论文检索

Deep Learning · Attention Mechanisms

Chuanyang Zheng, Jiankai Sun, Yihang Gao, Yuehao Wang, Peihao Wang, Jing Xiong, Liliang Ren, Hao Cheng, Janardhan Kulkarni, yelong shen 等

The attention mechanism is a core component of the Transformer architecture. Various methods have been developed to compute attention scores, including multi-head attention (MHA), multi-query attention, group-query attention and so on. We further analyze the MHA and observe that its performance improves as the number of attention heads increases, provided the hidden size per head remains sufficiently large. Therefore, increasing both the head count and hidden size per head with minimal parameter overhead can lead to significant performance gains at a low cost. Motivated by this insight, we introduce Simulated Attention Score (SAS), which **maintains a compact model size while simulating a larger number of attention heads and hidden feature dimension per head.** This is achieved by projecting a low-dimensional head representation into a higher-dimensional space, effectively increasing attention capacity without increasing parameter count. Beyond the head representations, we further extend the simulation approach to feature dimension of the key and query embeddings, enhancing expressiveness by mimicking the behavior of a larger model while preserving the original model size. **To control the parameter cost, we also propose Parameter-Efficient Attention Aggregation (PEAA).** Comprehensive experiments on a variety of datasets and tasks demonstrate the effectiveness of the proposed SAS method, achieving significant improvements over different attention variants.

Applications · Language, Speech and Dialog

Ansong Ni, Ruta Desai, Yang Li, Xinjie Lei, Dong Wang, Jiemin Zhang, Jane Yu, Ramya Raghavendra, Gargi Ghosh, Shang-Wen Li 等

With increasingly powerful large language models (LLMs) and LLM-based agents tackling an ever-growing list of tasks, we envision a future where numerous LLM agents work seamlessly with other AI agents and humans to solve complex problems and enhance daily life. To achieve these goals, LLM agents must develop collaborative skills such as effective persuasion, assertion and disagreement, which are often overlooked in the prevalent single-turn training and evaluation of LLMs. In this work, we present Collaborative Reasoner (Coral), a framework to evaluate and improve the collaborative reasoning abilities of language models. In particular, tasks and metrics in Coral necessitate agents to disagree with incorrect solutions, convince their partners of a correct solution, and ultimately agree as a team to commit to a final solution, all through a natural multi-turn conversation. Through comprehensive evaluation on six collaborative reasoning tasks covering domains of coding, math, scientific QA and social reasoning, we show that current models cannot effectively collaborate due to undesirable social behaviors, collapsing even on problems that they can solve singlehandedly. To improve the collaborative reasoning capabilities of LLMs, we propose a self-play method to generate synthetic multi-turn preference data and further train the language models to be better collaborators. Experiments with Llama-3.1, Ministral and Qwen-2.5 models show that our proposed self-improvement approach consistently outperforms finetuned chain-of-thought performance of the same base model, yielding gains up to 16.7% absolute. Human evaluations show that the models exhibit more effective disagreement and produce more natural conversations after training on our synthetic interaction data.

Applications · Physics

Panqi Chen, Yifan Sun, Lei Cheng, YANG YANG, Weichang Li, Yang Liu, Weiqing Liu, Jiang Bian, Shikai Fang

Modeling and reconstructing multidimensional physical dynamics from sparse and off-grid observations presents a fundamental challenge in scientific research. Recently, diffusion-based generative modeling shows promising potential for physical simulation. However, current approaches typically operate on on-grid data with preset spatiotemporal resolution, but struggle with the sparsely observed and continuous nature of real-world physical dynamics. To fill the gaps, we present SDIFT, Sequential DIffusion in Functional Tucker space, a novel framework that generates full-field evolution of physical dynamics from irregular sparse observations. SDIFT leverages the functional Tucker model as the latent space representer with proven universal approximation property, and represents sparse observations as latent functions and Tucker core sequences. We then construct a sequential diffusion model with temporally augmented UNet in the functional Tucker space, denoising noise drawn from a Gaussian process to generate the sequence of core tensors. At the posterior sampling stage, we propose a Message-Passing Posterior Sampling mechanism, enabling conditional generation of the entire sequence guided by observations at limited time steps. We validate SDIFT on three physical systems spanning astronomical (supernova explosions, light-year scale), environmental (ocean sound speed fields, kilometer scale), and molecular (organic liquid, millimeter scale) domains, demonstrating significant improvements in both reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.

