-the-shelf classifiers with barely any extra computational cost. With the proliferation of publicly available pretrained classifiers, our proposed approach has great potential and can be readily scaled up to text-to-image generation tasks. The code is available at https://github.com/AlexMaOLS/EluCD/tree/main.

Tianyang Hu, Fei Chen, Haonan Wang et al.

In generative modeling, numerous successful approaches leverage a low-dimensional latent space, e.g., Stable Diffusion models the latent space induced by an encoder and generates images through a paired decoder. Although the selection of the latent space is empirically pivotal, determining the optimal choice and the process of identifying it remain unclear. In this study, we aim to shed light on this under-explored topic by rethinking the latent space from the perspective of model complexity. Our investigation starts with the classic generative adversarial networks (GANs). Inspired by the GAN training objective, we propose a novel "distance" between the latent and data distributions, whose minimization coincides with that of the generator complexity. The minimizer of this distance is characterized as the optimal data-dependent latent that most effectively capitalizes on the generator's capacity. Then, we consider parameterizing such a latent distribution by an encoder network and propose a two-stage training strategy called Decoupled Autoencoder (DAE), where the encoder is only updated in the first stage with an auxiliary decoder and then frozen in the second stage while the actual decoder is being trained. DAE can improve the latent distribution and as a result, improve the generative performance. Our theoretical analyses are corroborated by comprehensive experiments on various models such as VQGAN and Diffusion Transformer, where our modifications yield significant improvements in sample quality with decreased model complexity.

Xuantong Liu, Jianfeng Zhang, Tianyang Hu et al.

Although deep neural networks achieve tremendous success on various classification tasks, the generalization ability drops sheer when training datasets exhibit long-tailed distributions. One of the reasons is that the learned representations (i.e. features) from the imbalanced datasets are less effective than those from balanced datasets. Specifically, the learned representation under class-balanced distribution will present the Neural Collapse (NC) phenomena. NC indicates the features from the same category are close to each other and from different categories are maximally distant, showing an optimal linear separable state of classification. However, the pattern differs on imbalanced datasets and is partially responsible for the reduced performance of the model. In this work, we propose two explicit feature regularization terms to learn high-quality representation for class-imbalanced data. With the proposed regularization, NC phenomena will appear under the class-imbalanced distribution, and the generalization ability can be significantly improved. Our method is easily implemented, highly effective, and can be plugged into most existing methods. The extensive experimental results on widely-used benchmarks show the effectiveness of our method

Weijian Luo, Hao Jiang, Tianyang Hu et al.

Energy-Based Models (EBMs) have been widely used for generative modeling. Contrastive Divergence (CD), a prevailing training objective for EBMs, requires sampling from the EBM with Markov Chain Monte Carlo methods (MCMCs), which leads to an irreconcilable trade-off between the computational burden and the validity of the CD. Running MCMCs till convergence is computationally intensive. On the other hand, short-run MCMC brings in an extra non-negligible parameter gradient term that is difficult to handle. In this paper, we provide a general interpretation of CD, viewing it as a special instance of our proposed Diffusion Contrastive Divergence (DCD) family. By replacing the Langevin dynamic used in CD with other EBM-parameter-free diffusion processes, we propose a more efficient divergence. We show that the proposed DCDs are both more computationally efficient than the CD and are not limited to a non-negligible gradient term. We conduct intensive experiments, including both synthesis data modeling and high-dimensional image denoising and generation, to show the advantages of the proposed DCDs. On the synthetic data learning and image denoising experiments, our proposed DCD outperforms CD by a large margin. In image generation experiments, the proposed DCD is capable of training an energy-based model for generating the Celab-A $32\times 32$ dataset, which is comparable to existing EBMs.

Hao Yang, Lanqing Hong, Aoxue Li et al.

Although many recent works have investigated generalizable NeRF-based novel view synthesis for unseen scenes, they seldom consider the synthetic-to-real generalization, which is desired in many practical applications. In this work, we first investigate the effects of synthetic data in synthetic-to-real novel view synthesis and surprisingly observe that models trained with synthetic data tend to produce sharper but less accurate volume densities. For pixels where the volume densities are correct, fine-grained details will be obtained. Otherwise, severe artifacts will be produced. To maintain the advantages of using synthetic data while avoiding its negative effects, we propose to introduce geometry-aware contrastive learning to learn multi-view consistent features with geometric constraints. Meanwhile, we adopt cross-view attention to further enhance the geometry perception of features by querying features across input views. Experiments demonstrate that under the synthetic-to-real setting, our method can render images with higher quality and better fine-grained details, outperforming existing generalizable novel view synthesis methods in terms of PSNR, SSIM, and LPIPS. When trained on real data, our method also achieves state-of-the-art results.

Qishi Dong, Awais Muhammad, Fengwei Zhou et al.

Recent advances on large-scale pre-training have shown great potentials of leveraging a large set of Pre-Trained Models (PTMs) for improving Out-of-Distribution (OoD) generalization, for which the goal is to perform well on possible unseen domains after fine-tuning on multiple training domains. However, maximally exploiting a zoo of PTMs is challenging since fine-tuning all possible combinations of PTMs is computationally prohibitive while accurate selection of PTMs requires tackling the possible data distribution shift for OoD tasks. In this work, we propose ZooD, a paradigm for PTMs ranking and ensemble with feature selection. Our proposed metric ranks PTMs by quantifying inter-class discriminability and inter-domain stability of the features extracted by the PTMs in a leave-one-domain-out cross-validation manner. The top-K ranked models are then aggregated for the target OoD task. To avoid accumulating noise induced by model ensemble, we propose an efficient variational EM algorithm to select informative features. We evaluate our paradigm on a diverse model zoo consisting of 35 models for various OoD tasks and demonstrate: (i) model ranking is better correlated with fine-tuning ranking than previous methods and up to 9859x faster than brute-force fine-tuning; (ii) OoD generalization after model ensemble with feature selection outperforms the state-of-the-art methods and the accuracy on most challenging task DomainNet is improved from 46.5\% to 50.6\%. Furthermore, we provide the fine-tuning results of 35 PTMs on 7 OoD datasets, hoping to help the research of model zoo and OoD generalization. Code will be available at https://gitee.com/mindspore/models/tree/master/research/cv/zood.

