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Difan Zou

Publications and source records attributed to Difan Zou.

At least 55 records · Page 3Linked to original sources
arXiv2025

F-Adapter: Frequency-Adaptive Parameter-Efficient Fine-Tuning in Scientific Machine Learning

Parameter-efficient fine-tuning (PEFT) of powerful pre-trained models for complex downstream tasks has proven effective in vision and language processing, yet this paradigm remains unexplored in scientific machine learning, where the objective is to model complex physical systems. We conduct the first systematic study of PEFT for pre-trained Large Operator Models (LOMs) obtained by scaling variants of Fourier Neural Operator. First, we observe that the widely used Low-Rank Adaptation (LoRA) yields markedly poorer performance on LOMs than Adapter tuning. Then, we further theoretically establish that stacked LoRA incurs a depth-amplified lower bound on approximation error within Fourier layers, whereas adapters retain universal approximation capacity and, by concentrating parameters on energy-dominant low-frequency modes, attain exponentially decaying error with bottleneck width in the Fourier domain. Motivated by the robust empirical gains of adapters and by our theoretical characterization of PDE solutions as spectrally sparse, we introduce Frequency-Adaptive Adapter (F-Adapter). F-Adapter allocates adapter capacity based on spectral complexity, assigning higher-dimension modules to low-frequency components and lower-dimension modules to high-frequency components. Our F-Adapters establish state-of-the-art (SOTA) results on multiple challenging 3D Navier-Stokes benchmarks, markedly enhancing both generalization and spectral fidelity over LoRA and other PEFT techniques commonly used in LLMs. To the best of our knowledge, this work is the first to explore PEFT for scientific machine-learning and establishes F-Adapter as an effective paradigm for this domain.

cs.LG↗
arXiv2025

Kernel Regression in Structured Non-IID Settings: Theory and Implications for Denoising Score Learning

Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d. setting, while real-world data often exhibits structured dependencies - particularly in applications like denoising score learning where multiple noisy observations derive from shared underlying signals. We present the first systematic study of KRR generalization for non-i.i.d. data with signal-noise causal structure, where observations represent different noisy views of common signals. By developing a novel blockwise decomposition method that enables precise concentration analysis for dependent data, we derive excess risk bounds for KRR that explicitly depend on: (1) the kernel spectrum, (2) causal structure parameters, and (3) sampling mechanisms (including relative sample sizes for signals and noises). We further apply our results to denoising score learning, establishing generalization guarantees and providing principled guidance for sampling noisy data points. This work advances KRR theory while providing practical tools for analyzing dependent data in modern machine learning applications.

stat.ML↗
arXiv2025

Hierarchical Koopman Diffusion: Fast Generation with Interpretable Diffusion Trajectory

Diffusion models have achieved impressive success in high-fidelity image generation but suffer from slow sampling due to their inherently iterative denoising process. While recent one-step methods accelerate inference by learning direct noise-to-image mappings, they sacrifice the interpretability and fine-grained control intrinsic to diffusion dynamics, key advantages that enable applications like editable generation. To resolve this dichotomy, we introduce \textbf{Hierarchical Koopman Diffusion}, a novel framework that achieves both one-step sampling and interpretable generative trajectories. Grounded in Koopman operator theory, our method lifts the nonlinear diffusion dynamics into a latent space where evolution is governed by globally linear operators, enabling closed-form trajectory solutions. This formulation not only eliminates iterative sampling but also provides full access to intermediate states, allowing manual intervention during generation. To model the multi-scale nature of images, we design a hierarchical architecture that disentangles generative dynamics across spatial resolutions via scale-specific Koopman subspaces, capturing coarse-to-fine details systematically. We empirically show that the Hierarchical Koopman Diffusion not only achieves competitive one-step generation performance but also provides a principled mechanism for interpreting and manipulating the generative process through spectral analysis. Our framework bridges the gap between fast sampling and interpretability in diffusion models, paving the way for explainable image synthesis in generative modeling.

cs.LG↗
arXiv2025

Understanding the Generalization of Stochastic Gradient Adam in Learning Neural Networks

Adam is a popular and widely used adaptive gradient method in deep learning, which has also received tremendous focus in theoretical research. However, most existing theoretical work primarily analyzes its full-batch version, which differs fundamentally from the stochastic variant used in practice. Unlike SGD, stochastic Adam does not converge to its full-batch counterpart even with infinitesimal learning rates. We present the first theoretical characterization of how batch size affects Adam's generalization, analyzing two-layer over-parameterized CNNs on image data. Our results reveal that while both Adam and AdamW with proper weight decay $λ$ converge to poor test error solutions, their mini-batch variants can achieve near-zero test error. We further prove Adam has a strictly smaller effective weight decay bound than AdamW, theoretically explaining why Adam requires more sensitive $λ$ tuning. Extensive experiments validate our findings, demonstrating the critical role of batch size and weight decay in Adam's generalization performance.