Applications · Health

Tarun Gogisetty, Naman Malpani, Gugan Chandrashekhar Mallika Thoppe, Sridharan Devarajan

Deep neural networks are increasingly applied in automated histopathology. Yet, whole-slide images (WSIs) are often acquired at gigapixel sizes, rendering them computationally infeasible to analyze entirely at high resolution. Diagnostic labels are largely available only at the slide-level, because expert annotation of images at a finer (patch) level is both laborious and expensive. Moreover, regions with diagnostic information typically occupy only a small fraction of the WSI, making it inefficient to examine the entire slide at full resolution. Here, we propose SASHA -- Sequential Attention-based Sampling for Histopathological Analysis -- a deep reinforcement learning approach for efficient analysis of histopathological images. First, SASHA learns informative features with a lightweight hierarchical, attention-based multiple instance learning (MIL) model. Second, SASHA samples intelligently and zooms selectively into a small fraction (10-20\%) of high-resolution patches to achieve reliable diagnoses. We show that SASHA matches state-of-the-art methods that analyze the WSI fully at high resolution, albeit at a fraction of their computational and memory costs. In addition, it significantly outperforms competing, sparse sampling methods. We propose SASHA as an intelligent sampling model for medical imaging challenges that involve automated diagnosis with exceptionally large images containing sparsely informative features. Model implementation is available at: https://github.com/coglabiisc/SASHA.

Computer Vision · 3D Rendering & Reconstruction

Xinran Han, Ko Nishino, Todd Zickler

Perceiving the shape and material of an object from a single image is inherently ambiguous, especially when lighting is unknown and unconstrained. Despite this, humans can often disentangle shape and material, and when they are uncertain, they often move their head slightly or rotate the object to help resolve the ambiguities. Inspired by this behavior, we introduce a novel conditional denoising-diffusion model that generates samples of shape-and-material maps from a short video of an object undergoing differential motions. Our parameter-efficient architecture allows training directly in pixel-space, and it generates many disentangled attributes of an object simultaneously. Trained on a modest number of synthetic object-motion videos with supervision on shape and material, the model exhibits compelling emergent behavior: For static observations, it produces diverse, multimodal predictions of plausible shape-and-material maps that capture the inherent ambiguities; and when objects move, the distributions converge to more accurate explanations. The model also produces high-quality shape-and-material estimates for less ambiguous, real-world objects. By moving beyond single-view to continuous motion observations, and by using generative perception to capture visual ambiguities, our work suggests ways to improve visual reasoning in physically-embodied systems.

Computer Vision · Image and Video Generation

Tianxiong Zhong, Xingye Tian, Boyuan Jiang, Xuebo Wang, Xin Tao, Pengfei Wan, Zhiwei Zhang

Modern video generation frameworks based on Latent Diffusion Models suffer from inefficiencies in tokenization due to the Frame-Proportional Information Assumption. Existing tokenizers provide fixed temporal compression rates, causing the computational cost of the diffusion model to scale linearly with the frame rate. The paper proposes the Duration-Proportional Information Assumption: the upper bound on the information capacity of a video is proportional to the duration rather than the number of frames. Based on this insight, the paper introduces VFRTok, a Transformer-based video tokenizer, that enables variable frame rate encoding and decoding through asymmetric frame rate training between the encoder and decoder. Furthermore, the paper proposes Partial Rotary Position Embeddings (RoPE) to decouple position and content modeling, which groups correlated patches into unified tokens. The Partial RoPE effectively improves content-awareness, enhancing the video generation capability. Benefiting from the compact and continuous spatio-temporal representation, VFRTok achieves competitive reconstruction quality and state-of-the-art generation fidelity while using only $1/8$ tokens compared to existing tokenizers.

Deep Learning · Generative Models and Autoencoders

Hao Sun, Huailiang Peng, Qiong Dai, Xu Bai, Yanan Cao

Activation steering is an efficient technique for aligning the behavior of large language models (LLMs) by injecting steering vectors directly into a model’s residual stream during inference. A pivotal challenge in this approach lies in choosing the right layers to intervene, as inappropriate selection can undermine behavioral alignment and even impair the model’s language fluency and other core capabilities. While single-layer steering allows straightforward evaluation on held-out data to identify the "best" layer, it offers only limited alignment improvements. Multi-layer steering promises stronger control but faces a combinatorial explosion of possible layer subsets, making exhaustive search impractical. To address these challenges, we propose LayerNavigator, which provides a principled and promising layer selection strategy. The core innovation of LayerNavigator lies in its novel, quantifiable criterion that evaluates each layer's steerability by jointly considering two key aspects: discriminability and consistency. By reusing the activations computed during steering vector generation, LayerNavigator requires no extra data and adds negligible overhead. Comprehensive experiments show that LayerNavigator achieves not only superior alignment but also greater scalability and interpretability compared to existing strategies. Our code is available at https://github.com/Bryson-Arrot/LayerNavigator