Yimeng Chen, Tianyang Hu, Fengwei Zhou et al.

The proliferation of pretrained models, as a result of advancements in pretraining techniques, has led to the emergence of a vast zoo of publicly available models. Effectively utilizing these resources to obtain models with robust out-of-distribution generalization capabilities for downstream tasks has become a crucial area of research. Previous research has primarily focused on identifying the most powerful models within the model zoo, neglecting to fully leverage the diverse inductive biases contained within. This paper argues that the knowledge contained in weaker models is valuable and presents a method for leveraging the diversity within the model zoo to improve out-of-distribution generalization capabilities. Specifically, we investigate the behaviors of various pretrained models across different domains of downstream tasks by characterizing the variations in their encoded representations in terms of two dimensions: diversity shift and correlation shift. This characterization enables us to propose a new algorithm for integrating diverse pretrained models, not limited to the strongest models, in order to achieve enhanced out-of-distribution generalization performance. Our proposed method demonstrates state-of-the-art empirical results on a variety of datasets, thus validating the benefits of utilizing diverse knowledge.

Chenhan Jiang, Yihan Zeng, Tianyang Hu et al.

Score Distillation Sampling (SDS) by well-trained 2D diffusion models has shown great promise in text-to-3D generation. However, this paradigm distills view-agnostic 2D image distributions into the rendering distribution of 3D representation for each view independently, overlooking the coherence across views and yielding 3D inconsistency in generations. In this work, we propose \textbf{J}oint \textbf{S}core \textbf{D}istillation (JSD), a new paradigm that ensures coherent 3D generations. Specifically, we model the joint image distribution, which introduces an energy function to capture the coherence among denoised images from the diffusion model. We then derive the joint score distillation on multiple rendered views of the 3D representation, as opposed to a single view in SDS. In addition, we instantiate three universal view-aware models as energy functions, demonstrating compatibility with JSD. Empirically, JSD significantly mitigates the 3D inconsistency problem in SDS, while maintaining text congruence. Moreover, we introduce the Geometry Fading scheme and Classifier-Free Guidance (CFG) Switching strategy to enhance generative details. Our framework, JointDreamer, establishes a new benchmark in text-to-3D generation, achieving outstanding results with an 88.5\% CLIP R-Precision and 27.7\% CLIP Score. These metrics demonstrate exceptional text congruence, as well as remarkable geometric consistency and texture fidelity.

Tianyang Hu, Zhili Liu, Fengwei Zhou et al.

Contrastive learning, especially self-supervised contrastive learning (SSCL), has achieved great success in extracting powerful features from unlabeled data. In this work, we contribute to the theoretical understanding of SSCL and uncover its connection to the classic data visualization method, stochastic neighbor embedding (SNE), whose goal is to preserve pairwise distances. From the perspective of preserving neighboring information, SSCL can be viewed as a special case of SNE with the input space pairwise similarities specified by data augmentation. The established correspondence facilitates deeper theoretical understanding of learned features of SSCL, as well as methodological guidelines for practical improvement. Specifically, through the lens of SNE, we provide novel analysis on domain-agnostic augmentations, implicit bias and robustness of learned features. To illustrate the practical advantage, we demonstrate that the modifications from SNE to $t$-SNE can also be adopted in the SSCL setting, achieving significant improvement in both in-distribution and out-of-distribution generalization.

Jiajun Ma, Tianyang Hu, Wenjia Wang

Self-supervised learning (SSL) aims to learn intrinsic features without labels. Despite the diverse architectures of SSL methods, the projection head always plays an important role in improving the performance of the downstream task. In this work, we systematically investigate the role of the projection head in SSL. Specifically, the projection head targets the uniformity part of SSL, which pushes the dissimilar samples away from each other, thus enabling the encoder to focus on extracting semantic features. Based on this understanding, we propose a Representation Evaluation Design (RED) in SSL models in which a shortcut connection between the representation and the projection vectors is built. Extensive experiments with different architectures, including SimCLR, MoCo-V2, and SimSiam, on various datasets, demonstrate that the representation evaluation design can consistently improve the baseline models in the downstream tasks. The learned representation from the RED-SSL models shows superior robustness to unseen augmentations and out-of-distribution data.

Paweł Piwek, Adam Klukowski, Tianyang Hu

Classic learning theory suggests that proper regularization is the key to good generalization and robustness. In classification, current training schemes only target the complexity of the classifier itself, which can be misleading and ineffective. Instead, we advocate directly measuring the complexity of the decision boundary. Existing literature is limited in this area with few well-established definitions of boundary complexity. As a proof of concept, we start by analyzing ReLU neural networks, whose boundary complexity can be conveniently characterized by the number of affine pieces. With the help of tropical geometry, we develop a novel method that can explicitly count the exact number of boundary pieces, and as a by-product, the exact number of total affine pieces. Numerical experiments are conducted and distinctive properties of our boundary complexity are uncovered. First, the boundary piece count appears largely independent of other measures, e.g., total piece count, and $l_2$ norm of weights, during the training process. Second, the boundary piece count is negatively correlated with robustness, where popular robust training techniques, e.g., adversarial training or random noise injection, are found to reduce the number of boundary pieces.

Xuantong Liu, Shaozhe Hao, Xianbiao Qi et al.

The success of autoregressive (AR) language models in text generation has inspired the computer vision community to adopt Large Language Models (LLMs) for image generation. However, considering the essential differences between text and image modalities, the design space of language models for image generation remains underexplored. We observe that image tokens exhibit greater randomness compared to text tokens, which presents challenges when training with token prediction. Nevertheless, AR models demonstrate their potential by effectively learning patterns even from a seemingly suboptimal optimization problem. Our analysis also reveals that while all models successfully grasp the importance of local information in image generation, smaller models struggle to capture the global context. In contrast, larger models showcase improved capabilities in this area, helping to explain the performance gains achieved when scaling up model size. We further elucidate the design space of language models for vision generation, including tokenizer choice, model choice, model scalability, vocabulary design, and sampling strategy through extensive comparative experiments. Our work is the first to analyze the optimization behavior of language models in vision generation, and we believe it can inspire more effective designs when applying LMs to other domains. Finally, our elucidated language model for image generation, termed as ELM, achieves state-of-the-art performance on the ImageNet 256*256 benchmark. The code is available at https://github.com/Pepperlll/LMforImageGeneration.git.

