Peihao Wang

Zhendong Wang, Yifan Jiang, Huangjie Zheng et al. · apple-ml, microsoft-research

Diffusion models are powerful, but they require a lot of time and data to train. We propose Patch Diffusion, a generic patch-wise training framework, to significantly reduce the training time costs while improving data efficiency, which thus helps democratize diffusion model training to broader users. At the core of our innovations is a new conditional score function at the patch level, where the patch location in the original image is included as additional coordinate channels, while the patch size is randomized and diversified throughout training to encode the cross-region dependency at multiple scales. Sampling with our method is as easy as in the original diffusion model. Through Patch Diffusion, we could achieve $\mathbf{\ge 2\times}$ faster training, while maintaining comparable or better generation quality. Patch Diffusion meanwhile improves the performance of diffusion models trained on relatively small datasets, $e.g.$, as few as 5,000 images to train from scratch. We achieve outstanding FID scores in line with state-of-the-art benchmarks: 1.77 on CelebA-64$\times$64, 1.93 on AFHQv2-Wild-64$\times$64, and 2.72 on ImageNet-256$\times$256. We share our code and pre-trained models at https://github.com/Zhendong-Wang/Patch-Diffusion.

Peihao Wang, Wenqing Zheng, Tianlong Chen et al.

Vision Transformer (ViT) has recently demonstrated promise in computer vision problems. However, unlike Convolutional Neural Networks (CNN), it is known that the performance of ViT saturates quickly with depth increasing, due to the observed attention collapse or patch uniformity. Despite a couple of empirical solutions, a rigorous framework studying on this scalability issue remains elusive. In this paper, we first establish a rigorous theory framework to analyze ViT features from the Fourier spectrum domain. We show that the self-attention mechanism inherently amounts to a low-pass filter, which indicates when ViT scales up its depth, excessive low-pass filtering will cause feature maps to only preserve their Direct-Current (DC) component. We then propose two straightforward yet effective techniques to mitigate the undesirable low-pass limitation. The first technique, termed AttnScale, decomposes a self-attention block into low-pass and high-pass components, then rescales and combines these two filters to produce an all-pass self-attention matrix. The second technique, termed FeatScale, re-weights feature maps on separate frequency bands to amplify the high-frequency signals. Both techniques are efficient and hyperparameter-free, while effectively overcoming relevant ViT training artifacts such as attention collapse and patch uniformity. By seamlessly plugging in our techniques to multiple ViT variants, we demonstrate that they consistently help ViTs benefit from deeper architectures, bringing up to 1.1% performance gains "for free" (e.g., with little parameter overhead). We publicly release our codes and pre-trained models at https://github.com/VITA-Group/ViT-Anti-Oversmoothing.

Keyu Duan, Zirui Liu, Peihao Wang et al.

Large-scale graph training is a notoriously challenging problem for graph neural networks (GNNs). Due to the nature of evolving graph structures into the training process, vanilla GNNs usually fail to scale up, limited by the GPU memory space. Up to now, though numerous scalable GNN architectures have been proposed, we still lack a comprehensive survey and fair benchmark of this reservoir to find the rationale for designing scalable GNNs. To this end, we first systematically formulate the representative methods of large-scale graph training into several branches and further establish a fair and consistent benchmark for them by a greedy hyperparameter searching. In addition, regarding efficiency, we theoretically evaluate the time and space complexity of various branches and empirically compare them w.r.t GPU memory usage, throughput, and convergence. Furthermore, We analyze the pros and cons for various branches of scalable GNNs and then present a new ensembling training manner, named EnGCN, to address the existing issues. Our code is available at https://github.com/VITA-Group/Large_Scale_GCN_Benchmarking.

Peihao Wang, Rameswar Panda, Lucas Torroba Hennigen et al. · mit

Scaling transformers has led to significant breakthroughs in many domains, leading to a paradigm in which larger versions of existing models are trained and released on a periodic basis. New instances of such models are typically trained completely from scratch, despite the fact that they are often just scaled-up versions of their smaller counterparts. How can we use the implicit knowledge in the parameters of smaller, extant models to enable faster training of newer, larger models? This paper describes an approach for accelerating transformer training by learning to grow pretrained transformers, where we learn to linearly map the parameters of the smaller model to initialize the larger model. For tractable learning, we factorize the linear transformation as a composition of (linear) width- and depth-growth operators, and further employ a Kronecker factorization of these growth operators to encode architectural knowledge. Extensive experiments across both language and vision transformers demonstrate that our learned Linear Growth Operator (LiGO) can save up to 50% computational cost of training from scratch, while also consistently outperforming strong baselines that also reuse smaller pretrained models to initialize larger models.

Tianlong Chen, Peihao Wang, Zhiwen Fan et al.

Neural Radiance Field (NeRF) regresses a neural parameterized scene by differentially rendering multi-view images with ground-truth supervision. However, when interpolating novel views, NeRF often yields inconsistent and visually non-smooth geometric results, which we consider as a generalization gap between seen and unseen views. Recent advances in convolutional neural networks have demonstrated the promise of advanced robust data augmentations, either random or learned, in enhancing both in-distribution and out-of-distribution generalization. Inspired by that, we propose Augmented NeRF (Aug-NeRF), which for the first time brings the power of robust data augmentations into regularizing the NeRF training. Particularly, our proposal learns to seamlessly blend worst-case perturbations into three distinct levels of the NeRF pipeline with physical grounds, including (1) the input coordinates, to simulate imprecise camera parameters at image capture; (2) intermediate features, to smoothen the intrinsic feature manifold; and (3) pre-rendering output, to account for the potential degradation factors in the multi-view image supervision. Extensive results demonstrate that Aug-NeRF effectively boosts NeRF performance in both novel view synthesis (up to 1.5dB PSNR gain) and underlying geometry reconstruction. Furthermore, thanks to the implicit smooth prior injected by the triple-level augmentations, Aug-NeRF can even recover scenes from heavily corrupted images, a highly challenging setting untackled before. Our codes are available in https://github.com/VITA-Group/Aug-NeRF.

