Daily Papers

Learning neural operators for solving partial differential equations (PDEs) has attracted great attention due to its high inference efficiency. However, training such operators requires generating a substantial amount of labeled data, i.e., PDE problems together with their solutions. The data generation process is exceptionally time-consuming, as it involves solving numerous systems of linear equations to obtain numerical solutions to the PDEs. Many existing methods solve these systems independently without considering their inherent similarities, resulting in extremely redundant computations. To tackle this problem, we propose a novel method, namely Sorting Krylov Recycling (SKR), to boost the efficiency of solving these systems, thus significantly accelerating data generation for neural operators training. To the best of our knowledge, SKR is the first attempt to address the time-consuming nature of data generation for learning neural operators. The working horse of SKR is Krylov subspace recycling, a powerful technique for solving a series of interrelated systems by leveraging their inherent similarities. Specifically, SKR employs a sorting algorithm to arrange these systems in a sequence, where adjacent systems exhibit high similarities. Then it equips a solver with Krylov subspace recycling to solve the systems sequentially instead of independently, thus effectively enhancing the solving efficiency. Both theoretical analysis and extensive experiments demonstrate that SKR can significantly accelerate neural operator data generation, achieving a remarkable speedup of up to 13.9 times.

Krylov subspace, which is generated by multiplying a given vector by the matrix of a linear transformation and its successive powers, has been extensively studied in classical optimization literature to design algorithms that converge quickly for large linear inverse problems. For example, the conjugate gradient method (CG), one of the most popular Krylov subspace methods, is based on the idea of minimizing the residual error in the Krylov subspace. However, with the recent advancement of high-performance diffusion solvers for inverse problems, it is not clear how classical wisdom can be synergistically combined with modern diffusion models. In this study, we propose a novel and efficient diffusion sampling strategy that synergistically combines the diffusion sampling and Krylov subspace methods. Specifically, we prove that if the tangent space at a denoised sample by Tweedie's formula forms a Krylov subspace, then the CG initialized with the denoised data ensures the data consistency update to remain in the tangent space. This negates the need to compute the manifold-constrained gradient (MCG), leading to a more efficient diffusion sampling method. Our method is applicable regardless of the parametrization and setting (i.e., VE, VP). Notably, we achieve state-of-the-art reconstruction quality on challenging real-world medical inverse imaging problems, including multi-coil MRI reconstruction and 3D CT reconstruction. Moreover, our proposed method achieves more than 80 times faster inference time than the previous state-of-the-art method. Code is available at https://github.com/HJ-harry/DDS

We analyze the stability of a class of eigensolvers that target interior eigenvalues with rational filters. We show that subspace iteration with a rational filter is robust even when an eigenvalue is near a filter's pole. These dangerous eigenvalues contribute to large round-off errors in the first iteration, but are self-correcting in later iterations. For matrices with orthogonal eigenvectors (e.g., real-symmetric or complex Hermitian), two iterations is enough to reduce round-off errors to the order of the unit-round off. In contrast, Krylov methods accelerated by rational filters with fixed poles typically fail to converge to unit round-off accuracy when an eigenvalue is close to a pole. In the context of Arnoldi with shift-and-invert enhancement, we demonstrate a simple restart strategy that recovers full precision in the target eigenpairs.

Despite substantial advances in all-in-one image restoration for addressing diverse degradations within a unified model, existing methods remain vulnerable to out-of-distribution degradations, thereby limiting their generalization in real-world scenarios. To tackle the challenge, this work is motivated by the intuition that multisource degraded feature distributions are induced by different degradation-specific shifts from an underlying degradation-agnostic distribution, and recovering such a shared distribution is thus crucial for achieving generalization across degradations. With this insight, we propose BaryIR, a representation learning framework that aligns multisource degraded features in the Wasserstein barycenter (WB) space, which models a degradation-agnostic distribution by minimizing the average of Wasserstein distances to multisource degraded distributions. We further introduce residual subspaces, whose embeddings are mutually contrasted while remaining orthogonal to the WB embeddings. Consequently, BaryIR explicitly decouples two orthogonal spaces: a WB space that encodes the degradation-agnostic invariant contents shared across degradations, and residual subspaces that adaptively preserve the degradation-specific knowledge. This disentanglement mitigates overfitting to in-distribution degradations and enables adaptive restoration grounded on the degradation-agnostic shared invariance. Extensive experiments demonstrate that BaryIR performs competitively against state-of-the-art all-in-one methods. Notably, BaryIR generalizes well to unseen degradations (e.g., types and levels) and shows remarkable robustness in learning generalized features, even when trained on limited degradation types and evaluated on real-world data with mixed degradations.

The Multi-Prize Lottery Ticket Hypothesis posits that randomly initialized neural networks contain several subnetworks that achieve comparable accuracy to fully trained models of the same architecture. However, current methods require that the network is sufficiently overparameterized. In this work, we propose a modification to two state-of-the-art algorithms (Edge-Popup and Biprop) that finds high-accuracy subnetworks with no additional storage cost or scaling. The algorithm, Iterative Weight Recycling, identifies subsets of important weights within a randomly initialized network for intra-layer reuse. Empirically we show improvements on smaller network architectures and higher prune rates, finding that model sparsity can be increased through the "recycling" of existing weights. In addition to Iterative Weight Recycling, we complement the Multi-Prize Lottery Ticket Hypothesis with a reciprocal finding: high-accuracy, randomly initialized subnetwork's produce diverse masks, despite being generated with the same hyperparameter's and pruning strategy. We explore the landscapes of these masks, which show high variability.

Deep subspace clustering (DSC) algorithms face several challenges that hinder their widespread adoption across variois application domains. First, clustering quality is typically assessed using only the encoder's output layer, disregarding valuable information present in the intermediate layers. Second, most DSC approaches treat representation learning and subspace clustering as independent tasks, limiting their effectiveness. Third, they assume the availability of a held-out dataset for hyperparameter tuning, which is often impractical in real-world scenarios. Fourth, learning termination is commonly based on clustering error monitoring, requiring external labels. Finally, their performance often depends on post-processing techniques that rely on labeled data. To address this limitations, we introduce a novel single-view DSC approach that: (i) minimizes a layer-wise self expression loss using a joint representation matrix; (ii) optimizes a subspace-structured norm to enhance clustering quality; (iii) employs a multi-stage sequential learning framework, consisting of pre-training and fine-tuning, enabling the use of multiple regularization terms without hyperparameter tuning; (iv) incorporates a relative error-based self-stopping mechanism to terminate training without labels; and (v) retains a fixed number of leading coefficients in the learned representation matrix based on prior knowledge. We evaluate the proposed method on six datasets representing faces, digits, and objects. The results show that our method outperforms most linear SC algorithms with careffulyl tuned hyperparameters while maintaining competitive performance with the best performing linear appoaches.

We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods with a provable improvement of the condition number, cutting the gaps between highest eigenvalues, without explicit knowledge of the actual spectrum. We give a stochastic interpretation of this preconditioning in terms of coordinate volume sampling and compare it with other classical approaches, including the Chebyshev polynomials. We show how to incorporate a polynomial preconditioning into the Gradient and Fast Gradient Methods and establish the corresponding global complexity bounds. Finally, we propose a simple adaptive search procedure that automatically chooses the best possible polynomial preconditioning for the Gradient Method, minimizing the objective along a low-dimensional Krylov subspace. Numerical experiments confirm the efficiency of our preconditioning strategies for solving various machine learning problems.

The success of Hyper-Connections (HC) in neural networks (NN) has also highlighted issues related to its training instability and restricted scalability. The Manifold-Constrained Hyper-Connections (mHC) mitigate these challenges by projecting the residual connection space onto a Birkhoff polytope, however, it faces two issues: 1) its iterative Sinkhorn-Knopp (SK) algorithm does not always yield exact doubly stochastic residual matrices; 2) mHC incurs a prohibitive O(n^3C) parameter complexity with n as the width of the residual stream and C as the feature dimension. The recently proposed mHC-lite reparametrizes the residual matrix via the Birkhoff-von-Neumann theorem to guarantee double stochasticity, but also faces a factorial explosion in its parameter complexity, O left( nC cdot n! right). To address both challenges, we propose KromHC, which uses the Kronecker products of smaller doubly stochastic matrices to parametrize the residual matrix in mHC. By enforcing manifold constraints across the factor residual matrices along each mode of the tensorized residual stream, KromHC guarantees exact double stochasticity of the residual matrices while reducing parameter complexity to O(n^2C). Comprehensive experiments demonstrate that KromHC matches or even outperforms state-of-the-art (SOTA) mHC variants, while requiring significantly fewer trainable parameters. The code is available at https://github.com/wz1119/KromHC.

Video imaging is often affected by complex degradations such as blur, noise, and compression artifacts. Traditional restoration methods follow a "single-task single-model" paradigm, resulting in poor generalization and high computational cost, limiting their applicability in real-world scenarios with diverse degradation types. We propose UniFlowRestore, a general video restoration framework that models restoration as a time-continuous evolution under a prompt-guided and physics-informed vector field. A physics-aware backbone PhysicsUNet encodes degradation priors as potential energy, while PromptGenerator produces task-relevant prompts as momentum. These components define a Hamiltonian system whose vector field integrates inertial dynamics, decaying physical gradients, and prompt-based guidance. The system is optimized via a fixed-step ODE solver to achieve efficient and unified restoration across tasks. Experiments show that UniFlowRestore delivers stateof-the-art performance with strong generalization and efficiency. Quantitative results demonstrate that UniFlowRestore achieves state-of-the-art performance, attaining the highest PSNR (33.89 dB) and SSIM (0.97) on the video denoising task, while maintaining top or second-best scores across all evaluated tasks.

Reinforcement Learning with Verifiable Rewards (RLVR) is increasingly viewed as a tree pruning mechanism. However, we identify a systemic pathology termed Recursive Space Contraction (RSC), an irreversible collapse driven by the combined dynamics of positive sharpening and negative squeezing, where the sampling probability of valid alternatives vanishes. While Kullback-Leibler (KL) regularization aims to mitigate this, it imposes a rigid Shape Matching constraint that forces the policy to mimic the reference model's full density, creating a gradient conflict with the sharpening required for correctness. We propose Anchored Policy Optimization (APO), shifting the paradigm from global Shape Matching to Support Coverage. By defining a Safe Manifold based on the reference model's high-confidence support, APO permits aggressive sharpening for efficiency while selectively invoking a restorative force during error correction to prevent collapse. We theoretically derive that APO serves as a gradient-aligned mechanism to maximize support coverage, enabling an Elastic Recovery that re-inflates valid branches. Empirical evaluations on mathematical benchmarks demonstrate that APO breaks the accuracy-diversity trade-off, significantly improving Pass@1 while restoring the Pass@K diversity typically lost by standard policy gradient methods.

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix {sf A} and a positive semi-definite matrix Win R^{ntimes n} with a sparse eigenbasis, we consider the task of maintaining the projection in the form of {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}, where {sf B}={sf A}(Wotimes I) or {sf B}={sf A}(W^{1/2}otimes W^{1/2}). At each iteration, the weight matrix W receives a low rank change and we receive a new vector h. The goal is to maintain the projection matrix and answer the query {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}h with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

While feed-forward Gaussian splatting models offer computational efficiency and can generalize to sparse input settings, their performance is fundamentally constrained by relying on a single forward pass for inference. We propose ReSplat, a feed-forward recurrent Gaussian splatting model that iteratively refines 3D Gaussians without explicitly computing gradients. Our key insight is that the Gaussian splatting rendering error serves as a rich feedback signal, guiding the recurrent network to learn effective Gaussian updates. This feedback signal naturally adapts to unseen data distributions at test time, enabling robust generalization across datasets, view counts and image resolutions. To initialize the recurrent process, we introduce a compact reconstruction model that operates in a 16 times subsampled space, producing 16 times fewer Gaussians than previous per-pixel Gaussian models. This substantially reduces computational overhead and allows for efficient Gaussian updates. Extensive experiments across varying of input views (2, 8, 16, 32), resolutions (256 times 256 to 540 times 960), and datasets (DL3DV, RealEstate10K and ACID) demonstrate that our method achieves state-of-the-art performance while significantly reducing the number of Gaussians and improving the rendering speed. Our project page is at https://haofeixu.github.io/resplat/.