Yihong Luo, Tianyang Hu, Weijian Luo et al.

While few-step generative models have enabled powerful image and video generation at significantly lower cost, generic reinforcement learning (RL) paradigms for few-step models remain an unsolved problem. Existing RL approaches for few-step diffusion models strongly rely on back-propagating through differentiable reward models, thereby excluding the majority of important real-world reward signals, e.g., non-differentiable rewards such as humans' binary likeness, object counts, etc. To properly incorporate non-differentiable rewards to improve few-step generative models, we introduce TDM-R1, a novel reinforcement learning paradigm built upon a leading few-step model, Trajectory Distribution Matching (TDM). TDM-R1 decouples the learning process into surrogate reward learning and generator learning. Furthermore, we developed practical methods to obtain per-step reward signals along the deterministic generation trajectory of TDM, resulting in a unified RL post-training method that significantly improves few-step models' ability with generic rewards. We conduct extensive experiments ranging from text-rendering, visual quality, and preference alignment. All results demonstrate that TDM-R1 is a powerful reinforcement learning paradigm for few-step text-to-image models, achieving state-of-the-art reinforcement learning performances on both in-domain and out-of-domain metrics. Furthermore, TDM-R1 also scales effectively to the recent strong Z-Image model, consistently outperforming both its 100-NFE and few-step variants with only 4 NFEs. Project page: https://github.com/Luo-Yihong/TDM-R1

Shuchen Xue, Tianyu Xie, Tianyang Hu et al. · pku

Large language models (LLMs) predominantly use autoregressive (AR) approaches, but masked diffusion models (MDMs) are emerging as viable alternatives. A key challenge in comparing AR and MDM paradigms is their typical architectural difference: AR models are often decoder-only, while MDMs have largely been encoder-only. This practice of changing both the modeling paradigm and architecture simultaneously makes direct comparisons unfair, as it's hard to distinguish whether observed differences stem from the paradigm itself or the architectural shift. This research evaluates MDMs within a decoder-only framework to: (1) equitably compare MDM (as Any-Order AR, or AO-AR) and standard AR paradigms. Our investigation suggests that the standard AO-AR objective, which averages over all token permutations, may benefit from refinement, as many permutations appear less informative compared to the language's inherent left-to-right structure. (2) Investigate architectural influences (decoder-only vs. encoder-only) within MDMs. We demonstrate that while encoder-only MDMs model a simpler conditional probability space, decoder-only MDMs can achieve dramatic generation speedups ($\sim25\times$) and comparable perplexity with temperature annealing despite modeling a vastly larger space, highlighting key trade-offs. This work thus decouples core paradigm differences from architectural influences, offering insights for future model design. Code is available at https://github.com/scxue/AO-GPT-MDM.

Yihong Luo, Tianyang Hu, Jing Tang

While reinforcement learning methods such as Group Relative Preference Optimization (GRPO) have significantly enhanced Large Language Models, adapting them to diffusion models remains challenging. In particular, GRPO demands a stochastic policy, yet the most cost-effective diffusion samplers are based on deterministic ODEs. Recent work addresses this issue by using inefficient SDE-based samplers to induce stochasticity, but this reliance on model-agnostic Gaussian noise leads to slow convergence. To resolve this conflict, we propose Direct Group Preference Optimization (DGPO), a new online RL algorithm that dispenses with the policy-gradient framework entirely. DGPO learns directly from group-level preferences, which utilize relative information of samples within groups. This design eliminates the need for inefficient stochastic policies, unlocking the use of efficient deterministic ODE samplers and faster training. Extensive results show that DGPO trains around 20 times faster than existing state-of-the-art methods and achieves superior performance on both in-domain and out-of-domain reward metrics. Code is available at https://github.com/Luo-Yihong/DGPO.

Yihong Luo, Shuchen Xue, Tianyang Hu et al.

The pursuit of efficient and controllable high-quality content generation remains a central challenge in artificial intelligence-generated content (AIGC). While one-step generators, enabled by diffusion distillation techniques, offer excellent generation quality and computational efficiency, adapting them to new control conditions--such as structural constraints, semantic guidelines, or external inputs--poses a significant challenge. Conventional approaches often necessitate computationally expensive modifications to the base model and subsequent diffusion distillation. This paper introduces Noise Consistency Training (NCT), a novel and lightweight approach to directly integrate new control signals into pre-trained one-step generators without requiring access to original training images or retraining the base diffusion model. NCT operates by introducing an adapter module and employs a noise consistency loss in the noise space of the generator. This loss aligns the adapted model's generation behavior across noises that are conditionally dependent to varying degrees, implicitly guiding it to adhere to the new control. Theoretically, this training objective can be understood as minimizing the distributional distance between the adapted generator and the conditional distribution induced by the new conditions. NCT is modular, data-efficient, and easily deployable, relying only on the pre-trained one-step generator and a control signal model. Extensive experiments demonstrate that NCT achieves state-of-the-art controllable generation in a single forward pass, surpassing existing multi-step and distillation-based methods in both generation quality and computational efficiency. Code is available at https://github.com/Luo-Yihong/NCT

Yihong Luo, Xiaolong Chen, Xinghua Qu et al.

Recently, some works have tried to combine diffusion and Generative Adversarial Networks (GANs) to alleviate the computational cost of the iterative denoising inference in Diffusion Models (DMs). However, existing works in this line suffer from either training instability and mode collapse or subpar one-step generation learning efficiency. To address these issues, we introduce YOSO, a novel generative model designed for rapid, scalable, and high-fidelity one-step image synthesis with high training stability and mode coverage. Specifically, we smooth the adversarial divergence by the denoising generator itself, performing self-cooperative learning. We show that our method can serve as a one-step generation model training from scratch with competitive performance. Moreover, we extend our YOSO to one-step text-to-image generation based on pre-trained models by several effective training techniques (i.e., latent perceptual loss and latent discriminator for efficient training along with the latent DMs; the informative prior initialization (IPI), and the quick adaption stage for fixing the flawed noise scheduler). Experimental results show that YOSO achieves the state-of-the-art one-step generation performance even with Low-Rank Adaptation (LoRA) fine-tuning. In particular, we show that the YOSO-PixArt-$α$ can generate images in one step trained on 512 resolution, with the capability of adapting to 1024 resolution without extra explicit training, requiring only ~10 A800 days for fine-tuning. Our code is provided at https://github.com/Luo-Yihong/YOSO.

