Daily Papers

Video matting is crucial for applications such as film production and virtual reality, yet deploying its computationally intensive models on resource-constrained devices presents challenges. Quantization is a key technique for model compression and acceleration. As an efficient approach, Post-Training Quantization (PTQ) is still in its nascent stages for video matting, facing significant hurdles in maintaining accuracy and temporal coherence. To address these challenges, this paper proposes a novel and general PTQ framework specifically designed for video matting models, marking, to the best of our knowledge, the first systematic attempt in this domain. Our contributions include: (1) A two-stage PTQ strategy that combines block-reconstruction-based optimization for fast, stable initial quantization and local dependency capture, followed by a global calibration of quantization parameters to minimize accuracy loss. (2) A Statistically-Driven Global Affine Calibration (GAC) method that enables the network to compensate for cumulative statistical distortions arising from factors such as neglected BN layer effects, even reducing the error of existing PTQ methods on video matting tasks up to 20%. (3) An Optical Flow Assistance (OFA) component that leverages temporal and semantic priors from frames to guide the PTQ process, enhancing the model's ability to distinguish moving foregrounds in complex scenes and ultimately achieving near full-precision performance even under ultra-low-bit quantization. Comprehensive quantitative and visual results show that our PTQ4VM achieves the state-of-the-art accuracy performance across different bit-widths compared to the existing quantization methods. We highlight that the 4-bit PTQ4VM even achieves performance close to the full-precision counterpart while enjoying 8x FLOP savings.

The recent advancements in 3D Gaussian Splatting (3DGS) have demonstrated remarkable potential in novel view synthesis tasks. The divide-and-conquer paradigm has enabled large-scale scene reconstruction, but significant challenges remain in scene partitioning, optimization, and merging processes. This paper introduces BlockGaussian, a novel framework incorporating a content-aware scene partition strategy and visibility-aware block optimization to achieve efficient and high-quality large-scale scene reconstruction. Specifically, our approach considers the content-complexity variation across different regions and balances computational load during scene partitioning, enabling efficient scene reconstruction. To tackle the supervision mismatch issue during independent block optimization, we introduce auxiliary points during individual block optimization to align the ground-truth supervision, which enhances the reconstruction quality. Furthermore, we propose a pseudo-view geometry constraint that effectively mitigates rendering degradation caused by airspace floaters during block merging. Extensive experiments on large-scale scenes demonstrate that our approach achieves state-of-the-art performance in both reconstruction efficiency and rendering quality, with a 5x speedup in optimization and an average PSNR improvement of 1.21 dB on multiple benchmarks. Notably, BlockGaussian significantly reduces computational requirements, enabling large-scale scene reconstruction on a single 24GB VRAM device. The project page is available at https://github.com/SunshineWYC/BlockGaussian

Scaling 3D Gaussian Splatting (3DGS) to large outdoor scenes is costly in both data acquisition and computation. Adopting panoramic images with equirectangular projection (ERP) can reduce capture effort via their full 360^{circ} field of view, yet the resulting omnipresent visibility invalidates existing partitioning strategies that rely on local camera frustums, causing block-wise optimization to degenerate into global training. Thus, we propose PanoLOG, a two-stage coarse-to-fine framework equipped with a Geometry and Gradient-based Partitioning Strategy tailored for large-scale panoramic 3DGS reconstruction. In the global coarse stage, PanoLOG leverages sky-sphere modeling and panoramic monocular depth supervision for reliable geometry, while in the refinement stage, G^2PS builds adaptive bounding volumes via parallax-driven uncertainty and assigns cameras via gradient-based importance scoring. Furthermore, we construct Pano360, the first benchmark on large-scale panoramic dataset for outdoor scene reconstruction. Extensive experiments demonstrate that G^2PS achieves state-of-the-art rendering quality while maintaining scalable, block-parallel training. Our models, training code, and dataset are publicly available.

We propose Long-LRM, a generalizable 3D Gaussian reconstruction model that is capable of reconstructing a large scene from a long sequence of input images. Specifically, our model can process 32 source images at 960x540 resolution within only 1.3 seconds on a single A100 80G GPU. Our architecture features a mixture of the recent Mamba2 blocks and the classical transformer blocks which allowed many more tokens to be processed than prior work, enhanced by efficient token merging and Gaussian pruning steps that balance between quality and efficiency. Unlike previous feed-forward models that are limited to processing 1~4 input images and can only reconstruct a small portion of a large scene, Long-LRM reconstructs the entire scene in a single feed-forward step. On large-scale scene datasets such as DL3DV-140 and Tanks and Temples, our method achieves performance comparable to optimization-based approaches while being two orders of magnitude more efficient. Project page: https://arthurhero.github.io/projects/llrm

We investigate a general formulation for clustering and transductive few-shot learning, which integrates prototype-based objectives, Laplacian regularization and supervision constraints from a few labeled data points. We propose a concave-convex relaxation of the problem, and derive a computationally efficient block-coordinate bound optimizer, with convergence guarantee. At each iteration,our optimizer computes independent (parallel) updates for each point-to-cluster assignment. Therefore, it could be trivially distributed for large-scale clustering and few-shot tasks. Furthermore, we provides a thorough convergence analysis based on point-to-set maps. Were port comprehensive clustering and few-shot learning experiments over various data sets, showing that our method yields competitive performances, in term of accuracy and optimization quality, while scaling up to large problems. Using standard training on the base classes, without resorting to complex meta-learning and episodic-training strategies, our approach outperforms state-of-the-art few-shot methods by significant margins, across various models, settings and data sets. Surprisingly, we found that even standard clustering procedures (e.g., K-means), which correspond to particular, non-regularized cases of our general model, already achieve competitive performances in comparison to the state-of-the-art in few-shot learning. These surprising results point to the limitations of the current few-shot benchmarks, and question the viability of a large body of convoluted few-shot learning techniques in the recent literature.

Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient descent largely without adapting to the non-convex nature of the problem and can be sensitive to initial values, impeding further performance improvement. In this paper, we propose an efficient amortized optimization scheme for inverse problems with a deep generative prior. Specifically, the optimization task with high degrees of difficulty is decomposed into optimizing a sequence of much easier ones. We provide a theoretical guarantee of the proposed algorithm and empirically validate it on different inverse problems. As a result, our approach outperforms baseline methods qualitatively and quantitatively by a large margin.

In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve mgg 1 lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its variance is more intricate due to the hierarchical sampling of blocks and data and the unique challenge of estimating hyper-gradient. We aim to achieve three nice properties for our algorithm: (a) matching the state-of-the-art complexity of standard BO problems with a single block; (b) achieving parallel speedup by sampling I blocks and sampling B samples for each sampled block per-iteration; (c) avoiding the computation of the inverse of a high-dimensional Hessian matrix estimator. However, it is non-trivial to achieve all of these by observing that existing works only achieve one or two of these properties. To address the involved challenges for achieving (a, b, c), we propose two stochastic algorithms by using advanced blockwise variance-reduction techniques for tracking the Hessian matrices (for low-dimensional problems) or the Hessian-vector products (for high-dimensional problems), and prove an iteration complexity of O(mepsilon^{-3I(I<m)}{II} + mepsilon^{-3}{IB}) for finding an epsilon-stationary point under appropriate conditions. We also conduct experiments to verify the effectiveness of the proposed algorithms comparing with existing MBBO algorithms.

Combinatorial optimization problems are ubiquitous in science and engineering. Still, learning-based approaches to accelerate combinatorial optimization often require solving a large number of difficult instances to collect training data, incurring significant computational cost. Existing learning-based methods require training dedicated models for each problem distribution, for each downstream task, severely limiting their scalability and generalization. We introduce Forge: Foundational Optimization Representations from Graph Embeddings, a framework that pre-trains a vector-quantized graph autoencoder on a large, diverse collection of mixed-integer programming (MIP) instances in an unsupervised manner, without relying on optimization solvers or optimal solutions. Vector quantization produces discrete code assignments that serve as a vocabulary for representing optimization instances. We evaluate Forge in both unsupervised and supervised settings. In the unsupervised setting, Forge embeddings effectively cluster unseen instances across problem domains and sizes. In the supervised setting, we fine-tune Forge embeddings and show that a single pre-trained model helps predicting both the integrality gap for cut-generation and variable hints for search guidance across multiple problem and size distributions. In both tasks, we improve the performance of a commercial optimization solver and outperform state-of-the-art learning-based methods. Finally, we open-source our training code, pre-trained Forge weights, and embeddings for multiple MIP distributions to foster further research in representation learning for optimization problems.

We propose PyTorchGeoNodes, a differentiable module for reconstructing 3D objects from images using interpretable shape programs. In comparison to traditional CAD model retrieval methods, the use of shape programs for 3D reconstruction allows for reasoning about the semantic properties of reconstructed objects, editing, low memory footprint, etc. However, the utilization of shape programs for 3D scene understanding has been largely neglected in past works. As our main contribution, we enable gradient-based optimization by introducing a module that translates shape programs designed in Blender, for example, into efficient PyTorch code. We also provide a method that relies on PyTorchGeoNodes and is inspired by Monte Carlo Tree Search (MCTS) to jointly optimize discrete and continuous parameters of shape programs and reconstruct 3D objects for input scenes. In our experiments, we apply our algorithm to reconstruct 3D objects in the ScanNet dataset and evaluate our results against CAD model retrieval-based reconstructions. Our experiments indicate that our reconstructions match well the input scenes while enabling semantic reasoning about reconstructed objects.

3D Gaussian Splatting has demonstrated notable success in large-scale scene reconstruction, but challenges persist due to high training memory consumption and storage overhead. Hybrid representations that integrate implicit and explicit features offer a way to mitigate these limitations. However, when applied in parallelized block-wise training, two critical issues arise since reconstruction accuracy deteriorates due to reduced data diversity when training each block independently, and parallel training restricts the number of divided blocks to the available number of GPUs. To address these issues, we propose Momentum-GS, a novel approach that leverages momentum-based self-distillation to promote consistency and accuracy across the blocks while decoupling the number of blocks from the physical GPU count. Our method maintains a teacher Gaussian decoder updated with momentum, ensuring a stable reference during training. This teacher provides each block with global guidance in a self-distillation manner, promoting spatial consistency in reconstruction. To further ensure consistency across the blocks, we incorporate block weighting, dynamically adjusting each block's weight according to its reconstruction accuracy. Extensive experiments on large-scale scenes show that our method consistently outperforms existing techniques, achieving a 12.8% improvement in LPIPS over CityGaussian with much fewer divided blocks and establishing a new state of the art. Project page: https://jixuan-fan.github.io/Momentum-GS_Page/

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting. The algorithmic insight obtained from our analysis extends to more general settings often considered in practice. Experimentally, we outperform previously proposed posterior sampling algorithms in a wide variety of problems including random inpainting, block inpainting, denoising, deblurring, destriping, and super-resolution.

A fundamental challenge in data science is to match disparate point sets with each other. While optimal transport efficiently minimizes point displacements under a bijectivity constraint, it is inherently sensitive to rotations. Conversely, minimizing distortions via the Gromov-Wasserstein (GW) framework addresses this limitation but introduces a non-convex, computationally demanding optimization problem. In this work, we identify a broad class of distortion penalties that reduce to a simple alignment problem within a lifted feature space. Leveraging this insight, we introduce an iterative GW solver with a linear memory footprint and quadratic (rather than cubic) time complexity. Our method is differentiable, comes with strong theoretical guarantees, and scales to hundreds of thousands of points in minutes. This efficiency unlocks a wide range of geometric applications and enables the exploration of the GW energy landscape, whose local minima encode the symmetries of the matching problem.

Diffusion models have recently revolutionized the field of image synthesis due to their ability to generate photorealistic images. However, one of the major drawbacks of diffusion models is that the image generation process is costly. A large image-to-image network has to be applied many times to iteratively refine an image from random noise. While many recent works propose techniques to reduce the number of required steps, they generally treat the underlying denoising network as a black box. In this work, we investigate the behavior of the layers within the network and find that 1) the layers' output changes smoothly over time, 2) the layers show distinct patterns of change, and 3) the change from step to step is often very small. We hypothesize that many layer computations in the denoising network are redundant. Leveraging this, we introduce block caching, in which we reuse outputs from layer blocks of previous steps to speed up inference. Furthermore, we propose a technique to automatically determine caching schedules based on each block's changes over timesteps. In our experiments, we show through FID, human evaluation and qualitative analysis that Block Caching allows to generate images with higher visual quality at the same computational cost. We demonstrate this for different state-of-the-art models (LDM and EMU) and solvers (DDIM and DPM).

Post-training quantization (PTQ) has driven attention to producing efficient large language models (LLMs) with ultra-low costs. Since hand-craft quantization parameters lead to low performance in low-bit quantization, recent methods optimize the quantization parameters through block-wise reconstruction between the floating-point and quantized models. However, these methods suffer from two challenges: accumulated errors from independent one-by-one block quantization and reconstruction difficulties from extreme weight and activation outliers. To address these two challenges, we propose CBQ, a cross-block reconstruction-based PTQ method for LLMs. To reduce error accumulation, we introduce a cross-block dependency with the aid of a homologous reconstruction scheme to build the long-range dependency between adjacent multi-blocks with overlapping. To reduce reconstruction difficulty, we design a coarse-to-fine pre-processing (CFP) to truncate weight outliers and dynamically scale activation outliers before optimization, and an adaptive rounding scheme, called LoRA-Rounding, with two low-rank learnable matrixes to further rectify weight quantization errors. Extensive experiments demonstrate that: (1) CBQ pushes both activation and weight quantization to low-bit settings W4A4, W4A8, and W2A16. (2) CBQ achieves better performance than the existing state-of-the-art methods on various LLMs and benchmark datasets.