Dejia Xu, Yifan Jiang, Peihao Wang et al. · gatech

Despite the rapid development of Neural Radiance Field (NeRF), the necessity of dense covers largely prohibits its wider applications. While several recent works have attempted to address this issue, they either operate with sparse views (yet still, a few of them) or on simple objects/scenes. In this work, we consider a more ambitious task: training neural radiance field, over realistically complex visual scenes, by "looking only once", i.e., using only a single view. To attain this goal, we present a Single View NeRF (SinNeRF) framework consisting of thoughtfully designed semantic and geometry regularizations. Specifically, SinNeRF constructs a semi-supervised learning process, where we introduce and propagate geometry pseudo labels and semantic pseudo labels to guide the progressive training process. Extensive experiments are conducted on complex scene benchmarks, including NeRF synthetic dataset, Local Light Field Fusion dataset, and DTU dataset. We show that even without pre-training on multi-view datasets, SinNeRF can yield photo-realistic novel-view synthesis results. Under the single image setting, SinNeRF significantly outperforms the current state-of-the-art NeRF baselines in all cases. Project page: https://vita-group.github.io/SinNeRF/

Ajay Jaiswal, Peihao Wang, Tianlong Chen et al.

Despite the enormous success of Graph Convolutional Networks (GCNs) in modeling graph-structured data, most of the current GCNs are shallow due to the notoriously challenging problems of over-smoothening and information squashing along with conventional difficulty caused by vanishing gradients and over-fitting. Previous works have been primarily focused on the study of over-smoothening and over-squashing phenomena in training deep GCNs. Surprisingly, in comparison with CNNs/RNNs, very limited attention has been given to understanding how healthy gradient flow can benefit the trainability of deep GCNs. In this paper, firstly, we provide a new perspective of gradient flow to understand the substandard performance of deep GCNs and hypothesize that by facilitating healthy gradient flow, we can significantly improve their trainability, as well as achieve state-of-the-art (SOTA) level performance from vanilla-GCNs. Next, we argue that blindly adopting the Glorot initialization for GCNs is not optimal, and derive a topology-aware isometric initialization scheme for vanilla-GCNs based on the principles of isometry. Additionally, contrary to ad-hoc addition of skip-connections, we propose to use gradient-guided dynamic rewiring of vanilla-GCNs} with skip connections. Our dynamic rewiring method uses the gradient flow within each layer during training to introduce on-demand skip-connections adaptively. We provide extensive empirical evidence across multiple datasets that our methods improve gradient flow in deep vanilla-GCNs and significantly boost their performance to comfortably compete and outperform many fancy state-of-the-art methods. Codes are available at: https://github.com/VITA-Group/GradientGCN.

Peihao Wang, Zhiwen Fan, Tianlong Chen et al.

Representing visual signals by coordinate-based deep fully-connected networks has been shown advantageous in fitting complex details and solving inverse problems than discrete grid-based representation. However, acquiring such a continuous Implicit Neural Representation (INR) requires tedious per-scene training on tons of signal measurements, which limits its practicality. In this paper, we present a generic INR framework that achieves both data and training efficiency by learning a Neural Implicit Dictionary (NID) from a data collection and representing INR as a functional combination of basis sampled from the dictionary. Our NID assembles a group of coordinate-based subnetworks which are tuned to span the desired function space. After training, one can instantly and robustly acquire an unseen scene representation by solving the coding coefficients. To parallelly optimize a large group of networks, we borrow the idea from Mixture-of-Expert (MoE) to design and train our network with a sparse gating mechanism. Our experiments show that, NID can improve reconstruction of 2D images or 3D scenes by 2 orders of magnitude faster with up to 98% less input data. We further demonstrate various applications of NID in image inpainting and occlusion removal, which are considered to be challenging with vanilla INR. Our codes are available in https://github.com/VITA-Group/Neural-Implicit-Dict.

Wenyan Cong, Hanxue Liang, Peihao Wang et al.

Cross-scene generalizable NeRF models, which can directly synthesize novel views of unseen scenes, have become a new spotlight of the NeRF field. Several existing attempts rely on increasingly end-to-end "neuralized" architectures, i.e., replacing scene representation and/or rendering modules with performant neural networks such as transformers, and turning novel view synthesis into a feed-forward inference pipeline. While those feedforward "neuralized" architectures still do not fit diverse scenes well out of the box, we propose to bridge them with the powerful Mixture-of-Experts (MoE) idea from large language models (LLMs), which has demonstrated superior generalization ability by balancing between larger overall model capacity and flexible per-instance specialization. Starting from a recent generalizable NeRF architecture called GNT, we first demonstrate that MoE can be neatly plugged in to enhance the model. We further customize a shared permanent expert and a geometry-aware consistency loss to enforce cross-scene consistency and spatial smoothness respectively, which are essential for generalizable view synthesis. Our proposed model, dubbed GNT with Mixture-of-View-Experts (GNT-MOVE), has experimentally shown state-of-the-art results when transferring to unseen scenes, indicating remarkably better cross-scene generalization in both zero-shot and few-shot settings. Our codes are available at https://github.com/VITA-Group/GNT-MOVE.

Mukund Varma T, Peihao Wang, Xuxi Chen et al.

We present Generalizable NeRF Transformer (GNT), a transformer-based architecture that reconstructs Neural Radiance Fields (NeRFs) and learns to renders novel views on the fly from source views. While prior works on NeRFs optimize a scene representation by inverting a handcrafted rendering equation, GNT achieves neural representation and rendering that generalizes across scenes using transformers at two stages. (1) The view transformer leverages multi-view geometry as an inductive bias for attention-based scene representation, and predicts coordinate-aligned features by aggregating information from epipolar lines on the neighboring views. (2) The ray transformer renders novel views using attention to decode the features from the view transformer along the sampled points during ray marching. Our experiments demonstrate that when optimized on a single scene, GNT can successfully reconstruct NeRF without an explicit rendering formula due to the learned ray renderer. When trained on multiple scenes, GNT consistently achieves state-of-the-art performance when transferring to unseen scenes and outperform all other methods by ~10% on average. Our analysis of the learned attention maps to infer depth and occlusion indicate that attention enables learning a physically-grounded rendering. Our results show the promise of transformers as a universal modeling tool for graphics. Please refer to our project page for video results: https://vita-group.github.io/GNT/.

Zhiwen Fan, Yifan Jiang, Peihao Wang et al.

Representing visual signals by implicit representation (e.g., a coordinate based deep network) has prevailed among many vision tasks. This work explores a new intriguing direction: training a stylized implicit representation, using a generalized approach that can apply to various 2D and 3D scenarios. We conduct a pilot study on a variety of implicit functions, including 2D coordinate-based representation, neural radiance field, and signed distance function. Our solution is a Unified Implicit Neural Stylization framework, dubbed INS. In contrary to vanilla implicit representation, INS decouples the ordinary implicit function into a style implicit module and a content implicit module, in order to separately encode the representations from the style image and input scenes. An amalgamation module is then applied to aggregate these information and synthesize the stylized output. To regularize the geometry in 3D scenes, we propose a novel self-distillation geometry consistency loss which preserves the geometry fidelity of the stylized scenes. Comprehensive experiments are conducted on multiple task settings, including novel view synthesis of complex scenes, stylization for implicit surfaces, and fitting images using MLPs. We further demonstrate that the learned representation is continuous not only spatially but also style-wise, leading to effortlessly interpolating between different styles and generating images with new mixed styles. Please refer to the video on our project page for more view synthesis results: https://zhiwenfan.github.io/INS.