Haonan Wang, Minbin Huang, Runhui Huang et al.

Contrastive Language-Image Pre-training (CLIP) has become the standard for cross-modal image-text representation learning. Improving CLIP typically requires additional data and retraining with new loss functions, but these demands raise resource and time costs, limiting practical use. In this work, we introduce HELIP, a cost-effective strategy that improves CLIP models by exploiting challenging text-image pairs within existing datasets in continuous training. This eliminates the need for additional data or extensive retraining. Moreover, HELIP integrates effortlessly into current training pipelines with minimal code modifications, allowing for quick and seamless implementation. On comprehensive benchmarks, HELIP consistently boosts existing models. In particular, within just two epochs of training, it improves zero-shot classification accuracy on ImageNet for SLIP models pre-trained on CC3M, CC12M, and YFCC15M datasets by 3.05%, 4.47%, and 10.1% , respectively. In addition, on fine-grained classification datasets, HELIP improves the zero-shot performance of CLIP and SLIP by an average of 8.4% and 18.6%, and their linear probe performance by an average of 9.5% and 3.0%. The code is publicly available at: https://github.com/haonan3/HELIP-NACCL-2025.git.

Bowen Zheng, Weijian Luo, Guang Yang et al.

In this work, we propose Prologue, an approach to bridging the reconstruction-generation gap in autoregressive (AR) image generation. Instead of modifying visual tokens to satisfy both reconstruction and generation, Prologue generates a small set of prologue tokens prepended to the visual token sequence. These prologue tokens are trained exclusively with the AR cross-entropy (CE) loss, while visual tokens remain dedicated to reconstruction. This decoupled design lets us optimize generation through the AR model's true distribution without affecting reconstruction quality, which we further formalize from an ELBO perspective. On ImageNet 256x256, Prologue-Base reduces gFID from 21.01 to 10.75 without classifier-free guidance while keeping reconstruction almost unchanged; Prologue-Large reaches a competitive rFID of 0.99 and gFID of 1.46 using a standard AR model without auxiliary semantic supervision. Interestingly, driven only by AR gradients, prologue tokens exhibit emergent semantic structure: linear probing on 16 prologue tokens reaches 35.88% Top-1, far above the 23.71% of the first 16 tokens from a standard tokenizer; resampling with fixed prologue tokens preserves a similar high-level semantic layout. Our results suggest a new direction: generation quality can be improved by introducing a separate learned generative representation while leaving the original representation intact.

Bowen Zheng, Yihong Luo, Tianyang Hu

Discrete image tokenizers are commonly trained in two stages: first for reconstruction, and then with a prior model fitted to the frozen token sequences. This decoupling leaves the tokenizer unaware of the model that will later generate its tokens. As a result, the learned tokens may preserve image information well but still be difficult for an autoregressive (AR) prior to predict from left to right. We analyze this mismatch using Tripartite Variational Consistency (TVC), which decomposes latent-variable learning into three consistency conditions: conditional-likelihood consistency, prior consistency, and posterior consistency. TVC shows that two-stage training preserves the reconstruction side but leaves prior consistency outside the tokenizer objective: the overall token distribution is fixed before the AR prior participates in training. Motivated by this view, we add a distribution-level prior-matching signal during tokenizer training, while keeping the reconstruction objective unchanged. We optimize this signal with a Wasserstein-gradient-flow update. For hard categorical tokens, the update reduces to a token-level contrast between an auxiliary AR model that tracks the tokenizer's current token distribution and the target AR prior. It requires only forward passes through the two AR models and does not backpropagate through either of them. The resulting tokenizer, wAR-Tok, reduces AR loss and improves generation FID on CIFAR-10 and ImageNet at comparable reconstruction quality.

Siquan Li, Kaiqi Jiang, Jiacheng Sun et al.

Despite the prevalence of the attention sink phenomenon in Large Language Models (LLMs), where initial tokens disproportionately monopolize attention scores, its structural origins remain elusive. This work provides a \textit{mechanistic explanation} for this phenomenon. First, we trace its root to the value aggregation process inherent in self-attention, which induces a systematic variance discrepancy. We further demonstrate that this discrepancy is drastically amplified by the activation of super neurons within Feed-Forward Network (FFN) layers. Specifically, the channel-sparse down-projections trigger a dimension disparity of the first-token representation, necessitating the formation of attention sinks as a structural anchor. Then, we validate this causal chain through two controlled interventions: (i) isolating the aggregation effect via attention mask modifications and (ii) amplifying the variance of targeted token representations. Both interventions can replicate attention sinks at arbitrary positions. Our mechanistic understanding offers a foundation for the systematic control of sink formation. Finally, as a proof of concept, we propose \textit{head-wise RMSNorm}, an architectural modification that stabilizes value aggregation outputs during pre-training. Our experiments demonstrate that restoring statistical parity across positions significantly accelerates convergence.

Bowen Zheng, Weijian Luo, Guang Yang et al.

Most discrete visual tokenizers rely on a default design: every position in the sequence shares the same codebook. Researchers try to scale the codebook size $K$ to get better reconstruction performance. Such a constant-codebook design hits a fundamental information-theoretic limit. We observe that the per-position conditional entropy of the training set decays so quickly along the sequence that, after a few positions, the conditional distribution becomes essentially deterministic. On ImageNet with $K=16384$, this happens within only 2 out of 256 positions, turning the remaining 254 into a memorization problem. We call this phenomenon the Entropy Cliff and formalize it with a simple expression: $t^{*} = \lceil \log_2 N / \log_2 K \rceil$. Interestingly, this phenomenon is not observed in language, as its natural structure keeps the effective entropy per position well below the codebook capacity. To address this, we propose Variable Codebook Size Quantization (VCQ), where the codebook size $K_t$ grows monotonically along the sequence from $K_{\min}=2$ to $K_{\max}$, leaving the loss function, parameter count, and AR training procedure unchanged. With a vanilla autoregressive Transformer and standard next-token prediction, a base version of VCQ reduces gFID w/o CFG from 27.98 to 14.80 on ImageNet $256\times256$ over the baseline. Scaled up, it reaches gFID 1.71 with 684M autoregressive parameters, without any extra training techniques such as semantic regularization or causal alignment. The extreme information bottleneck at $K_{\min}=2$ naturally induces a coarse-to-fine semantic hierarchy: a linear probe on only the first 10 tokens reaches 43.8% top-1 accuracy on ImageNet, compared to 27.1% for uniform codebooks. Ultimately, these results show that what matters is not only the total capacity of the codebook, but also how that capacity is distributed and organized.