We consider the block coordinate descent methods of Gauss-Seidel type with proximal regularization (BCD-PR), which is a classical method of minimizing general nonconvex objectives under constraints that has a wide range of practical applications. We theoretically establish the worst-case complexity bound for this algorithm. Namely, we show that for general nonconvex smooth objectives with block-wise constraints, the classical BCD-PR algorithm converges to an epsilon-stationary point within O(1/epsilon) iterations. Under a mild condition, this result still holds even if the algorithm is executed inexactly in each step. As an application, we propose a provable and efficient algorithm for `Wasserstein CP-dictionary learning', which seeks a set of elementary probability distributions that can well-approximate a given set of d-dimensional joint probability distributions. Our algorithm is a version of BCD-PR that operates in the dual space, where the primal problem is regularized both entropically and proximally.

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.

Nonconvex optimization is central in solving many machine learning problems, in which block-wise structure is commonly encountered. In this work, we propose cyclic block coordinate methods for nonconvex optimization problems with non-asymptotic gradient norm guarantees. Our convergence analysis is based on a gradient Lipschitz condition with respect to a Mahalanobis norm, inspired by a recent progress on cyclic block coordinate methods. In deterministic settings, our convergence guarantee matches the guarantee of (full-gradient) gradient descent, but with the gradient Lipschitz constant being defined w.r.t.~a Mahalanobis norm. In stochastic settings, we use recursive variance reduction to decrease the per-iteration cost and match the arithmetic operation complexity of current optimal stochastic full-gradient methods, with a unified analysis for both finite-sum and infinite-sum cases. We prove a faster linear convergence result when a Polyak-{\L}ojasiewicz (P{\L}) condition holds. To our knowledge, this work is the first to provide non-asymptotic convergence guarantees -- variance-reduced or not -- for a cyclic block coordinate method in general composite (smooth + nonsmooth) nonconvex settings. Our experimental results demonstrate the efficacy of the proposed cyclic scheme in training deep neural nets.

Vector-quantized networks (VQNs) have exhibited remarkable performance across various tasks, yet they are prone to training instability, which complicates the training process due to the necessity for techniques such as subtle initialization and model distillation. In this study, we identify the local minima issue as the primary cause of this instability. To address this, we integrate an optimal transport method in place of the nearest neighbor search to achieve a more globally informed assignment. We introduce OptVQ, a novel vector quantization method that employs the Sinkhorn algorithm to optimize the optimal transport problem, thereby enhancing the stability and efficiency of the training process. To mitigate the influence of diverse data distributions on the Sinkhorn algorithm, we implement a straightforward yet effective normalization strategy. Our comprehensive experiments on image reconstruction tasks demonstrate that OptVQ achieves 100% codebook utilization and surpasses current state-of-the-art VQNs in reconstruction quality.

3D Gaussian Splatting (3DGS) optimization is most commonly performed using standard optimizers (Adam, SGD). While stable across diverse scenes, standard optimizers are general-purpose and not tailored to the structure of the problem. In particular, they produce independent parameter updates that do not capture the structural and spatial relationships within a scene, leading to inefficient optimization and slow convergence. Recent works introduced learned optimizers that predict correlated updates informed by inter-parameter and inter-Gaussian dependencies. However, these methods are trained for a fixed number of optimization iterations and rely on manually scheduled learning rates to avoid degradation. In this paper, we introduce a learned optimizer for 3DGS that avoids degradation over extended optimization horizons without auxiliary mechanisms. To enable this, we propose a meta-learning scheme that extends the optimization horizon via a checkpoint buffer and an optimizer rollout strategy, combined with an architecture that encodes gradient scale information in its latent states. Results show improved early novel view synthesis quality while remaining stable over long horizons, with zero-shot generalization to unseen reconstruction settings. To support our findings, we introduce the first unified framework for training and evaluating both learned and conventional optimizers across sparse and dense view settings. Code and models will be released publicly. Our project page is available at https://naamapearl.github.io/learn2splat .

Recently, Flow Matching models have pushed the boundaries of high-fidelity data generation across a wide range of domains. It typically employs a single large network to learn the entire generative trajectory from noise to data. Despite their effectiveness, this design struggles to capture distinct signal characteristics across timesteps simultaneously and incurs substantial inference costs due to the iterative evaluation of the entire model. To address these limitations, we propose Blockwise Flow Matching (BFM), a novel framework that partitions the generative trajectory into multiple temporal segments, each modeled by smaller but specialized velocity blocks. This blockwise design enables each block to specialize effectively in its designated interval, improving inference efficiency and sample quality. To further enhance generation fidelity, we introduce a Semantic Feature Guidance module that explicitly conditions velocity blocks on semantically rich features aligned with pretrained representations. Additionally, we propose a lightweight Feature Residual Approximation strategy that preserves semantic quality while significantly reducing inference cost. Extensive experiments on ImageNet 256x256 demonstrate that BFM establishes a substantially improved Pareto frontier over existing Flow Matching methods, achieving 2.1x to 4.9x accelerations in inference complexity at comparable generation performance. Code is available at https://github.com/mlvlab/BFM.

We view the reconstruction of CAD models in the boundary representation (B-Rep) as the detection of geometric primitives of different orders, i.e. vertices, edges and surface patches, and the correspondence of primitives, which are holistically modeled as a chain complex, and show that by modeling such comprehensive structures more complete and regularized reconstructions can be achieved. We solve the complex generation problem in two steps. First, we propose a novel neural framework that consists of a sparse CNN encoder for input point cloud processing and a tri-path transformer decoder for generating geometric primitives and their mutual relationships with estimated probabilities. Second, given the probabilistic structure predicted by the neural network, we recover a definite B-Rep chain complex by solving a global optimization maximizing the likelihood under structural validness constraints and applying geometric refinements. Extensive tests on large scale CAD datasets demonstrate that the modeling of B-Rep chain complex structure enables more accurate detection for learning and more constrained reconstruction for optimization, leading to structurally more faithful and complete CAD B-Rep models than previous results.

Many modern iterative solvers for large-scale tomographic reconstruction incur two major computational costs per iteration: expensive forward/adjoint projections to update the data fidelity term and costly proximal computations for the regulariser, often done via inner iterations. This paper studies for the first time the application of methods that couple randomised skipping of the proximal with variance-reduced subset-based optimisation of data-fit term, to simultaneously reduce both costs in challenging tomographic reconstruction tasks. We provide a series of experiments using both synthetic and real data, demonstrating striking speed-ups of the order 5x--20x compared to the non-skipped counterparts which have been so far the standard approach for efficiently solving these problems. Our work lays the groundwork for broader adoption of these methods in inverse problems.

The remarkable success of diffusion and flow-matching models has ignited a surge of works on adapting them at test time for controlled generation tasks. Examples range from image editing to restoration, compression and personalization. However, due to the iterative nature of the sampling process in those models, it is computationally impractical to use gradient-based optimization to directly control the image generated at the end of the process. As a result, existing methods typically resort to manipulating each timestep separately. Here we introduce FlowOpt - a zero-order (gradient-free) optimization framework that treats the entire flow process as a black box, enabling optimization through the whole sampling path without backpropagation through the model. Our method is both highly efficient and allows users to monitor the intermediate optimization results and perform early stopping if desired. We prove a sufficient condition on FlowOpt's step-size, under which convergence to the global optimum is guaranteed. We further show how to empirically estimate this upper bound so as to choose an appropriate step-size. We demonstrate how FlowOpt can be used for image editing, showcasing two options: (i) inversion (determining the initial noise that generates a given image), and (ii) directly steering the edited image to be similar to the source image while conforming to a target text prompt. In both cases, FlowOpt achieves state-of-the-art results while using roughly the same number of neural function evaluations (NFEs) as existing methods. Code and examples are available on the project's webpage.

Large collections of matrices arise throughout modern machine learning, signal processing, and scientific computing, where they are commonly compressed by concatenation followed by truncated singular value decomposition (SVD). This strategy enables parameter sharing and efficient reconstruction and has been widely adopted across domains ranging from multi-view learning and signal processing to neural network compression. However, it leaves a fundamental question unanswered: which matrices can be safely concatenated and compressed together under explicit reconstruction error constraints? Existing approaches rely on heuristic or architecture-specific grouping and provide no principled guarantees on the resulting SVD approximation error. In the present work, we introduce a theory-driven framework for compression-aware clustering of matrices under SVD compression constraints. Our analysis establishes new spectral bounds for horizontally concatenated matrices, deriving global upper bounds on the optimal rank-r SVD reconstruction error from lower bounds on singular value growth. The first bound follows from Weyl-type monotonicity under blockwise extensions, while the second leverages singular values of incremental residuals to yield tighter, per-block guarantees. We further develop an efficient approximate estimator based on incremental truncated SVD that tracks dominant singular values without forming the full concatenated matrix. Therefore, we propose three clustering algorithms that merge matrices only when their predicted joint SVD compression error remains below a user-specified threshold. The algorithms span a trade-off between speed, provable accuracy, and scalability, enabling compression-aware clustering with explicit error control. Code is available online.

This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization and stochastic optimization. Our presentation of black-box optimization, strongly influenced by Nesterov's seminal book and Nemirovski's lecture notes, includes the analysis of cutting plane methods, as well as (accelerated) gradient descent schemes. We also pay special attention to non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror descent, and dual averaging) and discuss their relevance in machine learning. We provide a gentle introduction to structural optimization with FISTA (to optimize a sum of a smooth and a simple non-smooth term), saddle-point mirror prox (Nemirovski's alternative to Nesterov's smoothing), and a concise description of interior point methods. In stochastic optimization we discuss stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms. We also briefly touch upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods.

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this paradigm. PJAX composes projection operators for elementary operations, automatically deriving the solution operators for the feasibility problems (akin to autodiff for derivatives). It inherently supports GPU/TPU acceleration, provides a familiar NumPy-like API, and is extensible. We train diverse architectures (MLPs, CNNs, RNNs) on standard benchmarks using PJAX, demonstrating its functionality and generality. Our results show that this approach is as a compelling alternative to gradient-based training, with clear advantages in parallelism and the ability to handle non-differentiable operations.

We present MegaBlocks, a system for efficient Mixture-of-Experts (MoE) training on GPUs. Our system is motivated by the limitations of current frameworks, which restrict the dynamic routing in MoE layers to satisfy the constraints of existing software and hardware. These formulations force a tradeoff between model quality and hardware efficiency, as users must choose between dropping tokens from the computation or wasting computation and memory on padding. To address these limitations, we reformulate MoE computation in terms of block-sparse operations and develop new block-sparse GPU kernels that efficiently handle the dynamism present in MoEs. Our approach never drops tokens and maps efficiently to modern hardware, enabling end-to-end training speedups of up to 40% over MoEs trained with the state-of-the-art Tutel library and 2.4x over DNNs trained with the highly-optimized Megatron-LM framework.

Current state-of-the-art solutions for motion capture from a single camera are optimization driven: they optimize the parameters of a 3D human model so that its re-projection matches measurements in the video (e.g. person segmentation, optical flow, keypoint detections etc.). Optimization models are susceptible to local minima. This has been the bottleneck that forced using clean green-screen like backgrounds at capture time, manual initialization, or switching to multiple cameras as input resource. In this work, we propose a learning based motion capture model for single camera input. Instead of optimizing mesh and skeleton parameters directly, our model optimizes neural network weights that predict 3D shape and skeleton configurations given a monocular RGB video. Our model is trained using a combination of strong supervision from synthetic data, and self-supervision from differentiable rendering of (a) skeletal keypoints, (b) dense 3D mesh motion, and (c) human-background segmentation, in an end-to-end framework. Empirically we show our model combines the best of both worlds of supervised learning and test-time optimization: supervised learning initializes the model parameters in the right regime, ensuring good pose and surface initialization at test time, without manual effort. Self-supervision by back-propagating through differentiable rendering allows (unsupervised) adaptation of the model to the test data, and offers much tighter fit than a pretrained fixed model. We show that the proposed model improves with experience and converges to low-error solutions where previous optimization methods fail.

Reconstructing dynamic non-rigid objects from monocular video requires integrating visual cues from direct observations with data-driven priors over geometry and appearance. Prior approaches either learn to directly predict 4D representations from visual input or initialize a 3D representation that is subsequently deformed and refined based on video evidence. However, the former are constrained by the scarcity of 4D training data, while the latter leverage priors only for the initial reconstruction and rely solely on video supervision thereafter; neither handles complex in-the-wild scenarios with large deformations and occlusions well. We present Lift4D, a test-time optimization framework that addresses both limitations. First, we adapt an existing single-view 3D reconstruction model to yield temporally consistent per-frame predictions via causal latent conditioning, providing a coherent initialization for a deformable 3D Gaussian Splatting representation. We then ``sculpt'' this representation to match the input video through an occlusion-aware optimization that faithfully recovers visible surface details while completing unobserved regions using a view-conditioned diffusion prior. We demonstrate that Lift4D clearly improves over prior 4D reconstruction methods, particularly on challenging in-the-wild sequences with severe occlusions and non-rigid motion.

Optimizing high-dimensional black-box functions under black-box constraints is a pervasive task in a wide range of scientific and engineering problems. These problems are typically harder than unconstrained problems due to hard-to-find feasible regions. In this work, we reformulate constrained black-box optimization as posterior inference, and perform this inference in the latent space of generative models. Our method iterates through two stages. First, we train flow-based models to capture the data distribution and surrogate models that predict both function values and constraint violations. Second, we cast the candidate selection problem as a posterior inference problem to effectively search for promising candidates that have high objective values while not violating the constraints. Concretely, we utilize outsourced diffusion models to amortize the sampling from the posterior distribution in the latent space of flow-based models, which can bypass the issue of mode collapse. We empirically demonstrate that our method achieves superior performance across synthetic and real-world tasks. Our code is available https://github.com/umkiyoung/CiBO{here}.

