Jiacheng Sun

Hsiang-Wei Huang, Cheng-Yen Yang, Jiacheng Sun et al.

Deep learning-based object detectors have driven notable progress in multi-object tracking algorithms. Yet, current tracking methods mainly focus on simple, regular motion patterns in pedestrians or vehicles. This leaves a gap in tracking algorithms for targets with nonlinear, irregular motion, like athletes. Additionally, relying on the Kalman filter in recent tracking algorithms falls short when object motion defies its linear assumption. To overcome these issues, we propose a novel online and robust multi-object tracking approach named deep ExpansionIoU (Deep-EIoU), which focuses on multi-object tracking for sports scenarios. Unlike conventional methods, we abandon the use of the Kalman filter and leverage the iterative scale-up ExpansionIoU and deep features for robust tracking in sports scenarios. This approach achieves superior tracking performance without adopting a more robust detector, all while keeping the tracking process in an online fashion. Our proposed method demonstrates remarkable effectiveness in tracking irregular motion objects, achieving a score of 77.2% HOTA on the SportsMOT dataset and 85.4% HOTA on the SoccerNet-Tracking dataset. It outperforms all previous state-of-the-art trackers on various large-scale multi-object tracking benchmarks, covering various kinds of sports scenarios. The code and models are available at https://github.com/hsiangwei0903/Deep-EIoU.

Zebin You, Yong Zhong, Fan Bao et al.

In an effort to further advance semi-supervised generative and classification tasks, we propose a simple yet effective training strategy called dual pseudo training (DPT), built upon strong semi-supervised learners and diffusion models. DPT operates in three stages: training a classifier on partially labeled data to predict pseudo-labels; training a conditional generative model using these pseudo-labels to generate pseudo images; and retraining the classifier with a mix of real and pseudo images. Empirically, DPT consistently achieves SOTA performance of semi-supervised generation and classification across various settings. In particular, with one or two labels per class, DPT achieves a Fréchet Inception Distance (FID) score of 3.08 or 2.52 on ImageNet 256x256. Besides, DPT outperforms competitive semi-supervised baselines substantially on ImageNet classification tasks, achieving top-1 accuracies of 59.0 (+2.8), 69.5 (+3.0), and 74.4 (+2.0) with one, two, or five labels per class, respectively. Notably, our results demonstrate that diffusion can generate realistic images with only a few labels (e.g., <0.1%) and generative augmentation remains viable for semi-supervised classification. Our code is available at https://github.com/ML-GSAI/DPT.

Shuchen Xue, Mingyang Yi, Weijian Luo et al.

Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed. The majority of such techniques consider solving the diffusion ODE due to its superior efficiency. However, stochastic sampling could offer additional advantages in generating diverse and high-quality data. In this work, we engage in a comprehensive analysis of stochastic sampling from two aspects: variance-controlled diffusion SDE and linear multi-step SDE solver. Based on our analysis, we propose \textit{SA-Solver}, which is an improved efficient stochastic Adams method for solving diffusion SDE to generate data with high quality. Our experiments show that \textit{SA-Solver} achieves: 1) improved or comparable performance compared with the existing state-of-the-art (SOTA) sampling methods for few-step sampling; 2) SOTA FID on substantial benchmark datasets under a suitable number of function evaluations (NFEs). Code is available at https://github.com/scxue/SA-Solver.

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.

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.

Fan Bao, Chongxuan Li, Jiacheng Sun et al.

Diffusion probabilistic models (DPMs) are a class of powerful deep generative models (DGMs). Despite their success, the iterative generation process over the full timesteps is much less efficient than other DGMs such as GANs. Thus, the generation performance on a subset of timesteps is crucial, which is greatly influenced by the covariance design in DPMs. In this work, we consider diagonal and full covariances to improve the expressive power of DPMs. We derive the optimal result for such covariances, and then correct it when the mean of DPMs is imperfect. Both the optimal and the corrected ones can be decomposed into terms of conditional expectations over functions of noise. Building upon it, we propose to estimate the optimal covariance and its correction given imperfect mean by learning these conditional expectations. Our method can be applied to DPMs with both discrete and continuous timesteps. We consider the diagonal covariance in our implementation for computational efficiency. For an efficient practical implementation, we adopt a parameter sharing scheme and a two-stage training process. Empirically, our method outperforms a wide variety of covariance design on likelihood results, and improves the sample quality especially on a small number of timesteps.