Shuchen Xue, Zhaoqiang Liu, Fei Chen et al.

Diffusion probabilistic models (DPMs) have shown remarkable performance in high-resolution image synthesis, but their sampling efficiency is still to be desired due to the typically large number of sampling steps. Recent advancements in high-order numerical ODE solvers for DPMs have enabled the generation of high-quality images with much fewer sampling steps. While this is a significant development, most sampling methods still employ uniform time steps, which is not optimal when using a small number of steps. To address this issue, we propose a general framework for designing an optimization problem that seeks more appropriate time steps for a specific numerical ODE solver for DPMs. This optimization problem aims to minimize the distance between the ground-truth solution to the ODE and an approximate solution corresponding to the numerical solver. It can be efficiently solved using the constrained trust region method, taking less than $15$ seconds. Our extensive experiments on both unconditional and conditional sampling using pixel- and latent-space DPMs demonstrate that, when combined with the state-of-the-art sampling method UniPC, our optimized time steps significantly improve image generation performance in terms of FID scores for datasets such as CIFAR-10 and ImageNet, compared to using uniform time steps.

Siquan Li, Yao Tong, Haonan Wang et al.

Transformers underpin modern large language models (LLMs) and are commonly assumed to be behaviorally unstructured at random initialization, with all meaningful preferences emerging only through large-scale training. We challenge this assumption by showing that randomly initialized transformers already exhibit strong and systematic structural biases. In particular, untrained models display extreme token preferences: across random input sequences, certain tokens are predicted with probabilities orders of magnitude larger. We provide a mechanistic explanation for this phenomenon by dissecting the transformer architecture at initialization. We show that extreme token preference arises from a contraction of token representations along a random seed-dependent direction. This contraction is driven by two interacting forces: (i) asymmetric nonlinear activations in MLP sublayers induce global (inter-sequence) representation concentration, and (ii) self-attention further amplifies this effect through local (intra-sequence) aggregation. Together, these mechanisms align hidden representations along a direction determined solely by the random initialization, producing highly non-uniform next-token predictions. Beyond mechanistic insight, we demonstrate that these initialization-induced biases persist throughout training, forming a stable and intrinsic model identity. Leveraging this property, we introduce SeedPrint, a fingerprinting method that can reliably distinguish models that differ only in their random initialization, even after extensive training and under substantial distribution shift. Finally, we identify a fundamental positional discrepancy inherent to the attention mechanism's intra-sequence contraction that is causally linked to the attention-sink phenomenon. This discovery provides a principled explanation for the emergence of sinks and offers a pathway for their control.

Jiajun Ma, Shuchen Xue, Tianyang Hu et al.

With the incorporation of the UNet architecture, diffusion probabilistic models have become a dominant force in image generation tasks. One key design in UNet is the skip connections between the encoder and decoder blocks. Although skip connections have been shown to improve training stability and model performance, we reveal that such shortcuts can be a limiting factor for the complexity of the transformation. As the sampling steps decrease, the generation process and the role of the UNet get closer to the push-forward transformations from Gaussian distribution to the target, posing a challenge for the network's complexity. To address this challenge, we propose Skip-Tuning, a simple yet surprisingly effective training-free tuning method on the skip connections. Our method can achieve 100% FID improvement for pretrained EDM on ImageNet 64 with only 19 NFEs (1.75), breaking the limit of ODE samplers regardless of sampling steps. Surprisingly, the improvement persists when we increase the number of sampling steps and can even surpass the best result from EDM-2 (1.58) with only 39 NFEs (1.57). Comprehensive exploratory experiments are conducted to shed light on the surprising effectiveness. We observe that while Skip-Tuning increases the score-matching losses in the pixel space, the losses in the feature space are reduced, particularly at intermediate noise levels, which coincide with the most effective range accounting for image quality improvement.

Yihong Luo, Tianyang Hu, Jiacheng Sun et al.

Accelerating diffusion model sampling is crucial for efficient AIGC deployment. While diffusion distillation methods -- based on distribution matching and trajectory matching -- reduce sampling to as few as one step, they fall short on complex tasks like text-to-image generation. Few-step generation offers a better balance between speed and quality, but existing approaches face a persistent trade-off: distribution matching lacks flexibility for multi-step sampling, while trajectory matching often yields suboptimal image quality. To bridge this gap, we propose learning few-step diffusion models by Trajectory Distribution Matching (TDM), a unified distillation paradigm that combines the strengths of distribution and trajectory matching. Our method introduces a data-free score distillation objective, aligning the student's trajectory with the teacher's at the distribution level. Further, we develop a sampling-steps-aware objective that decouples learning targets across different steps, enabling more adjustable sampling. This approach supports both deterministic sampling for superior image quality and flexible multi-step adaptation, achieving state-of-the-art performance with remarkable efficiency. Our model, TDM, outperforms existing methods on various backbones, such as SDXL and PixArt-$α$, delivering superior quality and significantly reduced training costs. In particular, our method distills PixArt-$α$ into a 4-step generator that outperforms its teacher on real user preference at 1024 resolution. This is accomplished with 500 iterations and 2 A800 hours -- a mere 0.01% of the teacher's training cost. In addition, our proposed TDM can be extended to accelerate text-to-video diffusion. Notably, TDM can outperform its teacher model (CogVideoX-2B) by using only 4 NFE on VBench, improving the total score from 80.91 to 81.65. Project page: https://tdm-t2x.github.io/

Yihong Luo, Tianyang Hu, Weijian Luo et al.