Peihao Wang, Shenghao Yang, Yunyu Liu et al.

Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However, higher-order relations in practice contain complex patterns and are often highly irregular. So, it is often challenging to design an HNN that suffices to express those relations while keeping computational efficiency. Inspired by hypergraph diffusion algorithms, this work proposes a new HNN architecture named ED-HNN, which provably represents any continuous equivariant hypergraph diffusion operators that can model a wide range of higher-order relations. ED-HNN can be implemented efficiently by combining star expansions of hypergraphs with standard message passing neural networks. ED-HNN further shows great superiority in processing heterophilic hypergraphs and constructing deep models. We evaluate ED-HNN for node classification on nine real-world hypergraph datasets. ED-HNN uniformly outperforms the best baselines over these nine datasets and achieves more than 2\%$\uparrow$ in prediction accuracy over four datasets therein.

Dejia Xu, Peihao Wang, Yifan Jiang et al.

Implicit Neural Representations (INRs) encoding continuous multi-media data via multi-layer perceptrons has shown undebatable promise in various computer vision tasks. Despite many successful applications, editing and processing an INR remains intractable as signals are represented by latent parameters of a neural network. Existing works manipulate such continuous representations via processing on their discretized instance, which breaks down the compactness and continuous nature of INR. In this work, we present a pilot study on the question: how to directly modify an INR without explicit decoding? We answer this question by proposing an implicit neural signal processing network, dubbed INSP-Net, via differential operators on INR. Our key insight is that spatial gradients of neural networks can be computed analytically and are invariant to translation, while mathematically we show that any continuous convolution filter can be uniformly approximated by a linear combination of high-order differential operators. With these two knobs, INSP-Net instantiates the signal processing operator as a weighted composition of computational graphs corresponding to the high-order derivatives of INRs, where the weighting parameters can be data-driven learned. Based on our proposed INSP-Net, we further build the first Convolutional Neural Network (CNN) that implicitly runs on INRs, named INSP-ConvNet. Our experiments validate the expressiveness of INSP-Net and INSP-ConvNet in fitting low-level image and geometry processing kernels (e.g. blurring, deblurring, denoising, inpainting, and smoothening) as well as for high-level tasks on implicit fields such as image classification.

Zhiwen Fan, Panwang Pan, Peihao Wang et al.

In the field of novel-view synthesis, the necessity of knowing camera poses (e.g., via Structure from Motion) before rendering has been a common practice. However, the consistent acquisition of accurate camera poses remains elusive, and errors in pose extraction can adversely impact the view synthesis process. To address this challenge, we introduce PF-GRT, a new Pose-Free framework for Generalizable Rendering Transformer, eliminating the need for pre-computed camera poses and instead leveraging feature-matching learned directly from data. PF-GRT is parameterized using a local relative coordinate system, where one of the source images is set as the origin. An OmniView Transformer is designed for fusing multi-view cues under the pose-free setting, where unposed-view fusion and origin-centric aggregation are performed. The 3D point feature along target ray is sampled by projecting onto the selected origin plane. The final pixel intensities are modulated and decoded using another Transformer. PF-GRT demonstrates an impressive ability to generalize to new scenes that were not encountered during the training phase, without the need of pre-computing camera poses. Our experiments with zero-shot rendering on the LLFF, RealEstate-10k, Shiny, and Blender datasets reveal that it produces superior quality in generating photo-realistic images. Moreover, it demonstrates robustness against noise in test camera poses. Code is available at https://zhiwenfan.github.io/PF-GRT/.

Dejia Xu, Yifan Jiang, Peihao Wang et al.

Virtual reality and augmented reality (XR) bring increasing demand for 3D content. However, creating high-quality 3D content requires tedious work that a human expert must do. In this work, we study the challenging task of lifting a single image to a 3D object and, for the first time, demonstrate the ability to generate a plausible 3D object with 360° views that correspond well with the given reference image. By conditioning on the reference image, our model can fulfill the everlasting curiosity for synthesizing novel views of objects from images. Our technique sheds light on a promising direction of easing the workflows for 3D artists and XR designers. We propose a novel framework, dubbed NeuralLift-360, that utilizes a depth-aware neural radiance representation (NeRF) and learns to craft the scene guided by denoising diffusion models. By introducing a ranking loss, our NeuralLift-360 can be guided with rough depth estimation in the wild. We also adopt a CLIP-guided sampling strategy for the diffusion prior to provide coherent guidance. Extensive experiments demonstrate that our NeuralLift-360 significantly outperforms existing state-of-the-art baselines. Project page: https://vita-group.github.io/NeuralLift-360/

Zhiwen Fan, Peihao Wang, Yifan Jiang et al.

Neural volumetric representations have shown the potential that Multi-layer Perceptrons (MLPs) can be optimized with multi-view calibrated images to represent scene geometry and appearance, without explicit 3D supervision. Object segmentation can enrich many downstream applications based on the learned radiance field. However, introducing hand-crafted segmentation to define regions of interest in a complex real-world scene is non-trivial and expensive as it acquires per view annotation. This paper carries out the exploration of self-supervised learning for object segmentation using NeRF for complex real-world scenes. Our framework, called NeRF with Self-supervised Object Segmentation NeRF-SOS, couples object segmentation and neural radiance field to segment objects in any view within a scene. By proposing a novel collaborative contrastive loss in both appearance and geometry levels, NeRF-SOS encourages NeRF models to distill compact geometry-aware segmentation clusters from their density fields and the self-supervised pre-trained 2D visual features. The self-supervised object segmentation framework can be applied to various NeRF models that both lead to photo-realistic rendering results and convincing segmentation maps for both indoor and outdoor scenarios. Extensive results on the LLFF, Tank & Temple, and BlendedMVS datasets validate the effectiveness of NeRF-SOS. It consistently surpasses other 2D-based self-supervised baselines and predicts finer semantics masks than existing supervised counterparts. Please refer to the video on our project page for more details:https://zhiwenfan.github.io/NeRF-SOS.

Panwang Pan, Zhiwen Fan, Brandon Y. Feng et al.

