arXiv subjects

Difan Zou

Publications and source records attributed to Difan Zou.

At least 73 records · Page 4Linked to original sources

arXiv2025

Capturing Conditional Dependence via Auto-regressive Diffusion Models

Diffusion models have demonstrated appealing performance in both image and video generation. However, many works discover that they struggle to capture important, high-level relationships that are present in the real world. For example, they fail to learn physical laws from data, and even fail to understand that the objects in the world exist in a stable fashion. This is due to the fact that important conditional dependence structures are not adequately captured in the vanilla diffusion models. In this work, we initiate an in-depth study on strengthening the diffusion model to capture the conditional dependence structures in the data. In particular, we examine the efficacy of the auto-regressive (AR) diffusion models for such purpose and develop the first theoretical results on the sampling error of AR diffusion models under (possibly) the mildest data assumption. Our theoretical findings indicate that, compared with typical diffusion models, the AR variant produces samples with a reduced gap in approximating the data conditional distribution. On the other hand, the overall inference time of the AR-diffusion models is only moderately larger than that for the vanilla diffusion models, making them still practical for large scale applications. We also provide empirical results showing that when there is clear conditional dependence structure in the data, the AR diffusion models captures such structure, whereas vanilla DDPM fails to do so. On the other hand, when there is no obvious conditional dependence across patches of the data, AR diffusion does not outperform DDPM.

cs.LG↗

arXiv2025

How Does Critical Batch Size Scale in Pre-training?

Training large-scale models under given resources requires careful design of parallelism strategies. In particular, the efficiency notion of critical batch size (CBS), concerning the compromise between time and compute, marks the threshold beyond which greater data parallelism leads to diminishing returns. To operationalize it, we propose a measure of CBS and pre-train a series of auto-regressive language models, ranging from 85 million to 1.2 billion parameters, on the C4 dataset. Through extensive hyper-parameter sweeps and careful control of factors such as batch size, momentum, and learning rate along with its scheduling, we systematically investigate the impact of scale on CBS. Then we fit scaling laws with respect to model and data sizes to decouple their effects. Overall, our results demonstrate that CBS scales primarily with data size rather than model size, a finding we justify theoretically through the analysis of infinite-width limits of neural networks and infinite-dimensional least squares regression. Of independent interest, we highlight the importance of common hyper-parameter choices and strategies for studying large-scale pre-training beyond fixed training durations.

cs.LG↗

arXiv2025

FedEGG: Federated Learning with Explicit Global Guidance

Federated Learning (FL) holds great potential for diverse applications owing to its privacy-preserving nature. However, its convergence is often challenged by non-IID data distributions, limiting its effectiveness in real-world deployments. Existing methods help address these challenges via optimization-based client constraints, adaptive client selection, or the use of pre-trained models or synthetic data. In this work, we reinterpret these approaches as all introducing an \emph{implicit guiding task} to regularize and steer client learning. Following this insight, we propose to introduce an \emph{explicit global guiding task} into the current FL framework to improve convergence and performance. To this end, we present \textbf{FedEGG}, a new FL algorithm that constructs a global guiding task using a well-defined, easy-to-converge learning task based on a public dataset and Large Language Models (LLMs). This approach effectively combines the strengths of federated (the original FL task) and centralized (the global guiding task) learning. We provide a theoretical analysis of FedEGG's convergence, examining the impact of data heterogeneity between the guiding and FL tasks and the guiding strength. Our analysis derives an upper bound for the optimal guiding strength, offering practical insights for implementation. Empirically, FedEGG demonstrates superior performance over state-of-the-art FL methods under both IID and non-IID settings, and further improves their performances when combined.

cs.LG↗

arXiv2025

Gradient Descent Robustly Learns the Intrinsic Dimension of Data in Training Convolutional Neural Networks

Modern neural networks are usually highly over-parameterized. Behind the wide usage of over-parameterized networks is the belief that, if the data are simple, then the trained network will be automatically equivalent to a simple predictor. Following this intuition, many existing works have studied different notions of "ranks" of neural networks and their relation to the rank of data. In this work, we study the rank of convolutional neural networks (CNNs) trained by gradient descent, with a specific focus on the robustness of the rank to image background noises. Specifically, we point out that, when adding background noises to images, the rank of the CNN trained with gradient descent is affected far less compared with the rank of the data. We support our claim with a theoretical case study, where we consider a particular data model to characterize low-rank clean images with added background noises. We prove that CNNs trained by gradient descent can learn the intrinsic dimension of clean images, despite the presence of relatively large background noises. We also conduct experiments on synthetic and real datasets to further validate our claim.