Yuchuan Tian, Yuchen Liang, Jiacheng Sun et al.

Large language models (LLMs) excel at generation but dominant autoregressive (AR) decoding is inherently sequential, creating a throughput bottleneck. Diffusion Language Models (DLMs)--especially block-wise variants--enable parallel generation and intra-block bidirectional reasoning, yet training large DLMs from scratch is costly and wastes the knowledge in mature AR checkpoints. Prior "adaptation" attempts either modify logits or randomly grow attention masks to full-sequence diffusion, or simply transplant AR weights into a block-diffusion recipe, leaving a fundamental mismatch between AR causality and block-wise bidirectionality unaddressed. We reframe adaptation as a intra-paradigm path from AR to Block-Diffusion by viewing AR as Block-Diffusion with blocksize=1. Concretely, we design the pathway of adaptation as follows: we use a context-causal attention mask (causal in context, bidirectional only within the active block), an efficient parallel adaptation procedure, an auxiliary AR loss to maximize data utilization and retain pretrained knowledge, and gradual increment of the generation block size. The recipe integrates cleanly with masked block-diffusion and maintains train-inference consistency. Built on these components, NBDiff-7B (Base and Instruct) could inherit the long-context modeling and reasoning capabilities, and achieve state-of-the-art performance among the 7B-class DLMs, delivering strong gains on general-knowledge, math, and code benchmarks over strong baselines. These results demonstrate that principled AR-to-block-diffusion adaptation is an effective and compute-efficient alternative to training DLMs from scratch. Codes: https://github.com/YuchuanTian/NBDiff.

Fan Bao, Chongxuan Li, Jiacheng Sun et al.

Extensive empirical evidence demonstrates that conditional generative models are easier to train and perform better than unconditional ones by exploiting the labels of data. So do score-based diffusion models. In this paper, we analyze the phenomenon formally and identify that the key of conditional learning is to partition the data properly. Inspired by the analyses, we propose self-conditioned diffusion models (SCDM), which is trained conditioned on indices clustered by the k-means algorithm on the features extracted by a model pre-trained in a self-supervised manner. SCDM significantly improves the unconditional model across various datasets and achieves a record-breaking FID of 3.94 on ImageNet 64x64 without labels. Besides, SCDM achieves a slightly better FID than the corresponding conditional model on CIFAR10.

Hsiang-Wei Huang, Jiacheng Sun, Cheng-Yen Yang et al.

Assessing gross motor development in toddlers is crucial for understanding their physical development and identifying potential developmental delays or disorders. However, existing datasets for action recognition primarily focus on adults, lacking the diversity and specificity required for accurate assessment in toddlers. In this paper, we present ToddlerAct, a toddler gross motor action recognition dataset, aiming to facilitate research in early childhood development. The dataset consists of video recordings capturing a variety of gross motor activities commonly observed in toddlers aged under three years old. We describe the data collection process, annotation methodology, and dataset characteristics. Furthermore, we benchmarked multiple state-of-the-art methods including image-based and skeleton-based action recognition methods on our datasets. Our findings highlight the importance of domain-specific datasets for accurate assessment of gross motor development in toddlers and lay the foundation for future research in this critical area. Our dataset will be available at https://github.com/ipl-uw/ToddlerAct.

Fangyu Ding, Ding Ding, Sijin Chen et al.