The accurate estimation of six degrees-of-freedom (6DoF) object poses is essential for many applications in robotics and augmented reality. However, existing methods for 6DoF pose estimation often depend on CAD templates or dense support views, restricting their usefulness in realworld situations. In this study, we present a new cascade framework named Cas6D for few-shot 6DoF pose estimation that is generalizable and uses only RGB images. To address the false positives of target object detection in the extreme few-shot setting, our framework utilizes a selfsupervised pre-trained ViT to learn robust feature representations. Then, we initialize the nearest top-K pose candidates based on similarity score and refine the initial poses using feature pyramids to formulate and update the cascade warped feature volume, which encodes context at increasingly finer scales. By discretizing the pose search range using multiple pose bins and progressively narrowing the pose search range in each stage using predictions from the previous stage, Cas6D can overcome the large gap between pose candidates and ground truth poses, which is a common failure mode in sparse-view scenarios. Experimental results on the LINEMOD and GenMOP datasets demonstrate that Cas6D outperforms state-of-the-art methods by 9.2% and 3.8% accuracy (Proj-5) under the 32-shot setting compared to OnePose++ and Gen6D.

Peihao Wang, Shenghao Yang, Shu Li et al.

Set representation has become ubiquitous in deep learning for modeling the inductive bias of neural networks that are insensitive to the input order. DeepSets is the most widely used neural network architecture for set representation. It involves embedding each set element into a latent space with dimension $L$, followed by a sum pooling to obtain a whole-set embedding, and finally mapping the whole-set embedding to the output. In this work, we investigate the impact of the dimension $L$ on the expressive power of DeepSets. Previous analyses either oversimplified high-dimensional features to be one-dimensional features or were limited to analytic activations, thereby diverging from practical use or resulting in $L$ that grows exponentially with the set size $N$ and feature dimension $D$. To investigate the minimal value of $L$ that achieves sufficient expressive power, we present two set-element embedding layers: (a) linear + power activation (LP) and (b) linear + exponential activations (LE). We demonstrate that $L$ being poly$(N, D)$ is sufficient for set representation using both embedding layers. We also provide a lower bound of $L$ for the LP embedding layer. Furthermore, we extend our results to permutation-equivariant set functions and the complex field.

Jiajun Zhu, Ying Chen, Peihao Wang et al.

Graph foundation models (GFMs) aim to reuse a single backbone across diverse graph domains, yet their transfer is often uneven and can exhibit negative transfer. While most prior work improves transfer through architectural or adaptation choices, we ask a data-centric question: which properties of two graph domains determine how much a fixed representation model changes its outputs? Using a graphon-based continuous limit for dense graphs, we show that for both set-based and message-passing tokenizations, any Lipschitz backbone admits an explicit decomposition of cross-domain output shift into (i) graph-specific finite-sample approximation terms and (ii) an intrinsic, relabeling-invariant domain discrepancy capturing structural mismatch. A key ingredient is positional-encoding (PE) stability: we establish stability guarantees for spectral PEs and highlight contrasting behaviors of eigenvector- versus subspace-based PEs. Experiments on synthetic and real graphs validate the theory and translate the decomposition into guidance for data curation in GFM transfer.

Peihao Wang, Shan Yang, Xijun Wang et al.

Associative memory has long underpinned the design of sequential models. Beyond recall, humans reason by projecting future states and selecting goal-directed actions, a capability that modern language models increasingly require but do not natively encode. While prior work uses reinforcement learning or test-time training, planning remains external to the model architecture. We formulate reasoning as optimal control and introduce the Test-Time Control (TTC) layer, which performs finite-horizon LQR planning over latent states at inference time, represents a value function within neural architectures, and leverages it as the nested objective to enable planning before prediction. To ensure scalability, we derive a hardware-efficient LQR solver based on a symplectic formulation and implement it as a fused CUDA kernel, enabling parallel execution with minimal overhead. Integrated as an adapter into pretrained LLMs, TTC layers improve mathematical reasoning performance by up to +27.8% on MATH-500 and 2-3x Pass@8 improvements on AMC and AIME, demonstrating that embedding optimal control as an architectural component provides an effective and scalable mechanism for reasoning beyond test-time training.

Ruisi Cai, Yeonju Ro, Geon-Woo Kim et al.

The proliferation of large language models (LLMs) has led to the adoption of Mixture-of-Experts (MoE) architectures that dynamically leverage specialized subnetworks for improved efficiency and performance. Despite their benefits, MoE models face significant challenges during inference, including inefficient memory management and suboptimal batching, due to misaligned design choices between the model architecture and the system policies. Furthermore, the conventional approach of training MoEs from scratch is increasingly prohibitive in terms of cost. In this paper, we propose a novel framework Read-ME that transforms pre-trained dense LLMs into smaller MoE models (in contrast to "upcycling" generalist MoEs), avoiding the high costs of ground-up training. Our approach employs activation sparsity to extract experts. To compose experts, we examine the widely-adopted layer-wise router design and show its redundancy, and thus we introduce the pre-gating router decoupled from the MoE backbone that facilitates system-friendly pre-computing and lookahead scheduling, enhancing expert-aware batching and caching. Our codesign therefore addresses critical gaps on both the algorithmic and system fronts, establishing a scalable and efficient alternative for LLM inference in resource-constrained settings. Read-ME outperforms other popular open-source dense models of similar scales, achieving improvements of up to 10.1% on MMLU, and improving mean end-to-end latency up to 6.1%. Codes are available at: https://github.com/VITA-Group/READ-ME.

Zhangyang Wang, Peihao Wang, Kai Wang

Neural network checkpoints have quietly become a large-scale data resource: millions of trained weight vectors now exist, each encoding task-, domain-, and architecture-specific knowledge. This position paper argues that model checkpoints should be treated as a first-class data modality, and that generative modeling in weight space should be standardized as a core machine learning primitive. Recent advances demonstrate that neural weights can be synthesized on demand, often matching fine-tuning performance while reducing adaptation cost by orders of magnitude. We contend that these results reflect an underlying structural fact: high-performing models occupy low-dimensional, highly structured regions of weight space shaped by symmetry, flatness, modularity, and shared subspaces. Building on this view, we organize existing methods into a five-stage pipeline, survey applications where the approach is already practical, and clarify current limits: adapter-scale and conditional generation are advancing rapidly, while unrestricted frontier-scale checkpoint synthesis remains open. Our goal is to shift the community's default mindset from optimizing models per task to sampling models from learned weight distributions, accelerating toward an era in which AI systems routinely improve or create other AI systems.

Peihao Wang, Ruisi Cai, Yuehao Wang et al.