stat.ML↗

arXiv2025

Parallelized Autoregressive Visual Generation

Autoregressive models have emerged as a powerful approach for visual generation but suffer from slow inference speed due to their sequential token-by-token prediction process. In this paper, we propose a simple yet effective approach for parallelized autoregressive visual generation that improves generation efficiency while preserving the advantages of autoregressive modeling. Our key insight is that parallel generation depends on visual token dependencies-tokens with weak dependencies can be generated in parallel, while strongly dependent adjacent tokens are difficult to generate together, as their independent sampling may lead to inconsistencies. Based on this observation, we develop a parallel generation strategy that generates distant tokens with weak dependencies in parallel while maintaining sequential generation for strongly dependent local tokens. Our approach can be seamlessly integrated into standard autoregressive models without modifying the architecture or tokenizer. Experiments on ImageNet and UCF-101 demonstrate that our method achieves a 3.6x speedup with comparable quality and up to 9.5x speedup with minimal quality degradation across both image and video generation tasks. We hope this work will inspire future research in efficient visual generation and unified autoregressive modeling. Project page: https://yuqingwang1029.github.io/PAR-project.

cs.CV↗

arXiv2025

On the Feature Learning in Diffusion Models

The predominant success of diffusion models in generative modeling has spurred significant interest in understanding their theoretical foundations. In this work, we propose a feature learning framework aimed at analyzing and comparing the training dynamics of diffusion models with those of traditional classification models. Our theoretical analysis demonstrates that diffusion models, due to the denoising objective, are encouraged to learn more balanced and comprehensive representations of the data. In contrast, neural networks with a similar architecture trained for classification tend to prioritize learning specific patterns in the data, often focusing on easy-to-learn components. To support these theoretical insights, we conduct several experiments on both synthetic and real-world datasets, which empirically validate our findings and highlight the distinct feature learning dynamics in diffusion models compared to classification.

stat.ML↗

arXiv2025

STGAN: Spatial-temporal Graph Autoregression Network for Pavement Distress Deterioration Prediction

Pavement distress significantly compromises road integrity and poses risks to drivers. Accurate prediction of pavement distress deterioration is essential for effective road management, cost reduction in maintenance, and improvement of traffic safety. However, real-world data on pavement distress is usually collected irregularly, resulting in uneven, asynchronous, and sparse spatial-temporal datasets. This hinders the application of existing spatial-temporal models, such as DCRNN, since they are only applicable to regularly and synchronously collected data. To overcome these challenges, we propose the Spatial-Temporal Graph Autoregression Network (STGAN), a novel graph neural network model designed for accurately predicting irregular pavement distress deterioration using complex spatial-temporal data. Specifically, STGAN integrates the temporal domain into the spatial domain, creating a larger graph where nodes are represented by spatial-temporal tuples and edges are formed based on a similarity-based connection mechanism. Furthermore, based on the constructed spatiotemporal graph, we formulate pavement distress deterioration prediction as a graph autoregression task, i.e., the graph size increases incrementally and the prediction is performed sequentially. This is accomplished by a novel spatial-temporal attention mechanism deployed by STGAN. Utilizing the ConTrack dataset, which contains pavement distress records collected from different locations in Shanghai, we demonstrate the superior performance of STGAN in capturing spatial-temporal correlations and addressing the aforementioned challenges. Experimental results further show that STGAN outperforms baseline models, and ablation studies confirm the effectiveness of its novel modules. Our findings contribute to promoting proactive road maintenance decision-making and ultimately enhancing road safety and resilience.

cs.LG↗

arXiv2025

On the Robustness of Transformers against Context Hijacking for Linear Classification

Transformer-based Large Language Models (LLMs) have demonstrated powerful in-context learning capabilities. However, their predictions can be disrupted by factually correct context, a phenomenon known as context hijacking, revealing a significant robustness issue. To understand this phenomenon theoretically, we explore an in-context linear classification problem based on recent advances in linear transformers. In our setup, context tokens are designed as factually correct query-answer pairs, where the queries are similar to the final query but have opposite labels. Then, we develop a general theoretical analysis on the robustness of the linear transformers, which is formulated as a function of the model depth, training context lengths, and number of hijacking context tokens. A key finding is that a well-trained deeper transformer can achieve higher robustness, which aligns with empirical observations. We show that this improvement arises because deeper layers enable more fine-grained optimization steps, effectively mitigating interference from context hijacking. This is also well supported by our numerical experiments. Our findings provide theoretical insights into the benefits of deeper architectures and contribute to enhancing the understanding of transformer architectures.

cs.CL↗

arXiv2025

Can Diffusion Models Learn Hidden Inter-Feature Rules Behind Images?