Training large language models (LLMs) is often bottlenecked by extreme memory demands, with optimizer states dominating the footprint. Recent works mitigates this cost by projecting gradients into low-dimensional subspaces using sophisticated update strategies. In this paper, we analyze the dynamics of gradient space and its underlying subspaces. We find that while a small subspace captures most gradient energy, a significant portion still resides in the residual bulk; moreover, the influence of the core subspace diminishes over time and in deeper layers. We also observe that the gradient space exhibits near-flat curvature, calling for algorithms that explicitly account for this geometry. Motivated by these insights, we introduce a suite of randomized algorithms, GrassWalk and GrassJump, which exploit subspace and achieve state-of-the-art memory savings while improving performance on LLaMA-1B and LLaMA-7B pretraining.

Model customization necessitates high-quality and diverse datasets, but acquiring such data remains time-consuming and labor-intensive. Despite the great potential of large language models (LLMs) for data synthesis, current approaches are constrained by limited seed data, model biases, and low-variation prompts, resulting in limited diversity and biased distributions with the increase of data scales. To tackle this challenge, we introduce TREESYNTH, a tree-guided subspace-based data synthesis approach inspired by decision trees. It constructs a spatial partitioning tree to recursively divide a task-specific full data space (i.e., root node) into numerous atomic subspaces (i.e., leaf nodes) with mutually exclusive and exhaustive attributes to ensure both distinctiveness and comprehensiveness before synthesizing samples within each atomic subspace. This globally dividing-and-synthesizing method finally collects subspace samples into a comprehensive dataset, effectively circumventing repetition and space collapse to ensure the diversity of large-scale data synthesis. Furthermore, the spatial partitioning tree enables sample allocation into atomic subspaces, allowing the rebalancing of existing datasets for more balanced and comprehensive distributions. Empirically, extensive experiments across diverse benchmarks consistently demonstrate the superior data diversity, model performance, and robust scalability of TREESYNTH compared to both human-crafted datasets and peer data synthesis methods, with an average performance gain reaching 10%. Besides, the consistent improvements of TREESYNTH-balanced datasets highlight its efficacious application to redistribute existing datasets for more comprehensive coverage and the induced performance enhancement. The code is available at https://github.com/cpa2001/TreeSynth.

Automated waste recycling aims to efficiently separate the recyclable objects from the waste by employing vision-based systems. However, the presence of varying shaped objects having different material types makes it a challenging problem, especially in cluttered environments. Existing segmentation methods perform reasonably on many semantic segmentation datasets by employing multi-contextual representations, however, their performance is degraded when utilized for waste object segmentation in cluttered scenarios. In addition, plastic objects further increase the complexity of the problem due to their translucent nature. To address these limitations, we introduce an efficacious segmentation network, named COSNet, that uses boundary cues along with multi-contextual information to accurately segment the objects in cluttered scenes. COSNet introduces novel components including feature sharpening block (FSB) and boundary enhancement module (BEM) for enhancing the features and highlighting the boundary information of irregular waste objects in cluttered environment. Extensive experiments on three challenging datasets including ZeroWaste-f, SpectralWaste, and ADE20K demonstrate the effectiveness of the proposed method. Our COSNet achieves a significant gain of 1.8% on ZeroWaste-f and 2.1% on SpectralWaste datasets respectively in terms of mIoU metric.

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.

We generalize the class vectors found in neural networks to linear subspaces (i.e.~points in the Grassmann manifold) and show that the Grassmann Class Representation (GCR) enables the simultaneous improvement in accuracy and feature transferability. In GCR, each class is a subspace and the logit is defined as the norm of the projection of a feature onto the class subspace. We integrate Riemannian SGD into deep learning frameworks such that class subspaces in a Grassmannian are jointly optimized with the rest model parameters. Compared to the vector form, the representative capability of subspaces is more powerful. We show that on ImageNet-1K, the top-1 error of ResNet50-D, ResNeXt50, Swin-T and Deit3-S are reduced by 5.6%, 4.5%, 3.0% and 3.5%, respectively. Subspaces also provide freedom for features to vary and we observed that the intra-class feature variability grows when the subspace dimension increases. Consequently, we found the quality of GCR features is better for downstream tasks. For ResNet50-D, the average linear transfer accuracy across 6 datasets improves from 77.98% to 79.70% compared to the strong baseline of vanilla softmax. For Swin-T, it improves from 81.5% to 83.4% and for Deit3, it improves from 73.8% to 81.4%. With these encouraging results, we believe that more applications could benefit from the Grassmann class representation. Code is released at https://github.com/innerlee/GCR.

Model order reduction has been extensively studied over the last two decades. Projection-based methods such as the Proper Orthogonal Decomposition and the Reduced Basis Method enjoy the important advantages of Galerkin methods in the derivation of the reduced problem, but are limited to linear data compression for which the reduced solution is sought as a linear combination of spatial modes. Nonlinear data compression must be used when the solution manifold is not embedded in a low-dimensional subspace. Early methods involve piecewise linear data compression, by constructing a dictionary of reduced-order models tailored to a partition of the solution manifold. In this work, we introduce the concept of optimal partition of the solution manifold in terms of normalized Kolmogorov widths, and prove that the optimal partitions can be found by means of a representative-based clustering algorithm using the sine dissimilarity measure on the solution manifold.

Training modern neural networks on large datasets is computationally and environmentally costly. We introduce GRAFT, a scalable in-training subset selection method that (i) extracts a low-rank feature representation for each batch, (ii) applies a Fast MaxVol sampler to select a small, diverse subset that spans the batch's dominant subspace, and (iii) dynamically adjusts the subset size using a gradient-approximation criterion. By operating in low-rank subspaces and training on carefully chosen examples instead of full batches, GRAFT preserves the training trajectory while reducing wall-clock time, energy consumption, and CO_2 emissions. Across multiple benchmarks, GRAFT matches or exceeds recent selection baselines in both accuracy and efficiency, providing a favorable trade-off between accuracy, efficiency, and emissions.

Whether attention key value (KV) states computed for one prompt for a small LLM can be reused to accelerate inference on a new similar prompt, giving an increase to the space to its context memory using an approach called token recycling. Using a standard Hugging Face setup with DialoGPT-medium (a 345M parameter GPT-2 style decoder trained on 147M Reddit exchanges, 2005 to 2017) as the testbed, we build a cache of past activations and get entries by sentence embeddings, then reuse cached past key values when the cached prompt is an exact prefix of the new input. We compare recycled vs. baseline runs on latency and output fidelity, and log reuse depth in tokens. Reproducibility requires no model modifications, cached KVs are serialized to the CPU, reloaded, and supplied to the generate function to continue decoding from the cached prefix. In tests, we observe consistent speedups when prefix overlap exists, with no material degradation in output semantics, and when overlap is absent, behavior matches baseline.

The residual stream mediates communication between transformer decoder layers via linear reads and writes of non-linear computations. While sparse-dictionary learning-based methods locate features in the residual stream, and activation patching methods discover circuits within the model, the mechanism by which features flow through the residual stream remains understudied. Understanding this dynamic can better inform jailbreaking protections, enable early detection of model mistakes, and their correction. In this work, we propose Activation Transport Operators (ATO), linear maps from upstream to downstream residuals k layers later, evaluated in feature space using downstream SAE decoder projections. We empirically demonstrate that these operators can determine whether a feature has been linearly transported from a previous layer or synthesised from non-linear layer computation. We develop the notion of transport efficiency, for which we provide an upper bound, and use it to estimate the size of the residual stream subspace that corresponds to linear transport. We empirically demonstrate the linear transport, report transport efficiency and the size of the residual stream's subspace involved in linear transport. This compute-light (no finetuning, <50 GPU-h) method offers practical tools for safety, debugging, and a clearer picture of where computation in LLMs behaves linearly.

Model merging aims to cheaply combine individual task-specific models into a single multitask model. In this work, we view past merging methods as leveraging different notions of a ''task subspace'' in which models are matched before being merged. We connect the task subspace of a given model to its loss landscape and formalize how this approach to model merging can be seen as solving a linear system of equations. While past work has generally been limited to linear systems that have a closed-form solution, we consider using the conjugate gradient method to find a solution. We show that using the conjugate gradient method can outperform closed-form solutions, enables merging via linear systems that are otherwise intractable to solve, and flexibly allows choosing from a wide variety of initializations and estimates for the ''task subspace''. We ultimately demonstrate that our merging framework called ''Matching Models in their Task Subspace'' (MaTS) achieves state-of-the-art results in multitask and intermediate-task model merging. We release all of the code and checkpoints used in our work at https://github.com/r-three/mats.

Mixture of Experts (MoE) models scale capacity but often suffer from representation collapse and gradient instability. We propose Dynamic Subspace Composition (DSC), a framework that approximates context-dependent weights via a state-dependent, sparse expansion of a shared basis bank. Formally, DSC models the weight update as a residual trajectory within a Star- Shaped Domain, employing a Magnitude-Gated Simplex Interpolation to ensure continuity at the identity. Unlike standard Mixture-of-LoRAs, which incurs O(M rd) parameter complexity by retrieving independent rank-r matrices, DSC constructs a compositional rank-K approximation from decoupled unit-norm basis vectors. This reduces parameter complexity to O(M d) and memory traffic to O(Kd), while Frame-Theoretic regularization and spectral constraints provide rigorous worst-case bounds on the dynamic update. The code is available at https://github. com/VladimerKhasia/DSC

The learnable, linear neural network layers between tensor power spaces of R^{n} that are equivariant to the orthogonal group, O(n), the special orthogonal group, SO(n), and the symplectic group, Sp(n), were characterised in arXiv:2212.08630. We present an algorithm for multiplying a vector by any weight matrix for each of these groups, using category theoretic constructions to implement the procedure. We achieve a significant reduction in computational cost compared with a naive implementation by making use of Kronecker product matrices to perform the multiplication. We show that our approach extends to the symmetric group, S_n, recovering the algorithm of arXiv:2303.06208 in the process.

Model merging aims to integrate multiple task-adapted models into a unified model that preserves the knowledge of each task. In this paper, we identify that the key to this knowledge retention lies in maintaining the directional consistency of singular spaces between merged multi-task vector and individual task vectors. However, this consistency is frequently compromised by two issues: i) an imbalanced energy distribution within task vectors, where a small fraction of singular values dominate the total energy, leading to the neglect of semantically important but weaker components upon merging, and ii) the geometric inconsistency of task vectors in parameter space, which causes direct merging to distort their underlying directional geometry. To address these challenges, we propose DC-Merge, a method for directional-consistent model merging. It first balances the energy distribution of each task vector by smoothing its singular values, ensuring all knowledge components are adequately represented. These energy-balanced vectors are then projected onto a shared orthogonal subspace to align their directional geometries with minimal reconstruction error. Finally, the aligned vectors are aggregated in the shared orthogonal subspace and projected back to the original parameter space. Extensive experiments on vision and vision-language benchmarks show that DC-Merge consistently achieves state-of-the-art performance in both full fine-tuning and LoRA settings. The implementation code is available at https://github.com/Tobeginwith/DC-Merge.

The exploration of linear subspaces, particularly scattered subspaces, has garnered considerable attention across diverse mathematical disciplines in recent years, notably within finite geometries and coding theory. Scattered subspaces play a pivotal role in analyzing various geometric structures such as blocking sets, two-intersection sets, complete arcs, caps in affine and projective spaces over finite fields and rank metric codes. This paper introduces a new infinite family of h-subspaces, along with their associated MRD codes. Additionally, it addresses the task of determining the generalized weights of these codes. Notably, we demonstrate that these MRD codes exhibit some larger generalized weights compared to those previously identified.