While Masked Diffusion Language Models (MDLMs) relying on token masking and unmasking have shown promise in language modeling, their computational efficiency and generation flexibility remain constrained by the masking paradigm. In this paper, we propose Deletion-Insertion Diffusion language models (DID) that rigorously formulate token deletion and insertion as discrete diffusion processes, replacing the masking and unmasking processes in current MDLMs. DID improves training and inference efficiency by eliminating two major sources of computational overhead in MDLMs: the computations on non-informative 1) <MASK> tokens inherent to the paradigm, and 2) <PAD> tokens introduced in variable-length settings. Furthermore, DID offers greater flexibility by: 1) natively supporting variable-length sequences without requiring fixed-length padding, and 2) an intrinsic self-correction mechanism during generation due to insertion that dynamically adjusts token positions. To train DID, we design a score-based approach that assigns scores to token insertion operations and derive appropriate training objectives. The objectives involve subsequence counting problems, which we efficiently solve via a parallelized dynamic programming algorithm. Our experiments across fixed and variable-length settings demonstrate the advantage of DID over baselines of MDLMs and existing insertion-based LMs, in terms of modeling performance, sampling quality, and training/inference speed, without any hyperparameter tuning.

Zhipeng Bian, Jieming Zhu, Qijiong Liu et al.

Recent advances in multimodal large language models (MLLMs) and diffusion models (DMs) have opened new possibilities for AI-generated content. Yet, personalized cover image generation remains underexplored, despite its critical role in boosting user engagement on digital platforms. We propose ICG, a novel framework that integrates MLLM-based prompting with personalized preference alignment to generate high-quality, contextually relevant covers. ICG extracts semantic features from item titles and reference images via meta tokens, refines them with user embeddings, and injects the resulting personalized context into the diffusion model. To address the lack of labeled supervision, we adopt a multi-reward learning strategy that combines public aesthetic and relevance rewards with a personalized preference model trained from user behavior. Unlike prior pipelines relying on handcrafted prompts and disjointed modules, ICG employs an adapter to bridge MLLMs and diffusion models for end-to-end training. Experiments demonstrate that ICG significantly improves image quality, semantic fidelity, and personalization, leading to stronger user appeal and offline recommendation accuracy in downstream tasks. As a plug-and-play adapter bridging MLLMs and diffusion models, ICG is compatible with common checkpoints and requires no ground-truth labels during optimization.

Ruishu Zhu, Zhihao Huang, Jiacheng Sun et al.

Multi-view image generation from a single image and text description remains challenging due to the difficulty of maintaining geometric consistency across different viewpoints. Existing approaches typically rely on 3D-aware architectures or specialized diffusion models that require extensive multi-view training data and complex geometric priors. In this work, we introduce ViewMask-1-to-3, a pioneering approach to apply discrete diffusion models to multi-view image generation. Unlike continuous diffusion methods that operate in latent spaces, ViewMask-1-to-3 formulates multi-view synthesis as a discrete sequence modeling problem, where each viewpoint is represented as visual tokens obtained through MAGVIT-v2 tokenization. By unifying language and vision through masked token prediction, our approach enables progressive generation of multiple viewpoints through iterative token unmasking with text input. ViewMask-1-to-3 achieves cross-view consistency through simple random masking combined with self-attention, eliminating the requirement for complex 3D geometric constraints or specialized attention architectures. Our approach demonstrates that discrete diffusion provides a viable and simple alternative to existing multi-view generation methods, ranking first on average across GSO and 3D-FUTURE datasets in terms of PSNR, SSIM, and LPIPS, while maintaining architectural simplicity.

Shulei Wang, Wang Lin, Hai Huang et al.

We introduce a novel, training-free approach for enhancing alignment in Transformer-based Text-Guided Diffusion Models (TGDMs). Existing TGDMs often struggle to generate semantically aligned images, particularly when dealing with complex text prompts or multi-concept attribute binding challenges. Previous U-Net-based methods primarily optimized the latent space, but their direct application to Transformer-based architectures has shown limited effectiveness. Our method addresses these challenges by directly optimizing cross-attention maps during the generation process. Specifically, we introduce Self-Coherence Guidance, a method that dynamically refines attention maps using masks derived from previous denoising steps, ensuring precise alignment without additional training. To validate our approach, we constructed more challenging benchmarks for evaluating coarse-grained attribute binding, fine-grained attribute binding, and style binding. Experimental results demonstrate the superior performance of our method, significantly surpassing other state-of-the-art methods across all evaluated tasks. Our code is available at https://scg-diffusion.github.io/scg-diffusion.