cs.LG↗
arXiv2025

Speculative Jacobi-Denoising Decoding for Accelerating Autoregressive Text-to-image Generation

As a new paradigm of visual content generation, autoregressive text-to-image models suffer from slow inference due to their sequential token-by-token decoding process, often requiring thousands of model forward passes to generate a single image. To address this inefficiency, we propose Speculative Jacobi-Denoising Decoding (SJD2), a framework that incorporates the denoising process into Jacobi iterations to enable parallel token generation in autoregressive models. Our method introduces a next-clean-token prediction paradigm that enables the pre-trained autoregressive models to accept noise-perturbed token embeddings and predict the next clean tokens through low-cost fine-tuning. This denoising paradigm guides the model towards more stable Jacobi trajectories. During inference, our method initializes token sequences with Gaussian noise and performs iterative next-clean-token-prediction in the embedding space. We employ a probabilistic criterion to verify and accept multiple tokens in parallel, and refine the unaccepted tokens for the next iteration with the denoising trajectory. Experiments show that our method can accelerate generation by reducing model forward passes while maintaining the visual quality of generated images.

cs.CV↗
arXiv2025

Does higher interpretability imply better utility? A Pairwise Analysis on Sparse Autoencoders

Sparse Autoencoders (SAEs) are widely used to steer large language models (LLMs), based on the assumption that their interpretable features naturally enable effective model behavior steering. Yet, a fundamental question remains unanswered: does higher interpretability indeed imply better steering utility? To answer this question, we train 90 SAEs across three LLMs (Gemma-2-2B, Qwen-2.5-3B, Gemma-2-9B), spanning five architectures and six sparsity levels, and evaluate their interpretability and steering utility based on SAEBench (arXiv:2501.12345) and AxBench (arXiv:2502.23456) respectively, and perform a rank-agreement analysis via Kendall's rank coefficients (tau b). Our analysis reveals only a relatively weak positive association (tau b approx 0.298), indicating that interpretability is an insufficient proxy for steering performance. We conjecture the interpretability utility gap may stem from the selection of SAE features, as not all of them are equally effective for steering. To further find features that truly steer the behavior of LLMs, we propose a novel selection criterion called Delta Token Confidence, which measures how much amplifying a feature changes the next token distribution. We show that our method improves the steering performance of three LLMs by 52.52 percent compared to the current best output score based criterion (arXiv:2503.34567). Strikingly, after selecting features with high Delta Token Confidence, the correlation between interpretability and utility vanishes (tau b approx 0), and can even become negative. This further highlights the divergence between interpretability and utility for the most effective steering features.

cs.LG↗
arXiv2025

Reshaping Reasoning in LLMs: A Theoretical Analysis of RL Training Dynamics through Pattern Selection

While reinforcement learning (RL) demonstrated remarkable success in enhancing the reasoning capabilities of language models, the training dynamics of RL in LLMs remain unclear. In this work, we provide an explanation of the RL training process through empirical analysis and rigorous theoretical modeling. First, through systematic reasoning-pattern-level and token-level analysis across the RL training process, we show that while different reasoning patterns exhibit relatively stable success rates during training, RL primarily optimizes a sparse subset of critical tokens, thereby reshaping reasoning pattern distributions to affect model performance. Building on these empirical insights, we develop a theoretical framework to understand the training dynamics of RL with two typical rewards: verifiable reward (RLVR) and model's internal feedback (RLIF). For RLVR, we analyze the training dynamics under two special cases: one where models readily converge to optimal reasoning strategies, and another where optimization becomes challenging, revealing that the base model's reasoning quality is crucial for determining convergence behavior. For RLIF, we examine how internal rewards initially improve model performance but can potentially lead to degradation with continued training. Extensive experiments validate our findings, advancing both theoretical understanding and practical applications of RL in language model enhancement.

cs.LG↗
arXiv2025

Turning Internal Gap into Self-Improvement: Promoting the Generation-Understanding Unification in MLLMs