Theory · Learning Theory

Victor Li, Baiting Chen, Yuzhen Mao, Qi Lei, Zhun Deng

Calibrating blackbox machine learning models to achieve risk control is crucial to ensure reliable decision-making. A rich line of literature has been studying how to calibrate a model so that its predictions satisfy explicit finite-sample statistical guarantees under a _fixed_, _static_, and unknown data-generating distribution. However, prediction-supported decisions may influence the outcome they aim to predict, a phenomenon named _performativity_ of predictions, which is commonly seen in social science and economics. In this paper, we introduce _Performative Risk Control_, a framework to calibrate models to achieve risk control under performativity with provable theoretical guarantees. Specifically, we provide an iteratively refined calibration process, where we ensure the predictions are improved and risk-controlled throughout the process. We also study different types of risk measures and choices of tail bounds. Lastly, we demonstrate the effectiveness of our framework by numerical experiments on the task of predicting credit default risk. To the best of our knowledge, this work is the first one to study statistically rigorous risk control under performativity, which will serve as an important safeguard against a wide range of strategic manipulation in decision-making processes.

Applications

Yifeng Peng, Xinyi Li, Samuel Yen-Chi Chen, Kaining Zhang, Zhiding Liang, Ying Wang, Yuxuan Du

Variational quantum Eigensolver (VQE) is a leading candidate for harnessing quantum computers to advance quantum chemistry and materials simulations, yet its training efficiency deteriorates rapidly for large Hamiltonians. Two issues underlie this bottleneck: (i) the no-cloning theorem imposes a linear growth in circuit evaluations with the number of parameters per gradient step; and (ii) deeper circuits encounter barren plateaus (BPs), leading to exponentially increasing measurement overheads. To address these challenges, here we propose a deep learning framework, dubbed Titan, which identifies and freezes inactive parameters of a given ansätze at initialization for a specific class of Hamiltonians, reducing the optimization overhead without sacrificing accuracy. The motivation of Titan starts with our empirical findings that a subset of parameters consistently has negligible influence on training dynamics. Its design combines a theoretically grounded data construction strategy, ensuring each training example is informative and BP-resilient, with an adaptive neural architecture that generalizes across ansätze of varying sizes. Across benchmark transverse-field Ising models, Heisenberg models, and multiple molecule systems up to $30$ qubits, Titan achieves up to $3\times$ faster convergence and $40$–$60\%$ fewer circuit evaluations than state-of-the-art baselines, while matching or surpassing their estimation accuracy. By proactively trimming parameter space, Titan lowers hardware demands and offers a scalable path toward utilizing VQE to advance practical quantum chemistry and materials science.

Probabilistic Methods · Everything Else

Taeseong Yoon, Heeyoung Kim

Uncertainty quantification (UQ) is crucial for deploying machine learning models in high-stakes applications, where overconfident predictions can lead to serious consequences. An effective UQ method must balance computational efficiency with the ability to generalize across diverse scenarios. Evidential deep learning (EDL) achieves efficiency by modeling uncertainty through the prediction of a Dirichlet distribution over class probabilities. However, the restrictive assumption of Dirichlet-distributed class probabilities limits EDL's robustness, particularly in complex or unforeseen situations. To address this, we propose *flexible evidential deep learning* ($\mathcal{F}$-EDL), which extends EDL by predicting a flexible Dirichlet distribution—a generalization of the Dirichlet distribution—over class probabilities. This approach provides a more expressive and adaptive representation of uncertainty, significantly enhancing UQ generalization and reliability under challenging scenarios. We theoretically establish several advantages of $\mathcal{F}$-EDL and empirically demonstrate its state-of-the-art UQ performance across diverse evaluation settings, including classical, long-tailed, and noisy in-distribution scenarios.