Yixin Ou, Yunzhi Yao, Ningyu Zhang et al.

Despite exceptional capabilities in knowledge-intensive tasks, Large Language Models (LLMs) face a critical gap in understanding how they internalize new knowledge, particularly how to structurally embed acquired knowledge in their neural computations. We address this issue through the lens of knowledge circuit evolution, identifying computational subgraphs that facilitate knowledge storage and processing. Our systematic analysis of circuit evolution throughout continual pre-training reveals several key findings: (1) the acquisition of new knowledge is influenced by its relevance to pre-existing knowledge; (2) the evolution of knowledge circuits exhibits a distinct phase shift from formation to optimization; (3) the evolution of knowledge circuits follows a deep-to-shallow pattern. These insights not only advance our theoretical understanding of the mechanisms of new knowledge acquisition in LLMs, but also provide potential implications for improving continual pre-training strategies to enhance model performance. Code and data will be available at https://github.com/zjunlp/DynamicKnowledgeCircuits.

Haoxiong Liu, Jiacheng Sun, Zhenguo Li et al.

The synergy between deep learning models and traditional automation tools, such as built-in tactics of the proof assistant and off-the-shelf automated theorem provers, plays a crucial role in developing robust and efficient neural theorem provers(NTPs). However, for proof synthesis with LLMs, previous work applies automation tools either only when explicitly invoked by the model or at a single granularity level, failing to fully exploit their power. To solve this issue, we propose ProofAug, a procedure that equips LLMs with automation methods at various granularities through fine-grained structure analysis of model-generated proof proposals. ProofAug also serves as a versatile plug-and-play module that seamlessly integrates with any tree-search algorithm, enabling our construction of an efficient recursive proving (ERP) module to further enhance performance. The superiority of our method is validated on the miniF2F benchmark using the open-source deepseek-math-7b-base model and the Isabelle proof assistant. Notably, by additionally employing a mixed prompting strategy, we achieve a cumulative pass rate of 66.0% after curation of the dataset (61.9% for the original version) with 2100 queries to the model per problem (In contrast, the previous SOTA in Isabelle, Subgoal-XL, only achieves 56.1% using 16384 queries per problem). We also implement a Lean 4 version of ProofAug that can improve the pass@1 performance of Kimina-Prover-Preview-Distill-1.5B from 44.3% to 50.4% on miniF2F-test. Our code is available at https://github.com/haoxiongliu/ProofAug.

Jiacheng Sun, Hsiang-Wei Huang, Cheng-Yen Yang et al.

Multi-object tracking in sports scenarios has become one of the focal points in computer vision, experiencing significant advancements through the integration of deep learning techniques. Despite these breakthroughs, challenges remain, such as accurately re-identifying players upon re-entry into the scene and minimizing ID switches. In this paper, we propose an appearance-based global tracklet association algorithm designed to enhance tracking performance by splitting tracklets containing multiple identities and connecting tracklets seemingly from the same identity. This method can serve as a plug-and-play refinement tool for any multi-object tracker to further boost their performance. The proposed method achieved a new state-of-the-art performance on the SportsMOT dataset with HOTA score of 81.04%. Similarly, on the SoccerNet dataset, our method enhanced multiple trackers' performance, consistently increasing the HOTA score from 79.41% to 83.11%. These significant and consistent improvements across different trackers and datasets underscore our proposed method's potential impact on the application of sports player tracking. We open-source our project codebase at https://github.com/sjc042/gta-link.git.

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.

Jiacheng Sun, Jiaqi Lin, Wenlong Hu et al.