This paper addresses the challenge of achieving high-quality and fast image generation that aligns with complex human preferences. While recent advancements in diffusion models and distillation have enabled rapid generation, the effective integration of reward feedback for improved abilities like controllability and preference alignment remains a key open problem. Existing reward-guided post-training approaches targeting accelerated few-step generation often deem diffusion distillation losses indispensable. However, in this paper, we identify an interesting yet fundamental paradigm shift: as conditions become more specific, well-designed reward functions emerge as the primary driving force in training strong, few-step image generative models. Motivated by this insight, we introduce Reward-Instruct, a novel and surprisingly simple reward-centric approach for converting pre-trained base diffusion models into reward-enhanced few-step generators. Unlike existing methods, Reward-Instruct does not rely on expensive yet tricky diffusion distillation losses. Instead, it iteratively updates the few-step generator's parameters by directly sampling from a reward-tilted parameter distribution. Such a training approach entirely bypasses the need for expensive diffusion distillation losses, making it favorable to scale in high image resolutions. Despite its simplicity, Reward-Instruct yields surprisingly strong performance. Our extensive experiments on text-to-image generation have demonstrated that Reward-Instruct achieves state-of-the-art results in visual quality and quantitative metrics compared to distillation-reliant methods, while also exhibiting greater robustness to the choice of reward function.

Zhiwei Wang, Yunji Wang, Zhongwang Zhang et al.

Large language models have consistently struggled with complex reasoning tasks, such as mathematical problem-solving. Investigating the internal reasoning mechanisms of these models can help us design better model architectures and training strategies, ultimately enhancing their reasoning capability. In this study, we constructed a symbolic multi-step reasoning task to investigate the information propagation mechanisms in Transformer models when solving the task through direct answering and Chain-of-Thought (CoT) reasoning. We introduced the concept of buffer mechanism: the model stores various information in distinct buffers and selectively extracts it through the query-key matrix. We proposed a random matrix-based algorithm to enhance the model's reasoning ability. This algorithm introduces only 132 trainable parameters, yet leads to significant performance improvements on 7 multi-step reasoning datasets, including PrOntoQA, LogicAsker, and LogicInference. These findings provide new insights into understanding the large language models.

Yihang Gao, Chuanyang Zheng, Enze Xie et al.

Besides natural language processing, transformers exhibit extraordinary performance in solving broader applications, including scientific computing and computer vision. Previous works try to explain this from the expressive power and capability perspectives that standard transformers are capable of performing some algorithms. To empower transformers with algorithmic capabilities and motivated by the recently proposed looped transformer, we design a novel transformer framework, dubbed Algorithm Transformer (abbreviated as AlgoFormer). We provide an insight that efficient transformer architectures can be designed by leveraging prior knowledge of tasks and the underlying structure of potential algorithms. Compared with the standard transformer and vanilla looped transformer, the proposed AlgoFormer can perform efficiently in algorithm representation in some specific tasks. In particular, inspired by the structure of human-designed learning algorithms, our transformer framework consists of a pre-transformer that is responsible for task preprocessing, a looped transformer for iterative optimization algorithms, and a post-transformer for producing the desired results after post-processing. We provide theoretical evidence of the expressive power of the AlgoFormer in solving some challenging problems, mirroring human-designed algorithms. Furthermore, some theoretical and empirical results are presented to show that the designed transformer has the potential to perform algorithm representation and learning. Experimental results demonstrate the empirical superiority of the proposed transformer in that it outperforms the standard transformer and vanilla looped transformer in some specific tasks. An extensive experiment on real language tasks (e.g., neural machine translation of German and English, and text classification) further validates the expressiveness and effectiveness of AlgoFormer.

Xuantong Liu, Tianyang Hu, Wenjia Wang et al.

As a dominant force in text-to-image generation tasks, Diffusion Probabilistic Models (DPMs) face a critical challenge in controllability, struggling to adhere strictly to complex, multi-faceted instructions. In this work, we aim to address this alignment challenge for conditional generation tasks. First, we provide an alternative view of state-of-the-art DPMs as a way of inverting advanced Vision-Language Models (VLMs). With this formulation, we naturally propose a training-free approach that bypasses the conventional sampling process associated with DPMs. By directly optimizing images with the supervision of discriminative VLMs, the proposed method can potentially achieve a better text-image alignment. As proof of concept, we demonstrate the pipeline with the pre-trained BLIP-2 model and identify several key designs for improved image generation. To further enhance the image fidelity, a Score Distillation Sampling module of Stable Diffusion is incorporated. By carefully balancing the two components during optimization, our method can produce high-quality images with near state-of-the-art performance on T2I-Compbench.

Yihong Luo, Tianyang Hu, Yifan Song et al.

While diffusion distillation has enabled one-step generation through methods like Variational Score Distillation, adapting distilled models to emerging new controls -- such as novel structural constraints or latest user preferences -- remains challenging. Conventional approaches typically requires modifying the base diffusion model and redistilling it -- a process that is both computationally intensive and time-consuming. To address these challenges, we introduce Joint Distribution Matching (JDM), a novel approach that minimizes the reverse KL divergence between image-condition joint distributions. By deriving a tractable upper bound, JDM decouples fidelity learning from condition learning. This asymmetric distillation scheme enables our one-step student to handle controls unknown to the teacher model and facilitates improved classifier-free guidance (CFG) usage and seamless integration of human feedback learning (HFL). Experimental results demonstrate that JDM surpasses baseline methods such as multi-step ControlNet by mere one-step in most cases, while achieving state-of-the-art performance in one-step text-to-image synthesis through improved usage of CFG or HFL integration.

Tianyu Xie, Shuchen Xue, Zijin Feng et al. · pku

Discrete diffusion models have recently shown great promise for modeling complex discrete data, with masked diffusion models (MDMs) offering a compelling trade-off between quality and generation speed. MDMs denoise by progressively unmasking multiple dimensions from an all-masked input, but their performance can degrade when using few denoising steps due to limited modeling of inter-dimensional dependencies. In this paper, we propose Variational Autoencoding Discrete Diffusion (VADD), a novel framework that enhances discrete diffusion with latent variable modeling to implicitly capture correlations among dimensions. By introducing an auxiliary recognition model, VADD enables stable training via variational lower bounds maximization and amortized inference over the training set. Our approach retains the efficiency of traditional MDMs while significantly improving sample quality, especially when the number of denoising steps is small. Empirical results on 2D toy data, pixel-level image generation, and text generation demonstrate that VADD consistently outperforms MDM baselines.