Structured State Space Models (SSMs) have emerged as alternatives to transformers. While SSMs are often regarded as effective in capturing long-sequence dependencies, we rigorously demonstrate that they are inherently limited by strong recency bias. Our empirical studies also reveal that this bias impairs the models' ability to recall distant information and introduces robustness issues. Our scaling experiments then discovered that deeper structures in SSMs can facilitate the learning of long contexts. However, subsequent theoretical analysis reveals that as SSMs increase in depth, they exhibit another inevitable tendency toward over-smoothing, e.g., token representations becoming increasingly indistinguishable. This fundamental dilemma between recency and over-smoothing hinders the scalability of existing SSMs. Inspired by our theoretical findings, we propose to polarize two channels of the state transition matrices in SSMs, setting them to zero and one, respectively, simultaneously addressing recency bias and over-smoothing. Experiments demonstrate that our polarization technique consistently enhances the associative recall accuracy of long-range tokens and unlocks SSMs to benefit further from deeper architectures. All source codes are released at https://github.com/VITA-Group/SSM-Bottleneck.

Hengyu Liu, Yuehao Wang, Chenxin Li et al.

3D Gaussian splatting (3DGS) has enabled various applications in 3D scene representation and novel view synthesis due to its efficient rendering capabilities. However, 3DGS demands relatively significant GPU memory, limiting its use on devices with restricted computational resources. Previous approaches have focused on pruning less important Gaussians, effectively compressing 3DGS but often requiring a fine-tuning stage and lacking adaptability for the specific memory needs of different devices. In this work, we present an elastic inference method for 3DGS. Given an input for the desired model size, our method selects and transforms a subset of Gaussians, achieving substantial rendering performance without additional fine-tuning. We introduce a tiny learnable module that controls Gaussian selection based on the input percentage, along with a transformation module that adjusts the selected Gaussians to complement the performance of the reduced model. Comprehensive experiments on ZipNeRF, MipNeRF and Tanks\&Temples scenes demonstrate the effectiveness of our approach. Code is available at https://flexgs.github.io.

Jiajun Zhu, Peihao Wang, Ruisi Cai et al.

Transformers rely on both content-based and position-based addressing mechanisms to make predictions, but existing positional encoding techniques often diminish the effectiveness of position-based addressing. Many current methods enforce rigid patterns in attention maps, limiting the ability to model long-range dependencies and adapt to diverse tasks. Additionally, most positional encodings are learned as general biases, lacking the specialization required for different instances within a dataset. To address this, we propose con\textbf{T}extualized equivari\textbf{A}nt \textbf{P}osition \textbf{E}ncoding (\textbf{TAPE}), a novel framework that enhances positional embeddings by incorporating sequence content across layers. TAPE introduces dynamic, context-aware positional encodings, overcoming the constraints of traditional fixed patterns. We show that TAPE can provably facilitate LLM reasoning ability by emulating a broader class of algorithms. By enforcing permutation and orthogonal equivariance, TAPE ensures the stability of positional encodings during updates, improving long-context ability. Our method can be easily integrated into pre-trained transformers, offering parameter-efficient fine-tuning with minimal overhead. Extensive experiments show that TAPE achieves superior performance in language modeling, arithmetic reasoning, and long-context retrieval tasks compared to existing positional embedding techniques. Code is available at https://github.com/VITA-Group/TAPE.

Junjie Yang, Jinze Zhao, Peihao Wang et al.

Diffusion-based image synthesis has attracted extensive attention recently. In particular, ControlNet that uses image-based prompts exhibits powerful capability in image tasks such as canny edge detection and generates images well aligned with these prompts. However, vanilla ControlNet generally requires extensive training of around 5000 steps to achieve a desirable control for a single task. Recent context-learning approaches have improved its adaptability, but mainly for edge-based tasks, and rely on paired examples. Thus, two important open issues are yet to be addressed to reach the full potential of ControlNet: (i) zero-shot control for certain tasks and (ii) faster adaptation for non-edge-based tasks. In this paper, we introduce a novel Meta ControlNet method, which adopts the task-agnostic meta learning technique and features a new layer freezing design. Meta ControlNet significantly reduces learning steps to attain control ability from 5000 to 1000. Further, Meta ControlNet exhibits direct zero-shot adaptability in edge-based tasks without any finetuning, and achieves control within only 100 finetuning steps in more complex non-edge tasks such as Human Pose, outperforming all existing methods. The codes is available in https://github.com/JunjieYang97/Meta-ControlNet.

Wenqing Zheng, Qiangqiang Guo, Hao Yang et al.

Multi-agent control is a central theme in the Cyber-Physical Systems (CPS). However, current control methods either receive non-Markovian states due to insufficient sensing and decentralized design, or suffer from poor convergence. This paper presents the Delayed Propagation Transformer (DePT), a new transformer-based model that specializes in the global modeling of CPS while taking into account the immutable constraints from the physical world. DePT induces a cone-shaped spatial-temporal attention prior, which injects the information propagation and aggregation principles and enables a global view. With physical constraint inductive bias baked into its design, our DePT is ready to plug and play for a broad class of multi-agent systems. The experimental results on one of the most challenging CPS -- network-scale traffic signal control system in the open world -- show that our model outperformed the state-of-the-art expert methods on synthetic and real-world datasets. Our codes are released at: https://github.com/VITA-Group/DePT.

Tianlong Chen, Kaixiong Zhou, Keyu Duan et al.

Training deep graph neural networks (GNNs) is notoriously hard. Besides the standard plights in training deep architectures such as vanishing gradients and overfitting, it also uniquely suffers from over-smoothing, information squashing, and so on, which limits their potential power for encoding the high-order neighbor structure in large-scale graphs. Although numerous efforts are proposed to address these limitations, such as various forms of skip connections, graph normalization, and random dropping, it is difficult to disentangle the advantages brought by a deep GNN architecture from those "tricks" necessary to train such an architecture. Moreover, the lack of a standardized benchmark with fair and consistent experimental settings poses an almost insurmountable obstacle to gauge the effectiveness of new mechanisms. In view of those, we present the first fair and reproducible benchmark dedicated to assessing the "tricks" of training deep GNNs. We categorize existing approaches, investigate their hyperparameter sensitivity, and unify the basic configuration. Comprehensive evaluations are then conducted on tens of representative graph datasets including the recent large-scale Open Graph Benchmark, with diverse deep GNN backbones. We demonstrate that an organic combo of initial connection, identity mapping, group and batch normalization attains the new state-of-the-art results for deep GNNs on large datasets. Codes are available: https://github.com/VITA-Group/Deep_GCN_Benchmarking.

Peihao Wang, Dejia Xu, Zhiwen Fan et al.