One of the bottlenecks for instance segmentation today lies in the conflicting requirements of high-resolution inputs and lightweight, real-time inference. To address this bottleneck, we present a Polygon Detection Transformer (Poly-DETR) to reformulate instance segmentation as sparse vertex regression via Polar Representation, thereby eliminating the reliance on dense pixel-wise mask prediction. Considering the box-to-polygon reference shift in Detection Transformers, we propose Polar Deformable Attention and Position-Aware Training Scheme to dynamically update supervision and focus attention on boundary cues. Compared with state-of-the-art polar-based methods, Poly-DETR achieves a 4.7 mAP improvement on MS COCO test-dev. Moreover, we construct a parallel mask-based counterpart to support a systematic comparison between polar and mask representations. Experimental results show that Poly-DETR is more lightweight in high-resolution scenarios, reducing memory consumption by almost half on Cityscapes dataset. Notably, on PanNuke (cell segmentation) and SpaceNet (building footprints) datasets, Poly-DETR surpasses its mask-based counterpart on all metrics, which validates its advantage on regular-shaped instances in domain-specific settings.

Azim Ospanov, Zijin Feng, Jiacheng Sun et al.

Informal mathematics has been central to modern large language model (LLM) reasoning, offering flexibility and enabling efficient construction of arguments. However, purely informal reasoning is prone to logical gaps and subtle errors that are difficult to detect and correct. In contrast, formal theorem proving provides rigorous, verifiable mathematical reasoning, where each inference step is checked by a trusted compiler in systems such as Lean, but lacks the exploratory freedom of informal problem solving. This mismatch leaves current LLM-based math agents without a principled way to combine the strengths of both paradigms. In this work, we introduce Hermes, the first tool-assisted agent that explicitly interleaves informal reasoning with formally verified proof steps in Lean. The framework performs intermediate formal checking to prevent reasoning drift and employs a memory module that maintains proof continuity across long, multi-step reasoning chains, enabling both exploration and verification within a single workflow. We evaluate Hermes on four challenging mathematical reasoning benchmarks using LLMs of varying parameter scales, from small models to state-of-the-art systems. Across all settings, Hermes reliably improves the reasoning accuracy of base models while substantially reducing token usage and computational cost compared to reward-based approaches. On difficult datasets such as AIME'25, Hermes achieves up to a 67% accuracy improvement while using 80% fewer total inference FLOPs. The implementation and codebase are publicly available at https://github.com/aziksh-ospanov/HERMES.

Jingyang Ou, Shen Nie, Kaiwen Xue et al.

Discrete diffusion models with absorbing processes have shown promise in language modeling. The key quantities to be estimated are the ratios between the marginal probabilities of two transitive states at all timesteps, called the concrete score. In this paper, we reveal that the concrete score in absorbing diffusion can be expressed as conditional probabilities of clean data, multiplied by a time-dependent scalar in an analytic form. Motivated by this finding, we propose reparameterized absorbing discrete diffusion (RADD), a dedicated diffusion model without time-condition that characterizes the time-independent conditional probabilities. Besides its simplicity, RADD can reduce the number of function evaluations (NFEs) by caching the output of the time-independent network when the noisy sample remains unchanged in a sampling interval, which enables sampling acceleration. Built upon the new perspective of conditional distributions, we further unify absorbing discrete diffusion and any-order autoregressive models (AO-ARMs), showing that the upper bound on the negative log-likelihood for the diffusion model can be interpreted as an expected negative log-likelihood for AO-ARMs. Further, our RADD models achieve SOTA performance among diffusion models on 5 zero-shot language modeling benchmarks (measured by perplexity) at the GPT-2 scale. Our code is available at https://github.com/ML-GSAI/RADD.

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.

Guhao Feng, Kai Yang, Yuntian Gu et al. · pku

Despite the remarkable success of Transformer-based large language models (LLMs) across various domains, understanding and enhancing their mathematical capabilities remains a significant challenge. In this paper, we conduct a rigorous theoretical analysis of LLMs' mathematical abilities, with a specific focus on their arithmetic performances. We identify numerical precision as a key factor that influences their effectiveness in arithmetical tasks. Our results show that Transformers operating with low numerical precision fail to address arithmetic tasks, such as iterated addition and integer multiplication, unless the model size grows super-polynomially with respect to the input length. In contrast, Transformers with standard numerical precision can efficiently handle these tasks with significantly smaller model sizes. We further support our theoretical findings through empirical experiments that explore the impact of varying numerical precision on arithmetic tasks, providing valuable insights for improving the mathematical reasoning capabilities of LLMs.