Reinforcement Learning · Multi-agent

Yang Zhang, Xinran Li, Jianing Ye, Shuang Qiu, Delin Qu, Xiu Li, Chongjie Zhang, Chenjia Bai

World models have recently attracted growing interest in Multi-Agent Reinforcement Learning (MARL) due to their ability to improve sample efficiency for policy learning. However, accurately modeling environments in MARL is challenging due to the exponentially large joint action space and highly uncertain dynamics inherent in multi-agent systems. To address this, we reduce modeling complexity by shifting from jointly modeling the entire state-action transition dynamics to focusing on the state space alone at each timestep through sequential agent modeling. Specifically, our approach enables the model to progressively resolve uncertainty while capturing the structured dependencies among agents, providing a more accurate representation of how agents influence the state. Interestingly, this sequential revelation of agents' actions in a multi-agent system aligns with the reverse process in diffusion models—a class of powerful generative models known for their expressiveness and training stability compared to autoregressive or latent variable models. Leveraging this insight, we develop a flexible and robust world model for MARL using diffusion models. Our method, \textbf{D}iffusion-\textbf{I}nspired \textbf{M}ulti-\textbf{A}gent world model (DIMA), achieves state-of-the-art performance across multiple multi-agent control benchmarks, significantly outperforming prior world models in terms of final return and sample efficiency, including MAMuJoCo and Bi-DexHands. DIMA establishes a new paradigm for constructing multi-agent world models, advancing the frontier of MARL research.

Mingyang Yi, Bohan Wang

Recently, optimization on the Riemannian manifold have provided valuable insights to the optimization community. In this regard, extending these methods to to the Wasserstein space is of particular interest, since optimization on Wasserstein space is closely connected to practical sampling processes. Generally, the standard (continuous) optimization method on Wasserstein space is Riemannian gradient flow (i.e., Langevin dynamics when minimizing KL divergence). In this paper, we aim to enrich the family of continuous optimization methods in the Wasserstein space, by extending the gradient flow on it into the stochastic gradient descent (SGD) flow and stochastic variance reduction gradient (SVRG) flow. By leveraging the property of Wasserstein space, we construct stochastic differential equations (SDEs) to approximate the corresponding discrete Euclidean dynamics of the desired Riemannian stochastic methods. Then, we obtain the flows in Wasserstein space by Fokker-Planck equation. Finally, we establish convergence rates of the proposed stochastic flows, which align with those known in the Euclidean setting.

Reinforcement Learning · Everything Else

Xiaoxue Cheng, Junyi Li, Zhenduo Zhang, Xinyu Tang, Xin Zhao, Xinyu Kong, Zhiqiang Zhang

Large reasoning models (LRMs) have demonstrated strong performance on complex reasoning tasks, but often suffer from overthinking, generating redundant content regardless of task difficulty. Inspired by the dual process theory in cognitive science, we propose Adaptive Cognition Policy Optimization (ACPO), a reinforcement learning framework that enables LRMs to achieve efficient reasoning through adaptive cognitive allocation and dynamic system switch. ACPO incorporates two key components: (1) introducing system-aware reasoning tokens to explicitly represent the thinking modes thereby making the model's cognitive process transparent, and (2) integrating online difficulty estimation and token length budget to guide adaptive system switch and reasoning during reinforcement learning. To this end, we propose a two-stage training strategy. The first stage begins with supervised fine-tuning to cold start the model, enabling it to generate reasoning paths with explicit thinking modes. In the second stage, we apply ACPO to further enhance adaptive system switch for difficulty-aware reasoning. Experimental results demonstrate that ACPO effectively reduces redundant reasoning while adaptively adjusting cognitive allocation based on task complexity, achieving efficient hybrid reasoning.

Probabilistic Methods · Bayesian Models and Methods

Junxi Xiao, Qinliang Su, Zexin Yuan

Mean-field variational inference (VI), despite its scalability, is limited by the independence assumption, making it unsuitable for scenarios with correlated data instances. Existing structured VI methods either focus on correlations among latent dimensions which lack scalability for modeling instance-level correlations, or are restricted to simple first-order dependencies, limiting their expressiveness. In this paper, we propose High-order Tree-structured Variational Inference (HoT-VI), that explicitly models $k$-order instance-level correlations among latent variables. By expressing the global posterior through overlapping $k$-dimensional local marginals, our method enables efficient parameterized sampling via a sequential procedure. To ensure the validity of these marginals, we introduce a conditional correlation parameterization method that guarantees positive definiteness of their correlation matrices. We further extend our method with a tree-structured backbone to capture more flexible dependency patterns. Extensive experiments on time-series and graph-structured datasets demonstrate that modeling higher-order correlations leads to significantly improved posterior approximations and better performance across various downstream tasks.