Although unified MLLMs aim to unify generation and understanding, they are considered to exhibit an internal gap, with understanding outperforming generation. Through large-scale evaluation across multiple MLLMs and tasks, we confirm the widespread non-unification of MLLMs, and demonstrate that it indeed stems from weak generation rather than misunderstanding. This finding motivates us to propose a simple yet effective internal gap-based self-improvement framework, which mitigates internal gaps by leveraging stronger understanding to guide weaker generation without relying on any external signals. We validate this strategy through comprehensive experiments: scoring generations with understanding to construct image data for post-training (e.g., SFT and DPO) significantly improves generation while promoting unification. Furthermore, we empirically discover a co-improvement effect of such self-improvement, a phenomenon well known in pre-training but underexplored in post-training. Specifically, as generation improves, understanding becomes more effective at detecting false positives that were previously misclassified as prompt-aligned. To explain this effect, we extend learning dynamic theory to the MLLM setting, showing that the shared empirical neural tangent kernel between generation and understanding encourages aligned learning dynamics, thereby driving co-improvement. This interplay between generation and understanding further motivates a curriculum learning approach for stronger self-improvement: progressively enhanced understanding and generation revisit samples underutilized by pre-trained MLLMs, dynamically expanding post-training data and leading to improved performance and unification.

cs.CL↗
arXiv2025

From Channel Bias to Feature Redundancy: Uncovering the "Less is More" Principle in Few-Shot Learning

Deep neural networks often fail to adapt representations to novel tasks under distribution shifts, especially when only a few examples are available. This paper identifies a core obstacle behind this failure: channel bias, where networks develop a rigid emphasis on feature dimensions that were discriminative for the source task, but this emphasis is misaligned and fails to adapt to the distinct needs of a novel task. This bias leads to a striking and detrimental consequence: feature redundancy. We demonstrate that for few-shot tasks, classification accuracy is significantly improved by using as few as 1-5% of the most discriminative feature dimensions, revealing that the vast majority are actively harmful. Our theoretical analysis confirms that this redundancy originates from confounding feature dimensions-those with high intra-class variance but low inter-class separability-which are especially problematic in low-data regimes. This "less is more" phenomenon is a defining characteristic of the few-shot setting, diminishing as more samples become available. To address this, we propose a simple yet effective soft-masking method, Augmented Feature Importance Adjustment (AFIA), which estimates feature importance from augmented data to mitigate the issue. By establishing the cohesive link from channel bias to its consequence of extreme feature redundancy, this work provides a foundational principle for few-shot representation transfer and a practical method for developing more robust few-shot learning algorithms.

cs.CV↗
arXiv2025

On the Collapse Errors Induced by the Deterministic Sampler for Diffusion Models

Despite the widespread adoption of deterministic samplers in diffusion models (DMs), their potential limitations remain largely unexplored. In this paper, we identify collapse errors, a previously unrecognized phenomenon in ODE-based diffusion sampling, where the sampled data is overly concentrated in local data space. To quantify this effect, we introduce a novel metric and demonstrate that collapse errors occur across a variety of settings. When investigating its underlying causes, we observe a see-saw effect, where score learning in low noise regimes adversely impacts the one in high noise regimes. This misfitting in high noise regimes, coupled with the dynamics of deterministic samplers, ultimately causes collapse errors. Guided by these insights, we apply existing techniques from sampling, training, and architecture to empirically support our explanation of collapse errors. This work provides intensive empirical evidence of collapse errors in ODE-based diffusion sampling, emphasizing the need for further research into the interplay between score learning and deterministic sampling, an overlooked yet fundamental aspect of diffusion models.

cs.LG↗
arXiv2025

Towards Theoretical Understanding of Transformer Test-Time Computing: Investigation on In-Context Linear Regression

Using more test-time computation during language model inference, such as generating more intermediate thoughts or sampling multiple candidate answers, has proven effective in significantly improving model performance. This paper takes an initial step toward bridging the gap between practical language model inference and theoretical transformer analysis by incorporating randomness and sampling. We focus on in-context linear regression with continuous/binary coefficients, where our framework simulates language model decoding through noise injection and binary coefficient sampling. Through this framework, we provide detailed analyses of widely adopted inference techniques. Supported by empirical results, our theoretical framework and analysis demonstrate the potential for offering new insights into understanding inference behaviors in real-world language models.