We present SHINOBI, an end-to-end framework for the reconstruction of shape, material, and illumination from object images captured with varying lighting, pose, and background. Inverse rendering of an object based on unconstrained image collections is a long-standing challenge in computer vision and graphics and requires a joint optimization over shape, radiance, and pose. We show that an implicit shape representation based on a multi-resolution hash encoding enables faster and robust shape reconstruction with joint camera alignment optimization that outperforms prior work. Further, to enable the editing of illumination and object reflectance (i.e. material) we jointly optimize BRDF and illumination together with the object's shape. Our method is class-agnostic and works on in-the-wild image collections of objects to produce relightable 3D assets for several use cases such as AR/VR, movies, games, etc. Project page: https://shinobi.aengelhardt.com Video: https://www.youtube.com/watch?v=iFENQ6AcYd8&feature=youtu.be

Subspace clustering seeks to identify subspaces that segment a set of n data points into k (k<<n) groups, which has emerged as a powerful tool for analyzing data from various domains, especially images and videos. Recently, several studies have demonstrated the great potential of subspace clustering models for partitioning vertices in attributed graphs, referred to as SCAG. However, these works either demand significant computational overhead for constructing the nxn self-expressive matrix, or fail to incorporate graph topology and attribute data into the subspace clustering framework effectively, and thus, compromise result quality. Motivated by this, this paper presents two effective and efficient algorithms, S2CAG and M-S2CAG, for SCAG computation. Particularly, S2CAG obtains superb performance through three major contributions. First, we formulate a new objective function for SCAG with a refined representation model for vertices and two non-trivial constraints. On top of that, an efficient linear-time optimization solver is developed based on our theoretically grounded problem transformation and well-thought-out adaptive strategy. We then conduct an in-depth analysis to disclose the theoretical connection of S2CAG to conductance minimization, which further inspires the design of M-S2CAG that maximizes the modularity. Our extensive experiments, comparing S2CAG and M-S2CAG against 17 competitors over 8 benchmark datasets, exhibit that our solutions outperform all baselines in terms of clustering quality measured against the ground truth while delivering high efficiency

Reconstructing dynamic 4D scenes remains challenging due to the presence of moving objects that corrupt camera pose estimation. Existing optimization methods alleviate this issue with additional supervision, but they are mostly computationally expensive and impractical in real-time applications. To address these limitations, we propose MoRe, a feedforward 4D reconstruction network that efficiently recovers dynamic 3D scenes from monocular videos. Built upon a strong static reconstruction backbone, MoRe employs an attention-forcing strategy to disentangle dynamic motion from static structure. To further enhance robustness, we fine-tune the model on large-scale, diverse datasets encompassing both dynamic and static scenes. Moreover, our grouped causal attention captures temporal dependencies and adapts to varying token lengths across frames, ensuring temporally coherent geometry reconstruction. Extensive experiments on multiple benchmarks demonstrate that MoRe achieves high-quality dynamic reconstructions with exceptional efficiency.

Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing. We overcome these challenges by employing a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core operation of BSP involves recursive subdivision of 3D space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition without supervision. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built over a set of planes, where the planes and convexes are both defined by learned network weights. BSP-Net directly outputs polygonal meshes from the inferred convexes. The generated meshes are watertight, compact (i.e., low-poly), and well suited to represent sharp geometry. We show that the reconstruction quality by BSP-Net is competitive with those from state-of-the-art methods while using much fewer primitives. We also explore variations to BSP-Net including using a more generic decoder for reconstruction, more general primitives than planes, as well as training a generative model with variational auto-encoders. Code is available at https://github.com/czq142857/BSP-NET-original.

The discovery of extremal structures in mathematics requires navigating vast and nonconvex landscapes where analytical methods offer little guidance and brute-force search becomes intractable. We introduce FlowBoost, a closed-loop generative framework that learns to discover rare and extremal geometric structures by combining three components: (i) a geometry-aware conditional flow-matching model that learns to sample high-quality configurations, (ii) reward-guided policy optimization with action exploration that directly optimizes the generation process toward the objective while maintaining diversity, and (iii) stochastic local search for both training-data generation and final refinement. Unlike prior open-loop approaches, such as PatternBoost that retrains on filtered discrete samples, or AlphaEvolve which relies on frozen Large Language Models (LLMs) as evolutionary mutation operators, FlowBoost enforces geometric feasibility during sampling, and propagates reward signal directly into the generative model, closing the optimization loop and requiring much smaller training sets and shorter training times, and reducing the required outer-loop iterations by orders of magnitude, while eliminating dependence on LLMs. We demonstrate the framework on four geometric optimization problems: sphere packing in hypercubes, circle packing maximizing sum of radii, the Heilbronn triangle problem, and star discrepancy minimization. In several cases, FlowBoost discovers configurations that match or exceed the best known results. For circle packings, we improve the best known lower bounds, surpassing the LLM-based system AlphaEvolve while using substantially fewer computational resources.

Inverse rendering aims to recover both 3D geometry and physically meaningful material properties from images, enabling applications such as relighting and novel view synthesis. Optimization-based methods achieve high fidelity but require costly per-scene fitting, while image-space learning-based approaches often suffer from multi-view inconsistencies and lack an explicit 3D representation for stable novel view rendering. We present a feed-forward multi-view reconstruction framework for inverse rendering that directly predicts a structured 3D Gaussian representation with intrinsic material attributes. Each Gaussian primitive is parameterized by mean, normal, opacity, rotation, scale, albedo, metallic, and roughness, enabling a disentangled and physically grounded scene representation. Our model integrates priors from a material estimation network with a multi-view 3D reconstruction backbone, allowing joint prediction of geometry and reflectance parameters in a single forward pass. Experiments on synthetic and real-world datasets demonstrate improved multi-view consistency compared to 2D baselines, accurate material recovery, and stable novel view rendering. Our representation further supports physically-based relighting and more faithful modeling of view-dependent effects compared to existing RGB-based feed-forward reconstruction methods. Our project webpage is: https://poliik.github.io/invsplat/{https://poliik.github.io/invsplat/}.

Recent feed-forward 3D reconstruction transformers have scaled to over a billion parameters, following the broader trend of increasing model capacity in computer vision. Yet emerging evidence suggests that contiguous transformer layers often behave like repeated applications of similar operations, and multi-view reconstruction transformers refine their predictions progressively across decoder depth. We posit that model depth partially buys iteration, paid for inefficiently in unique parameters, and instead make that iteration explicit in architecture. Our model, DéjàView, applies a single looped transformer block recurrently to per-view features for K refinement steps. Trained once, it exposes K as an inference-time compute knob, matching or outperforming substantially larger feed-forward baselines across five reconstruction benchmarks spanning indoor, outdoor, object-centric, and driving scenes, while using a fraction of their parameters and comparable or lower compute. Importantly, the same looped block formulation outperforms an otherwise identical variant with independent per-step parameters under matched training data and compute, suggesting that explicit iteration is not merely a compute-efficient substitute for capacity but a stronger inductive bias for multi-view 3D reconstruction.

Speculative decoding accelerates inference by using a lightweight draft model to generate candidate tokens in parallel, and are then verified by the target model, enabling lossless acceleration. Recently, diffusion-based speculative decoding further improves parallelism by generating multiple tokens per forward pass via block-level diffusion, achieving state-of-the-art (SOTA) performance. However, existing methods adopt a fixed inference block size and assume a uniform optimal decoding strategy across all inputs. In this paper, we show that this assumption is suboptimal, as the optimal block size varies across samples and plays a critical role in speculative decoding performance. Moreover, these values exhibit a clear local structure, concentrating around the training block size, which reduces the problem to a low-dimensional and structured decision space. Based on these insights, we propose BlockPilot, a sample-adaptive policy that predicts the optimal block size from the prefilling representation. Specifically, we formulate block size selection as a lightweight policy learning problem and propose an instance-adaptive decision mechanism that predicts the optimal block size based on the representation of the prefilling stage. The prediction is performed only once after prefilling, allowing for seamless integration. Extensive experiments demonstrate that our method is plug-and-play, introduces minimal overhead, and consistently improves efficiency, achieving an acceptance length of 5.92 and a 4.20times speedup on Qwen3-4B under temperature T=1.

We introduce an inference-time scene optimization algorithm utilizing triangle soup, a collection of disconnected translucent triangle primitives, as the representation for the geometry and appearance of a scene. Unlike full-rank Gaussian kernels, triangles are a natural, locally-flat proxy for surfaces that can be connected to achieve highly complex geometry. When coupled with per-vertex Spherical Harmonics (SH), triangles provide a rich visual representation without incurring an expensive increase in primitives. We leverage our new representation to incorporate optimization objectives and enforce spatial regularization directly on the underlying primitives. The main differentiator of our approach is the definition and enforcement of soft connectivity forces between triangles during optimization, encouraging explicit, but soft, surface continuity in 3D. Experiments on representative 3D reconstruction and novel view synthesis datasets show improvements in geometric accuracy compared to current state-of-the-art algorithms without sacrificing visual fidelity.

We present a scalable 3D reconstruction model that addresses a critical limitation in offline feed-forward methods: their computational and memory requirements grow quadratically w.r.t. the number of input images. Our approach is built on the key insight that this bottleneck stems from the varying-length Key-Value (KV) space representation of scene geometry, which we distill into a fixed-size Multi-Layer Perceptron (MLP) via test-time training. VGG-T^3 (Visual Geometry Grounded Test Time Training) scales linearly w.r.t. the number of input views, similar to online models, and reconstructs a 1k image collection in just 54 seconds, achieving a 11.6times speed-up over baselines that rely on softmax attention. Since our method retains global scene aggregation capability, our point map reconstruction error outperforming other linear-time methods by large margins. Finally, we demonstrate visual localization capabilities of our model by querying the scene representation with unseen images.

The field of 3D reconstruction from images has rapidly evolved in the past few years, first with the introduction of Neural Radiance Field (NeRF) and more recently with 3D Gaussian Splatting (3DGS). The latter provides a significant edge over NeRF in terms of the training and inference speed, as well as the reconstruction quality. Although 3DGS works well for dense input images, the unstructured point-cloud like representation quickly overfits to the more challenging setup of extremely sparse input images (e.g., 3 images), creating a representation that appears as a jumble of needles from novel views. To address this issue, we propose regularized optimization and depth-based initialization. Our key idea is to introduce a structured Gaussian representation that can be controlled in 2D image space. We then constraint the Gaussians, in particular their position, and prevent them from moving independently during optimization. Specifically, we introduce single and multiview constraints through an implicit convolutional decoder and a total variation loss, respectively. With the coherency introduced to the Gaussians, we further constrain the optimization through a flow-based loss function. To support our regularized optimization, we propose an approach to initialize the Gaussians using monocular depth estimates at each input view. We demonstrate significant improvements compared to the state-of-the-art sparse-view NeRF-based approaches on a variety of scenes.

3D reconstruction and view synthesis are foundational problems in computer vision, graphics, and immersive technologies such as augmented reality (AR), virtual reality (VR), and digital twins. Traditional methods rely on computationally intensive iterative optimization in a complex chain, limiting their applicability in real-world scenarios. Recent advances in feed-forward approaches, driven by deep learning, have revolutionized this field by enabling fast and generalizable 3D reconstruction and view synthesis. This survey offers a comprehensive review of feed-forward techniques for 3D reconstruction and view synthesis, with a taxonomy according to the underlying representation architectures including point cloud, 3D Gaussian Splatting (3DGS), Neural Radiance Fields (NeRF), etc. We examine key tasks such as pose-free reconstruction, dynamic 3D reconstruction, and 3D-aware image and video synthesis, highlighting their applications in digital humans, SLAM, robotics, and beyond. In addition, we review commonly used datasets with detailed statistics, along with evaluation protocols for various downstream tasks. We conclude by discussing open research challenges and promising directions for future work, emphasizing the potential of feed-forward approaches to advance the state of the art in 3D vision.

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce suboptimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion

Learning decompositions of expensive-to-evaluate black-box functions promises to scale Bayesian optimisation (BO) to high-dimensional problems. However, the success of these techniques depends on finding proper decompositions that accurately represent the black-box. While previous works learn those decompositions based on data, we investigate data-independent decomposition sampling rules in this paper. We find that data-driven learners of decompositions can be easily misled towards local decompositions that do not hold globally across the search space. Then, we formally show that a random tree-based decomposition sampler exhibits favourable theoretical guarantees that effectively trade off maximal information gain and functional mismatch between the actual black-box and its surrogate as provided by the decomposition. Those results motivate the development of the random decomposition upper-confidence bound algorithm (RDUCB) that is straightforward to implement - (almost) plug-and-play - and, surprisingly, yields significant empirical gains compared to the previous state-of-the-art on a comprehensive set of benchmarks. We also confirm the plug-and-play nature of our modelling component by integrating our method with HEBO, showing improved practical gains in the highest dimensional tasks from Bayesmark.