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/

Yu Xuejun, Jianyuan Zhong, Zijin Feng et al.

Recent advances in large language models show strong promise for formal reasoning. However, most LLM-based theorem provers have long been constrained by the need for expert-written formal statements as inputs, limiting their applicability to real-world problems expressed in natural language. We tackle this gap with Mathesis, the first end-to-end theorem proving pipeline processing informal problem statements. It contributes Mathesis-Autoformalizer, the first autoformalizer using reinforcement learning to enhance the formalization ability of natural language problems, aided by our novel LeanScorer framework for nuanced formalization quality assessment. It also proposes a Mathesis-Prover, which generates formal proofs from the formalized statements. To evaluate the real-world applicability of end-to-end formal theorem proving, we introduce Gaokao-Formal, a benchmark of 488 complex problems from China's national college entrance exam. Our approach is carefully designed, with a thorough study of each component. Experiments demonstrate Mathesis's effectiveness, with the autoformalizer outperforming the best baseline by 22% in pass-rate on Gaokao-Formal. The full system surpasses other model combinations, achieving 64% accuracy on MiniF2F with pass@32 and a state-of-the-art 18% on Gaokao-Formal.

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.

Youquan Fu, Ruiyang Si, Hongfa Wang et al.

There is a high demand for audio-visual editing in video post-production and the film making field. While numerous models have explored audio and video editing, they struggle with object-level audio-visual operations. Specifically, object-level audio-visual editing requires the ability to perform object addition, replacement, and removal across both audio and visual modalities, while preserving the structural information of the source instances during the editing process. In this paper, we present \textbf{Object-AVEdit}, achieving the object-level audio-visual editing based on the inversion-regeneration paradigm. To achieve the object-level controllability during editing, we develop a word-to-sounding-object well-aligned audio generation model, bridging the gap in object-controllability between audio and current video generation models. Meanwhile, to achieve the better structural information preservation and object-level editing effect, we propose an inversion-regeneration holistically-optimized editing algorithm, ensuring both information retention during the inversion and better regeneration effect. Extensive experiments demonstrate that our editing model achieved advanced results in both audio-video object-level editing tasks with fine audio-visual semantic alignment. In addition, our developed audio generation model also achieved advanced performance. More results on our project page: https://gewu-lab.github.io/Object_AVEdit-website/.

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.

Sitong Chen, Shen Nie, Jiacheng Sun et al.

We present a systematic theoretical framework that interprets masked diffusion models (MDMs) as solutions to energy minimization problems in discrete optimal transport. Specifically, we prove that three distinct energy formulations--kinetic, conditional kinetic, and geodesic energy--are mathematically equivalent under the structure of MDMs, and that MDMs minimize all three when the mask schedule satisfies a closed-form optimality condition. This unification not only clarifies the theoretical foundations of MDMs, but also motivates practical improvements in sampling. By parameterizing interpolation schedules via Beta distributions, we reduce the schedule design space to a tractable 2D search, enabling efficient post-training tuning without model modification. Experiments on synthetic and real-world benchmarks demonstrate that our energy-inspired schedules outperform hand-crafted baselines, particularly in low-step sampling settings.

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.

Mingyang Yi, Jiacheng Sun, Zhenguo Li

The diffusion probabilistic generative models are widely used to generate high-quality data. Though they can synthetic data that does not exist in the training set, the rationale behind such generalization is still unexplored. In this paper, we formally define the generalization of the generative model, which is measured by the mutual information between the generated data and the training set. The definition originates from the intuition that the model which generates data with less correlation to the training set exhibits better generalization ability. Meanwhile, we show that for the empirical optimal diffusion model, the data generated by a deterministic sampler are all highly related to the training set, thus poor generalization. This result contradicts the observation of the trained diffusion model's (approximating empirical optima) extrapolation ability (generating unseen data). To understand this contradiction, we empirically verify the difference between the sufficiently trained diffusion model and the empirical optima. We found, though obtained through sufficient training, there still exists a slight difference between them, which is critical to making the diffusion model generalizable. Moreover, we propose another training objective whose empirical optimal solution has no potential generalization problem. We empirically show that the proposed training objective returns a similar model to the original one, which further verifies the generalization ability of the trained diffusion model.