cs.LG↗
arXiv2025

SIDE: Surrogate Conditional Data Extraction from Diffusion Models

As diffusion probabilistic models (DPMs) become central to Generative AI (GenAI), understanding their memorization behavior is essential for evaluating risks such as data leakage, copyright infringement, and trustworthiness. While prior research finds conditional DPMs highly susceptible to data extraction attacks using explicit prompts, unconditional models are often assumed to be safe. We challenge this view by introducing \textbf{Surrogate condItional Data Extraction (SIDE)}, a general framework that constructs data-driven surrogate conditions to enable targeted extraction from any DPM. Through extensive experiments on CIFAR-10, CelebA, ImageNet, and LAION-5B, we show that SIDE can successfully extract training data from so-called safe unconditional models, outperforming baseline attacks even on conditional models. Complementing these findings, we present a unified theoretical framework based on informative labels, demonstrating that all forms of conditioning, explicit or surrogate, amplify memorization. Our work redefines the threat landscape for DPMs, establishing precise conditioning as a fundamental vulnerability and setting a new, stronger benchmark for model privacy evaluation.

cs.LG↗
arXiv2025

Towards Understanding Fine-Tuning Mechanisms of LLMs via Circuit Analysis

Fine-tuning significantly improves the performance of Large Language Models (LLMs), yet its underlying mechanisms remain poorly understood. This paper aims to provide an in-depth interpretation of the fine-tuning process through circuit analysis, a popular tool in Mechanistic Interpretability (MI). Unlike previous studies (Prakash et al. 2024; Chhabra et al. 2024) that focus on tasks where pre-trained models already perform well, we develop a set of mathematical tasks where fine-tuning yields substantial performance gains, which are closer to the practical setting. In our experiments, we identify circuits at various checkpoints during fine-tuning and examine the interplay between circuit analysis, fine-tuning methods, and task complexities. First, we find that while circuits maintain high node similarity before and after fine-tuning, their edges undergo significant changes, in contrast to prior work that shows circuits only add some additional components after fine-tuning. Based on these observations, we develop a circuit-aware Low-Rank Adaptation (LoRA) method, which assigns ranks to layers based on edge changes in the circuits. Experimental results demonstrate that our circuit-based LoRA algorithm achieves an average performance improvement of 2.46% over standard LoRA with similar parameter sizes. Furthermore, we explore how combining circuits from subtasks can enhance fine-tuning in compositional tasks, providing new insights into the design of such tasks and deepening the understanding of circuit dynamics and fine-tuning mechanisms.

cs.CL↗
arXiv2025

Masked Autoencoders Are Effective Tokenizers for Diffusion Models

Recent advances in latent diffusion models have demonstrated their effectiveness for high-resolution image synthesis. However, the properties of the latent space from tokenizer for better learning and generation of diffusion models remain under-explored. Theoretically and empirically, we find that improved generation quality is closely tied to the latent distributions with better structure, such as the ones with fewer Gaussian Mixture modes and more discriminative features. Motivated by these insights, we propose MAETok, an autoencoder (AE) leveraging mask modeling to learn semantically rich latent space while maintaining reconstruction fidelity. Extensive experiments validate our analysis, demonstrating that the variational form of autoencoders is not necessary, and a discriminative latent space from AE alone enables state-of-the-art performance on ImageNet generation using only 128 tokens. MAETok achieves significant practical improvements, enabling a gFID of 1.69 with 76x faster training and 31x higher inference throughput for 512x512 generation. Our findings show that the structure of the latent space, rather than variational constraints, is crucial for effective diffusion models. Code and trained models are released.

cs.CV↗
arXiv2025

Hyper-SET: Designing Transformers via Hyperspherical Energy Minimization

Transformer-based models have achieved remarkable success, but their core components, Transformer layers, are largely heuristics-driven and engineered from the bottom up, calling for a prototypical model with high interpretability and practical competence. To this end, we conceptualize a principled, top-down approach grounded in energy-based interpretation. Specifically, we formalize token dynamics as a joint maximum likelihood estimation on the hypersphere, featuring two properties: semantic alignment in the high-dimensional space and distributional uniformity in the low-dimensional space. By quantifying them with extended Hopfield energy functions, we instantiate this idea as a constrained energy minimization problem, which enables designs of symmetric attention and feedforward modules with RMS normalization. We further present \textit{Hyper-Spherical Energy Transformer} (Hyper-SET), a recurrent-depth alternative to vanilla Transformers naturally emerging from iterative energy optimization on the hypersphere. With shared parameters across layers, Hyper-SET can scale to arbitrary depth with fewer parameters. Theoretically grounded and compact, it achieves competitive or superior performance across diverse tasks, including Sudoku solving, image classification, and masked image modeling. We also design novel variations under the proposed general principle, such as linear attention and gated feedforward layer. Moreover, we showcase its scalability with depth-wise LoRA. Our results highlight Hyper-SET as a step toward interpretable and principled Transformer design.