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the reverse generation process, without modifying the original denoising diffusion process. However, since the degraded images already include low-frequency information, starting from Gaussian white noise will result in increased sampling steps. We propose Resfusion, a general framework that incorporates the residual term into the diffusion forward process, starting the reverse process directly from the noisy degraded images. The form of our inference process is consistent with the DDPM. We introduced a weighted residual noise, named resnoise, as the prediction target and explicitly provide the quantitative relationship between the residual term and the noise term in resnoise. By leveraging a smooth equivalence transformation, Resfusion determine the optimal acceleration step and maintains the integrity of existing noise schedules, unifying the training and inference processes. The experimental results demonstrate that Resfusion exhibits competitive performance on ISTD dataset, LOL dataset and Raindrop dataset with only five sampling steps. Furthermore, Resfusion can be easily applied to image generation and emerges with strong versatility. Our code and model are available at https://github.com/nkicsl/Resfusion.

Orbit recovery problems are a class of problems that often arise in practice and various forms. In these problems, we aim to estimate an unknown function after being distorted by a group action and observed via a known operator. Typically, the observations are contaminated with a non-trivial level of noise. Two particular orbit recovery problems of interest in this paper are multireference alignment and single-particle cryo-EM modelling. In order to suppress the noise, we suggest using the method of moments approach for both problems while introducing deep neural network priors. In particular, our neural networks should output the signals and the distribution of group elements, with moments being the input. In the multireference alignment case, we demonstrate the advantage of using the NN to accelerate the convergence for the reconstruction of signals from the moments. Finally, we use our method to reconstruct simulated and biological volumes in the cryo-EM setting.

The increase in non-biodegradable waste is a worldwide concern. Recycling facilities play a crucial role, but their automation is hindered by the complex characteristics of waste recycling lines like clutter or object deformation. In addition, the lack of publicly available labeled data for these environments makes developing robust perception systems challenging. Our work explores the benefits of multimodal perception for object segmentation in real waste management scenarios. First, we present SpectralWaste, the first dataset collected from an operational plastic waste sorting facility that provides synchronized hyperspectral and conventional RGB images. This dataset contains labels for several categories of objects that commonly appear in sorting plants and need to be detected and separated from the main trash flow for several reasons, such as security in the management line or reuse. Additionally, we propose a pipeline employing different object segmentation architectures and evaluate the alternatives on our dataset, conducting an extensive analysis for both multimodal and unimodal alternatives. Our evaluation pays special attention to efficiency and suitability for real-time processing and demonstrates how HSI can bring a boost to RGB-only perception in these realistic industrial settings without much computational overhead.

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

Mixture-of-Experts (MoE) architectures achieve parameter efficiency through conditional computation, yet contemporary designs suffer from two fundamental limitations: structural parameter isolation that causes catastrophic forgetting, and instruction-overfitting that degrades performance in instruction-free scenarios. We propose CDSP-MoE (Conflict-Driven Subspace Pruning MoE), a framework that addresses these issues through a paradigm shift from isolated expert containers to dynamic expert instantiation within a shared physical subspace. Grounded in the Universal Weight Subspace Hypothesis, CDSP-MoE maintains a super-complete parameter backbone where logical experts are carved out via learnable topology masks. Unlike prior work that uses gradient conflict for token reassignment or optimization surgery, we leverage it as a structural supervisory signal: a Lagged Gradient Game penalizes interfering connections in the shared manifold, enabling the topology to spontaneously prune conflicting pathways and evolve interpretable modular structures. Experimental results demonstrate that CDSP-MoE achieves robust content-driven routing without human-defined task labels, maintaining semantic specialization even under strict blind inference protocols where explicit instructions are absent. Code is available at: https://github.com/konodiodaaaaa1/Conflict-Driven-Subspace-Pruning-Mixture-of-Experts

Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems involve non-Euclidean distributions, such as hyperspherical manifolds, where class-specific patterns are governed by angular geometry within hypercones. When modeled in Euclidean space, these angular subtleties are lost, leading to suboptimal generative performance. To address this limitation, we introduce HyperSphereDiff to align hyperspherical structures with directional noise, preserving class geometry and effectively capturing angular uncertainty. We demonstrate both theoretically and empirically that this approach aligns the generative process with the intrinsic geometry of hyperspherical data, resulting in more accurate and geometry-aware generative models. We evaluate our framework on four object datasets and two face datasets, showing that incorporating angular uncertainty better preserves the underlying hyperspherical manifold. Resources are available at: {https://github.com/IAB-IITJ/Harmonizing-Geometry-and-Uncertainty-Diffusion-with-Hyperspheres/}

Kolmogorov-Arnold Networks (KANs) replace scalar weights with per-edge vectors of basis coefficients, thereby boosting expressivity and accuracy but at the same time resulting in a multiplicative increase in parameters and memory. We propose MetaCluster, a framework that makes KANs highly compressible without sacrificing accuracy. Specifically, a lightweight meta-learner, trained jointly with the KAN, is used to map low-dimensional embedding to coefficient vectors, shaping them to lie on a low-dimensional manifold that is amenable to clustering. We then run K-means in coefficient space and replace per-edge vectors with shared centroids. Afterwards, the meta-learner can be discarded, and a brief fine-tuning of the centroid codebook recovers any residual accuracy loss. The resulting model stores only a small codebook and per-edge indices, exploiting the vector nature of KAN parameters to amortize storage across multiple coefficients. On MNIST, CIFAR-10, and CIFAR-100, across standard KANs and ConvKANs using multiple basis functions, MetaCluster achieves a reduction of up to 80times in parameter storage, with no loss in accuracy. Code will be released upon publication.

We show that deep neural networks trained across diverse tasks exhibit remarkably similar low-dimensional parametric subspaces. We provide the first large-scale empirical evidence that demonstrates that neural networks systematically converge to shared spectral subspaces regardless of initialization, task, or domain. Through mode-wise spectral analysis of over 1100 models - including 500 Mistral-7B LoRAs, 500 Vision Transformers, and 50 LLaMA-8B models - we identify universal subspaces capturing majority variance in just a few principal directions. By applying spectral decomposition techniques to the weight matrices of various architectures trained on a wide range of tasks and datasets, we identify sparse, joint subspaces that are consistently exploited, within shared architectures across diverse tasks and datasets. Our findings offer new insights into the intrinsic organization of information within deep networks and raise important questions about the possibility of discovering these universal subspaces without the need for extensive data and computational resources. Furthermore, this inherent structure has significant implications for model reusability, multi-task learning, model merging, and the development of training and inference-efficient algorithms, potentially reducing the carbon footprint of large-scale neural models.

While 3D Gaussian Splatting has recently become popular for neural rendering, current methods rely on carefully engineered cloning and splitting strategies for placing Gaussians, which can lead to poor-quality renderings, and reliance on a good initialization. In this work, we rethink the set of 3D Gaussians as a random sample drawn from an underlying probability distribution describing the physical representation of the scene-in other words, Markov Chain Monte Carlo (MCMC) samples. Under this view, we show that the 3D Gaussian updates can be converted as Stochastic Gradient Langevin Dynamics (SGLD) updates by simply introducing noise. We then rewrite the densification and pruning strategies in 3D Gaussian Splatting as simply a deterministic state transition of MCMC samples, removing these heuristics from the framework. To do so, we revise the 'cloning' of Gaussians into a relocalization scheme that approximately preserves sample probability. To encourage efficient use of Gaussians, we introduce a regularizer that promotes the removal of unused Gaussians. On various standard evaluation scenes, we show that our method provides improved rendering quality, easy control over the number of Gaussians, and robustness to initialization.

3D reconstruction methods such as Neural Radiance Fields (NeRFs) excel at rendering photorealistic novel views of complex scenes. However, recovering a high-quality NeRF typically requires tens to hundreds of input images, resulting in a time-consuming capture process. We present ReconFusion to reconstruct real-world scenes using only a few photos. Our approach leverages a diffusion prior for novel view synthesis, trained on synthetic and multiview datasets, which regularizes a NeRF-based 3D reconstruction pipeline at novel camera poses beyond those captured by the set of input images. Our method synthesizes realistic geometry and texture in underconstrained regions while preserving the appearance of observed regions. We perform an extensive evaluation across various real-world datasets, including forward-facing and 360-degree scenes, demonstrating significant performance improvements over previous few-view NeRF reconstruction approaches.

Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics. This creates three practical limitations. First, linear averaging, task vectors, and related rules operate on Euclidean coordinates, even though the desired goal is to merge functionality, i.e., predictive behaviors across tasks. Second, when the source checkpoints are farther apart or more heterogeneous, Euclidean blends often trigger representation collapse, manifested as activation variance shrinkage and effective-rank degradation, which sharply degrades accuracy. Third, many geometry-inspired methods are most natural for two-model interpolation and do not extend cleanly to merging N>2 experts with a principled objective. We address these issues by formulating model merging as computing a weighted Karcher mean on the Fisher--Rao manifold, which is locally equivalent to minimizing a KL-based function distance between predictive distributions. We derive a practical fixed-point algorithm using a lightweight spherical proxy that preserves norms and generalizes directly to multi-expert merging. Across various benchmarks and collapse diagnostics, our method remains stable as the number and heterogeneity of merged models increase, consistently outperforming prior baselines.

Large-scale text-to-image diffusion models excel in generating high-quality images from textual inputs, yet concerns arise as research indicates their tendency to memorize and replicate training data, raising We also addressed the issue of memorization in diffusion models, where models tend to replicate exact training samples raising copyright infringement and privacy issues. Efforts within the text-to-image community to address memorization explore causes such as data duplication, replicated captions, or trigger tokens, proposing per-prompt inference-time or training-time mitigation strategies. In this paper, we focus on the feed-forward layers and begin by contrasting neuron activations of a set of memorized and non-memorized prompts. Experiments reveal a surprising finding: many different sets of memorized prompts significantly activate a common subspace in the model, demonstrating, for the first time, that memorization in the diffusion models lies in a special subspace. Subsequently, we introduce a novel post-hoc method for editing pre-trained models, whereby memorization is mitigated through the straightforward pruning of weights in specialized subspaces, avoiding the need to disrupt the training or inference process as seen in prior research. Finally, we demonstrate the robustness of the pruned model against training data extraction attacks, thereby unveiling new avenues for a practical and one-for-all solution to memorization.

By interpreting the product of the Principal Component Analysis, that is the covariance matrix, as a sequence of nested subspaces naturally coming with weights according to the level of approximation they provide, we are able to embed all d--dimensional Grassmannians into a stratified space of covariance matrices. We observe that Grassmannians constitute the lowest dimensional skeleton of the stratification while it is possible to define a Riemaniann metric on the highest dimensional and dense stratum, such a metric being compatible with the global stratification. With such a Riemaniann metric at hand, it is possible to look for geodesics between two linear subspaces of different dimensions that do not go through higher dimensional linear subspaces as would euclidean geodesics. Building upon the proposed embedding of Grassmannians into the stratified space of covariance matrices, we generalize the concept of varifolds to what we call flagfolds in order to model multi-dimensional shapes.

Addressing the critical theme of recycling electronic waste (E-waste), this contribution is dedicated to developing advanced automated data processing pipelines as a basis for decision-making and process control. Aligning with the broader goals of the circular economy and the United Nations (UN) Sustainable Development Goals (SDG), our work leverages non-invasive analysis methods utilizing RGB and hyperspectral imaging data to provide both quantitative and qualitative insights into the E-waste stream composition for optimizing recycling efficiency. In this paper, we introduce 'PCB-Vision'; a pioneering RGB-hyperspectral printed circuit board (PCB) benchmark dataset, comprising 53 RGB images of high spatial resolution paired with their corresponding high spectral resolution hyperspectral data cubes in the visible and near-infrared (VNIR) range. Grounded in open science principles, our dataset provides a comprehensive resource for researchers through high-quality ground truths, focusing on three primary PCB components: integrated circuits (IC), capacitors, and connectors. We provide extensive statistical investigations on the proposed dataset together with the performance of several state-of-the-art (SOTA) models, including U-Net, Attention U-Net, Residual U-Net, LinkNet, and DeepLabv3+. By openly sharing this multi-scene benchmark dataset along with the baseline codes, we hope to foster transparent, traceable, and comparable developments of advanced data processing across various scientific communities, including, but not limited to, computer vision and remote sensing. Emphasizing our commitment to supporting a collaborative and inclusive scientific community, all materials, including code, data, ground truth, and masks, will be accessible at https://github.com/hifexplo/PCBVision.