Despite the remarkable success of diffusion models (DMs) in data generation, they exhibit specific failure cases with unsatisfactory outputs. We focus on one such limitation: the ability of DMs to learn hidden rules between image features. Specifically, for image data with dependent features ($\mathbf{x}$) and ($\mathbf{y}$) (e.g., the height of the sun ($\mathbf{x}$) and the length of the shadow ($\mathbf{y}$)), we investigate whether DMs can accurately capture the inter-feature rule ($p(\mathbf{y}|\mathbf{x})$). Empirical evaluations on mainstream DMs (e.g., Stable Diffusion 3.5) reveal consistent failures, such as inconsistent lighting-shadow relationships and mismatched object-mirror reflections. Inspired by these findings, we design four synthetic tasks with strongly correlated features to assess DMs' rule-learning abilities. Extensive experiments show that while DMs can identify coarse-grained rules, they struggle with fine-grained ones. Our theoretical analysis demonstrates that DMs trained via denoising score matching (DSM) exhibit constant errors in learning hidden rules, as the DSM objective is not compatible with rule conformity. To mitigate this, we introduce a common technique - incorporating additional classifier guidance during sampling, which achieves (limited) improvements. Our analysis reveals that the subtle signals of fine-grained rules are challenging for the classifier to capture, providing insights for future exploration.

cs.CV↗

arXiv2024

Beyond Surface Structure: A Causal Assessment of LLMs' Comprehension Ability

Large language models (LLMs) have shown remarkable capability in natural language tasks, yet debate persists on whether they truly comprehend deep structure (i.e., core semantics) or merely rely on surface structure (e.g., presentation format). Prior studies observe that LLMs' performance declines when intervening on surface structure, arguing their success relies on surface structure recognition. However, surface structure sensitivity does not prevent deep structure comprehension. Rigorously evaluating LLMs' capability requires analyzing both, yet deep structure is often overlooked. To this end, we assess LLMs' comprehension ability using causal mediation analysis, aiming to fully discover the capability of using both deep and surface structures. Specifically, we formulate the comprehension of deep structure as direct causal effect (DCE) and that of surface structure as indirect causal effect (ICE), respectively. To address the non-estimability of original DCE and ICE -- stemming from the infeasibility of isolating mutual influences of deep and surface structures, we develop the corresponding quantifiable surrogates, including approximated DCE (ADCE) and approximated ICE (AICE). We further apply the ADCE to evaluate a series of mainstream LLMs, showing that most of them exhibit deep structure comprehension ability, which grows along with the prediction accuracy. Comparing ADCE and AICE demonstrates closed-source LLMs rely more on deep structure, while open-source LLMs are more surface-sensitive, which decreases with model scale. Theoretically, ADCE is a bidirectional evaluation, which measures both the sufficiency and necessity of deep structure changes in causing output variations, thus offering a more comprehensive assessment than accuracy, a common evaluation in LLMs. Our work provides new insights into LLMs' deep structure comprehension and offers novel methods for LLMs evaluation.

cs.CL↗

arXiv2024

An In-depth Investigation of Sparse Rate Reduction in Transformer-like Models

Deep neural networks have long been criticized for being black-box. To unveil the inner workings of modern neural architectures, a recent work \cite{yu2024white} proposed an information-theoretic objective function called Sparse Rate Reduction (SRR) and interpreted its unrolled optimization as a Transformer-like model called Coding Rate Reduction Transformer (CRATE). However, the focus of the study was primarily on the basic implementation, and whether this objective is optimized in practice and its causal relationship to generalization remain elusive. Going beyond this study, we derive different implementations by analyzing layer-wise behaviors of CRATE, both theoretically and empirically. To reveal the predictive power of SRR on generalization, we collect a set of model variants induced by varied implementations and hyperparameters and evaluate SRR as a complexity measure based on its correlation with generalization. Surprisingly, we find out that SRR has a positive correlation coefficient and outperforms other baseline measures, such as path-norm and sharpness-based ones. Furthermore, we show that generalization can be improved using SRR as regularization on benchmark image classification datasets. We hope this paper can shed light on leveraging SRR to design principled models and study their generalization ability.