Despite the remarkable performance of score distillation in text-to-3D generation, such techniques notoriously suffer from view inconsistency issues, also known as "Janus" artifact, where the generated objects fake each view with multiple front faces. Although empirically effective methods have approached this problem via score debiasing or prompt engineering, a more rigorous perspective to explain and tackle this problem remains elusive. In this paper, we reveal that the existing score distillation-based text-to-3D generation frameworks degenerate to maximal likelihood seeking on each view independently and thus suffer from the mode collapse problem, manifesting as the Janus artifact in practice. To tame mode collapse, we improve score distillation by re-establishing the entropy term in the corresponding variational objective, which is applied to the distribution of rendered images. Maximizing the entropy encourages diversity among different views in generated 3D assets, thereby mitigating the Janus problem. Based on this new objective, we derive a new update rule for 3D score distillation, dubbed Entropic Score Distillation (ESD). We theoretically reveal that ESD can be simplified and implemented by just adopting the classifier-free guidance trick upon variational score distillation. Although embarrassingly straightforward, our extensive experiments successfully demonstrate that ESD can be an effective treatment for Janus artifacts in score distillation.

Zhiwen Fan, Jian Zhang, Wenyan Cong et al.

Reconstructing and understanding 3D structures from a limited number of images is a well-established problem in computer vision. Traditional methods usually break this task into multiple subtasks, each requiring complex transformations between different data representations. For instance, dense reconstruction through Structure-from-Motion (SfM) involves converting images into key points, optimizing camera parameters, and estimating structures. Afterward, accurate sparse reconstructions are required for further dense modeling, which is subsequently fed into task-specific neural networks. This multi-step process results in considerable processing time and increased engineering complexity. In this work, we present the Large Spatial Model (LSM), which processes unposed RGB images directly into semantic radiance fields. LSM simultaneously estimates geometry, appearance, and semantics in a single feed-forward operation, and it can generate versatile label maps by interacting with language at novel viewpoints. Leveraging a Transformer-based architecture, LSM integrates global geometry through pixel-aligned point maps. To enhance spatial attribute regression, we incorporate local context aggregation with multi-scale fusion, improving the accuracy of fine local details. To tackle the scarcity of labeled 3D semantic data and enable natural language-driven scene manipulation, we incorporate a pre-trained 2D language-based segmentation model into a 3D-consistent semantic feature field. An efficient decoder then parameterizes a set of semantic anisotropic Gaussians, facilitating supervised end-to-end learning. Extensive experiments across various tasks show that LSM unifies multiple 3D vision tasks directly from unposed images, achieving real-time semantic 3D reconstruction for the first time.

Peihao Wang, Zhiwen Fan, Dejia Xu et al.

Score distillation has emerged as one of the most prevalent approaches for text-to-3D asset synthesis. Essentially, score distillation updates 3D parameters by lifting and back-propagating scores averaged over different views. In this paper, we reveal that the gradient estimation in score distillation is inherent to high variance. Through the lens of variance reduction, the effectiveness of SDS and VSD can be interpreted as applications of various control variates to the Monte Carlo estimator of the distilled score. Motivated by this rethinking and based on Stein's identity, we propose a more general solution to reduce variance for score distillation, termed Stein Score Distillation (SSD). SSD incorporates control variates constructed by Stein identity, allowing for arbitrary baseline functions. This enables us to include flexible guidance priors and network architectures to explicitly optimize for variance reduction. In our experiments, the overall pipeline, dubbed SteinDreamer, is implemented by instantiating the control variate with a monocular depth estimator. The results suggest that SSD can effectively reduce the distillation variance and consistently improve visual quality for both object- and scene-level generation. Moreover, we demonstrate that SteinDreamer achieves faster convergence than existing methods due to more stable gradient updates.

Mukund Varma T, Peihao Wang, Zhiwen Fan et al.

In recent years, there has been an explosion of 2D vision models for numerous tasks such as semantic segmentation, style transfer or scene editing, enabled by large-scale 2D image datasets. At the same time, there has been renewed interest in 3D scene representations such as neural radiance fields from multi-view images. However, the availability of 3D or multiview data is still substantially limited compared to 2D image datasets, making extending 2D vision models to 3D data highly desirable but also very challenging. Indeed, extending a single 2D vision operator like scene editing to 3D typically requires a highly creative method specialized to that task and often requires per-scene optimization. In this paper, we ask the question of whether any 2D vision model can be lifted to make 3D consistent predictions. We answer this question in the affirmative; our new Lift3D method trains to predict unseen views on feature spaces generated by a few visual models (i.e. DINO and CLIP), but then generalizes to novel vision operators and tasks, such as style transfer, super-resolution, open vocabulary segmentation and image colorization; for some of these tasks, there is no comparable previous 3D method. In many cases, we even outperform state-of-the-art methods specialized for the task in question. Moreover, Lift3D is a zero-shot method, in the sense that it requires no task-specific training, nor scene-specific optimization.

Zekai Li, Xinhao Zhong, Samir Khaki et al.

In recent years, dataset distillation has provided a reliable solution for data compression, where models trained on the resulting smaller synthetic datasets achieve performance comparable to those trained on the original datasets. To further improve the performance of synthetic datasets, various training pipelines and optimization objectives have been proposed, greatly advancing the field of dataset distillation. Recent decoupled dataset distillation methods introduce soft labels and stronger data augmentation during the post-evaluation phase and scale dataset distillation up to larger datasets (e.g., ImageNet-1K). However, this raises a question: Is accuracy still a reliable metric to fairly evaluate dataset distillation methods? Our empirical findings suggest that the performance improvements of these methods often stem from additional techniques rather than the inherent quality of the images themselves, with even randomly sampled images achieving superior results. Such misaligned evaluation settings severely hinder the development of DD. Therefore, we propose DD-Ranking, a unified evaluation framework, along with new general evaluation metrics to uncover the true performance improvements achieved by different methods. By refocusing on the actual information enhancement of distilled datasets, DD-Ranking provides a more comprehensive and fair evaluation standard for future research advancements.

Wenyan Cong, Hanqing Zhu, Peihao Wang et al.

World foundation models, which simulate the physical world by predicting future states from current observations and inputs, have become central to many applications in physical intelligence, including autonomous driving and robotics. However, these models require substantial computational resources for pretraining and are further constrained by available data during post-training. As such, scaling computation at test time emerges as both a critical and practical alternative to traditional model enlargement or re-training. In this work, we introduce SWIFT, a test-time scaling framework tailored for WFMs. SWIFT integrates our extensible WFM evaluation toolkit with process-level inference strategies, including fast tokenization, probability-based Top-K pruning, and efficient beam search. Empirical results on the COSMOS model demonstrate that test-time scaling exists even in a compute-optimal way. Our findings reveal that test-time scaling laws hold for WFMs and that SWIFT provides a scalable and effective pathway for improving WFM inference without retraining or increasing model size. Project page: https://scalingwfm.github.io/.