Yichen Xu, Yuyang Liang, Shan Dai et al.

As large language models (LLMs) continue to grow, the cost of full-parameter fine-tuning has made parameter-efficient fine-tuning (PEFT) the default strategy for downstream adaptation. Constraints from inference latency in scalable serving and fine-tuning cost in edge or rapid-deployment settings make the choice of which layers to fine-tune unavoidable. Yet current practice typically applies PEFT uniformly across all layers, with limited understanding or leverage of layer selection. This paper develops a unified projected residual view of PEFT on top of a frozen base model. Under a local quadratic approximation, layerwise adaptation is governed by three quantities: (i) the projected residual norm (resnorm), which measures how much correctable bias a layer can capture; (ii) the activation energy, which determines feature conditioning; and (iii) layer coupling, which quantifies how strongly residuals interact across layers. We show that, for squared loss and linear adapters, the resnorm equals a normalized gradient norm, activation energy controls ill-conditioning and noise amplification, and weak coupling yields approximately additive layerwise contributions. Building on these insights, we introduce the Layer Card, a reusable diagnostic that summarizes residual signal strength, compute cost, and performance for each layer of a given model. With an identical model and LoRA configuration, Layer Card-guided placement refines the choice of adapted layers to flexibly prioritize different objectives, such as maximizing performance or reducing fine-tuning cost. Moreover, on Qwen3-8B, we show that selectively adapting a subset of layers can achieve performance close to full-layer LoRA while substantially reducing fine-tuning cost and the number of adapter-augmented layers during inference, offering a more cost-performance-aware alternative to full-layer insertion.

Yao Tong, Haonan Wang, Siquan Li et al.

Fingerprinting Large Language Models (LLMs) is essential for provenance verification and model attribution. Existing methods typically extract post-hoc signatures based on training dynamics, data exposure, or hyperparameters -- properties that only emerge after training begins. In contrast, we propose a stronger and more intrinsic notion of LLM fingerprinting: SeedPrints, a method that leverages random initialization biases as persistent, seed-dependent identifiers present even before training. We show that untrained models exhibit reproducible token selection biases conditioned solely on their parameters at initialization. These biases are stable and measurable throughout training, enabling our statistical detection method to recover a model's lineage with high confidence. Unlike prior techniques, unreliable before convergence and vulnerable to distribution shifts, SeedPrints remains effective across all training stages and robust under domain shifts or parameter modifications. Experiments on LLaMA-style and Qwen-style models show that SeedPrints achieves seed-level distinguishability and can provide birth-to-lifecycle identity verification akin to a biometric fingerprint. Evaluations on large-scale pretrained models and fingerprinting benchmarks further confirm its effectiveness under practical deployment scenarios. These results suggest that initialization itself imprints a unique and persistent identity on neural language models, forming a true ''Galtonian'' fingerprint.

Haonan Wang, Brian Chen, Siquan Li et al.

Parameter-Efficient Fine-Tuning (PEFT) methods have become crucial for rapidly adapting large language models (LLMs) to downstream tasks. Prefix-Tuning, an early and effective PEFT technique, demonstrated the ability to achieve performance comparable to full fine-tuning with significantly reduced computational and memory overhead. However, despite its earlier success, its effectiveness in training modern state-of-the-art LLMs has been very limited. In this work, we demonstrate empirically that Prefix-Tuning underperforms on LLMs because of an inherent tradeoff between input and prefix significance within the attention head. This motivates us to introduce Prefix-Tuning+, a novel architecture that generalizes the principles of Prefix-Tuning while addressing its shortcomings by shifting the prefix module out of the attention head itself. We further provide an overview of our construction process to guide future users when constructing their own context-based methods. Our experiments show that, across a diverse set of benchmarks, Prefix-Tuning+ consistently outperforms existing Prefix-Tuning methods. Notably, it achieves performance on par with the widely adopted LoRA method on several general benchmarks, highlighting the potential modern extension of Prefix-Tuning approaches. Our findings suggest that by overcoming its inherent limitations, Prefix-Tuning can remain a competitive and relevant research direction in the landscape of parameter-efficient LLM adaptation.

Brian K Chen, Tianyang Hu, Hui Jin et al.

In-Context Learning (ICL) has been a powerful emergent property of large language models that has attracted increasing attention in recent years. In contrast to regular gradient-based learning, ICL is highly interpretable and does not require parameter updates. In this paper, we show that, for linearized transformer networks, ICL can be made explicit and permanent through the inclusion of bias terms. We mathematically demonstrate the equivalence between a model with ICL demonstration prompts and the same model with the additional bias terms. Our algorithm (ICLCA) allows for exact conversion in an inexpensive manner. Existing methods are not exact and require expensive parameter updates. We demonstrate the efficacy of our approach through experiments that show the exact incorporation of ICL tokens into a linear transformer. We further suggest how our method can be adapted to achieve cheap approximate conversion of ICL tokens, even in regular transformer networks that are not linearized. Our experiments on GPT-2 show that, even though the conversion is only approximate, the model still gains valuable context from the included bias terms.

Weijian Luo, Tianyang Hu, Shifeng Zhang et al.

Due to the ease of training, ability to scale, and high sample quality, diffusion models (DMs) have become the preferred option for generative modeling, with numerous pre-trained models available for a wide variety of datasets. Containing intricate information about data distributions, pre-trained DMs are valuable assets for downstream applications. In this work, we consider learning from pre-trained DMs and transferring their knowledge to other generative models in a data-free fashion. Specifically, we propose a general framework called Diff-Instruct to instruct the training of arbitrary generative models as long as the generated samples are differentiable with respect to the model parameters. Our proposed Diff-Instruct is built on a rigorous mathematical foundation where the instruction process directly corresponds to minimizing a novel divergence we call Integral Kullback-Leibler (IKL) divergence. IKL is tailored for DMs by calculating the integral of the KL divergence along a diffusion process, which we show to be more robust in comparing distributions with misaligned supports. We also reveal non-trivial connections of our method to existing works such as DreamFusion, and generative adversarial training. To demonstrate the effectiveness and universality of Diff-Instruct, we consider two scenarios: distilling pre-trained diffusion models and refining existing GAN models. The experiments on distilling pre-trained diffusion models show that Diff-Instruct results in state-of-the-art single-step diffusion-based models. The experiments on refining GAN models show that the Diff-Instruct can consistently improve the pre-trained generators of GAN models across various settings.