cs.LG↗

arXiv2024

Slight Corruption in Pre-training Data Makes Better Diffusion Models

Diffusion models (DMs) have shown remarkable capabilities in generating realistic high-quality images, audios, and videos. They benefit significantly from extensive pre-training on large-scale datasets, including web-crawled data with paired data and conditions, such as image-text and image-class pairs. Despite rigorous filtering, these pre-training datasets often inevitably contain corrupted pairs where conditions do not accurately describe the data. This paper presents the first comprehensive study on the impact of such corruption in pre-training data of DMs. We synthetically corrupt ImageNet-1K and CC3M to pre-train and evaluate over 50 conditional DMs. Our empirical findings reveal that various types of slight corruption in pre-training can significantly enhance the quality, diversity, and fidelity of the generated images across different DMs, both during pre-training and downstream adaptation stages. Theoretically, we consider a Gaussian mixture model and prove that slight corruption in the condition leads to higher entropy and a reduced 2-Wasserstein distance to the ground truth of the data distribution generated by the corruptly trained DMs. Inspired by our analysis, we propose a simple method to improve the training of DMs on practical datasets by adding condition embedding perturbations (CEP). CEP significantly improves the performance of various DMs in both pre-training and downstream tasks. We hope that our study provides new insights into understanding the data and pre-training processes of DMs and all models are released at https://huggingface.co/DiffusionNoise.

cs.CV↗

arXiv2024

Initialization Matters: On the Benign Overfitting of Two-Layer ReLU CNN with Fully Trainable Layers

Benign overfitting refers to how over-parameterized neural networks can fit training data perfectly and generalize well to unseen data. While this has been widely investigated theoretically, existing works are limited to two-layer networks with fixed output layers, where only the hidden weights are trained. We extend the analysis to two-layer ReLU convolutional neural networks (CNNs) with fully trainable layers, which is closer to the practice. Our results show that the initialization scaling of the output layer is crucial to the training dynamics: large scales make the model training behave similarly to that with the fixed output, the hidden layer grows rapidly while the output layer remains largely unchanged; in contrast, small scales result in more complex layer interactions, the hidden layer initially grows to a specific ratio relative to the output layer, after which both layers jointly grow and maintain that ratio throughout training. Furthermore, in both settings, we provide nearly matching upper and lower bounds on the test errors, identifying the sharp conditions on the initialization scaling and signal-to-noise ratio (SNR) in which the benign overfitting can be achieved or not. Numerical experiments back up the theoretical results.

cs.LG↗

arXiv2024

Extracting Training Data from Unconditional Diffusion Models

As diffusion probabilistic models (DPMs) are being employed as mainstream models for generative artificial intelligence (AI), the study of their memorization of the raw training data has attracted growing attention. Existing works in this direction aim to establish an understanding of whether or to what extent DPMs learn by memorization. Such an understanding is crucial for identifying potential risks of data leakage and copyright infringement in diffusion models and, more importantly, for more controllable generation and trustworthy application of Artificial Intelligence Generated Content (AIGC). While previous works have made important observations of when DPMs are prone to memorization, these findings are mostly empirical, and the developed data extraction methods only work for conditional diffusion models. In this work, we aim to establish a theoretical understanding of memorization in DPMs with 1) a memorization metric for theoretical analysis, 2) an analysis of conditional memorization with informative and random labels, and 3) two better evaluation metrics for measuring memorization. Based on the theoretical analysis, we further propose a novel data extraction method called \textbf{Surrogate condItional Data Extraction (SIDE)} that leverages a classifier trained on generated data as a surrogate condition to extract training data directly from unconditional diffusion models. Our empirical results demonstrate that SIDE can extract training data from diffusion models where previous methods fail, and it is on average over 50\% more effective across different scales of the CelebA dataset.

cs.CR↗

arXiv2024

Self-Control of LLM Behaviors by Compressing Suffix Gradient into Prefix Controller

We propose SelfControl, an inference-time model control method utilizing gradients to control the behavior of large language models (LLMs) without explicit human annotations. Given a desired behavior expressed in a natural language suffix string concatenated to the input prompt, SelfControl computes gradients of the LLM's self-evaluation of the suffix with respect to its latent representations. The gradients are used to directly control the auto-regressive generation process towards desired behaviors, which eliminates human supervision, achieves precise and transparent control, and offers on-the-fly adaptability. To further enhance efficiency, we introduce SelfControl_{Prefix}, a compact module that encapsulates the learned representations from gradients into a SelfControl_{Prefix}, facilitating efficient inference-time control with no latency compared to the original model and allowing control for multiple behaviors simultaneously. Our experiments demonstrate SelfControl's efficacy across multiple domains, where it improves over SOTA for 8.3% in detoxification, 3.1% in truthfulness enhancement, 4%~10% in controlling on emotion tones, and 48.2% in privacy protection, i.e., completely remove privacy leakage issue. Additionally, we demonstrate that SelfControl can be used for data synthesis and to improve reasoning abilities.