Qi Sun, Hexin Dong, Zewei Chen et al.

Gradient-based methods for the distributed training of residual networks (ResNets) typically require a forward pass of the input data, followed by back-propagating the error gradient to update model parameters, which becomes time-consuming as the network goes deeper. To break the algorithmic locking and exploit synchronous module parallelism in both the forward and backward modes, auxiliary-variable methods have attracted much interest lately but suffer from significant communication overhead and lack of data augmentation. In this work, a novel joint learning framework for training realistic ResNets across multiple compute devices is established by trading off the storage and recomputation of external auxiliary variables. More specifically, the input data of each independent processor is generated from its low-capacity auxiliary network (AuxNet), which permits the use of data augmentation and realizes forward unlocking. The backward passes are then executed in parallel, each with a local loss function that originates from the penalty or augmented Lagrangian (AL) methods. Finally, the proposed AuxNet is employed to reproduce the updated auxiliary variables through an end-to-end training process. We demonstrate the effectiveness of our methods on ResNets and WideResNets across CIFAR-10, CIFAR-100, and ImageNet datasets, achieving speedup over the traditional layer-serial training method while maintaining comparable testing accuracy.

Yao Zhu, Jiacheng Ma, Jiacheng Sun et al.

Recently, some works found an interesting phenomenon that adversarially robust classifiers can generate good images comparable to generative models. We investigate this phenomenon from an energy perspective and provide a novel explanation. We reformulate adversarial example generation, adversarial training, and image generation in terms of an energy function. We find that adversarial training contributes to obtaining an energy function that is flat and has low energy around the real data, which is the key for generative capability. Based on our new understanding, we further propose a better adversarial training method, Joint Energy Adversarial Training (JEAT), which can generate high-quality images and achieve new state-of-the-art robustness under a wide range of attacks. The Inception Score of the images (CIFAR-10) generated by JEAT is 8.80, much better than original robust classifiers (7.50).

Mingyang Yi, Lu Hou, Jiacheng Sun et al.

Recently, learning a model that generalizes well on out-of-distribution (OOD) data has attracted great attention in the machine learning community. In this paper, after defining OOD generalization via Wasserstein distance, we theoretically show that a model robust to input perturbation generalizes well on OOD data. Inspired by previous findings that adversarial training helps improve input-robustness, we theoretically show that adversarially trained models have converged excess risk on OOD data, and empirically verify it on both image classification and natural language understanding tasks. Besides, in the paradigm of first pre-training and then fine-tuning, we theoretically show that a pre-trained model that is more robust to input perturbation provides a better initialization for generalization on downstream OOD data. Empirically, after fine-tuning, this better-initialized model from adversarial pre-training also has better OOD generalization.

Xiao-Yun Zhou, Jiacheng Sun, Nanyang Ye et al.