Computer Vision · Classification and Understanding

Chanhyeong Yang, Taehoon song, Jihwan Park, Hyunwoo J. Kim

Zero-shot Human-Object Interaction detection aims to localize humans and objects in an image and recognize their interaction, even when specific verb-object pairs are unseen during training. Recent works have shown promising results using prompt learning with pretrained vision-language models such as CLIP, which align natural language prompts with visual features in a shared embedding space. However, existing approaches still fail to handle the *visual complexity of interaction*—including (1) *intra-class visual diversity*, where instances of the same verb appear in diverse poses and contexts, and (2) *inter-class visual entanglement*, where distinct verbs yield visually similar patterns. To address these challenges, we propose **VDRP**, a framework for *Visual Diversity and Region-aware Prompt learning*. First, we introduce a visual diversity-aware prompt learning strategy that injects group-wise visual variance into the context embedding. We further apply Gaussian perturbation to encourage the prompt to capture diverse visual variations of a verb. Second, we retrieve region-specific concepts from the human, object, and union regions. These are used to augment the diversity-aware prompt embeddings, yielding region-aware prompts that improve verb-level discrimination. Experiments on the HICO-DET benchmark demonstrate that our method achieves state-of-the-art performance under four zero-shot evaluation settings, effectively addressing both intra-class diversity and inter-class visual entanglement. Code is available at https://github.com/mlvlab/VDRP.

Computer Vision · Vision Models & Multimodal

Wenbo Hu, Yining Hong, Yanjun Wang, Leison Gao, Zibu Wei, Xingcheng Yao, Nanyun Peng, Yonatan Bitton, Idan Szpektor, Kai-Wei Chang

Humans excel at performing complex tasks by leveraging long-term memory across temporal and spatial experiences. In contrast, current Large Language Models (LLMs) struggle to effectively plan and act in dynamic, multi-room 3D environments. We posit that part of this limitation is due to the lack of proper 3D spatial-temporal memory modeling in LLMs. To address this, we first introduce 3DMem-Bench, a comprehensive benchmark comprising over 26,000 trajectories and 2,892 embodied tasks, question-answering and captioning, designed to evaluate an agent's ability to reason over long-term memory in 3D environments. Second, we propose 3DLLM-Mem, a novel dynamic memory management and fusion model for embodied spatial-temporal reasoning and actions in LLMs. Our model uses working memory tokens, which represents current observations, as queries to selectively attend to and fuse the most useful spatial and temporal features from episodic memory, which stores past observations and interactions. Our approach allows the agent to focus on task-relevant information while maintaining memory efficiency in complex, long-horizon environments. Experimental results demonstrate that 3DLLM-Mem achieves state-of-the-art performance across various tasks, outperforming the strongest baselines by 16.5\% in success rate on 3DMem-Bench's most challenging in-the-wild embodied tasks.

Computer Vision · Vision Models & Multimodal

Ling Yang, Ye Tian, Bowen Li, Xinchen Zhang, Ke Shen, Yunhai Tong, Mengdi Wang

We introduce MMaDA, a novel class of multimodal diffusion foundation models designed to achieve superior performance across diverse domains such as textual reasoning, multimodal understanding, and text-to-image generation. The approach is distinguished by three key innovations: (i) MMaDA adopts a unified diffusion architecture with a shared probabilistic formulation and a modality-agnostic design, eliminating the need for modality-specific components. This architecture ensures seamless integration and processing across different data types. (ii) We implement a mixed long chain-of-thought (CoT) fine-tuning strategy that curates a unified CoT format across modalities. By aligning reasoning processes between textual and visual domains, this strategy facilitates cold-start training for the final reinforcement learning (RL) stage, thereby enhancing the model's ability to handle complex tasks from the outset. (iii) We propose UniGRPO, a unified policy-gradient-based RL algorithm specifically tailored for diffusion foundation models. Utilizing diversified reward modeling, UniGRPO unifies post-training across both reasoning and generation tasks, ensuring consistent performance improvements. Experimental results demonstrate that MMaDA-8B exhibits strong generalization capabilities as a unified multimodal foundation model. It surpasses powerful models like LLaMA-3-7B and Qwen2-7B in textual reasoning, outperforms Show-o and SEED-X in multimodal understanding, and excels over SDXL and Janus in text-to-image generation. These achievements highlight MMaDA's effectiveness in bridging the gap between pretraining and post-training within unified diffusion architectures, providing a comprehensive framework for future research and development. We open-source our code and trained models at: https://github.com/Gen-Verse/MMaDA