Pruning neural networks, which involves removing a fraction of their weights, can often maintain high accuracy while significantly reducing model complexity, at least up to a certain limit. We present a neural network pruning technique that builds upon the Combinatorial Brain Surgeon, but solves an optimization problem over a subset of the network weights in an iterative, block-wise manner using block coordinate descent. The iterative, block-based nature of this pruning technique, which we dub ``iterative Combinatorial Brain Surgeon'' (iCBS) allows for scalability to very large models, including large language models (LLMs), that may not be feasible with a one-shot combinatorial optimization approach. When applied to large models like Mistral and DeiT, iCBS achieves higher performance metrics at the same density levels compared to existing pruning methods such as Wanda. This demonstrates the effectiveness of this iterative, block-wise pruning method in compressing and optimizing the performance of large deep learning models, even while optimizing over only a small fraction of the weights. Moreover, our approach allows for a quality-time (or cost) tradeoff that is not available when using a one-shot pruning technique alone. The block-wise formulation of the optimization problem enables the use of hardware accelerators, potentially offsetting the increased computational costs compared to one-shot pruning methods like Wanda. In particular, the optimization problem solved for each block is quantum-amenable in that it could, in principle, be solved by a quantum computer.

Score Distillation Sampling (SDS) leverages pretrained 2D diffusion models to advance text-to-3D generation but neglects multi-view correlations, being prone to geometric inconsistencies and multi-face artifacts in the generated 3D content. In this work, we propose Coupled Score Distillation (CSD), a framework that couples multi-view joint distribution priors to ensure geometrically consistent 3D generation while enabling the stable and direct optimization of 3D Gaussian Splatting. Specifically, by reformulating the optimization as a multi-view joint optimization problem, we derive an effective optimization rule that effectively couples multi-view priors to guide optimization across different viewpoints while preserving the diversity of generated 3D assets. Additionally, we propose a framework that directly optimizes 3D Gaussian Splatting (3D-GS) with random initialization to generate geometrically consistent 3D content. We further employ a deformable tetrahedral grid, initialized from 3D-GS and refined through CSD, to produce high-quality, refined meshes. Quantitative and qualitative experimental results demonstrate the efficiency and competitive quality of our approach.

In this paper, we propose an algorithm that allows joint refinement of camera pose and scene geometry represented by decomposed low-rank tensor, using only 2D images as supervision. First, we conduct a pilot study based on a 1D signal and relate our findings to 3D scenarios, where the naive joint pose optimization on voxel-based NeRFs can easily lead to sub-optimal solutions. Moreover, based on the analysis of the frequency spectrum, we propose to apply convolutional Gaussian filters on 2D and 3D radiance fields for a coarse-to-fine training schedule that enables joint camera pose optimization. Leveraging the decomposition property in decomposed low-rank tensor, our method achieves an equivalent effect to brute-force 3D convolution with only incurring little computational overhead. To further improve the robustness and stability of joint optimization, we also propose techniques of smoothed 2D supervision, randomly scaled kernel parameters, and edge-guided loss mask. Extensive quantitative and qualitative evaluations demonstrate that our proposed framework achieves superior performance in novel view synthesis as well as rapid convergence for optimization.

Given a matrix Min R^{mtimes n}, the low rank matrix completion problem asks us to find a rank-k approximation of M as UV^top for Uin R^{mtimes k} and Vin R^{ntimes k} by only observing a few entries specified by a set of entries Omegasubseteq [m]times [n]. In particular, we examine an approach that is widely used in practice -- the alternating minimization framework. Jain, Netrapalli and Sanghavi~jns13 showed that if M has incoherent rows and columns, then alternating minimization provably recovers the matrix M by observing a nearly linear in n number of entries. While the sample complexity has been subsequently improved~glz17, alternating minimization steps are required to be computed exactly. This hinders the development of more efficient algorithms and fails to depict the practical implementation of alternating minimization, where the updates are usually performed approximately in favor of efficiency. In this paper, we take a major step towards a more efficient and error-robust alternating minimization framework. To this end, we develop an analytical framework for alternating minimization that can tolerate moderate amount of errors caused by approximate updates. Moreover, our algorithm runs in time widetilde O(|Omega| k), which is nearly linear in the time to verify the solution while preserving the sample complexity. This improves upon all prior known alternating minimization approaches which require widetilde O(|Omega| k^2) time.

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

Stateful optimizers maintain gradient statistics over time, e.g., the exponentially smoothed sum (SGD with momentum) or squared sum (Adam) of past gradient values. This state can be used to accelerate optimization compared to plain stochastic gradient descent but uses memory that might otherwise be allocated to model parameters, thereby limiting the maximum size of models trained in practice. In this paper, we develop the first optimizers that use 8-bit statistics while maintaining the performance levels of using 32-bit optimizer states. To overcome the resulting computational, quantization, and stability challenges, we develop block-wise dynamic quantization. Block-wise quantization divides input tensors into smaller blocks that are independently quantized. Each block is processed in parallel across cores, yielding faster optimization and high precision quantization. To maintain stability and performance, we combine block-wise quantization with two additional changes: (1) dynamic quantization, a form of non-linear optimization that is precise for both large and small magnitude values, and (2) a stable embedding layer to reduce gradient variance that comes from the highly non-uniform distribution of input tokens in language models. As a result, our 8-bit optimizers maintain 32-bit performance with a small fraction of the memory footprint on a range of tasks, including 1.5B parameter language modeling, GLUE finetuning, ImageNet classification, WMT'14 machine translation, MoCo v2 contrastive ImageNet pretraining+finetuning, and RoBERTa pretraining, without changes to the original optimizer hyperparameters. We open-source our 8-bit optimizers as a drop-in replacement that only requires a two-line code change.

Reconstructing an animatable 3D human from casually captured images of an articulated subject without camera or human pose information is a practical yet challenging task due to view misalignment, occlusions, and the absence of structural priors. While optimization-based methods can produce high-fidelity results from monocular or multi-view videos, they require accurate pose estimation and slow iterative optimization, limiting scalability in unconstrained scenarios. Recent feed-forward approaches enable efficient single-image reconstruction but struggle to effectively leverage multiple input images to reduce ambiguity and improve reconstruction accuracy. To address these challenges, we propose PF-LHM, a large human reconstruction model that generates high-quality 3D avatars in seconds from one or multiple casually captured pose-free images. Our approach introduces an efficient Encoder-Decoder Point-Image Transformer architecture, which fuses hierarchical geometric point features and multi-view image features through multimodal attention. The fused features are decoded to recover detailed geometry and appearance, represented using 3D Gaussian splats. Extensive experiments on both real and synthetic datasets demonstrate that our method unifies single- and multi-image 3D human reconstruction, achieving high-fidelity and animatable 3D human avatars without requiring camera and human pose annotations. Code and models will be released to the public.

Distributed training of foundation models via DDP is limited by interconnect bandwidth. While infrequent communication strategies reduce synchronization frequency, they remain bottlenecked by the memory and communication requirements of optimizer states. Low-rank optimizers can alleviate these constraints; however, in the local-update regime, workers lack access to the full-batch gradients required to compute low-rank projections, which degrades performance. We propose LoRDO, a principled framework unifying low-rank optimization with infrequent synchronization. We first demonstrate that, while global projections based on pseudo-gradients are theoretically superior, they permanently restrict the optimization trajectory to a low-rank subspace. To restore subspace exploration, we introduce a full-rank quasi-hyperbolic update. LoRDO achieves near-parity with low-rank DDP in language modeling and downstream tasks at model scales of 125M--720M, while reducing communication by approx 10 times. Finally, we show that LoRDO improves performance even more in very low-memory settings with small rank/batch size.

Advancements in 3D scene reconstruction have transformed 2D images from the real world into 3D models, producing realistic 3D results from hundreds of input photos. Despite great success in dense-view reconstruction scenarios, rendering a detailed scene from insufficient captured views is still an ill-posed optimization problem, often resulting in artifacts and distortions in unseen areas. In this paper, we propose ReconX, a novel 3D scene reconstruction paradigm that reframes the ambiguous reconstruction challenge as a temporal generation task. The key insight is to unleash the strong generative prior of large pre-trained video diffusion models for sparse-view reconstruction. However, 3D view consistency struggles to be accurately preserved in directly generated video frames from pre-trained models. To address this, given limited input views, the proposed ReconX first constructs a global point cloud and encodes it into a contextual space as the 3D structure condition. Guided by the condition, the video diffusion model then synthesizes video frames that are both detail-preserved and exhibit a high degree of 3D consistency, ensuring the coherence of the scene from various perspectives. Finally, we recover the 3D scene from the generated video through a confidence-aware 3D Gaussian Splatting optimization scheme. Extensive experiments on various real-world datasets show the superiority of our ReconX over state-of-the-art methods in terms of quality and generalizability.

Recent advances in image editing with diffusion models have achieved impressive results, offering fine-grained control over the generation process. However, these methods are computationally intensive because of their iterative nature. While distilled diffusion models enable faster inference, their editing capabilities remain limited, primarily because of poor inversion quality. High-fidelity inversion and reconstruction are essential for precise image editing, as they preserve the structural and semantic integrity of the source image. In this work, we propose a novel framework that enhances image inversion using consistency models, enabling high-quality editing in just four steps. Our method introduces a cycle-consistency optimization strategy that significantly improves reconstruction accuracy and enables a controllable trade-off between editability and content preservation. We achieve state-of-the-art performance across various image editing tasks and datasets, demonstrating that our method matches or surpasses full-step diffusion models while being substantially more efficient. The code of our method is available on GitHub at https://github.com/ControlGenAI/Inverse-and-Edit.

Efficient and accurate feed-forward multi-view reconstruction has long been an important task in computer vision. Recent transformer-based models like VGGT and pi^3 have achieved impressive results with simple architectures, yet they face an inherent runtime bottleneck, due to the quadratic complexity of the global attention layers, that limits the scalability to large image sets. In this paper, we empirically analyze the global attention matrix of these models and observe that probability mass concentrates on a small subset of patch-patch interactions that correspond to cross-view geometric matches. Motivated by the structured attention and inspired by recent advancement in large language models, we propose a replacement for the dense global attention operation based on highly optimized block-sparse kernels, yielding up to 4times faster inference with comparable task performance. Our retrofit requires no retraining of the backbone, extends to both VGGT and pi^3, and supports large image collections. Evaluations on a comprehensive suite of multi-view benchmarks demonstrate the effectiveness of our approach.

Batch Bayesian optimisation (BO) is a successful technique for the optimisation of expensive black-box functions. Asynchronous BO can reduce wallclock time by starting a new evaluation as soon as another finishes, thus maximising resource utilisation. To maximise resource allocation, we develop a novel asynchronous BO method, AEGiS (Asynchronous epsilon-Greedy Global Search) that combines greedy search, exploiting the surrogate's mean prediction, with Thompson sampling and random selection from the approximate Pareto set describing the trade-off between exploitation (surrogate mean prediction) and exploration (surrogate posterior variance). We demonstrate empirically the efficacy of AEGiS on synthetic benchmark problems, meta-surrogate hyperparameter tuning problems and real-world problems, showing that AEGiS generally outperforms existing methods for asynchronous BO. When a single worker is available performance is no worse than BO using expected improvement.

Diffusion Transformers (DiTs) have become a leading backbone for video generation, yet their quadratic attention cost remains a major bottleneck. Sparse attention reduces this cost by computing only a subset of attention blocks. However, prior methods often either drop the remaining blocks, which incurs information loss, or rely on learned predictors to approximate them, introducing training overhead and potential output distribution shifting. In this paper, we show that the missing contributions can be recovered without training: after semantic clustering, keys and values within each block exhibit strong similarity and can be well summarized by a small set of cluster centroids. Based on this observation, we introduce SVG-EAR, a parameter-free linear compensation branch that uses the centroid to approximate skipped blocks and recover their contributions. While centroid compensation is accurate for most blocks, it can fail on a small subset. Standard sparsification typically selects blocks by attention scores, which indicate where the model places its attention mass, but not where the approximation error would be largest. SVG-EAR therefore performs error-aware routing: a lightweight probe estimates the compensation error for each block, and we compute exactly the blocks with the highest error-to-cost ratio while compensating for skipped blocks. We provide theoretical guarantees that relate attention reconstruction error to clustering quality, and empirically show that SVG-EAR improves the quality-efficiency trade-off and increases throughput at the same generation fidelity on video diffusion tasks. Overall, SVG-EAR establishes a clear Pareto frontier over prior approaches, achieving up to 1.77times and 1.93times speedups while maintaining PSNRs of up to 29.759 and 31.043 on Wan2.2 and HunyuanVideo, respectively.

Generative foundation models are increasingly scaled in both width and depth, posing significant challenges for stable feature learning and reliable hyperparameter (HP) transfer across model sizes. While maximal update parameterization (μP) has provided a principled solution to both problems for width scaling, existing extensions to the joint width-depth scaling regime remain fragmented, architecture- and optimizer-specific, and often rely on technically involved theories. In this work, we develop a simple and unified spectral framework for μP under joint width-depth scaling. Considering residual networks of varying block depths, we first introduce a spectral μP condition that precisely characterizes how the norms of weights and their per-step updates should scale with width and depth, unifying previously disparate μP formulations as special cases. Building on this condition, we then derive a general recipe for implementing μP across a broad class of optimizers by mapping the spectral constraints to concrete HP parameterizations. This approach not only recovers existing μP formulations (e.g., for SGD and AdamW) but also naturally extends to a wider range of optimizers. Finally, experiments on GPT-2 style language models demonstrate that the proposed spectral μP condition preserves stable feature learning and enables robust HP transfer under width-depth scaling.