cs.CL↗

arXiv2024

How Transformers Utilize Multi-Head Attention in In-Context Learning? A Case Study on Sparse Linear Regression

Despite the remarkable success of transformer-based models in various real-world tasks, their underlying mechanisms remain poorly understood. Recent studies have suggested that transformers can implement gradient descent as an in-context learner for linear regression problems and have developed various theoretical analyses accordingly. However, these works mostly focus on the expressive power of transformers by designing specific parameter constructions, lacking a comprehensive understanding of their inherent working mechanisms post-training. In this study, we consider a sparse linear regression problem and investigate how a trained multi-head transformer performs in-context learning. We experimentally discover that the utilization of multi-heads exhibits different patterns across layers: multiple heads are utilized and essential in the first layer, while usually only a single head is sufficient for subsequent layers. We provide a theoretical explanation for this observation: the first layer preprocesses the context data, and the following layers execute simple optimization steps based on the preprocessed context. Moreover, we demonstrate that such a preprocess-then-optimize algorithm can significantly outperform naive gradient descent and ridge regression algorithms. Further experimental results support our explanations. Our findings offer insights into the benefits of multi-head attention and contribute to understanding the more intricate mechanisms hidden within trained transformers.

cs.LG↗

arXiv2024

On the Limitation and Experience Replay for GNNs in Continual Learning

Continual learning seeks to empower models to progressively acquire information from a sequence of tasks. This approach is crucial for many real-world systems, which are dynamic and evolve over time. Recent research has witnessed a surge in the exploration of Graph Neural Networks (GNN) in Node-wise Graph Continual Learning (NGCL), a practical yet challenging paradigm involving the continual training of a GNN on node-related tasks. Despite recent advancements in continual learning strategies for GNNs in NGCL, a thorough theoretical understanding, especially regarding its learnability, is lacking. Learnability concerns the existence of a learning algorithm that can produce a good candidate model from the hypothesis/weight space, which is crucial for model selection in NGCL development. This paper introduces the first theoretical exploration of the learnability of GNN in NGCL, revealing that learnability is heavily influenced by structural shifts due to the interconnected nature of graph data. Specifically, GNNs may not be viable for NGCL under significant structural changes, emphasizing the need to manage structural shifts. To mitigate the impact of structural shifts, we propose a novel experience replay method termed Structure-Evolution-Aware Experience Replay (SEA-ER). SEA-ER features an innovative experience selection strategy that capitalizes on the topological awareness of GNNs, alongside a unique replay strategy that employs structural alignment to effectively counter catastrophic forgetting and diminish the impact of structural shifts on GNNs in NGCL. Our extensive experiments validate our theoretical insights and the effectiveness of SEA-ER.

cs.LG↗

arXiv2024

Explainable Bayesian Recurrent Neural Smoother to Capture Global State Evolutionary Correlations

Through integrating the evolutionary correlations across global states in the bidirectional recursion, an explainable Bayesian recurrent neural smoother (EBRNS) is proposed for offline data-assisted fixed-interval state smoothing. At first, the proposed model, containing global states in the evolutionary interval, is transformed into an equivalent model with bidirectional memory. This transformation incorporates crucial global state information with support for bi-directional recursive computation. For the transformed model, the joint state-memory-trend Bayesian filtering and smoothing frameworks are derived by introducing the bidirectional memory iteration mechanism and offline data into Bayesian estimation theory. The derived frameworks are implemented using the Gaussian approximation to ensure analytical properties and computational efficiency. Finally, the neural network modules within EBRNS and its two-stage training scheme are designed. Unlike most existing approaches that artificially combine deep learning and model-based estimation, the bidirectional recursion and internal gated structures of EBRNS are naturally derived from Bayesian estimation theory, explainably integrating prior model knowledge, online measurement, and offline data. Experiments on representative real-world datasets demonstrate that the high smoothing accuracy of EBRNS is accompanied by data efficiency and a lightweight parameter scale.

eess.SP↗