Yan Zheng, Zhenxiao Liang, Xiaoyan Cong et al.

We explore the oscillatory behavior observed in inversion methods applied to large-scale text-to-image diffusion models, with a focus on the "Flux" model. By employing a fixed-point-inspired iterative approach to invert real-world images, we observe that the solution does not achieve convergence, instead oscillating between distinct clusters. Through both toy experiments and real-world diffusion models, we demonstrate that these oscillating clusters exhibit notable semantic coherence. We offer theoretical insights, showing that this behavior arises from oscillatory dynamics in rectified flow models. Building on this understanding, we introduce a simple and fast distribution transfer technique that facilitates image enhancement, stroke-based recoloring, as well as visual prompt-guided image editing. Furthermore, we provide quantitative results demonstrating the effectiveness of our method for tasks such as image enhancement, makeup transfer, reconstruction quality, and guided sampling quality. Higher-quality examples of videos and images are available at \href{https://yanyanzheng96.github.io/oscillation_inversion/}{this link}.

Peihao Wang, Ruisi Cai, Zhen Wang et al.

Scaling inference-time compute for Large Language Models (LLMs) has unlocked unprecedented reasoning capabilities. However, existing inference-time scaling methods typically rely on inefficient and suboptimal discrete search algorithms or trial-and-error prompting to improve the online policy. In this paper, we propose $\nabla$-Reasoner, an iterative generation framework that integrates differentiable optimization over token logits into the decoding loop to refine the policy on the fly. Our core component, Differentiable Textual Optimization (DTO), leverages gradient signals from both the LLM's likelihood and a reward model to refine textual representations. $\nabla$-Reasoner further incorporates rejection sampling and acceleration design to robustify and speed up decoding. Theoretically, we show that performing inference-time gradient descent in the sample space to maximize reward is dual to aligning an LLM policy via KL-regularized reinforcement learning. Empirically, $\nabla$-Reasoner achieves over 20% accuracy improvement on a challenging mathematical reasoning benchmark, while reducing number of model calls by approximately 10-40% compared to strong baselines. Overall, our work introduces a paradigm shift from zeroth-order search to first-order optimization at test time, offering a cost-effective path to amplify LLM reasoning.

Zhiyuan Liang, Dongwen Tang, Yuhao Zhou et al.

Modern Parameter-Efficient Fine-Tuning (PEFT) methods such as low-rank adaptation (LoRA) reduce the cost of customizing large language models (LLMs), yet still require a separate optimization run for every downstream dataset. We introduce \textbf{Drag-and-Drop LLMs (\textit{DnD})}, a prompt-conditioned parameter generator that eliminates per-task training by mapping a handful of unlabeled task prompts directly to LoRA weight updates. A lightweight text encoder distills each prompt batch into condition embeddings, which are then transformed by a cascaded hyper-convolutional decoder into the full set of LoRA matrices. Once trained in a diverse collection of prompt-checkpoint pairs, DnD produces task-specific parameters in seconds, yielding i) up to \textbf{12,000$\times$} lower overhead than full fine-tuning, ii) average gains up to \textbf{30\%} in performance over the strongest training LoRAs on unseen common-sense reasoning, math, coding, and multimodal benchmarks, and iii) robust cross-domain generalization despite never seeing the target data or labels. Our results demonstrate that prompt-conditioned parameter generation is a viable alternative to gradient-based adaptation for rapidly specializing LLMs. Our project is available at \href{https://jerryliang24.github.io/DnD}{https://jerryliang24.github.io/DnD}.

Jinze Zhao, Peihao Wang, Zhangyang Wang

Mixture-of-Experts (MoE) represents an ensemble methodology that amalgamates predictions from several specialized sub-models (referred to as experts). This fusion is accomplished through a router mechanism, dynamically assigning weights to each expert's contribution based on the input data. Conventional MoE mechanisms select all available experts, incurring substantial computational costs. In contrast, Sparse Mixture-of-Experts (Sparse MoE) selectively engages only a limited number, or even just one expert, significantly reducing computation overhead while empirically preserving, and sometimes even enhancing, performance. Despite its wide-ranging applications and these advantageous characteristics, MoE's theoretical underpinnings have remained elusive. In this paper, we embark on an exploration of Sparse MoE's generalization error concerning various critical factors. Specifically, we investigate the impact of the number of data samples, the total number of experts, the sparsity in expert selection, the complexity of the routing mechanism, and the complexity of individual experts. Our analysis sheds light on \textit{how \textbf{sparsity} contributes to the MoE's generalization}, offering insights from the perspective of classical learning theory.

Peihao Wang, Yuehao Wang, Dilin Wang et al.

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for real-time, high-resolution novel view synthesis. By representing scenes as a mixture of Gaussian primitives, 3DGS leverages GPU rasterization pipelines for efficient rendering and reconstruction. To optimize scene coverage and capture fine details, 3DGS employs a densification algorithm to generate additional points. However, this process often leads to redundant point clouds, resulting in excessive memory usage, slower performance, and substantial storage demands - posing significant challenges for deployment on resource-constrained devices. To address this limitation, we propose a theoretical framework that demystifies and improves density control in 3DGS. Our analysis reveals that splitting is crucial for escaping saddle points. Through an optimization-theoretic approach, we establish the necessary conditions for densification, determine the minimal number of offspring Gaussians, identify the optimal parameter update direction, and provide an analytical solution for normalizing off-spring opacity. Building on these insights, we introduce SteepGS, incorporating steepest density control, a principled strategy that minimizes loss while maintaining a compact point cloud. SteepGS achieves a ~50% reduction in Gaussian points without compromising rendering quality, significantly enhancing both efficiency and scalability.

Chuanyang Zheng, Jiankai Sun, Yihang Gao et al.