We introduce the Large Sparse Reconstruction Model to study how scaling transformer context windows impacts feed-forward 3D reconstruction. Although recent object-centric feed-forward methods deliver robust, high-quality reconstruction, they still lag behind dense-view optimization in recovering fine-grained texture and appearance. We show that expanding the context window -- by substantially increasing the number of active object and image tokens -- remarkably narrows this gap and enables high-fidelity 3D object reconstruction and inverse rendering. To scale effectively, we adapt native sparse attention in our architecture design, unlocking its capacity for 3D reconstruction with three key contributions: (1) an efficient coarse-to-fine pipeline that focuses computation on informative regions by predicting sparse high-resolution residuals; (2) a 3D-aware spatial routing mechanism that establishes accurate 2D-3D correspondences using explicit geometric distances rather than standard attention scores; and (3) a custom block-aware sequence parallelism strategy utilizing an All-gather-KV protocol to balance dynamic, sparse workloads across GPUs. As a result, LSRM handles 20x more object tokens and >2x more image tokens than prior state-of-the-art (SOTA) methods. Extensive evaluations on standard novel-view synthesis benchmarks show substantial gains over the current SOTA, yielding 2.5 dB higher PSNR and 40% lower LPIPS. Furthermore, when extending LSRM to inverse rendering tasks, qualitative and quantitative evaluations on widely-used benchmarks demonstrate consistent improvements in texture and geometry details, achieving an LPIPS that matches or exceeds that of SOTA dense-view optimization methods. Code and model will be released on our project page.

This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance of adapting to the structures in the problem. We then cover how to make these algorithms agnostic to the scale of the problem. Our exposition is intended as an introduction for both practitioners and researchers who wish to be involved in these exciting new developments.

Faithfully reconstructing textured shapes and physical properties from videos presents an intriguing yet challenging problem. Significant efforts have been dedicated to advancing such a system identification problem in this area. Previous methods often rely on heavy optimization pipelines with a differentiable simulator and renderer to estimate physical parameters. However, these approaches frequently necessitate extensive hyperparameter tuning for each scene and involve a costly optimization process, which limits both their practicality and generalizability. In this work, we propose a novel framework, Vid2Sim, a generalizable video-based approach for recovering geometry and physical properties through a mesh-free reduced simulation based on Linear Blend Skinning (LBS), offering high computational efficiency and versatile representation capability. Specifically, Vid2Sim first reconstructs the observed configuration of the physical system from video using a feed-forward neural network trained to capture physical world knowledge. A lightweight optimization pipeline then refines the estimated appearance, geometry, and physical properties to closely align with video observations within just a few minutes. Additionally, after the reconstruction, Vid2Sim enables high-quality, mesh-free simulation with high efficiency. Extensive experiments demonstrate that our method achieves superior accuracy and efficiency in reconstructing geometry and physical properties from video data.

3D Gaussian Splatting (3DGS) employs Gaussian primitives for explicit scene representation, facilitating real-time, high-fidelity reconstruction and novel view synthesis of complex scenes. However, the explicit modeling inherent in 3DGS introduces a gradient bias during optimization, rendering its non-convex optimization process highly susceptible to convergence toward local suboptimal solutions. This constitutes a fundamental limitation in 3DGS optimization, which we term the Blur Trap. To address this limitation, we integrate simple explicit exploration into the 3DGS optimization framework. First, through rigorous mathematical analysis of the 3DGS optimization formulation, we identify the underlying optimization bias responsible for the Blur Trap and categorize it into two distinct subtypes: the Far-Side Blur Trap and the Near-Side Blur Trap. Subsequently, we propose two highly straightforward exploration strategies (Random Seeding and Random Splitting) to mitigate the far-side and near-side blur traps, respectively. Experimental validation demonstrates that the incorporation of these exploration operators effectively and complementarily overcome the Blur Trap, achieving high-quality rendering performance across multiple datasets. Project page: https://chengbo-wang.github.io/ExploreGS/

We revisit the problem of large-scale bundle adjustment and propose a technique called Multidirectional Conjugate Gradients that accelerates the solution of the normal equation by up to 61%. The key idea is that we enlarge the search space of classical preconditioned conjugate gradients to include multiple search directions. As a consequence, the resulting algorithm requires fewer iterations, leading to a significant speedup of large-scale reconstruction, in particular for denser problems where traditional approaches notoriously struggle. We provide a number of experimental ablation studies revealing the robustness to variations in the hyper-parameters and the speedup as a function of problem density.

Bayesian Optimization (BO) is typically used to optimize an unknown function f that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Even if provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open problem, often tackled by assuming an additive structure for f. By doing so, BO algorithms typically introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. This paper contains two main contributions: (i) we relax the restrictive assumptions on the additive structure of f without weakening the maximization guarantees of the acquisition function, and (ii) we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of f comprises high-dimensional factors.

Implicit neural networks have emerged as a crucial technology in 3D surface reconstruction. To reconstruct continuous surfaces from discrete point clouds, encoding the input points into regular grid features (plane or volume) has been commonly employed in existing approaches. However, these methods typically use the grid as an index for uniformly scattering point features. Compared with the irregular point features, the regular grid features may sacrifice some reconstruction details but improve efficiency. To take full advantage of these two types of features, we introduce a novel and high-efficiency attention mechanism between the grid and point features named Point-Grid Transformer (GridFormer). This mechanism treats the grid as a transfer point connecting the space and point cloud. Our method maximizes the spatial expressiveness of grid features and maintains computational efficiency. Furthermore, optimizing predictions over the entire space could potentially result in blurred boundaries. To address this issue, we further propose a boundary optimization strategy incorporating margin binary cross-entropy loss and boundary sampling. This approach enables us to achieve a more precise representation of the object structure. Our experiments validate that our method is effective and outperforms the state-of-the-art approaches under widely used benchmarks by producing more precise geometry reconstructions. The code is available at https://github.com/list17/GridFormer.

Supervised dictionary learning (SDL) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. The goal of SDL is to learn a class-discriminative dictionary, which is a set of latent feature vectors that can well-explain both the features as well as labels of observed data. In this paper, we provide a systematic study of SDL, including the theory, algorithm, and applications of SDL. First, we provide a novel framework that `lifts' SDL as a convex problem in a combined factor space and propose a low-rank projected gradient descent algorithm that converges exponentially to the global minimizer of the objective. We also formulate generative models of SDL and provide global estimation guarantees of the true parameters depending on the hyperparameter regime. Second, viewed as a nonconvex constrained optimization problem, we provided an efficient block coordinate descent algorithm for SDL that is guaranteed to find an varepsilon-stationary point of the objective in O(varepsilon^{-1}(log varepsilon^{-1})^{2}) iterations. For the corresponding generative model, we establish a novel non-asymptotic local consistency result for constrained and regularized maximum likelihood estimation problems, which may be of independent interest. Third, we apply SDL for imbalanced document classification by supervised topic modeling and also for pneumonia detection from chest X-ray images. We also provide simulation studies to demonstrate that SDL becomes more effective when there is a discrepancy between the best reconstructive and the best discriminative dictionaries.

Multi-resolution hash encoding has recently been proposed to reduce the computational cost of neural renderings, such as NeRF. This method requires accurate camera poses for the neural renderings of given scenes. However, contrary to previous methods jointly optimizing camera poses and 3D scenes, the naive gradient-based camera pose refinement method using multi-resolution hash encoding severely deteriorates performance. We propose a joint optimization algorithm to calibrate the camera pose and learn a geometric representation using efficient multi-resolution hash encoding. Showing that the oscillating gradient flows of hash encoding interfere with the registration of camera poses, our method addresses the issue by utilizing smooth interpolation weighting to stabilize the gradient oscillation for the ray samplings across hash grids. Moreover, the curriculum training procedure helps to learn the level-wise hash encoding, further increasing the pose refinement. Experiments on the novel-view synthesis datasets validate that our learning frameworks achieve state-of-the-art performance and rapid convergence of neural rendering, even when initial camera poses are unknown.

We focus on the problem of black-box adversarial attacks, where the aim is to generate adversarial examples for deep learning models solely based on information limited to output label~(hard label) to a queried data input. We propose a simple and efficient Bayesian Optimization~(BO) based approach for developing black-box adversarial attacks. Issues with BO's performance in high dimensions are avoided by searching for adversarial examples in a structured low-dimensional subspace. We demonstrate the efficacy of our proposed attack method by evaluating both ell_infty and ell_2 norm constrained untargeted and targeted hard label black-box attacks on three standard datasets - MNIST, CIFAR-10 and ImageNet. Our proposed approach consistently achieves 2x to 10x higher attack success rate while requiring 10x to 20x fewer queries compared to the current state-of-the-art black-box adversarial attacks.

We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for highly non-rigid shapes. To this end, we introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic and extrinsic geometric information to measure the deformation quality induced by predicted correspondences. We integrate the PLBO, together with an orientation-aware regulariser, into a novel MIP formulation that can be solved to global optimality for many practical problems. In contrast to previous methods, our approach is provably invariant to rigid transformations and global scaling, initialisation-free, has optimality guarantees, and scales to high resolution meshes with (empirically observed) linear time. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets, including data with inconsistent meshing, as well as applications in mesh-to-point-cloud matching.

We aim to address sparse-view reconstruction of a 3D scene by leveraging priors from large-scale vision models. While recent advancements such as 3D Gaussian Splatting (3DGS) have demonstrated remarkable successes in 3D reconstruction, these methods typically necessitate hundreds of input images that densely capture the underlying scene, making them time-consuming and impractical for real-world applications. However, sparse-view reconstruction is inherently ill-posed and under-constrained, often resulting in inferior and incomplete outcomes. This is due to issues such as failed initialization, overfitting on input images, and a lack of details. To mitigate these challenges, we introduce LM-Gaussian, a method capable of generating high-quality reconstructions from a limited number of images. Specifically, we propose a robust initialization module that leverages stereo priors to aid in the recovery of camera poses and the reliable point clouds. Additionally, a diffusion-based refinement is iteratively applied to incorporate image diffusion priors into the Gaussian optimization process to preserve intricate scene details. Finally, we utilize video diffusion priors to further enhance the rendered images for realistic visual effects. Overall, our approach significantly reduces the data acquisition requirements compared to previous 3DGS methods. We validate the effectiveness of our framework through experiments on various public datasets, demonstrating its potential for high-quality 360-degree scene reconstruction. Visual results are on our website.

The idea of video super resolution is to use different view points of a single scene to enhance the overall resolution and quality. Classical energy minimization approaches first establish a correspondence of the current frame to all its neighbors in some radius and then use this temporal information for enhancement. In this paper, we propose the first variational super resolution approach that computes several super resolved frames in one batch optimization procedure by incorporating motion information between the high-resolution image frames themselves. As a consequence, the number of motion estimation problems grows linearly in the number of frames, opposed to a quadratic growth of classical methods and temporal consistency is enforced naturally. We use infimal convolution regularization as well as an automatic parameter balancing scheme to automatically determine the reliability of the motion information and reweight the regularization locally. We demonstrate that our approach yields state-of-the-art results and even is competitive with machine learning approaches.

Training learned image compression (LIC) models entails navigating a challenging optimization landscape defined by the fundamental trade-off between rate and distortion. Standard first-order optimizers, such as SGD and Adam, struggle with gradient conflicts arising from competing objectives, leading to slow convergence and suboptimal rate-distortion performance. In this work, we demonstrate that a simple utilization of a second-order quasi-Newton optimizer, SOAP, dramatically improves both training efficiency and final performance across diverse LICs. Our theoretical and empirical analyses reveal that Newton preconditioning inherently resolves the intra-step and inter-step update conflicts intrinsic to the R-D objective, facilitating faster, more stable convergence. Beyond acceleration, we uncover a critical deployability benefit: second-order trained models exhibit significantly fewer activation and latent outliers. This substantially enhances robustness to post-training quantization. Together, these results establish second-order optimization, achievable as a seamless drop-in replacement of the imported optimizer, as a powerful, practical tool for advancing the efficiency and real-world readiness of LICs.

We introduce RealX3D, a real-capture benchmark for multi-view visual restoration and 3D reconstruction under diverse physical degradations. RealX3D groups corruptions into four families, including illumination, scattering, occlusion, and blurring, and captures each at multiple severity levels using a unified acquisition protocol that yields pixel-aligned LQ/GT views. Each scene includes high-resolution capture, RAW images, and dense laser scans, from which we derive world-scale meshes and metric depth. Benchmarking a broad range of optimization-based and feed-forward methods shows substantial degradation in reconstruction quality under physical corruptions, underscoring the fragility of current multi-view pipelines in real-world challenging environments.

Diffusion-based image restoration (IR) methods aim to use diffusion models to recover high-quality (HQ) images from degraded images and achieve promising performance. Due to the inherent property of diffusion models, most of these methods need long serial sampling chains to restore HQ images step-by-step. As a result, it leads to expensive sampling time and high computation costs. Moreover, such long sampling chains hinder understanding the relationship between the restoration results and the inputs since it is hard to compute the gradients in the whole chains. In this work, we aim to rethink the diffusion-based IR models through a different perspective, i.e., a deep equilibrium (DEQ) fixed point system. Specifically, we derive an analytical solution by modeling the entire sampling chain in diffusion-based IR models as a joint multivariate fixed point system. With the help of the analytical solution, we are able to conduct single-image sampling in a parallel way and restore HQ images without training. Furthermore, we compute fast gradients in DEQ and found that initialization optimization can boost performance and control the generation direction. Extensive experiments on benchmarks demonstrate the effectiveness of our proposed method on typical IR tasks and real-world settings. The code and models will be made publicly available.