We introduce the Subspace Power Method (SPM) for calculating the CP decomposition of low-rank real symmetric tensors. This algorithm calculates one new CP component at a time, alternating between applying the shifted symmetric higher-order power method (SS-HOPM) to a certain modified tensor, constructed from a matrix flattening of the original tensor; and using appropriate deflation steps. We obtain rigorous guarantees for SPM regarding convergence and global optima for input tensors of dimension d and order m of CP rank up to O(d^{lfloor m/2rfloor}), via results in classical algebraic geometry and optimization theory. As a by-product of our analysis we prove that SS-HOPM converges unconditionally, settling a conjecture in [Kolda, T.G., Mayo, J.R.: Shifted power method for computing tensor eigenpairs. SIAM Journal on Matrix Analysis and Applications 32(4), 1095-1124 (2011)]. We present numerical experiments which demonstrate that SPM is efficient and robust to noise, being up to one order of magnitude faster than state-of-the-art CP decomposition algorithms in certain experiments. Furthermore, prior knowledge of the CP rank is not required by SPM.

Model merging aims to combine multiple fine-tuned models into a single set of weights that performs well across all source tasks. While prior work has shown that merging can approximate the performance of individual fine-tuned models for each task, it largely overlooks scenarios where models are compressed into low-rank representations, either through low-rank adaptation (LoRA) or post-training singular value decomposition (SVD). We first demonstrate that applying conventional merging methods to low-rank weights leads to severe performance degradation in the merged model. Motivated by this phenomenon, we propose a fundamentally different approach: instead of collapsing all adapters into one set of weights, we construct a compact basis (e.g., an equivalent of holding two or more models) from which original task-specific models can be recovered via linear combination. This reframes merging as generating a reconstruction-capable model space rather than producing a single merged model. Crucially, this allows us to ``revert'' to each individual model when needed, recognizing that no merged model can consistently outperform one specialized for its task. Building on this insight, we introduce our method, Reversible Model Merging (RMM), an efficient, data-free, and flexible method that provides a closed-form solution for selecting the optimal basis of model weights and task-specific coefficients for linear combination. Extensive experiments across diverse datasets and model scales demonstrate that RMM consistently outperforms existing merging approaches, preserving the performance of low-rank compressed models by a significant margin.

In recent years, diffusion models have become the most popular and powerful methods in the field of image synthesis, even rivaling human artists in artistic creativity. However, the key issue currently limiting the application of diffusion models is its extremely slow generation process. Although several methods were proposed to speed up the generation process, there still exists a trade-off between efficiency and quality. In this paper, we first provide a detailed theoretical and empirical analysis of the generation process of the diffusion models based on schedulers. We transform the designing problem of schedulers into the determination of several parameters, and further transform the accelerated generation process into an expansion process of the linear subspace. Based on these analyses, we consequently propose a novel method called Optimal Linear Subspace Search (OLSS), which accelerates the generation process by searching for the optimal approximation process of the complete generation process in the linear subspaces spanned by latent variables. OLSS is able to generate high-quality images with a very small number of steps. To demonstrate the effectiveness of our method, we conduct extensive comparative experiments on open-source diffusion models. Experimental results show that with a given number of steps, OLSS can significantly improve the quality of generated images. Using an NVIDIA A100 GPU, we make it possible to generate a high-quality image by Stable Diffusion within only one second without other optimization techniques.

Online novel view synthesis remains challenging, requiring robust scene reconstruction from sequential, often unposed, observations. We present ReCoSplat, an autoregressive feed-forward Gaussian Splatting model supporting posed or unposed inputs, with or without camera intrinsics. While assembling local Gaussians using camera poses scales better than canonical-space prediction, it creates a dilemma during training: using ground-truth poses ensures stability but causes a distribution mismatch when predicted poses are used at inference. To address this, we introduce a Render-and-Compare (ReCo) module. ReCo renders the current reconstruction from the predicted viewpoint and compares it with the incoming observation, providing a stable conditioning signal that compensates for pose errors. To support long sequences, we propose a hybrid KV cache compression strategy combining early-layer truncation with chunk-level selective retention, reducing the KV cache size by over 90% for 100+ frames. ReCoSplat achieves state-of-the-art performance across different input settings on both in- and out-of-distribution benchmarks. Code and pretrained models will be released. Our project page is at https://freemancheng.com/ReCoSplat .

Model pruning is an effective approach for compressing large language models. However, this process often leads to significant degradation of model capabilities. While post-training techniques such as instruction tuning are commonly employed to recover model performance, existing methods often overlook the uneven deterioration of model capabilities and incur high computational costs. Moreover, some instruction data irrelevant to model capability recovery may introduce negative effects. To address these challenges, we propose the Post-training dAta Selection method for Efficient pruned large language model Recovery (PASER). PASER aims to identify instructions where model capabilities are most severely compromised within a certain recovery data budget. Our approach first applies manifold learning and spectral clustering to group recovery data in the semantic space, revealing capability-specific instruction sets. We then adaptively allocate the data budget to different clusters based on the degrees of model capability degradation. In each cluster, we prioritize data samples where model performance has declined dramatically. To mitigate potential negative transfer, we also detect and filter out conflicting or irrelevant recovery data. Extensive experiments demonstrate that PASER significantly outperforms conventional baselines, effectively recovering the general capabilities of pruned LLMs while utilizing merely 4\%-20\% of the original post-training data.

Modern neural models trained on textual data rely on pre-trained representations that emerge without direct supervision. As these representations are increasingly being used in real-world applications, the inability to control their content becomes an increasingly important problem. We formulate the problem of identifying and erasing a linear subspace that corresponds to a given concept, in order to prevent linear predictors from recovering the concept. We model this problem as a constrained, linear maximin game, and show that existing solutions are generally not optimal for this task. We derive a closed-form solution for certain objectives, and propose a convex relaxation, \method, that works well for others. When evaluated in the context of binary gender removal, the method recovers a low-dimensional subspace whose removal mitigates bias by intrinsic and extrinsic evaluation. We show that the method is highly expressive, effectively mitigating bias in deep nonlinear classifiers while maintaining tractability and interpretability.

In person re-identification (re-ID) task, it is still challenging to learn discriminative representation by deep learning, due to limited data. Generally speaking, the model will get better performance when increasing the amount of data. The addition of similar classes strengthens the ability of the classifier to identify similar identities, thereby improving the discrimination of representation. In this paper, we propose a Diverse and Compact Transformer (DC-Former) that can achieve a similar effect by splitting embedding space into multiple diverse and compact subspaces. Compact embedding subspace helps model learn more robust and discriminative embedding to identify similar classes. And the fusion of these diverse embeddings containing more fine-grained information can further improve the effect of re-ID. Specifically, multiple class tokens are used in vision transformer to represent multiple embedding spaces. Then, a self-diverse constraint (SDC) is applied to these spaces to push them away from each other, which makes each embedding space diverse and compact. Further, a dynamic weight controller(DWC) is further designed for balancing the relative importance among them during training. The experimental results of our method are promising, which surpass previous state-of-the-art methods on several commonly used person re-ID benchmarks.

We present Franca (pronounced Fran-ka): free one; the first fully open-source (data, code, weights) vision foundation model that matches and in many cases surpasses the performance of state-of-the-art proprietary models, e.g., DINOv2, CLIP, SigLIPv2, etc. Our approach is grounded in a transparent training pipeline inspired by Web-SSL and uses publicly available data: ImageNet-21K and a subset of ReLAION-2B. Beyond model release, we tackle critical limitations in SSL clustering methods. While modern models rely on assigning image features to large codebooks via clustering algorithms like Sinkhorn-Knopp, they fail to account for the inherent ambiguity in clustering semantics. To address this, we introduce a parameter-efficient, multi-head clustering projector based on nested Matryoshka representations. This design progressively refines features into increasingly fine-grained clusters without increasing the model size, enabling both performance and memory efficiency. Additionally, we propose a novel positional disentanglement strategy that explicitly removes positional biases from dense representations, thereby improving the encoding of semantic content. This leads to consistent gains on several downstream benchmarks, demonstrating the utility of cleaner feature spaces. Our contributions establish a new standard for transparent, high-performance vision models and open a path toward more reproducible and generalizable foundation models for the broader AI community. The code and model checkpoints are available at https://github.com/valeoai/Franca.

Despite their immense success, deep convolutional neural networks (CNNs) can be difficult to optimize and costly to train due to hundreds of layers within the network depth. Conventional convolutional operations are fundamentally limited by their linear nature along with fixed activations, where many layers are needed to learn meaningful patterns in data. Because of the sheer size of these networks, this approach is simply computationally inefficient, and poses overfitting or gradient explosion risks, especially in small datasets. As a result, we introduce a "plug-in" module, called Residual Kolmogorov-Arnold Network (RKAN). Our module is highly compact, so it can be easily added into any stage (level) of traditional deep networks, where it learns to integrate supportive polynomial feature transformations to existing convolutional frameworks. RKAN offers consistent improvements over baseline models in different vision tasks and widely tested benchmarks, accomplishing cutting-edge performance on them.

Driven by the rapid growth of model parameters, parameter-efficient fine-tuning (PEFT) has become essential for adapting large models to diverse downstream tasks under constrained computational resources. Within this paradigm, orthogonal fine-tuning and its variants preserve semantic representations of pre-trained models, but struggle to achieve both expressiveness and efficiency in terms of parameter counts, memory, and computation. To overcome this limitation, we propose efficient Orthogonal Fine-Tuning with Principal Subspace adaptation (PSOFT), which confines orthogonal transformations to the principal subspace of pre-trained weights. Specifically, PSOFT constructs this subspace via matrix decomposition to enable compatible transformations with higher effective rank, establishes a theoretical condition that strictly maintains the geometry of this subspace for essential semantic preservation, and introduces efficient tunable vectors that gradually relax orthogonality during training to enhance adaptability. Extensive experiments on 35 NLP and CV tasks across four representative models demonstrate that PSOFT offers a practical and scalable solution to simultaneously achieve semantic preservation, expressiveness, and multi-dimensional efficiency in PEFT. The code is publicly available at https://github.com/fei407/PSOFT.

The growing demand for Embodied AI and VR applications has highlighted the need for synthesizing high-quality 3D indoor scenes from sparse inputs. However, existing approaches struggle to infer massive amounts of missing geometry in large unseen areas while maintaining global consistency, often producing locally plausible but globally inconsistent reconstructions. We present Rein3D, a framework that reconstructs full 360-degree indoor environments by coupling explicit 3D Gaussian Splatting (3DGS) with temporally coherent priors from video diffusion models. Our approach follows a "restore-and-refine" paradigm: we employ a radial exploration strategy to render imperfect panoramic videos along trajectories starting from the origin, effectively uncovering occluded regions from a coarse 3DGS initialization. These sequences are restored by a panoramic video-to-video diffusion model and further enhanced via video super-resolution to synthesize high-fidelity geometry and textures. Finally, these refined videos serve as pseudo-ground truths to update the global 3D Gaussian field. To support this task, we construct PanoV2V-15K, a dataset of over 15K paired clean and degraded panoramic videos for diffusion-based scene restoration. Experiments demonstrate that Rein3D produces photorealistic and globally consistent 3D scenes and significantly improves long-range camera exploration compared with existing baselines.