Shoukang Hu, Kaichen Zhou, Kaiyu Li et al.

Neural Radiance Fields (NeRF) has demonstrated remarkable 3D reconstruction capabilities with dense view images. However, its performance significantly deteriorates under sparse view settings. We observe that learning the 3D consistency of pixels among different views is crucial for improving reconstruction quality in such cases. In this paper, we propose ConsistentNeRF, a method that leverages depth information to regularize both multi-view and single-view 3D consistency among pixels. Specifically, ConsistentNeRF employs depth-derived geometry information and a depth-invariant loss to concentrate on pixels that exhibit 3D correspondence and maintain consistent depth relationships. Extensive experiments on recent representative works reveal that our approach can considerably enhance model performance in sparse view conditions, achieving improvements of up to 94% in PSNR, 76% in SSIM, and 31% in LPIPS compared to the vanilla baselines across various benchmarks, including DTU, NeRF Synthetic, and LLFF.

Liang Ding, Tianyang Hu, Jiahang Jiang et al.

Random smoothing data augmentation is a unique form of regularization that can prevent overfitting by introducing noise to the input data, encouraging the model to learn more generalized features. Despite its success in various applications, there has been a lack of systematic study on the regularization ability of random smoothing. In this paper, we aim to bridge this gap by presenting a framework for random smoothing regularization that can adaptively and effectively learn a wide range of ground truth functions belonging to the classical Sobolev spaces. Specifically, we investigate two underlying function spaces: the Sobolev space of low intrinsic dimension, which includes the Sobolev space in $D$-dimensional Euclidean space or low-dimensional sub-manifolds as special cases, and the mixed smooth Sobolev space with a tensor structure. By using random smoothing regularization as novel convolution-based smoothing kernels, we can attain optimal convergence rates in these cases using a kernel gradient descent algorithm, either with early stopping or weight decay. It is noteworthy that our estimator can adapt to the structural assumptions of the underlying data and avoid the curse of dimensionality. This is achieved through various choices of injected noise distributions such as Gaussian, Laplace, or general polynomial noises, allowing for broad adaptation to the aforementioned structural assumptions of the underlying data. The convergence rate depends only on the effective dimension, which may be significantly smaller than the actual data dimension. We conduct numerical experiments on simulated data to validate our theoretical results.

Tianyang Hu, Jun Wang, Wenjia Wang et al.

Deep learning has achieved many breakthroughs in modern classification tasks. Numerous architectures have been proposed for different data structures but when it comes to the loss function, the cross-entropy loss is the predominant choice. Recently, several alternative losses have seen revived interests for deep classifiers. In particular, empirical evidence seems to promote square loss but a theoretical justification is still lacking. In this work, we contribute to the theoretical understanding of square loss in classification by systematically investigating how it performs for overparametrized neural networks in the neural tangent kernel (NTK) regime. Interesting properties regarding the generalization error, robustness, and calibration error are revealed. We consider two cases, according to whether classes are separable or not. In the general non-separable case, fast convergence rate is established for both misclassification rate and calibration error. When classes are separable, the misclassification rate improves to be exponentially fast. Further, the resulting margin is proven to be lower bounded away from zero, providing theoretical guarantees for robustness. We expect our findings to hold beyond the NTK regime and translate to practical settings. To this end, we conduct extensive empirical studies on practical neural networks, demonstrating the effectiveness of square loss in both synthetic low-dimensional data and real image data. Comparing to cross-entropy, square loss has comparable generalization error but noticeable advantages in robustness and model calibration.

Tianyang Hu, Wenjia Wang, Cong Lin et al.

Overparametrized neural networks trained by gradient descent (GD) can provably overfit any training data. However, the generalization guarantee may not hold for noisy data. From a nonparametric perspective, this paper studies how well overparametrized neural networks can recover the true target function in the presence of random noises. We establish a lower bound on the $L_2$ estimation error with respect to the GD iterations, which is away from zero without a delicate scheme of early stopping. In turn, through a comprehensive analysis of $\ell_2$-regularized GD trajectories, we prove that for overparametrized one-hidden-layer ReLU neural network with the $\ell_2$ regularization: (1) the output is close to that of the kernel ridge regression with the corresponding neural tangent kernel; (2) minimax {optimal} rate of $L_2$ estimation error can be achieved. Numerical experiments confirm our theory and further demonstrate that the $\ell_2$ regularization approach improves the training robustness and works for a wider range of neural networks.

Tianyang Hu, Zuofeng Shang, Guang Cheng

Classifiers built with neural networks handle large-scale high dimensional data, such as facial images from computer vision, extremely well while traditional statistical methods often fail miserably. In this paper, we attempt to understand this empirical success in high dimensional classification by deriving the convergence rates of excess risk. In particular, a teacher-student framework is proposed that assumes the Bayes classifier to be expressed as ReLU neural networks. In this setup, we obtain a sharp rate of convergence, i.e., $\tilde{O}_d(n^{-2/3})$, for classifiers trained using either 0-1 loss or hinge loss. This rate can be further improved to $\tilde{O}_d(n^{-1})$ when the data distribution is separable. Here, $n$ denotes the sample size. An interesting observation is that the data dimension only contributes to the $\log(n)$ term in the above rates. This may provide one theoretical explanation for the empirical successes of deep neural networks in high dimensional classification, particularly for structured data.

Tianyang Hu, Zixiang Chen, Hanxi Sun et al.

We propose two novel samplers to generate high-quality samples from a given (un-normalized) probability density. Motivated by the success of generative adversarial networks, we construct our samplers using deep neural networks that transform a reference distribution to the target distribution. Training schemes are developed to minimize two variations of the Stein discrepancy, which is designed to work with un-normalized densities. Once trained, our samplers are able to generate samples instantaneously. We show that the proposed methods are theoretically sound and experience fewer convergence issues compared with traditional sampling approaches according to our empirical studies.