Mixture-of-Experts (MoE) has become a cornerstone in recent state-of-the-art large language models (LLMs). Traditionally, MoE relies on $\mathrm{Softmax}$ as the router score function to aggregate expert output, a designed choice that has persisted from the earliest MoE models to modern LLMs, and is now widely regarded as standard practice. However, the necessity of using $\mathrm{Softmax}$ to project router weights into a probability simplex remains an unchallenged assumption rather than a principled design choice. In this work, we first revisit the classical Nadaraya-Watson regression and observe that MoE shares the same mathematical formulation as Nadaraya-Watson regression. Furthermore, we show that both feed-forward neural network (FFN) and MoE can be interpreted as a special case of Nadaraya-Watson regression, where the kernel function corresponds to the input neurons of the output layer. Motivated by these insights, we propose the \textbf{zero-additional-cost} Kernel Inspired Router with Normalization (KERN), an FFN-style router function, as an alternative to $\mathrm{Softmax}$. We demonstrate that this router generalizes both $\mathrm{Sigmoid}$- and $\mathrm{Softmax}$-based routers. \textbf{Based on empirical observations and established practices in FFN implementation, we recommend the use of $\mathrm{ReLU}$ activation and $\ell_2$-normalization in $\mathrm{KERN}$ router function.} Comprehensive experiments in MoE and LLM validate the effectiveness of the proposed FFN-style router function \methodNorm.

Haoyu Wang, Peihao Wang, Mufei Li et al. · gatech

Modern large language models (LLMs) are inherently auto-regressive, requiring input to be serialized into flat sequences regardless of their structural dependencies. This serialization hinders the model's ability to leverage structural inductive biases, especially in tasks such as retrieval-augmented generation (RAG) and reasoning on data with native graph structures, where inter-segment dependencies are crucial. We introduce Graph-KV with the potential to overcome this limitation. Graph-KV leverages the KV-cache of text segments as condensed representations and governs their interaction through structural inductive biases. In this framework, 'target' segments selectively attend only to the KV-caches of their designated 'source' segments, rather than all preceding segments in a serialized sequence. This approach induces a graph-structured block mask, sparsifying attention and enabling a message-passing-like step within the LLM. Furthermore, strategically allocated positional encodings for source and target segments reduce positional bias and context window consumption. We evaluate Graph-KV across three scenarios: (1) seven RAG benchmarks spanning direct inference, multi-hop reasoning, and long-document understanding; (2) Arxiv-QA, a novel academic paper QA task with full-text scientific papers structured as citation ego-graphs; and (3) paper topic classification within a citation network. By effectively reducing positional bias and harnessing structural inductive biases, Graph-KV substantially outperforms baselines, including standard costly sequential encoding, across various settings. Code and the Graph-KV data are publicly available.

Jinze Zhao, Peihao Wang, Junjie Yang et al.

Sparse Mixture-of-Experts (SMoE) architectures have gained prominence for their ability to scale neural networks, particularly transformers, without a proportional increase in computational cost. Despite their success, their role in compositional generalization, i.e., adapting to novel combinations of known components, remains under-explored. This study challenges the assumption that minimal expert activation suffices for task generalization and investigates the relationship between task complexity and optimal sparsity in SMoE models. Through empirical evaluations on the SRAVEN symbolic reasoning task and the SKILL-MIX benchmark, we demonstrate that (i) the number of activated experts consistently increases with the perceived task difficulty to maintain performance; and (ii) the optimal number of activated experts scales proportionally with task complexity. Our theoretical analysis derives a scaling law for optimal sparsity by balancing approximation and estimation errors, revealing alignment with empirical observations. We formally show that the optimal sparsity lies between minimal activation (1-2 experts) and full activation, with the exact number scaling proportionally to task complexity and further influenced by the size of the training data and the complexity of the model. These findings offer practical insights for designing SMoE models that achieve computational efficiency while enabling robust compositional generalization.

Chuanyang Zheng, Jiankai Sun, Yihang Gao et al.

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.

Peihao Wang, Zhangyang Wang

We develop a theoretical framework that explains how discrete symbolic structures can emerge naturally from continuous neural network training dynamics. By lifting neural parameters to a measure space and modeling training as Wasserstein gradient flow, we show that under geometric constraints, such as group invariance, the parameter measure $μ_t$ undergoes two concurrent phenomena: (1) a decoupling of the gradient flow into independent optimization trajectories over some potential functions, and (2) a progressive contraction on the degree of freedom. These potentials encode algebraic constraints relevant to the task and act as ring homomorphisms under a commutative semi-ring structure on the measure space. As training progresses, the network transitions from a high-dimensional exploration to compositional representations that comply with algebraic operations and exhibit a lower degree of freedom. We further establish data scaling laws for realizing symbolic tasks, linking representational capacity to the group invariance that facilitates symbolic solutions. This framework charts a principled foundation for understanding and designing neurosymbolic systems that integrate continuous learning with discrete algebraic reasoning.

Zhiwen Fan, Panwang Pan, Peihao Wang et al.

Despite the significant progress in six degrees-of-freedom (6DoF) object pose estimation, existing methods have limited applicability in real-world scenarios involving embodied agents and downstream 3D vision tasks. These limitations mainly come from the necessity of 3D models, closed-category detection, and a large number of densely annotated support views. To mitigate this issue, we propose a general paradigm for object pose estimation, called Promptable Object Pose Estimation (POPE). The proposed approach POPE enables zero-shot 6DoF object pose estimation for any target object in any scene, while only a single reference is adopted as the support view. To achieve this, POPE leverages the power of the pre-trained large-scale 2D foundation model, employs a framework with hierarchical feature representation and 3D geometry principles. Moreover, it estimates the relative camera pose between object prompts and the target object in new views, enabling both two-view and multi-view 6DoF pose estimation tasks. Comprehensive experimental results demonstrate that POPE exhibits unrivaled robust performance in zero-shot settings, by achieving a significant reduction in the averaged Median Pose Error by 52.38% and 50.47% on the LINEMOD and OnePose datasets, respectively. We also conduct more challenging testings in causally captured images (see Figure 1), which further demonstrates the robustness of POPE. Project page can be found with https://paulpanwang.github.io/POPE/.

Peihao Wang, Yuehao Wang, Hua Lin et al.

Graph Convolutional Networks (GCN) with multi-hop aggregation is more expressive than one-hop GCN but suffers from higher model complexity. Finding the shortest aggregation range that achieves comparable expressiveness and minimizes this side effect remains an open question. We answer this question by showing that multi-layer second-order graph convolution (SoGC) is sufficient to attain the ability of expressing polynomial spectral filters with arbitrary coefficients. Compared to models with one-hop aggregation, multi-hop propagation, and jump connections, SoGC possesses filter representational completeness while being lightweight, efficient, and easy to implement. Thereby, we suggest that SoGC is a simple design capable of forming the basic building block of GCNs, playing the same role as $3 \times 3$ kernels in CNNs. We build our Second-Order Graph Convolutional Networks (SoGCN) with SoGC and design a synthetic dataset to verify its filter fitting capability to validate these points. For real-world tasks, we present the state-of-the-art performance of SoGCN on the benchmark of node classification, graph classification, and graph regression datasets.