Merging models fine-tuned from a common, extensively pre-trained large model but specialized for different tasks has been demonstrated as a cheap and scalable strategy to construct a multi-task model that performs well across diverse tasks. Recent research, exemplified by task arithmetic, highlights that this multi-task model can be derived through arithmetic operations on task vectors. Nevertheless, current merging techniques frequently resolve potential conflicts among parameters from task-specific models by evaluating individual attributes, such as the parameters' magnitude or sign, overlooking their collective impact on the overall functionality of the model. In this work, we propose the CONtinuous relaxation of disCRETE (Concrete) subspace learning method to identify a common low-dimensional subspace and utilize its shared information to track the interference problem without sacrificing much performance. Specifically, we model the problem as a bi-level optimization problem and introduce a meta-learning framework to find the Concrete subspace mask through gradient-based techniques. At the upper level, we focus on learning a shared Concrete mask to identify the subspace, while at the inner level, model merging is performed to maximize the performance of the merged model. We conduct extensive experiments on both vision domain and language domain, and the results demonstrate the effectiveness of our method. The code is available at https://github.com/tanganke/subspace_fusion

Semidefinite programming is a fundamental problem class in convex optimization, but despite recent advances in solvers, solving large-scale semidefinite programs remains challenging. Generally the matrix functions involved are spectral or unitarily invariant, i.e., they depend only on the eigenvalues or singular values of the matrix. This paper investigates how spectral matrix cones -- cones defined from epigraphs and perspectives of spectral or unitarily invariant functions -- can be used to enhance first-order conic solvers for semidefinite programs. Our main result shows that projecting a matrix can be reduced to projecting its eigenvalues or singular values, which we demonstrate can be done at a negligible cost compared to the eigenvalue or singular value decomposition itself. We have integrated support for spectral matrix cone projections into the Splitting Conic Solver (SCS). Numerical experiments show that SCS with this enhancement can achieve speedups of up to an order of magnitude for solving semidefinite programs arising in experimental design, robust principal component analysis, and graph partitioning.

We present an algorithm for decomposing low rank tensors of any symmetry type, from fully asymmetric to fully symmetric. It generalizes the recent subspace power method from symmetric tensors to all tensors. The algorithm transforms an input tensor into a tensor with orthonormal slices. We show that for tensors with orthonormal slices and low rank, the summands of their decomposition are in one-to-one correspondence with the partially symmetric singular vector tuples (pSVTs) with singular value one. We use this to show correctness of the algorithm. We introduce a shifted power method for computing pSVTs and establish its global convergence. Numerical experiments demonstrate that our decomposition algorithm achieves higher accuracy and faster runtime than existing methods.

Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several fine-tuning techniques have been developed to update the pre-trained model weights in a more resource-efficient manner, such as through low-rank adjustments. Yet, almost all of these methods focus on linear weights, neglecting the intricacies of parameter spaces in higher dimensions like 4D. Alternatively, some methods can be adapted for high-dimensional parameter space by compressing changes in the original space into two dimensions and then employing low-rank matrix decomposition. However, these approaches destructs the structural integrity of the involved high-dimensional spaces. To tackle the diversity of dimensional spaces across different foundation models and provide a more precise representation of the changes within these spaces, this paper introduces a generalized parameter-efficient fine-tuning framework, FLoRA, designed for various dimensional parameter space. Specifically, utilizing Tucker decomposition, FLoRA asserts that changes in each dimensional parameter space are based on a low-rank core space which maintains the consistent topological structure with the original space. It then models the changes through this core space alongside corresponding weights to reconstruct alterations in the original space. FLoRA effectively preserves the structural integrity of the change of original N-dimensional parameter space, meanwhile decomposes it via low-rank tensor decomposition. Extensive experiments on computer vision, natural language processing and multi-modal tasks validate FLoRA's effectiveness. Codes are available at https://github.com/SJTU-DeepVisionLab/FLoRA.

Deep subspace clustering (DSC) networks based on self-expressive model learn representation matrix, often implemented in terms of fully connected network, in the embedded space. After the learning is finished, representation matrix is used by spectral clustering module to assign labels to clusters. However, such approach ignores complementary information that exist in other layers of the encoder (including the input data themselves). Herein, we apply selected linear subspace clustering algorithm to learn representation matrices from representations learned by all layers of encoder network including the input data. Afterward, we learn a multilayer graph that in a multi-view like manner integrates information from graph Laplacians of all used layers. That improves further performance of selected DSC network. Furthermore, we also provide formulation of our approach to cluster out-of-sample/test data points. We validate proposed approach on four well-known datasets with two DSC networks as baseline models. In almost all the cases, proposed approach achieved statistically significant improvement in three performance metrics. MATLAB code of proposed algorithm is posted on https://github.com/lovro-sinda/MLG-DSC.

Most existing Image Restoration (IR) models are task-specific, which can not be generalized to different degradation operators. In this work, we propose the Denoising Diffusion Null-Space Model (DDNM), a novel zero-shot framework for arbitrary linear IR problems, including but not limited to image super-resolution, colorization, inpainting, compressed sensing, and deblurring. DDNM only needs a pre-trained off-the-shelf diffusion model as the generative prior, without any extra training or network modifications. By refining only the null-space contents during the reverse diffusion process, we can yield diverse results satisfying both data consistency and realness. We further propose an enhanced and robust version, dubbed DDNM+, to support noisy restoration and improve restoration quality for hard tasks. Our experiments on several IR tasks reveal that DDNM outperforms other state-of-the-art zero-shot IR methods. We also demonstrate that DDNM+ can solve complex real-world applications, e.g., old photo restoration.

Unlike the predictable scaling laws in natural language processing and computer vision, protein language models (PLMs) scale poorly: for many tasks, models within the same family plateau or even decrease in performance, with mid-sized models often outperforming the largest in the family. We introduce Reverse Distillation, a principled framework that decomposes large PLM representations into orthogonal subspaces guided by smaller models of the same family. The resulting embeddings have a nested, Matryoshka-style structure: the first k dimensions of a larger model's embedding are exactly the representation from the smaller model. This ensures that larger reverse-distilled models consistently outperform smaller ones. A motivating intuition is that smaller models, constrained by capacity, preferentially encode broadly-shared protein features. Reverse distillation isolates these shared features and orthogonally extracts additional contributions from larger models, preventing interference between the two. On ProteinGym benchmarks, reverse-distilled ESM-2 variants outperform their respective baselines at the same embedding dimensionality, with the reverse-distilled 15 billion parameter model achieving the strongest performance. Our framework is generalizable to any model family where scaling challenges persist. Code and trained models are available at https://github.com/rohitsinghlab/plm_reverse_distillation.

Continual learning aims to learn multiple tasks sequentially while preserving prior knowledge, but faces the challenge of catastrophic forgetting when adapting to new tasks. Recently, approaches leveraging pre-trained models have gained increasing popularity in mitigating this issue, due to the strong generalization ability of foundation models. To adjust pre-trained models for new tasks, existing methods usually employ low-rank adaptation, which restricts parameter updates to a fixed low-rank subspace. However, constraining the optimization space inherently compromises the model's learning capacity, resulting in inferior performance. To address this limitation, we propose Continuous Subspace Optimization for Continual Learning (CoSO) to fine-tune the model in a series of subspaces rather than a single one. These sequential subspaces are dynamically determined through the singular value decomposition of the gradients. CoSO updates the model by projecting gradients onto these subspaces, ensuring memory-efficient optimization. To mitigate forgetting, the optimization subspace of each task is constrained to be orthogonal to the historical task subspace. During task learning, CoSO maintains a task-specific component that captures the critical update directions for the current task. Upon completing a task, this component is used to update the historical task subspace, laying the groundwork for subsequent learning. Extensive experiments on multiple datasets demonstrate that CoSO significantly outperforms state-of-the-art methods, especially in challenging scenarios with long task sequences.

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student t mixture or Gaussian mixture. We apply the inverse Fourier transform to obtain the covariance function (by Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. Next, we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability, without low-rank approximations. We show the advantage of our method in systematic experiments. The code is released at https://github.com/xuangu-fang/Gaussian-Process-Slover-for-High-Freq-PDE.

Generative models trained on extensive high-quality datasets effectively capture the structural and statistical properties of clean images, rendering them powerful priors for transforming degraded features into clean ones in image restoration. VAR, a novel image generative paradigm, surpasses diffusion models in generation quality by applying a next-scale prediction approach. It progressively captures both global structures and fine-grained details through the autoregressive process, consistent with the multi-scale restoration principle widely acknowledged in the restoration community. Furthermore, we observe that during the image reconstruction process utilizing VAR, scale predictions automatically modulate the input, facilitating the alignment of representations at subsequent scales with the distribution of clean images. To harness VAR's adaptive distribution alignment capability in image restoration tasks, we formulate the multi-scale latent representations within VAR as the restoration prior, thus advancing our delicately designed VarFormer framework. The strategic application of these priors enables our VarFormer to achieve remarkable generalization on unseen tasks while also reducing training computational costs. Extensive experiments underscores that our VarFormer outperforms existing multi-task image restoration methods across various restoration tasks.

Large Language Models (LLMs) rely on safety alignment to produce socially acceptable responses. This is typically achieved through instruction tuning and reinforcement learning from human feedback. However, this alignment is known to be brittle: further fine-tuning, even on benign or lightly contaminated data, can degrade safety and reintroduce harmful behaviors. A growing body of work suggests that alignment may correspond to identifiable geometric directions in weight space, forming subspaces that could, in principle, be isolated or preserved to defend against misalignment. In this work, we conduct a comprehensive empirical study of this geometric perspective. We examine whether safety-relevant behavior is concentrated in specific subspaces, whether it can be separated from general-purpose learning, and whether harmfulness arises from distinguishable patterns in internal representations. Across both parameter and activation space, our findings are consistent: subspaces that amplify safe behaviors also amplify unsafe ones, and prompts with different safety implications activate overlapping representations. We find no evidence of a subspace that selectively governs safety. These results challenge the assumption that alignment is geometrically localized. Rather than residing in distinct directions, safety appears to emerge from entangled, high-impact components of the model's broader learning dynamics. This suggests that subspace-based defenses may face fundamental limitations and underscores the need for alternative strategies to preserve alignment under continued training. We corroborate these findings through multiple experiments on five open-source LLMs. Our code is publicly available at: https://github.com/CERT-Lab/safety-subspaces.

Diffusion models have achieved impressive advancements in various vision tasks. However, these gains often rely on increasing model size, which escalates computational complexity and memory demands, complicating deployment, raising inference costs, and causing environmental impact. While some studies have explored pruning techniques to improve the memory efficiency of diffusion models, most existing methods require extensive retraining to retain the model performance. Retraining a modern large diffusion model is extremely costly and resource-intensive, which limits the practicality of these methods. In this work, we achieve low-cost diffusion pruning without retraining by proposing a model-agnostic structural pruning framework for diffusion models that learns a differentiable mask to sparsify the model. To ensure effective pruning that preserves the quality of the final denoised latent, we design a novel end-to-end pruning objective that spans the entire diffusion process. As end-to-end pruning is memory-intensive, we further propose time step gradient checkpointing, a technique that significantly reduces memory usage during optimization, enabling end-to-end pruning within a limited memory budget. Results on state-of-the-art U-Net diffusion models SDXL and diffusion transformers (FLUX) demonstrate that our method can effectively prune up to 20% parameters with minimal perceptible performance degradation, and notably, without the need for model retraining. We also showcase that our method can still prune on top of time step distilled diffusion models.

3D Gaussian Splatting (3DGS) has made significant strides in scene representation and neural rendering, with intense efforts focused on adapting it for dynamic scenes. Despite delivering remarkable rendering quality and speed, existing methods struggle with storage demands and representing complex real-world motions. To tackle these issues, we propose MoDecGS, a memory-efficient Gaussian splatting framework designed for reconstructing novel views in challenging scenarios with complex motions. We introduce GlobaltoLocal Motion Decomposition (GLMD) to effectively capture dynamic motions in a coarsetofine manner. This approach leverages Global Canonical Scaffolds (Global CS) and Local Canonical Scaffolds (Local CS), extending static Scaffold representation to dynamic video reconstruction. For Global CS, we propose Global Anchor Deformation (GAD) to efficiently represent global dynamics along complex motions, by directly deforming the implicit Scaffold attributes which are anchor position, offset, and local context features. Next, we finely adjust local motions via the Local Gaussian Deformation (LGD) of Local CS explicitly. Additionally, we introduce Temporal Interval Adjustment (TIA) to automatically control the temporal coverage of each Local CS during training, allowing MoDecGS to find optimal interval assignments based on the specified number of temporal segments. Extensive evaluations demonstrate that MoDecGS achieves an average 70% reduction in model size over stateoftheart methods for dynamic 3D Gaussians from realworld dynamic videos while maintaining or even improving rendering quality.