Applications · Health

Felix Wagner, Pramit Saha, Harry Anthony, Alison Noble, Konstantinos Kamnitsas

Safe deployment of machine learning (ML) models in safety-critical domains such as medical imaging requires detecting inputs with characteristics not seen during training, known as out-of-distribution (OOD) detection, to prevent unreliable predictions. Effective OOD detection after deployment could benefit from access to the training data, enabling direct comparison between test samples and the training data distribution to identify differences. State-of-the-art OOD detection methods, however, either discard the training data after deployment or assume that test samples and training data are centrally stored together, an assumption that rarely holds in real-world settings. This is because shipping the training data with the deployed model is usually impossible due to the size of training databases, as well as proprietary or privacy constraints. We introduce the Isolation Network, an OOD detection framework that quantifies the difficulty of separating a target test sample from the training data by solving a binary classification task. We then propose Decentralized Isolation Networks (DIsoN), which enables the comparison of training and test data when data-sharing is impossible, by exchanging only model parameters between the remote computational nodes of training and deployment. We further extend DIsoN with class-conditioning, comparing a target sample solely with training data of its predicted class. We evaluate DIsoN on four medical imaging datasets (dermatology, chest X-ray, breast ultrasound, histopathology) across 12 OOD detection tasks. DIsoN performs favorably against existing methods while respecting data-privacy. This decentralized OOD detection framework opens the way for a new type of service that ML developers could provide along with their models: providing remote, secure utilization of their training data for OOD detection services. Code available at: https://github.com/FelixWag/DIsoN

Computer Vision · Image and Video Generation

Yu Shang, Xin Zhang, Yinzhou Tang, Lei Jin, Chen Gao, Wei Wu, Yong Li

World models have become indispensable tools for embodied intelligence, serving as powerful simulators capable of generating realistic robotic videos while addressing critical data scarcity challenges. However, current embodied world models exhibit limited physical awareness, particularly in modeling 3D geometry and motion dynamics, resulting in unrealistic video generation for contact-rich robotic scenarios. In this paper, we present RoboScape, a unified physics-informed world model that jointly learns RGB video generation and physics knowledge within an integrated framework. We introduce two key physics-informed joint training tasks: temporal depth prediction that enhances 3D geometric consistency in video rendering, and keypoint dynamics learning that implicitly encodes physical properties (e.g., object shape and material characteristics) while improving complex motion modeling. Extensive experiments demonstrate that RoboScape generates videos with superior visual fidelity and physical plausibility across diverse robotic scenarios. We further validate its practical utility through downstream applications including robotic policy training with generated data and policy evaluation. Our work provides new insights for building efficient physics-informed world models to advance embodied intelligence research. Our code and demos are available at: https://github.com/tsinghua-fib-lab/RoboScape.

Theory · Learning Theory

Guoji Fu, Wee Sun Lee

This paper studies the approximation and generalization abilities of score-based neural network generative models (SGMs) in estimating an unknown distribution $P_0$ from $n$ i.i.d. observations in $d$ dimensions. Assuming merely that $P_0$ is $\alpha$-sub-Gaussian, we prove that for any time step $t \in [t_0, n^{\mathcal{O}(1)}]$, where $t_0 > \mathcal{O}(\alpha^2n^{-2/d}\log n)$, there exists a deep ReLU neural network with width $\leq \mathcal{O}(n^{\frac{3}{d}}\log_2n)$ and depth $\leq \mathcal{O}(\log^2n)$ that can approximate the scores with $\tilde{\mathcal{O}}(n^{-1})$ mean square error and achieve a nearly optimal rate of $\tilde{\mathcal{O}}(n^{-1}t_0^{-d/2})$ for score estimation, as measured by the score matching loss. Our framework is universal and can be used to establish convergence rates for SGMs under milder assumptions than previous work. For example, assuming further that the target density function $p_0$ lies in Sobolev or Besov classes, with an appropriately early stopping strategy, we demonstrate that neural network-based SGMs can attain nearly minimax convergence rates up to logarithmic factors. Our analysis removes several crucial assumptions, such as Lipschitz continuity of the score function or a strictly positive lower bound on the target density.