Deep Convolutional Neural Networks (DCNNs) are hard and time-consuming to train. Normalization is one of the effective solutions. Among previous normalization methods, Batch Normalization (BN) performs well at medium and large batch sizes and is with good generalizability to multiple vision tasks, while its performance degrades significantly at small batch sizes. In this paper, we find that BN saturates at extreme large batch sizes, i.e., 128 images per worker, i.e., GPU, as well and propose that the degradation/saturation of BN at small/extreme large batch sizes is caused by noisy/confused statistic calculation. Hence without adding new trainable parameters, using multiple-layer or multi-iteration information, or introducing extra computation, Batch Group Normalization (BGN) is proposed to solve the noisy/confused statistic calculation of BN at small/extreme large batch sizes with introducing the channel, height and width dimension to compensate. The group technique in Group Normalization (GN) is used and a hyper-parameter G is used to control the number of feature instances used for statistic calculation, hence to offer neither noisy nor confused statistic for different batch sizes. We empirically demonstrate that BGN consistently outperforms BN, Instance Normalization (IN), Layer Normalization (LN), GN, and Positional Normalization (PN), across a wide spectrum of vision tasks, including image classification, Neural Architecture Search (NAS), adversarial learning, Few Shot Learning (FSL) and Unsupervised Domain Adaptation (UDA), indicating its good performance, robust stability to batch size and wide generalizability. For example, for training ResNet-50 on ImageNet with a batch size of 2, BN achieves Top1 accuracy of 66.512% while BGN achieves 76.096% with notable improvement.

Qi Sun, Hexin Dong, Zewei Chen et al.

Gradient-based algorithms for training ResNets typically require a forward pass of the input data, followed by back-propagating the objective gradient to update parameters, which are time-consuming for deep ResNets. To break the dependencies between modules in both the forward and backward modes, auxiliary-variable methods such as the penalty and augmented Lagrangian (AL) approaches have attracted much interest lately due to their ability to exploit layer-wise parallelism. However, we observe that large communication overhead and lacking data augmentation are two key challenges of these methods, which may lead to low speedup ratio and accuracy drop across multiple compute devices. Inspired by the optimal control formulation of ResNets, we propose a novel serial-parallel hybrid training strategy to enable the use of data augmentation, together with downsampling filters to reduce the communication cost. The proposed strategy first trains the network parameters by solving a succession of independent sub-problems in parallel and then corrects the network parameters through a full serial forward-backward propagation of data. Such a strategy can be applied to most of the existing layer-parallel training methods using auxiliary variables. As an example, we validate the proposed strategy using penalty and AL methods on ResNet and WideResNet across MNIST, CIFAR-10 and CIFAR-100 datasets, achieving significant speedup over the traditional layer-serial training methods while maintaining comparable accuracy.

Jiacheng Sun, Xiangyong Cao, Hanwen Liang et al.

In recent years, a variety of normalization methods have been proposed to help train neural networks, such as batch normalization (BN), layer normalization (LN), weight normalization (WN), group normalization (GN), etc. However, mathematical tools to analyze all these normalization methods are lacking. In this paper, we first propose a lemma to define some necessary tools. Then, we use these tools to make a deep analysis on popular normalization methods and obtain the following conclusions: 1) Most of the normalization methods can be interpreted in a unified framework, namely normalizing pre-activations or weights onto a sphere; 2) Since most of the existing normalization methods are scaling invariant, we can conduct optimization on a sphere with scaling symmetry removed, which can help stabilize the training of network; 3) We prove that training with these normalization methods can make the norm of weights increase, which could cause adversarial vulnerability as it amplifies the attack. Finally, a series of experiments are conducted to verify these claims.

Hanwen Liang, Shifeng Zhang, Jiacheng Sun et al.

Recently, there has been a growing interest in automating the process of neural architecture design, and the Differentiable Architecture Search (DARTS) method makes the process available within a few GPU days. However, the performance of DARTS is often observed to collapse when the number of search epochs becomes large. Meanwhile, lots of "{\em skip-connect}s" are found in the selected architectures. In this paper, we claim that the cause of the collapse is that there exists overfitting in the optimization of DARTS. Therefore, we propose a simple and effective algorithm, named "DARTS+", to avoid the collapse and improve the original DARTS, by "early stopping" the search procedure when meeting a certain criterion. We also conduct comprehensive experiments on benchmark datasets and different search spaces and show the effectiveness of our DARTS+ algorithm, and DARTS+ achieves $2.32\%$ test error on CIFAR10, $14.87\%$ on CIFAR100, and $23.7\%$ on ImageNet. We further remark that the idea of "early stopping" is implicitly included in some existing DARTS variants by manually setting a small number of search epochs, while we give an {\em explicit} criterion for "early stopping".