We address the computational challenges of solving parametric PDEs with non parametrized geometric variations and non-reducible problems, such as those involving shocks and discontinuities of variable positions. Traditional dimensionality reduction methods like POD struggle with these scenarios due to slowly decaying Kolmogorov widths. To overcome this, we propose a novel non-linear dimensionality reduction technique to reduce the required modes for representation. The non-linear reduction is obtained through a POD after applying a transformation on the fields, which we call optimal mappings, and is a solution to an optimization problem in infinite dimension. The proposed learning framework combines morphing techniques, non-linear dimensionality reduction, and Gaussian Process Regression (GPR). The problem is reformulated on a reference geometry before applying the dimensionality reduction. Our method learns both the optimal mapping, and the solution fields, using a series of GPR models, enabling efficient and accurate modeling of complex parametric PDEs with geometrical variability. The results obtained concur with current state-of-the-art models. We mainly compare our method with the winning solution of the ML4CFD NeurIPS 2024 competition.

Diffusion models have recently received a surge of interest due to their impressive performance for image restoration, especially in terms of noise robustness. However, existing diffusion-based methods are trained on a large amount of training data and perform very well in-distribution, but can be quite susceptible to distribution shift. This is especially inappropriate for data-starved hyperspectral image (HSI) restoration. To tackle this problem, this work puts forth a self-supervised diffusion model for HSI restoration, namely Denoising Diffusion Spatio-Spectral Model (DDS2M), which works by inferring the parameters of the proposed Variational Spatio-Spectral Module (VS2M) during the reverse diffusion process, solely using the degraded HSI without any extra training data. In VS2M, a variational inference-based loss function is customized to enable the untrained spatial and spectral networks to learn the posterior distribution, which serves as the transitions of the sampling chain to help reverse the diffusion process. Benefiting from its self-supervised nature and the diffusion process, DDS2M enjoys stronger generalization ability to various HSIs compared to existing diffusion-based methods and superior robustness to noise compared to existing HSI restoration methods. Extensive experiments on HSI denoising, noisy HSI completion and super-resolution on a variety of HSIs demonstrate DDS2M's superiority over the existing task-specific state-of-the-arts.

The inherent generative power of denoising diffusion models makes them well-suited for image restoration tasks where the objective is to find the optimal high-quality image within the generative space that closely resembles the input image. We propose a method to adapt a pretrained diffusion model for image restoration by simply adding noise to the input image to be restored and then denoise. Our method is based on the observation that the space of a generative model needs to be constrained. We impose this constraint by finetuning the generative model with a set of anchor images that capture the characteristics of the input image. With the constrained space, we can then leverage the sampling strategy used for generation to do image restoration. We evaluate against previous methods and show superior performances on multiple real-world restoration datasets in preserving identity and image quality. We also demonstrate an important and practical application on personalized restoration, where we use a personal album as the anchor images to constrain the generative space. This approach allows us to produce results that accurately preserve high-frequency details, which previous works are unable to do. Project webpage: https://gen2res.github.io.

Class-Incremental Learning (CIL) requires a learning system to continually learn new classes without forgetting. Despite the strong performance of Pre-Trained Models (PTMs) in CIL, a critical issue persists: learning new classes often results in the overwriting of old ones. Excessive modification of the network causes forgetting, while minimal adjustments lead to an inadequate fit for new classes. As a result, it is desired to figure out a way of efficient model updating without harming former knowledge. In this paper, we propose ExpAndable Subspace Ensemble (EASE) for PTM-based CIL. To enable model updating without conflict, we train a distinct lightweight adapter module for each new task, aiming to create task-specific subspaces. These adapters span a high-dimensional feature space, enabling joint decision-making across multiple subspaces. As data evolves, the expanding subspaces render the old class classifiers incompatible with new-stage spaces. Correspondingly, we design a semantic-guided prototype complement strategy that synthesizes old classes' new features without using any old class instance. Extensive experiments on seven benchmark datasets verify EASE's state-of-the-art performance. Code is available at: https://github.com/sun-hailong/CVPR24-Ease

Neural rendering methods have significantly advanced photo-realistic 3D scene rendering in various academic and industrial applications. The recent 3D Gaussian Splatting method has achieved the state-of-the-art rendering quality and speed combining the benefits of both primitive-based representations and volumetric representations. However, it often leads to heavily redundant Gaussians that try to fit every training view, neglecting the underlying scene geometry. Consequently, the resulting model becomes less robust to significant view changes, texture-less area and lighting effects. We introduce Scaffold-GS, which uses anchor points to distribute local 3D Gaussians, and predicts their attributes on-the-fly based on viewing direction and distance within the view frustum. Anchor growing and pruning strategies are developed based on the importance of neural Gaussians to reliably improve the scene coverage. We show that our method effectively reduces redundant Gaussians while delivering high-quality rendering. We also demonstrates an enhanced capability to accommodate scenes with varying levels-of-detail and view-dependent observations, without sacrificing the rendering speed.

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

Working over infinite dimensional separable Hilbert spaces, residual results have been achieved for the space of contractive C_{0}-semigroups under the topology of uniform weak operator convergence on compact subsets of R_{+}. Eisner and Serény raised in 2009 the open problem: Does this space constitute a Baire space? Observing that the subspace of unitary semigroups is completely metrisable and appealing to known density results, we solve this problem positively by showing that certain topological properties can in general be transferred from dense subspaces to larger spaces. The transfer result in turn relies upon classification of topological properties via infinite games. Our approach is sufficiently general and can be applied to other contexts, e.g. the space of contractions under the pw-topology.

Plasma modeling is central to the design of nuclear fusion reactors, yet simulating collisional plasma kinetics from first principles remains a formidable computational challenge: the Vlasov-Maxwell-Landau (VML) system describes six-dimensional phase-space transport under self-consistent electromagnetic fields together with the nonlinear, nonlocal Landau collision operator. A recent deterministic particle method for the full VML system estimates the velocity score function via the blob method, a kernel-based approximation with O(n^2) cost. In this work, we replace the blob score estimator with score-based transport modeling (SBTM), in which a neural network is trained on-the-fly via implicit score matching at O(n) cost. We prove that the approximated collision operator preserves momentum and kinetic energy, and dissipates an estimated entropy. We also characterize the unique global steady state of the VML system and its electrostatic reduction, providing the ground truth for numerical validation. On three canonical benchmarks -- Landau damping, two-stream instability, and Weibel instability -- SBTM is more accurate than the blob method, achieves correct long-time relaxation to Maxwellian equilibrium where the blob method fails, and delivers 50% faster runtime with 4times lower peak memory.

Magnetic Resonance Imaging can produce detailed images of the anatomy and physiology of the human body that can assist doctors in diagnosing and treating pathologies such as tumours. However, MRI suffers from very long acquisition times that make it susceptible to patient motion artifacts and limit its potential to deliver dynamic treatments. Conventional approaches such as Parallel Imaging and Compressed Sensing allow for an increase in MRI acquisition speed by reconstructing MR images from sub-sampled MRI data acquired using multiple receiver coils. Recent advancements in Deep Learning combined with Parallel Imaging and Compressed Sensing techniques have the potential to produce high-fidelity reconstructions from highly accelerated MRI data. In this work we present a novel Deep Learning-based Inverse Problem solver applied to the task of Accelerated MRI Reconstruction, called the Recurrent Variational Network (RecurrentVarNet), by exploiting the properties of Convolutional Recurrent Neural Networks and unrolled algorithms for solving Inverse Problems. The RecurrentVarNet consists of multiple recurrent blocks, each responsible for one iteration of the unrolled variational optimization scheme for solving the inverse problem of multi-coil Accelerated MRI Reconstruction. Contrary to traditional approaches, the optimization steps are performed in the observation domain (k-space) instead of the image domain. Each block of the RecurrentVarNet refines the observed k-space and comprises a data consistency term and a recurrent unit which takes as input a learned hidden state and the prediction of the previous block. Our proposed method achieves new state of the art qualitative and quantitative reconstruction results on 5-fold and 10-fold accelerated data from a public multi-coil brain dataset, outperforming previous conventional and deep learning-based approaches.

Manual modeling of material parameters and 3D geometry is a time consuming yet essential task in the gaming and film industries. While recent advances in 3D reconstruction have enabled accurate approximations of scene geometry and appearance, these methods often fall short in relighting scenarios due to the lack of precise, spatially varying material parameters. At the same time, diffusion models operating on 2D images have shown strong performance in predicting physically based rendering (PBR) properties such as albedo, roughness, and metallicity. However, transferring these 2D material maps onto reconstructed 3D geometry remains a significant challenge. We propose a framework for fusing 2D material data into 3D geometry using a combination of novel learning-based and projection-based approaches. We begin by reconstructing scene geometry via Gaussian Splatting. From the input images, a diffusion model generates 2D maps for albedo, roughness, and metallic parameters. Any existing diffusion model that can convert images or videos to PBR materials can be applied. The predictions are further integrated into the 3D representation either by optimizing an image-based loss or by directly projecting the material parameters onto the Gaussians using Gaussian ray tracing. To enhance fine-scale accuracy and multi-view consistency, we further introduce a light-weight neural refinement step (Neural Merger), which takes ray-traced material features as input and produces detailed adjustments. Our results demonstrate that the proposed methods outperform existing techniques in both quantitative metrics and perceived visual realism. This enables more accurate, relightable, and photorealistic renderings from reconstructed scenes, significantly improving the realism and efficiency of asset creation workflows in content production pipelines.

Satellite image inpainting is a crucial task in remote sensing, where accurately restoring missing or occluded regions is essential for robust image analysis. In this paper, we propose KAO, a novel framework that utilizes Kernel-Adaptive Optimization within diffusion models for satellite image inpainting. KAO is specifically designed to address the challenges posed by very high-resolution (VHR) satellite datasets, such as DeepGlobe and the Massachusetts Roads Dataset. Unlike existing methods that rely on preconditioned models requiring extensive retraining or postconditioned models with significant computational overhead, KAO introduces a Latent Space Conditioning approach, optimizing a compact latent space to achieve efficient and accurate inpainting. Furthermore, we incorporate Explicit Propagation into the diffusion process, facilitating forward-backward fusion, which improves the stability and precision of the method. Experimental results demonstrate that KAO sets a new benchmark for VHR satellite image restoration, providing a scalable, high-performance solution that balances the efficiency of preconditioned models with the flexibility of postconditioned models.

We present NeRFVS, a novel neural radiance fields (NeRF) based method to enable free navigation in a room. NeRF achieves impressive performance in rendering images for novel views similar to the input views while suffering for novel views that are significantly different from the training views. To address this issue, we utilize the holistic priors, including pseudo depth maps and view coverage information, from neural reconstruction to guide the learning of implicit neural representations of 3D indoor scenes. Concretely, an off-the-shelf neural reconstruction method is leveraged to generate a geometry scaffold. Then, two loss functions based on the holistic priors are proposed to improve the learning of NeRF: 1) A robust depth loss that can tolerate the error of the pseudo depth map to guide the geometry learning of NeRF; 2) A variance loss to regularize the variance of implicit neural representations to reduce the geometry and color ambiguity in the learning procedure. These two loss functions are modulated during NeRF optimization according to the view coverage information to reduce the negative influence brought by the view coverage imbalance. Extensive results demonstrate that our NeRFVS outperforms state-of-the-art view synthesis methods quantitatively and qualitatively on indoor scenes, achieving high-fidelity free navigation results.