Quantizing large language models has become a standard way to reduce their memory and computational costs. Typically, existing methods focus on breaking down the problem into individual layer-wise sub-problems, and minimizing per-layer error, measured via various metrics. Yet, this approach currently lacks theoretical justification and the metrics employed may be sub-optimal. In this paper, we present a "linearity theorem" establishing a direct relationship between the layer-wise ell_2 reconstruction error and the model perplexity increase due to quantization. This insight enables two novel applications: (1) a simple data-free LLM quantization method using Hadamard rotations and MSE-optimal grids, dubbed HIGGS, which outperforms all prior data-free approaches such as the extremely popular NF4 quantized format, and (2) an optimal solution to the problem of finding non-uniform per-layer quantization levels which match a given compression constraint in the medium-bitwidth regime, obtained by reduction to dynamic programming. On the practical side, we demonstrate improved accuracy-compression trade-offs on Llama-3.1 and 3.2-family models, as well as on Qwen-family models. Further, we show that our method can be efficiently supported in terms of GPU kernels at various batch sizes, advancing both data-free and non-uniform quantization for LLMs.

We present an algorithm for reconstructing the radiance field of a large-scale scene from a single casually captured video. The task poses two core challenges. First, most existing radiance field reconstruction approaches rely on accurate pre-estimated camera poses from Structure-from-Motion algorithms, which frequently fail on in-the-wild videos. Second, using a single, global radiance field with finite representational capacity does not scale to longer trajectories in an unbounded scene. For handling unknown poses, we jointly estimate the camera poses with radiance field in a progressive manner. We show that progressive optimization significantly improves the robustness of the reconstruction. For handling large unbounded scenes, we dynamically allocate new local radiance fields trained with frames within a temporal window. This further improves robustness (e.g., performs well even under moderate pose drifts) and allows us to scale to large scenes. Our extensive evaluation on the Tanks and Temples dataset and our collected outdoor dataset, Static Hikes, show that our approach compares favorably with the state-of-the-art.

3D Gaussian Splatting (3DGS) has revolutionized neural rendering with its efficiency and quality, but like many novel view synthesis methods, it heavily depends on accurate camera poses from Structure-from-Motion (SfM) systems. Although recent SfM pipelines have made impressive progress, questions remain about how to further improve both their robust performance in challenging conditions (e.g., textureless scenes) and the precision of camera parameter estimation simultaneously. We present 3R-GS, a 3D Gaussian Splatting framework that bridges this gap by jointly optimizing 3D Gaussians and camera parameters from large reconstruction priors MASt3R-SfM. We note that naively performing joint 3D Gaussian and camera optimization faces two challenges: the sensitivity to the quality of SfM initialization, and its limited capacity for global optimization, leading to suboptimal reconstruction results. Our 3R-GS, overcomes these issues by incorporating optimized practices, enabling robust scene reconstruction even with imperfect camera registration. Extensive experiments demonstrate that 3R-GS delivers high-quality novel view synthesis and precise camera pose estimation while remaining computationally efficient. Project page: https://zsh523.github.io/3R-GS/

Recent feed-forward reconstruction models, such as VGGT, have proven competitive with traditional optimization-based reconstructors while also providing geometry-aware features useful for other tasks. Here, we show that the quality of these models scales predictably with model and data size. We do so by introducing VGGT-Ω, which substantially improves reconstruction accuracy, efficiency, and capabilities for both static and dynamic scenes. To enable training this model at an unprecedented scale, we introduce architectural changes that improve training efficiency, a high-quality data annotation pipeline that supports dynamic scenes, and a self-supervised learning protocol. We simplify VGGT's architecture by using a single dense prediction head with multi-task supervision and removing the expensive high-resolution convolutional layers. We also use registers to aggregate scene information into a compact representation and introduce register attention, which restricts inter-frame information exchange to these registers, in part replacing global attention. In this way, during training, VGGT-Ω uses only about 30% of the GPU memory of its predecessor, allowing us to train with 15x more supervised data than prior work and to leverage vast amounts of unlabeled video data. VGGT-Ω achieves strong results for reconstruction of static and dynamic scenes across multiple benchmarks, for example, improving over the previous best camera estimation accuracy on Sintel by 77%. We also show that the learned registers can improve vision-language-action models and support alignment with language, suggesting that reconstruction can be a powerful and scalable proxy task for spatial understanding. Project Page: http://vggt-omega.github.io/

Post-training quantization at the 2-bit level enables low-cost deployment and inference acceleration for large language models (LLMs). Scalar quantization (SQ) and vector quantization (VQ) are two primary quantization methods, however, the former suffers from significant performance degradation, and the latter incurs computational and storage overhead. We propose UniSVQ, a unified 2-bit quantization framework that bridges scalar and vector quantization by parameterizing codewords as an affine transform of integer lattices. This structure preserves compatibility with optimized integer kernels while retaining much of VQ's flexibility. We further introduce a data-driven block-wise fine-tuning strategy to directly minimize quantization reconstruction error. Extensive experiments across multiple LLM families and zero-shot benchmarks demonstrate that UniSVQ consistently outperforms state-of-the-art SQ methods and achieves performance comparable to advanced VQ methods, while providing higher inference throughput. Codes are publicly available at https://github.com/AI9Stars/UniSVQ.

Sparse-view 3D reconstruction is essential for modeling scenes from casual captures, but remain challenging for non-generative reconstruction. Existing diffusion-based approaches mitigates this issues by synthesizing novel views, but they often condition on only one or two capture frames, which restricts geometric consistency and limits scalability to large or diverse scenes. We propose AnyRecon, a scalable framework for reconstruction from arbitrary and unordered sparse inputs that preserves explicit geometric control while supporting flexible conditioning cardinality. To support long-range conditioning, our method constructs a persistent global scene memory via a prepended capture view cache, and removes temporal compression to maintain frame-level correspondence under large viewpoint changes. Beyond better generative model, we also find that the interplay between generation and reconstruction is crucial for large-scale 3D scenes. Thus, we introduce a geometry-aware conditioning strategy that couples generation and reconstruction through an explicit 3D geometric memory and geometry-driven capture-view retrieval. To ensure efficiency, we combine 4-step diffusion distillation with context-window sparse attention to reduce quadratic complexity. Extensive experiments demonstrate robust and scalable reconstruction across irregular inputs, large viewpoint gaps, and long trajectories.

This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary objective of the proposed optimization model is to achieve a good balance between denoising and the preservation of fine details and edges, overcoming the performance of the popular and largely used Total Variation (TV) regularization through the application of appropriate pixel-dependent weights. The proposed strategy leverages the role of gradient approximations for the computation of the space-variant TV weights. For this reason, a convolutional neural network is designed, to approximate both the ground truth image and its gradient using an elastic loss function in its training. Additionally, the paper provides a theoretical analysis of the proposed model, showing the uniqueness of its solution, and illustrates a Chambolle-Pock algorithm tailored to address the specific problem at hand. This comprehensive framework integrates innovative regularization techniques with advanced neural network capabilities, demonstrating promising results in achieving high-quality reconstructions from low-sampled tomographic data.

Decompositional reconstruction of 3D scenes, with complete shapes and detailed texture of all objects within, is intriguing for downstream applications but remains challenging, particularly with sparse views as input. Recent approaches incorporate semantic or geometric regularization to address this issue, but they suffer significant degradation in underconstrained areas and fail to recover occluded regions. We argue that the key to solving this problem lies in supplementing missing information for these areas. To this end, we propose DP-Recon, which employs diffusion priors in the form of Score Distillation Sampling (SDS) to optimize the neural representation of each individual object under novel views. This provides additional information for the underconstrained areas, but directly incorporating diffusion prior raises potential conflicts between the reconstruction and generative guidance. Therefore, we further introduce a visibility-guided approach to dynamically adjust the per-pixel SDS loss weights. Together these components enhance both geometry and appearance recovery while remaining faithful to input images. Extensive experiments across Replica and ScanNet++ demonstrate that our method significantly outperforms SOTA methods. Notably, it achieves better object reconstruction under 10 views than the baselines under 100 views. Our method enables seamless text-based editing for geometry and appearance through SDS optimization and produces decomposed object meshes with detailed UV maps that support photorealistic Visual effects (VFX) editing. The project page is available at https://dp-recon.github.io/.

Reconstructing human motion and its surrounding environment is crucial for understanding human-scene interaction and predicting human movements in the scene. While much progress has been made in capturing human-scene interaction in constrained environments, those prior methods can hardly reconstruct the natural and diverse human motion and scene context from web videos. In this work, we propose JOSH, a novel optimization-based method for 4D human-scene reconstruction in the wild from monocular videos. JOSH uses techniques in both dense scene reconstruction and human mesh recovery as initialization, and then it leverages the human-scene contact constraints to jointly optimize the scene, the camera poses, and the human motion. Experiment results show JOSH achieves better results on both global human motion estimation and dense scene reconstruction by joint optimization of scene geometry and human motion. We further design a more efficient model, JOSH3R, and directly train it with pseudo-labels from web videos. JOSH3R outperforms other optimization-free methods by only training with labels predicted from JOSH, further demonstrating its accuracy and generalization ability.

We present an explicit-grid based method for efficiently reconstructing streaming radiance fields for novel view synthesis of real world dynamic scenes. Instead of training a single model that combines all the frames, we formulate the dynamic modeling problem with an incremental learning paradigm in which per-frame model difference is trained to complement the adaption of a base model on the current frame. By exploiting the simple yet effective tuning strategy with narrow bands, the proposed method realizes a feasible framework for handling video sequences on-the-fly with high training efficiency. The storage overhead induced by using explicit grid representations can be significantly reduced through the use of model difference based compression. We also introduce an efficient strategy to further accelerate model optimization for each frame. Experiments on challenging video sequences demonstrate that our approach is capable of achieving a training speed of 15 seconds per-frame with competitive rendering quality, which attains 1000 times speedup over the state-of-the-art implicit methods. Code is available at https://github.com/AlgoHunt/StreamRF.

Optimizing high-dimensional and complex black-box functions is crucial in numerous scientific applications. While Bayesian optimization (BO) is a powerful method for sample-efficient optimization, it struggles with the curse of dimensionality and scaling to thousands of evaluations. Recently, leveraging generative models to solve black-box optimization problems has emerged as a promising framework. However, those methods often underperform compared to BO methods due to limited expressivity and difficulty of uncertainty estimation in high-dimensional spaces. To overcome these issues, we introduce DiBO, a novel framework for solving high-dimensional black-box optimization problems. Our method iterates two stages. First, we train a diffusion model to capture the data distribution and deep ensembles to predict function values with uncertainty quantification. Second, we cast the candidate selection as a posterior inference problem to balance exploration and exploitation in high-dimensional spaces. Concretely, we fine-tune diffusion models to amortize posterior inference. Extensive experiments demonstrate that our method outperforms state-of-the-art baselines across synthetic and real-world tasks. Our code is publicly available https://github.com/umkiyoung/DiBO{here}.

We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in optimal-approximation theory, we train a network to decompose an implicit approximation operator by minimizing the reconstruction error in the learned basis over a chosen distribution of probe functions. For suitable distributions, they can be seen as an approximation of the Laplacian operator and its eigendecomposition, which are fundamental in geometry processing. Furthermore, our method recovers in a unified manner not only the spectral basis, but also the implicit metric's sampling density and the eigenvalues of the underlying operator. Notably, our unsupervised method makes no assumption on the data manifold, such as meshing or manifold dimensionality, allowing it to scale to arbitrary datasets of any dimension. On point clouds lying on surfaces in 3D and high-dimensional image manifolds, our approach yields meaningful spectral bases, that can resemble those of the Laplacian, without explicit construction of an operator. By replacing the traditional operator selection, construction, and eigendecomposition with a learning-based approach, our framework offers a principled, data-driven alternative to conventional pipelines. This opens new possibilities in geometry processing for unstructured data, particularly in high-dimensional spaces.

Capturing the shape and spatially-varying appearance (SVBRDF) of an object from images is a challenging task that has applications in both computer vision and graphics. Traditional optimization-based approaches often need a large number of images taken from multiple views in a controlled environment. Newer deep learning-based approaches require only a few input images, but the reconstruction quality is not on par with optimization techniques. We propose a novel deep learning architecture with a stage-wise estimation of shape and SVBRDF. The previous predictions guide each estimation, and a joint refinement network later refines both SVBRDF and shape. We follow a practical mobile image capture setting and use unaligned two-shot flash and no-flash images as input. Both our two-shot image capture and network inference can run on mobile hardware. We also create a large-scale synthetic training dataset with domain-randomized geometry and realistic materials. Extensive experiments on both synthetic and real-world datasets show that our network trained on a synthetic dataset can generalize well to real-world images. Comparisons with recent approaches demonstrate the superior performance of the proposed approach.

High-resolution video generation faces a coupled bottleneck of optimization instability and prohibitive computational costs. The massive expansion of the token sequence not only biases optimization toward local textures at the expense of global coherence, leading to structural collapse, but also imposes prohibitive training costs and severe inference latency. To address this, we propose PixelWizard, a framework that hierarchically decouples global structure modeling from fine-grained detail synthesis. PixelWizard first establishes a compact spatiotemporal anchor to concentrate dense structural priors, which then guides fine-grained generation at high resolution. This mitigates the local optimization bias to ensure structural stability without compromising high-frequency details. Leveraging this structural stability, we introduce Noise-Span Aligned Shortcut Training to break the inference bottleneck. By explicitly modeling the step size, this mechanism allows the model to traverse the generation trajectory with large steps. Crucially, we incorporate Exponential Index-Biased Sampling and Adaptive Noise-Span Calibration to align optimization with the shifted noise schedules of high-resolution grids, ensuring robust few-step inference without incurring the heavy overhead of distillation. Extensive experiments demonstrate that PixelWizard achieves superior visual quality while accelerating the generative sampling of native 2K/4K videos by over 10x.