cs.LG↗
arXiv2025

Model Unlearning via Sparse Autoencoder Subspace Guided Projections

Large language models (LLMs) store vast amounts of information, making them powerful yet raising privacy and safety concerns when selective knowledge removal is required. Existing unlearning strategies, ranging from gradient-based fine-tuning and model editing to sparse autoencoder (SAE) steering, either lack interpretability or fail to provide a robust defense against adversarial prompts. We propose SAE-Guided Subspace Projection Unlearning (SSPU), a novel framework that leverages SAE features to drive targeted updates in the model's parameter space, enabling precise, interpretable, and robust unlearning. SSPU's three-stage pipeline performs data-driven layer and feature selection, subspace construction via QR decomposition, and constrained optimization that controls activations into an "irrelevant" subspace while preserving retained knowledge. Overall, we use SAE features to construct a subspace that supervises unlearning, refining the loss and adding a regularization term to guide interpretable parameter updates. In experiments on the WMDP-Cyber forget set and three utility benchmarks (MMLU, TruthfulQA, GSM8K), SSPU reduces harmful knowledge accuracy by 3.22% compared to the strongest baseline. It also improves adversarial robustness, lowering malicious accuracy under jailbreak prompts compared to baselines. Our findings expose the limitations of prior unlearning methods and demonstrate how interpretable subspace-guided optimization can achieve robust, controllable model behavior.

cs.CL↗
arXiv2025

Almost Linear Convergence under Minimal Score Assumptions: Quantized Transition Diffusion

Continuous diffusion models have demonstrated remarkable performance in data generation across various domains, yet their efficiency remains constrained by two critical limitations: (1) the local adjacency structure of the forward Markov process, which restricts long-range transitions in the data space, and (2) inherent biases introduced during the simulation of time-inhomogeneous reverse denoising processes. To address these challenges, we propose Quantized Transition Diffusion (QTD), a novel approach that integrates data quantization with discrete diffusion dynamics. Our method first transforms the continuous data distribution $p_*$ into a discrete one $q_*$ via histogram approximation and binary encoding, enabling efficient representation in a structured discrete latent space. We then design a continuous-time Markov chain (CTMC) with Hamming distance-based transitions as the forward process, which inherently supports long-range movements in the original data space. For reverse-time sampling, we introduce a \textit{truncated uniformization} technique to simulate the reverse CTMC, which can provably provide unbiased generation from $q_*$ under minimal score assumptions. Through a novel KL dynamic analysis of the reverse CTMC, we prove that QTD can generate samples with $O(d\ln^2(d/ε))$ score evaluations in expectation to approximate the $d$--dimensional target distribution $p_*$ within an $ε$ error tolerance. Our method not only establishes state-of-the-art inference efficiency but also advances the theoretical foundations of diffusion-based generative modeling by unifying discrete and continuous diffusion paradigms.

stat.ML↗
arXiv2025

SWE-Fixer: Training Open-Source LLMs for Effective and Efficient GitHub Issue Resolution

Large Language Models (LLMs) have demonstrated remarkable proficiency across a variety of complex tasks. One significant application of LLMs is in tackling software engineering challenges, particularly in resolving real-world tasks on GitHub by fixing code based on the issues reported by the users. However, many current approaches rely on proprietary LLMs, which limits reproducibility, accessibility, and transparency. The critical components of LLMs for addressing software engineering issues and how their capabilities can be effectively enhanced remain unclear. To address these challenges, we introduce SWE-Fixer, a novel open-source framework designed to effectively and efficiently resolve GitHub issues. SWE-Fixer comprises two essential modules: a code file retrieval module and a code editing module. The retrieval module employs BM25 along with a lightweight model to achieve coarse-to-fine file retrieval. Subsequently, the code editing module utilizes the other model to generate patches for the identified files. To mitigate the lack of publicly available datasets, we compile an extensive dataset that includes 110K GitHub issues along with their corresponding patches and train the two models of SWE-Fixer separately. We assess our approach on the SWE-Bench Lite and Verified benchmarks, achieving competitive performance among open-source models with scores of 22.0% and 30.2%. Furthermore, SWE-Fixer reaches state-of-the-art performance (24.7% on Lite and 32.8% on Verified) with PASS_TO_PASS (P2P) filtering. Additionally, our approach requires only two model calls per instance, making it significantly more efficient than existing methods. These results highlight the effectiveness of SWE-Fixer in real-world code-fixing scenarios. We will make our model, dataset, and code publicly available at https://github.com/InternLM/SWE-Fixer.

cs.CL↗