Learned representations are a central component in modern ML systems, serving a multitude of downstream tasks. When training such representations, it is often the case that computational and statistical constraints for each downstream task are unknown. In this context rigid, fixed capacity representations can be either over or under-accommodating to the task at hand. This leads us to ask: can we design a flexible representation that can adapt to multiple downstream tasks with varying computational resources? Our main contribution is Matryoshka Representation Learning (MRL) which encodes information at different granularities and allows a single embedding to adapt to the computational constraints of downstream tasks. MRL minimally modifies existing representation learning pipelines and imposes no additional cost during inference and deployment. MRL learns coarse-to-fine representations that are at least as accurate and rich as independently trained low-dimensional representations. The flexibility within the learned Matryoshka Representations offer: (a) up to 14x smaller embedding size for ImageNet-1K classification at the same level of accuracy; (b) up to 14x real-world speed-ups for large-scale retrieval on ImageNet-1K and 4K; and (c) up to 2% accuracy improvements for long-tail few-shot classification, all while being as robust as the original representations. Finally, we show that MRL extends seamlessly to web-scale datasets (ImageNet, JFT) across various modalities -- vision (ViT, ResNet), vision + language (ALIGN) and language (BERT). MRL code and pretrained models are open-sourced at https://github.com/RAIVNLab/MRL.

We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels (cc-universal) on the metric spaces, which results in reproducing kernel Hilbert spaces for the predictor and response that are rich enough to characterize the conditional independence that determines sufficient dimension reduction. For univariate distributions, we construct the universal kernel using the Wasserstein distance, while for multivariate distributions, we resort to the sliced Wasserstein distance. The sliced Wasserstein distance ensures that the metric space possesses similar topological properties to the Wasserstein space while also offering significant computation benefits. Numerical results based on synthetic data show that our method outperforms possible competing methods. The method is also applied to several data sets, including fertility and mortality data and Calgary temperature data.

Transformers have revolutionized medical image restoration, but the quadratic complexity still poses limitations for their application to high-resolution medical images. The recent advent of the Receptance Weighted Key Value (RWKV) model in the natural language processing field has attracted much attention due to its ability to process long sequences efficiently. To leverage its advanced design, we propose Restore-RWKV, the first RWKV-based model for medical image restoration. Since the original RWKV model is designed for 1D sequences, we make two necessary modifications for modeling spatial relations in 2D medical images. First, we present a recurrent WKV (Re-WKV) attention mechanism that captures global dependencies with linear computational complexity. Re-WKV incorporates bidirectional attention as basic for a global receptive field and recurrent attention to effectively model 2D dependencies from various scan directions. Second, we develop an omnidirectional token shift (Omni-Shift) layer that enhances local dependencies by shifting tokens from all directions and across a wide context range. These adaptations make the proposed Restore-RWKV an efficient and effective model for medical image restoration. Even a lightweight variant of Restore-RWKV, with only 1.16 million parameters, achieves comparable or even superior results compared to existing state-of-the-art (SOTA) methods. Extensive experiments demonstrate that the resulting Restore-RWKV achieves SOTA performance across a range of medical image restoration tasks, including PET image synthesis, CT image denoising, MRI image super-resolution, and all-in-one medical image restoration. Code is available at: https://github.com/Yaziwel/Restore-RWKV.

Growing waste streams and the transition to a circular economy require efficient automated waste sorting. In industrial settings, materials move on fast conveyor belts, where reliable identification and ejection demand pixel-accurate segmentation. RGB imaging delivers high-resolution spatial detail, which is essential for accurate segmentation, but it confuses materials that look similar in the visible spectrum. Hyperspectral imaging (HSI) provides spectral signatures that separate such materials, yet its lower spatial resolution limits detail. Effective waste sorting therefore needs methods that fuse both modalities to exploit their complementary strengths. We present Bidirectional Cross-Attention Fusion (BCAF), which aligns high-resolution RGB with low-resolution HSI at their native grids via localized, bidirectional cross-attention, avoiding pre-upsampling or early spectral collapse. BCAF uses two independent backbones: a standard Swin Transformer for RGB and an HSI-adapted Swin backbone that preserves spectral structure through 3D tokenization with spectral self-attention. We also analyze trade-offs between RGB input resolution and the number of HSI spectral slices. Although our evaluation targets RGB-HSI fusion, BCAF is modality-agnostic and applies to co-registered RGB with lower-resolution, high-channel auxiliary sensors. On the benchmark SpectralWaste dataset, BCAF achieves state-of-the-art performance of 76.4% mIoU at 31 images/s and 75.4% mIoU at 55 images/s. We further evaluate a novel industrial dataset: K3I-Cycling (first RGB subset already released on Fordatis). On this dataset, BCAF reaches 62.3% mIoU for material segmentation (paper, metal, plastic, etc.) and 66.2% mIoU for plastic-type segmentation (PET, PP, HDPE, LDPE, PS, etc.).

The increasing demand for virtual reality applications has highlighted the significance of crafting immersive 3D assets. We present a text-to-3D 360^{circ} scene generation pipeline that facilitates the creation of comprehensive 360^{circ} scenes for in-the-wild environments in a matter of minutes. Our approach utilizes the generative power of a 2D diffusion model and prompt self-refinement to create a high-quality and globally coherent panoramic image. This image acts as a preliminary "flat" (2D) scene representation. Subsequently, it is lifted into 3D Gaussians, employing splatting techniques to enable real-time exploration. To produce consistent 3D geometry, our pipeline constructs a spatially coherent structure by aligning the 2D monocular depth into a globally optimized point cloud. This point cloud serves as the initial state for the centroids of 3D Gaussians. In order to address invisible issues inherent in single-view inputs, we impose semantic and geometric constraints on both synthesized and input camera views as regularizations. These guide the optimization of Gaussians, aiding in the reconstruction of unseen regions. In summary, our method offers a globally consistent 3D scene within a 360^{circ} perspective, providing an enhanced immersive experience over existing techniques. Project website at: http://dreamscene360.github.io/

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.

Model merging combines multiple fine-tuned checkpoints into a single model without additional training, offering an attractive approach to reusing models and efficiently improving performance. However, it remains unclear whether the advantages reported for settings where all merged experts have distinct roles and are tuned on clearly separated tasks also hold in settings where the merged experts do not have clearly distinct roles, but are trained on overlapping or even conflicting objectives. To evaluate this setting, we present a large-scale, systematic evaluation of "in-the-wild" model merging of heterogeneous experts, that may have been trained on overlapping or conflicting objectives. Concretely, we evaluate six state-of-the-art merging methods, including recent subspace methods, across four open-weight LLMs, twelve fine-tuned checkpoints per base model, and sixteen standard LLM benchmarks. Evaluating through standardized benchmarks, we measure both the probability that a model merged from a heterogeneous set of experts outperforms the base model and we measure relative gains over the best individual checkpoint. Our results show that the oldest and simplest method, Task Arithmetic, is the only approach that reliably yields performance gains on LLMs in this "in-the-wild" setting. Other interference-aware and subspace merging methods typically do not result in notable improvements over the base model. Our findings indicate that current merging techniques mostly do not enable extracting useful weight updates from heterogeneous and potentially conflicting versions. This motivates the design of LLM-specific merging algorithms and merging-aware fine-tuning methods.

Visual retrieval systems face significant challenges when updating models with improved representations due to misalignment between the old and new representations. The costly and resource-intensive backfilling process involves recalculating feature vectors for images in the gallery set whenever a new model is introduced. To address this, prior research has explored backward-compatible training methods that enable direct comparisons between new and old representations without backfilling. Despite these advancements, achieving a balance between backward compatibility and the performance of independently trained models remains an open problem. In this paper, we address it by expanding the representation space with additional dimensions and learning an orthogonal transformation to achieve compatibility with old models and, at the same time, integrate new information. This transformation preserves the original feature space's geometry, ensuring that our model aligns with previous versions while also learning new data. Our Orthogonal Compatible Aligned (OCA) approach eliminates the need for re-indexing during model updates and ensures that features can be compared directly across different model updates without additional mapping functions. Experimental results on CIFAR-100 and ImageNet-1k demonstrate that our method not only maintains compatibility with previous models but also achieves state-of-the-art accuracy, outperforming several existing methods.

Recent studies suggest that with sufficiently wide models, most SGD solutions can, up to permutation, converge into the same basin. This phenomenon, known as the model re-basin regime, has significant implications for model averaging by ensuring the linear mode connectivity. However, current re-basin strategies are ineffective in many scenarios due to a lack of comprehensive understanding of underlying mechanisms. Addressing this gap, this paper provides novel insights into understanding and improving the standard practice. Firstly, we decompose re-normalization into rescaling and reshift, uncovering that rescaling plays a crucial role in re-normalization while re-basin performance is sensitive to shifts in model activation. The finding calls for a more nuanced handling of the activation shift. Secondly, we identify that the merged model suffers from the issue of activation collapse and magnitude collapse. Varying the learning rate, weight decay, and initialization method can mitigate the issues and improve model performance. Lastly, we propose a new perspective to unify the re-basin and pruning, under which a lightweight yet effective post-pruning technique is derived, which can significantly improve the model performance after pruning. Our implementation is available at https://github.com/XingyuQu/rethink-re-basin.

KV cache has become a de facto technique for the inference of large language models (LLMs), where tensors of shape (layer number, head number, sequence length, feature dimension) are introduced to cache historical information for self-attention. As the size of the model and data grows, the KV cache can quickly become a bottleneck within the system in both storage and memory transfer. To address this, prior studies usually focus on the first three axes of the cache tensors for compression. This paper supplements them, focusing on the feature dimension axis, by utilizing low-rank projection matrices to transform the cache features into spaces with reduced dimensions. We begin by investigating the canonical orthogonal projection method for data compression through principal component analysis (PCA). We observe the issue with PCA projection where significant performance degradation is observed at low compression rates. To bridge the gap, we propose to directly tune the orthogonal projection matrices with a distillation objective using an elaborate Matryoshka training strategy. After training, we adaptively search for the optimal compression rates for various layers and heads given varying compression budgets. Compared to previous works, our method can easily embrace pre-trained LLMs and hold a smooth tradeoff between performance and compression rate. We empirically witness the high data efficiency of our training procedure and find that our method can sustain over 90% performance with an average KV cache compression rate of 60% (and up to 75% in certain extreme scenarios) for popular LLMs like LLaMA2-7B-base and Mistral-7B-v0.3-base.

Policy gradient methods hold great potential for solving complex continuous control tasks. Still, their training efficiency can be improved by exploiting structure within the optimization problem. Recent work indicates that supervised learning can be accelerated by leveraging the fact that gradients lie in a low-dimensional and slowly-changing subspace. In this paper, we conduct a thorough evaluation of this phenomenon for two popular deep policy gradient methods on various simulated benchmark tasks. Our results demonstrate the existence of such gradient subspaces despite the continuously changing data distribution inherent to reinforcement learning. These findings reveal promising directions for future work on more efficient reinforcement learning, e.g., through improving parameter-space exploration or enabling second-order optimization.

4D Gaussian Splatting (4DGS) has recently gained considerable attention as a method for reconstructing dynamic scenes. Despite achieving superior quality, 4DGS typically requires substantial storage and suffers from slow rendering speed. In this work, we delve into these issues and identify two key sources of temporal redundancy. (Q1) Short-Lifespan Gaussians: 4DGS uses a large portion of Gaussians with short temporal span to represent scene dynamics, leading to an excessive number of Gaussians. (Q2) Inactive Gaussians: When rendering, only a small subset of Gaussians contributes to each frame. Despite this, all Gaussians are processed during rasterization, resulting in redundant computation overhead. To address these redundancies, we present 4DGS-1K, which runs at over 1000 FPS on modern GPUs. For Q1, we introduce the Spatial-Temporal Variation Score, a new pruning criterion that effectively removes short-lifespan Gaussians while encouraging 4DGS to capture scene dynamics using Gaussians with longer temporal spans. For Q2, we store a mask for active Gaussians across consecutive frames, significantly reducing redundant computations in rendering. Compared to vanilla 4DGS, our method achieves a 41times reduction in storage and 9times faster rasterization speed on complex dynamic scenes, while maintaining comparable visual quality. Please see our project page at https://4DGS-1K.github.io.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

We introduce two complementary techniques for efficient adaptive optimization that reduce memory requirements while accelerating training of large-scale neural networks. The first technique, Subset-Norm adaptive step size, generalizes AdaGrad-Norm and AdaGrad(-Coordinate) by reducing the second moment term's memory footprint from O(d) to O(d) through step-size sharing, where d is the model size. For non-convex smooth objectives under coordinate-wise sub-gaussian gradient noise, we prove a noise-adapted high-probability convergence guarantee showing improved dimensional dependence over existing methods. Our second technique, Subspace-Momentum, reduces the momentum state's memory footprint by operating in a low-dimensional subspace while applying standard SGD in the orthogonal complement. We establish high-probability convergence rates under similar relaxed assumptions. Empirical evaluation on LLaMA models from 60M to 1B parameters demonstrates the effectiveness of our methods, where combining subset-norm with subspace-momentum achieves Adam's validation perplexity in approximately half the training tokens (6.8B vs 13.1B) while using only 20% of the Adam's optimizer-states memory footprint and requiring minimal additional hyperparameter tuning.