We propose a compressive yet effective mesh representation, Blocked and Patchified Tokenization (BPT), facilitating the generation of meshes exceeding 8k faces. BPT compresses mesh sequences by employing block-wise indexing and patch aggregation, reducing their length by approximately 75\% compared to the original sequences. This compression milestone unlocks the potential to utilize mesh data with significantly more faces, thereby enhancing detail richness and improving generation robustness. Empowered with the BPT, we have built a foundation mesh generative model training on scaled mesh data to support flexible control for point clouds and images. Our model demonstrates the capability to generate meshes with intricate details and accurate topology, achieving SoTA performance on mesh generation and reaching the level for direct product usage.

We tackle the challenge of efficiently reconstructing a 3D asset from a single image with growing demands for automated 3D content creation pipelines. Previous methods primarily rely on Score Distillation Sampling (SDS) and Neural Radiance Fields (NeRF). Despite their significant success, these approaches encounter practical limitations due to lengthy optimization and considerable memory usage. In this report, we introduce Gamba, an end-to-end amortized 3D reconstruction model from single-view images, emphasizing two main insights: (1) 3D representation: leveraging a large number of 3D Gaussians for an efficient 3D Gaussian splatting process; (2) Backbone design: introducing a Mamba-based sequential network that facilitates context-dependent reasoning and linear scalability with the sequence (token) length, accommodating a substantial number of Gaussians. Gamba incorporates significant advancements in data preprocessing, regularization design, and training methodologies. We assessed Gamba against existing optimization-based and feed-forward 3D generation approaches using the real-world scanned OmniObject3D dataset. Here, Gamba demonstrates competitive generation capabilities, both qualitatively and quantitatively, while achieving remarkable speed, approximately 0.6 second on a single NVIDIA A100 GPU.

Exploiting partial first-order information in a cyclic way is arguably the most natural strategy to obtain scalable first-order methods. However, despite their wide use in practice, cyclic schemes are far less understood from a theoretical perspective than their randomized counterparts. Motivated by a recent success in analyzing an extrapolated cyclic scheme for generalized variational inequalities, we propose an Accelerated Cyclic Coordinate Dual Averaging with Extrapolation (A-CODER) method for composite convex optimization, where the objective function can be expressed as the sum of a smooth convex function accessible via a gradient oracle and a convex, possibly nonsmooth, function accessible via a proximal oracle. We show that A-CODER attains the optimal convergence rate with improved dependence on the number of blocks compared to prior work. Furthermore, for the setting where the smooth component of the objective function is expressible in a finite sum form, we introduce a variance-reduced variant of A-CODER, VR-A-CODER, with state-of-the-art complexity guarantees. Finally, we demonstrate the effectiveness of our algorithms through numerical experiments.

3D reconstruction of dynamic scenes is a long-standing problem in computer graphics and increasingly difficult the less information is available. Shape-from-Template (SfT) methods aim to reconstruct a template-based geometry from RGB images or video sequences, often leveraging just a single monocular camera without depth information, such as regular smartphone recordings. Unfortunately, existing reconstruction methods are either unphysical and noisy or slow in optimization. To solve this problem, we propose a novel SfT reconstruction algorithm for cloth using a pre-trained neural surrogate model that is fast to evaluate, stable, and produces smooth reconstructions due to a regularizing physics simulation. Differentiable rendering of the simulated mesh enables pixel-wise comparisons between the reconstruction and a target video sequence that can be used for a gradient-based optimization procedure to extract not only shape information but also physical parameters such as stretching, shearing, or bending stiffness of the cloth. This allows to retain a precise, stable, and smooth reconstructed geometry while reducing the runtime by a factor of 400-500 compared to phi-SfT, a state-of-the-art physics-based SfT approach.

This work focuses on addressing two major challenges in the context of large-scale nonconvex Bi-Level Optimization (BLO) problems, which are increasingly applied in machine learning due to their ability to model nested structures. These challenges involve ensuring computational efficiency and providing theoretical guarantees. While recent advances in scalable BLO algorithms have primarily relied on lower-level convexity simplification, our work specifically tackles large-scale BLO problems involving nonconvexity in both the upper and lower levels. We simultaneously address computational and theoretical challenges by introducing an innovative single-loop gradient-based algorithm, utilizing the Moreau envelope-based reformulation, and providing non-asymptotic convergence analysis for general nonconvex BLO problems. Notably, our algorithm relies solely on first-order gradient information, enhancing its practicality and efficiency, especially for large-scale BLO learning tasks. We validate our approach's effectiveness through experiments on various synthetic problems, two typical hyper-parameter learning tasks, and a real-world neural architecture search application, collectively demonstrating its superior performance.

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees, while achieving competitive empirical performance.

Capturing geometric and material information from images remains a fundamental challenge in computer vision and graphics. Traditional optimization-based methods often require hours of computational time to reconstruct geometry, material properties, and environmental lighting from dense multi-view inputs, while still struggling with inherent ambiguities between lighting and material. On the other hand, learning-based approaches leverage rich material priors from existing 3D object datasets but face challenges with maintaining multi-view consistency. In this paper, we introduce IDArb, a diffusion-based model designed to perform intrinsic decomposition on an arbitrary number of images under varying illuminations. Our method achieves accurate and multi-view consistent estimation on surface normals and material properties. This is made possible through a novel cross-view, cross-domain attention module and an illumination-augmented, view-adaptive training strategy. Additionally, we introduce ARB-Objaverse, a new dataset that provides large-scale multi-view intrinsic data and renderings under diverse lighting conditions, supporting robust training. Extensive experiments demonstrate that IDArb outperforms state-of-the-art methods both qualitatively and quantitatively. Moreover, our approach facilitates a range of downstream tasks, including single-image relighting, photometric stereo, and 3D reconstruction, highlighting its broad applications in realistic 3D content creation.

Modern VLSI designs comprise tens of billions of components, making scalable hypergraph partitioning critical for parallel and hierarchical optimization. Although multilevel partitioning remains the dominant paradigm, its coarsening stage can distort structural information, especially in hypergraphs with many high-degree hyperedges, leading to increased refinement overhead and limited scalability. Recent approaches incorporate spectral information to guide coarsening, but only in a heuristic manner, without directly optimizing the partitioning objectives. We introduce HySpecPro, a single-level hypergraph partitioner that performs end-to-end optimization in a spectral embedding space. HySpecPro constructs embeddings from a bipartite Laplacian and performs efficient projection-based search, supported by a fully GPU-accelerated implementation. Experiments show that HySpecPro delivers cut quality comparable to state-of-the-art multilevel methods while scaling linearly with the total hyperedge degree.

This paper studies the black-box optimization task which aims to find the maxima of a black-box function using a static set of its observed input-output pairs. This is often achieved via learning and optimizing a surrogate function with that offline data. Alternatively, it can also be framed as an inverse modeling task that maps a desired performance to potential input candidates that achieve it. Both approaches are constrained by the limited amount of offline data. To mitigate this limitation, we introduce a new perspective that casts offline optimization as a distributional translation task. This is formulated as learning a probabilistic bridge transforming an implicit distribution of low-value inputs (i.e., offline data) into another distribution of high-value inputs (i.e., solution candidates). Such probabilistic bridge can be learned using low- and high-value inputs sampled from synthetic functions that resemble the target function. These synthetic functions are constructed as the mean posterior of multiple Gaussian processes fitted with different parameterizations on the offline data, alleviating the data bottleneck. The proposed approach is evaluated on an extensive benchmark comprising most recent methods, demonstrating significant improvement and establishing a new state-of-the-art performance. Our code is publicly available at https://github.com/cuong-dm/ROOT.

We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator's output. We assume that queries to the operator (such as running a high-fidelity simulator or physical experiment) are costly, while functional evaluations on the operator's output are inexpensive. Our algorithm employs a sample-then-optimize approach using neural operator surrogates. This strategy avoids explicit uncertainty quantification by treating trained neural operators as approximate samples from a Gaussian process (GP) posterior. We derive regret bounds and theoretical results connecting neural operators with GPs in infinite-dimensional settings. Experiments benchmark our method against other Bayesian optimization baselines on functional optimization tasks involving partial differential equations of physical systems, demonstrating better sample efficiency and significant performance gains.

Despite advances in physics-based 3D motion synthesis, current methods face key limitations: reliance on pre-reconstructed 3D Gaussian Splatting (3DGS) built from dense multi-view images with time-consuming per-scene optimization; physics integration via either inflexible, hand-specified attributes or unstable, optimization-heavy guidance from video models using Score Distillation Sampling (SDS); and naive concatenation of prebuilt 3DGS with physics modules, which ignores physical information embedded in appearance and yields suboptimal performance. To address these issues, we propose PhysGM, a feed-forward framework that jointly predicts 3D Gaussian representation and physical properties from a single image, enabling immediate simulation and high-fidelity 4D rendering. Unlike slow appearance-agnostic optimization methods, we first pre-train a physics-aware reconstruction model that directly infers both Gaussian and physical parameters. We further refine the model with Direct Preference Optimization (DPO), aligning simulations with the physically plausible reference videos and avoiding the high-cost SDS optimization. To address the absence of a supporting dataset for this task, we propose PhysAssets, a dataset of 50K+ 3D assets annotated with physical properties and corresponding reference videos. Experiments show that PhysGM produces high-fidelity 4D simulations from a single image in one minute, achieving a significant speedup over prior work while delivering realistic renderings.Our project page is at:https://hihixiaolv.github.io/PhysGM.github.io/

We introduce Power Bundle Adjustment as an expansion type algorithm for solving large-scale bundle adjustment problems. It is based on the power series expansion of the inverse Schur complement and constitutes a new family of solvers that we call inverse expansion methods. We theoretically justify the use of power series and we prove the convergence of our approach. Using the real-world BAL dataset we show that the proposed solver challenges the state-of-the-art iterative methods and significantly accelerates the solution of the normal equation, even for reaching a very high accuracy. This easy-to-implement solver can also complement a recently presented distributed bundle adjustment framework. We demonstrate that employing the proposed Power Bundle Adjustment as a sub-problem solver significantly improves speed and accuracy of the distributed optimization.

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network - where every weight is a hyperparameter tuned for validation performance - outputting augmented training examples. Jointly tuning weights and hyperparameters with our approach is only a few times more costly in memory and compute than standard training.

Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains unresolved: beyond a few special dimensions, neither optimal packings nor tight upper bounds are known. Even a major breakthrough in dimension n=8, later recognised with a Fields Medal, underscores its difficulty. A leading technique for upper bounds, the three-point method, reduces the problem to solving large, high-precision semidefinite programs (SDPs). Because each candidate SDP may take days to evaluate, standard data-intensive AI approaches are infeasible. We address this challenge by formulating SDP construction as a sequential decision process, the SDP game, in which a policy assembles SDP formulations from a set of admissible components. Using a sample-efficient model-based framework that combines Bayesian optimisation with Monte Carlo Tree Search, we obtain new state-of-the-art upper bounds in dimensions 4-16, showing that model-based search can advance computational progress in longstanding geometric problems. Together, these results demonstrate that sample-efficient, model-based search can make tangible progress on mathematically rigid, evaluation limited problems, pointing towards a complementary direction for AI-assisted discovery beyond large-scale LLM-driven exploration.

Bayesian optimisation is a popular, surrogate model-based approach for optimising expensive black-box functions. Given a surrogate model, the next location to expensively evaluate is chosen via maximisation of a cheap-to-query acquisition function. We present an epsilon-greedy procedure for Bayesian optimisation in batch settings in which the black-box function can be evaluated multiple times in parallel. Our epsilon-shotgun algorithm leverages the model's prediction, uncertainty, and the approximated rate of change of the landscape to determine the spread of batch solutions to be distributed around a putative location. The initial target location is selected either in an exploitative fashion on the mean prediction, or -- with probability epsilon -- from elsewhere in the design space. This results in locations that are more densely sampled in regions where the function is changing rapidly and in locations predicted to be good (i.e close to predicted optima), with more scattered samples in regions where the function is flatter and/or of poorer quality. We empirically evaluate the epsilon-shotgun methods on a range of synthetic functions and two real-world problems, finding that they perform at least as well as state-of-the-art batch methods and in many cases exceed their performance.

Recent inverse problem solvers that leverage generative diffusion priors have garnered significant attention due to their exceptional quality. However, adaptation of the prior is necessary when there exists a discrepancy between the training and testing distributions. In this work, we propose deep diffusion image prior (DDIP), which generalizes the recent adaptation method of SCD by introducing a formal connection to the deep image prior. Under this framework, we propose an efficient adaptation method dubbed D3IP, specified for 3D measurements, which accelerates DDIP by orders of magnitude while achieving superior performance. D3IP enables seamless integration of 3D inverse solvers and thus leads to coherent 3D reconstruction. Moreover, we show that meta-learning techniques can also be applied to yield even better performance. We show that our method is capable of solving diverse 3D reconstructive tasks from the generative prior trained only with phantom images that are vastly different from the training set, opening up new opportunities of applying diffusion inverse solvers even when training with gold standard data is impossible. Code: https://github.com/HJ-harry/DDIP3D

Single image 3D reconstruction is an important but challenging task that requires extensive knowledge of our natural world. Many existing methods solve this problem by optimizing a neural radiance field under the guidance of 2D diffusion models but suffer from lengthy optimization time, 3D inconsistency results, and poor geometry. In this work, we propose a novel method that takes a single image of any object as input and generates a full 360-degree 3D textured mesh in a single feed-forward pass. Given a single image, we first use a view-conditioned 2D diffusion model, Zero123, to generate multi-view images for the input view, and then aim to lift them up to 3D space. Since traditional reconstruction methods struggle with inconsistent multi-view predictions, we build our 3D reconstruction module upon an SDF-based generalizable neural surface reconstruction method and propose several critical training strategies to enable the reconstruction of 360-degree meshes. Without costly optimizations, our method reconstructs 3D shapes in significantly less time than existing methods. Moreover, our method favors better geometry, generates more 3D consistent results, and adheres more closely to the input image. We evaluate our approach on both synthetic data and in-the-wild images and demonstrate its superiority in terms of both mesh quality and runtime. In addition, our approach can seamlessly support the text-to-3D task by integrating with off-the-shelf text-to-image diffusion models.

Real-time dense scene reconstruction during unstable camera motions is crucial for robotics, yet current RGB-D SLAM systems fail when cameras experience large viewpoint changes, fast motions, or sudden shaking. Classical optimization-based methods deliver high accuracy but fail with poor initialization during large motions, while learning-based approaches provide robustness but lack sufficient accuracy for dense reconstruction. We address this challenge through a combination of learning-based initialization with optimization-based refinement. Our method employs a camera pose regression network to predict metric-aware relative poses from consecutive RGB-D frames, which serve as reliable starting points for a randomized optimization algorithm that further aligns depth images with the scene geometry. Extensive experiments demonstrate promising results: our approach outperforms the best competitor on challenging benchmarks, while maintaining comparable accuracy on stable motion sequences. The system operates in real-time, showcasing that combining simple and principled techniques can achieve both robustness for unstable motions and accuracy for dense reconstruction. Project page: https://github.com/siyandong/PROFusion.

We present BlockFusion, a diffusion-based model that generates 3D scenes as unit blocks and seamlessly incorporates new blocks to extend the scene. BlockFusion is trained using datasets of 3D blocks that are randomly cropped from complete 3D scene meshes. Through per-block fitting, all training blocks are converted into the hybrid neural fields: with a tri-plane containing the geometry features, followed by a Multi-layer Perceptron (MLP) for decoding the signed distance values. A variational auto-encoder is employed to compress the tri-planes into the latent tri-plane space, on which the denoising diffusion process is performed. Diffusion applied to the latent representations allows for high-quality and diverse 3D scene generation. To expand a scene during generation, one needs only to append empty blocks to overlap with the current scene and extrapolate existing latent tri-planes to populate new blocks. The extrapolation is done by conditioning the generation process with the feature samples from the overlapping tri-planes during the denoising iterations. Latent tri-plane extrapolation produces semantically and geometrically meaningful transitions that harmoniously blend with the existing scene. A 2D layout conditioning mechanism is used to control the placement and arrangement of scene elements. Experimental results indicate that BlockFusion is capable of generating diverse, geometrically consistent and unbounded large 3D scenes with unprecedented high-quality shapes in both indoor and outdoor scenarios.

What do auto-encoders learn about the underlying data generating distribution? Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of data. This paper clarifies some of these previous observations by showing that minimizing a particular form of regularized reconstruction error yields a reconstruction function that locally characterizes the shape of the data generating density. We show that the auto-encoder captures the score (derivative of the log-density with respect to the input). It contradicts previous interpretations of reconstruction error as an energy function. Unlike previous results, the theorems provided here are completely generic and do not depend on the parametrization of the auto-encoder: they show what the auto-encoder would tend to if given enough capacity and examples. These results are for a contractive training criterion we show to be similar to the denoising auto-encoder training criterion with small corruption noise, but with contraction applied on the whole reconstruction function rather than just encoder. Similarly to score matching, one can consider the proposed training criterion as a convenient alternative to maximum likelihood because it does not involve a partition function. Finally, we show how an approximate Metropolis-Hastings MCMC can be setup to recover samples from the estimated distribution, and this is confirmed in sampling experiments.

Recent works show that reducing the number of layers in a convolutional neural network can enhance efficiency while maintaining the performance of the network. Existing depth compression methods remove redundant non-linear activation functions and merge the consecutive convolution layers into a single layer. However, these methods suffer from a critical drawback; the kernel size of the merged layers becomes larger, significantly undermining the latency reduction gained from reducing the depth of the network. We show that this problem can be addressed by jointly pruning convolution layers and activation functions. To this end, we propose LayerMerge, a novel depth compression method that selects which activation layers and convolution layers to remove, to achieve a desired inference speed-up while minimizing performance loss. Since the corresponding selection problem involves an exponential search space, we formulate a novel surrogate optimization problem and efficiently solve it via dynamic programming. Empirical results demonstrate that our method consistently outperforms existing depth compression and layer pruning methods on various network architectures, both on image classification and generation tasks. We release the code at https://github.com/snu-mllab/LayerMerge.

In many real-world scenarios, obtaining fully observed samples is prohibitively expensive or even infeasible, while partial and noisy observations are comparatively easy to collect. In this work, we study distribution restoration with abundant noisy samples, assuming the corruption process is available as a black-box generator. We show that this task can be framed as a one-sided entropic optimal transport problem and solved via an EM-like algorithm. We further provide a test criterion to determine whether the true underlying distribution is recoverable under per-sample information loss, and show that in otherwise unrecoverable cases, a small number of clean samples can render the distribution largely recoverable. Building on these insights, we introduce SFBD-OMNI, a bridge model-based framework that maps corrupted sample distributions to the ground-truth distribution. Our method generalizes Stochastic Forward-Backward Deconvolution (SFBD; Lu et al., 2025) to handle arbitrary measurement models beyond Gaussian corruption. Experiments across benchmark datasets and diverse measurement settings demonstrate significant improvements in both qualitative and quantitative performance.

We propose a method for in-hand 3D scanning of an unknown object with a monocular camera. Our method relies on a neural implicit surface representation that captures both the geometry and the appearance of the object, however, by contrast with most NeRF-based methods, we do not assume that the camera-object relative poses are known. Instead, we simultaneously optimize both the object shape and the pose trajectory. As direct optimization over all shape and pose parameters is prone to fail without coarse-level initialization, we propose an incremental approach that starts by splitting the sequence into carefully selected overlapping segments within which the optimization is likely to succeed. We reconstruct the object shape and track its poses independently within each segment, then merge all the segments before performing a global optimization. We show that our method is able to reconstruct the shape and color of both textured and challenging texture-less objects, outperforms classical methods that rely only on appearance features, and that its performance is close to recent methods that assume known camera poses.

Prior studies in learned image compression (LIC) consistently show that only a small subset of latent channels is critical for reconstruction, while many others carry limited information. Exploiting this imbalance could improve both coding and computational efficiency, yet existing approaches often rely on costly, dataset-specific ablation tests and typically analyze channels in isolation, ignoring their interdependencies. We propose a generalizable, dataset-agnostic method to identify and organize important channels in pretrained VAE-based LIC models. Instead of brute-force empirical evaluations, our approach leverages intrinsic parameter statistics-weight variances, bias magnitudes, and pairwise correlations-to estimate channel importance. This analysis reveals a consistent organizational structure, termed the Invariant Salient Channel Space (ISCS), where Salient-Core channels capture dominant structures and Salient-Auxiliary channels provide complementary details. Building on ISCS, we introduce a deterministic channel ordering and grouping strategy that enables slice-parallel decoding, reduces redundancy, and improves bitrate efficiency. Experiments across multiple LIC architectures demonstrate that our method effectively reduces bitrate and computation while maintaining reconstruction quality, providing a practical and modular enhancement to existing learned compression frameworks.

In this paper, we propose RI3D, a novel 3DGS-based approach that harnesses the power of diffusion models to reconstruct high-quality novel views given a sparse set of input images. Our key contribution is separating the view synthesis process into two tasks of reconstructing visible regions and hallucinating missing regions, and introducing two personalized diffusion models, each tailored to one of these tasks. Specifically, one model ('repair') takes a rendered image as input and predicts the corresponding high-quality image, which in turn is used as a pseudo ground truth image to constrain the optimization. The other model ('inpainting') primarily focuses on hallucinating details in unobserved areas. To integrate these models effectively, we introduce a two-stage optimization strategy: the first stage reconstructs visible areas using the repair model, and the second stage reconstructs missing regions with the inpainting model while ensuring coherence through further optimization. Moreover, we augment the optimization with a novel Gaussian initialization method that obtains per-image depth by combining 3D-consistent and smooth depth with highly detailed relative depth. We demonstrate that by separating the process into two tasks and addressing them with the repair and inpainting models, we produce results with detailed textures in both visible and missing regions that outperform state-of-the-art approaches on a diverse set of scenes with extremely sparse inputs.

Per-scene optimization methods such as 3D Gaussian Splatting provide state-of-the-art novel view synthesis quality but extrapolate poorly to under-observed areas. Methods that leverage generative priors to correct artifacts in these areas hold promise but currently suffer from two shortcomings. The first is scalability, as existing methods use image diffusion models or bidirectional video models that are limited in the number of views they can generate in a single pass (and thus require a costly iterative distillation process for consistency). The second is quality itself, as generators used in prior work tend to produce outputs that are inconsistent with existing scene content and fail entirely in completely unobserved regions. To solve these, we propose a two-stage pipeline that leverages two key insights. First, we train a powerful bidirectional generative model with a novel opacity mixing strategy that encourages consistency with existing observations while retaining the model's ability to extrapolate novel content in unseen areas. Second, we distill it into a causal auto-regressive model that generates hundreds of frames in a single pass. This model can directly produce novel views or serve as pseudo-supervision to improve the underlying 3D representation in a simple and highly efficient manner. We evaluate our method extensively and demonstrate that it can generate plausible reconstructions in scenarios where existing approaches fail completely. When measured on commonly benchmarked datasets, we outperform all existing baselines by a wide margin, exceeding prior state-of-the-art methods by 1-3 dB PSNR.

Reconstructing meshes from point clouds is an important task in fields such as robotics, autonomous systems, and medical imaging. This survey examines state-of-the-art learning-based approaches to mesh reconstruction, categorizing them into five paradigms: PointNet family, autoencoder architectures, deformation-based methods, point-move techniques, and primitive-based approaches. Each paradigm is explored in depth, detailing the primary approaches and their underlying methodologies. By comparing these techniques, our study serves as a comprehensive guide, and equips researchers and practitioners with the knowledge to navigate the landscape of learning-based mesh reconstruction techniques. The findings underscore the transformative potential of these methods, which often surpass traditional techniques in allowing detailed and efficient reconstructions.

Optimization-based approaches, such as score distillation sampling (SDS), show promise in zero-shot 3D generation but suffer from low efficiency, primarily due to the high number of function evaluations (NFEs) required for each sample. In this paper, we introduce score-based iterative reconstruction (SIR), an efficient and general algorithm for 3D generation with a multi-view score-based diffusion model. Given the images produced by the diffusion model, SIR reduces NFEs by repeatedly optimizing 3D parameters, unlike the single optimization in SDS, mimicking the 3D reconstruction process. With other improvements including optimization in the pixel space, we present an efficient approach called MicroDreamer that generally applies to various 3D representations and 3D generation tasks. In particular, retaining a comparable performance, MicroDreamer is 5-20 times faster than SDS in generating neural radiance field and takes about 20 seconds to generate meshes from 3D Gaussian splitting on a single A100 GPU, halving the time of the fastest zero-shot baseline, DreamGaussian. Our code is available at https://github.com/ML-GSAI/MicroDreamer.

We introduce 4DGS360, a diffusion-free framework for 360^{circ} dynamic object reconstruction from casual monocular video. Existing methods often fail to reconstruct consistent 360^{circ} geometry, as their heavy reliance on 2D-native priors causes initial points to overfit to visible surface in each training view. 4DGS360 addresses this challenge through a advanced 3D-native initialization that mitigates the geometric ambiguity of occluded regions. Our proposed 3D tracker, AnchorTAP3D, produces reinforced 3D point trajectories by leveraging confident 2D track points as anchors, suppressing drift and providing reliable initialization that preserves geometry in occluded regions. This initialization, combined with optimization, yields coherent 360^{circ} 4D reconstructions. We further present iPhone360, a new benchmark where test cameras are placed up to 135^{circ} apart from training views, enabling 360^{circ} evaluation that existing datasets cannot provide. Experiments show that 4DGS360 achieves state-of-the-art performance on the iPhone360, iPhone, and DAVIS datasets, both qualitatively and quantitatively.

We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximation quality and regularity of the models, any such algorithm drives a natural stationarity measure to zero at the rate O(k^{-1/4}). As a consequence, we obtain the first complexity guarantees for the stochastic proximal point, proximal subgradient, and regularized Gauss-Newton methods for minimizing compositions of convex functions with smooth maps. The guiding principle, underlying the complexity guarantees, is that all algorithms under consideration can be interpreted as approximate descent methods on an implicit smoothing of the problem, given by the Moreau envelope. Specializing to classical circumstances, we obtain the long-sought convergence rate of the stochastic projected gradient method, without batching, for minimizing a smooth function on a closed convex set.

Modern ML applications increasingly rely on complex deep learning models and large datasets. There has been an exponential growth in the amount of computation needed to train the largest models. Therefore, to scale computation and data, these models are inevitably trained in a distributed manner in clusters of nodes, and their updates are aggregated before being applied to the model. However, a distributed setup is prone to Byzantine failures of individual nodes, components, and software. With data augmentation added to these settings, there is a critical need for robust and efficient aggregation systems. We define the quality of workers as reconstruction ratios in (0,1], and formulate aggregation as a Maximum Likelihood Estimation procedure using Beta densities. We show that the Regularized form of log-likelihood wrt subspace can be approximately solved using iterative least squares solver, and provide convergence guarantees using recent Convex Optimization landscape results. Our empirical findings demonstrate that our approach significantly enhances the robustness of state-of-the-art Byzantine resilient aggregators. We evaluate our method in a distributed setup with a parameter server, and show simultaneous improvements in communication efficiency and accuracy across various tasks. The code is publicly available at https://github.com/hamidralmasi/FlagAggregator