Low-rank optimization has emerged as a promising approach to enabling memory-efficient training of large language models (LLMs). Existing low-rank optimization methods typically project gradients onto a low-rank subspace, reducing the memory cost of storing optimizer states. A key challenge in these methods is selecting suitable subspaces to ensure an effective optimization trajectory. Most existing approaches select the dominant subspace to preserve gradient information, as this intuitively provides the best approximation. However, we find that in practice, the dominant subspace stops changing during pretraining, thereby constraining weight updates to similar subspaces. In this paper, we propose importance sampling for low-rank optimization in LLM pretraining with a provable convergence guarantee, which the dominant subspace approach does not have. Empirically, we demonstrate that our method significantly outperforms previous methods in LLM pretraining tasks.

Matrix manifolds, such as manifolds of Symmetric Positive Definite (SPD) matrices and Grassmann manifolds, appear in many applications. Recently, by applying the theory of gyrogroups and gyrovector spaces that is a powerful framework for studying hyperbolic geometry, some works have attempted to build principled generalizations of Euclidean neural networks on matrix manifolds. However, due to the lack of many concepts in gyrovector spaces for the considered manifolds, e.g., the inner product and gyroangles, techniques and mathematical tools provided by these works are still limited compared to those developed for studying hyperbolic geometry. In this paper, we generalize some notions in gyrovector spaces for SPD and Grassmann manifolds, and propose new models and layers for building neural networks on these manifolds. We show the effectiveness of our approach in two applications, i.e., human action recognition and knowledge graph completion.

Diffusion models deliver high-fidelity synthesis but remain slow due to iterative sampling. We empirically observe there exists feature invariance in deterministic sampling, and present InvarDiff, a training-free acceleration method that exploits the relative temporal invariance across timestep-scale and layer-scale. From a few deterministic runs, we compute a per-timestep, per-layer, per-module binary cache plan matrix and use a re-sampling correction to avoid drift when consecutive caches occur. Using quantile-based change metrics, this matrix specifies which module at which step is reused rather than recomputed. The same invariance criterion is applied at the step scale to enable cross-timestep caching, deciding whether an entire step can reuse cached results. During inference, InvarDiff performs step-first and layer-wise caching guided by this matrix. When applied to DiT and FLUX, our approach reduces redundant compute while preserving fidelity. Experiments show that InvarDiff achieves 2-3times end-to-end speed-ups with minimal impact on standard quality metrics. Qualitatively, we observe almost no degradation in visual quality compared with full computations.

The rapid growth of large models has raised concerns about their environmental impact and equity in accessibility due to significant computational costs. Low-Rank Adapters (LoRA) offer a lightweight solution for finetuning large models, resulting in an abundance of publicly available adapters tailored to diverse domains. We ask: Can these pretrained adapters be leveraged to further streamline adaptation to new tasks while addressing these challenges? We introduce EigenLoRAx, a parameter-efficient finetuning method that recycles existing adapters to create a principal subspace aligned with their shared domain knowledge which can be further augmented with orthogonal basis vectors in low-resource scenarios. This enables rapid adaptation to new tasks by learning only lightweight coefficients on the principal components of the subspace - eliminating the need to finetune entire adapters. EigenLoRAx requires significantly fewer parameters and memory, improving efficiency for both training and inference. Our method demonstrates strong performance across diverse domains and tasks, offering a scalable for edge-based applications, personalization, and equitable deployment of large models in resource-constrained environments.

Recent works in inverse rendering have shown promise in using multi-view images of an object to recover shape, albedo, and materials. However, the recovered components often fail to render accurately under new lighting conditions due to the intrinsic challenge of disentangling albedo and material properties from input images. To address this challenge, we introduce MaterialFusion, an enhanced conventional 3D inverse rendering pipeline that incorporates a 2D prior on texture and material properties. We present StableMaterial, a 2D diffusion model prior that refines multi-lit data to estimate the most likely albedo and material from given input appearances. This model is trained on albedo, material, and relit image data derived from a curated dataset of approximately ~12K artist-designed synthetic Blender objects called BlenderVault. we incorporate this diffusion prior with an inverse rendering framework where we use score distillation sampling (SDS) to guide the optimization of the albedo and materials, improving relighting performance in comparison with previous work. We validate MaterialFusion's relighting performance on 4 datasets of synthetic and real objects under diverse illumination conditions, showing our diffusion-aided approach significantly improves the appearance of reconstructed objects under novel lighting conditions. We intend to publicly release our BlenderVault dataset to support further research in this field.

Recent text-to-video (T2V) diffusion models have demonstrated impressive generation capabilities across various domains. However, these models often generate videos that have misalignments with text prompts, especially when the prompts describe complex scenes with multiple objects and attributes. To address this, we introduce VideoRepair, a novel model-agnostic, training-free video refinement framework that automatically identifies fine-grained text-video misalignments and generates explicit spatial and textual feedback, enabling a T2V diffusion model to perform targeted, localized refinements. VideoRepair consists of four stages: In (1) video evaluation, we detect misalignments by generating fine-grained evaluation questions and answering those questions with MLLM. In (2) refinement planning, we identify accurately generated objects and then create localized prompts to refine other areas in the video. Next, in (3) region decomposition, we segment the correctly generated area using a combined grounding module. We regenerate the video by adjusting the misaligned regions while preserving the correct regions in (4) localized refinement. On two popular video generation benchmarks (EvalCrafter and T2V-CompBench), VideoRepair substantially outperforms recent baselines across various text-video alignment metrics. We provide a comprehensive analysis of VideoRepair components and qualitative examples.

3D Gaussian splatting (3DGS) has shown its detailed expressive ability and highly efficient rendering speed in the novel view synthesis (NVS) task. The application to inverse rendering still faces several challenges, as the discrete nature of Gaussian primitives makes it difficult to apply geometry constraints. Recent works introduce the signed distance field (SDF) as an extra continuous representation to regularize the geometry defined by Gaussian primitives. It improves the decomposition quality, at the cost of increasing memory usage and complicating training. Unlike these works, we introduce a discretized SDF to represent the continuous SDF in a discrete manner by encoding it within each Gaussian using a sampled value. This approach allows us to link the SDF with the Gaussian opacity through an SDF-to-opacity transformation, enabling rendering the SDF via splatting and avoiding the computational cost of ray marching.The key challenge is to regularize the discrete samples to be consistent with the underlying SDF, as the discrete representation can hardly apply the gradient-based constraints (\eg Eikonal loss). For this, we project Gaussians onto the zero-level set of SDF and enforce alignment with the surface from splatting, namely a projection-based consistency loss. Thanks to the discretized SDF, our method achieves higher relighting quality, while requiring no extra memory beyond GS and avoiding complex manually designed optimization. The experiments reveal that our method outperforms existing Gaussian-based inverse rendering methods. Our code is available at https://github.com/NK-CS-ZZL/DiscretizedSDF.

Most kernel-based methods, such as kernel or Gaussian process regression, kernel PCA, ICA, or k-means clustering, do not scale to large datasets, because constructing and storing the kernel matrix K_n requires at least O(n^2) time and space for n samples. Recent works show that sampling points with replacement according to their ridge leverage scores (RLS) generates small dictionaries of relevant points with strong spectral approximation guarantees for K_n. The drawback of RLS-based methods is that computing exact RLS requires constructing and storing the whole kernel matrix. In this paper, we introduce SQUEAK, a new algorithm for kernel approximation based on RLS sampling that sequentially processes the dataset, storing a dictionary which creates accurate kernel matrix approximations with a number of points that only depends on the effective dimension d_{eff}(γ) of the dataset. Moreover since all the RLS estimations are efficiently performed using only the small dictionary, SQUEAK is the first RLS sampling algorithm that never constructs the whole matrix K_n, runs in linear time mathcal{O}(nd_{eff}(γ)^3) w.r.t. n, and requires only a single pass over the dataset. We also propose a parallel and distributed version of SQUEAK that linearly scales across multiple machines, achieving similar accuracy in as little as mathcal{O}(log(n)d_{eff}(γ)^3) time.

Image restoration (IR) in real-world scenarios presents significant challenges due to the lack of high-capacity models and comprehensive datasets. To tackle these issues, we present a dual strategy: GenIR, an innovative data curation pipeline, and DreamClear, a cutting-edge Diffusion Transformer (DiT)-based image restoration model. GenIR, our pioneering contribution, is a dual-prompt learning pipeline that overcomes the limitations of existing datasets, which typically comprise only a few thousand images and thus offer limited generalizability for larger models. GenIR streamlines the process into three stages: image-text pair construction, dual-prompt based fine-tuning, and data generation & filtering. This approach circumvents the laborious data crawling process, ensuring copyright compliance and providing a cost-effective, privacy-safe solution for IR dataset construction. The result is a large-scale dataset of one million high-quality images. Our second contribution, DreamClear, is a DiT-based image restoration model. It utilizes the generative priors of text-to-image (T2I) diffusion models and the robust perceptual capabilities of multi-modal large language models (MLLMs) to achieve photorealistic restoration. To boost the model's adaptability to diverse real-world degradations, we introduce the Mixture of Adaptive Modulator (MoAM). It employs token-wise degradation priors to dynamically integrate various restoration experts, thereby expanding the range of degradations the model can address. Our exhaustive experiments confirm DreamClear's superior performance, underlining the efficacy of our dual strategy for real-world image restoration. Code and pre-trained models will be available at: https://github.com/shallowdream204/DreamClear.

In applications of diffusion models, controllable generation is of practical significance, but is also challenging. Current methods for controllable generation primarily focus on modifying the score function of diffusion models, while Mean Reverting (MR) Diffusion directly modifies the structure of the stochastic differential equation (SDE), making the incorporation of image conditions simpler and more natural. However, current training-free fast samplers are not directly applicable to MR Diffusion. And thus MR Diffusion requires hundreds of NFEs (number of function evaluations) to obtain high-quality samples. In this paper, we propose a new algorithm named MRS (MR Sampler) to reduce the sampling NFEs of MR Diffusion. We solve the reverse-time SDE and the probability flow ordinary differential equation (PF-ODE) associated with MR Diffusion, and derive semi-analytical solutions. The solutions consist of an analytical function and an integral parameterized by a neural network. Based on this solution, we can generate high-quality samples in fewer steps. Our approach does not require training and supports all mainstream parameterizations, including noise prediction, data prediction and velocity prediction. Extensive experiments demonstrate that MR Sampler maintains high sampling quality with a speedup of 10 to 20 times across ten different image restoration tasks. Our algorithm accelerates the sampling procedure of MR Diffusion, making it more practical in controllable generation.

In this paper, we develop and implement an efficient asymptotic-preserving (AP) scheme to solve the gas mixture of Boltzmann equations under the disparate mass scaling relevant to the so-called "epochal relaxation" phenomenon. The disparity in molecular masses, ranging across several orders of magnitude, leads to significant challenges in both the evaluation of collision operators and the designing of time-stepping schemes to capture the multi-scale nature of the dynamics. A direct implementation of the spectral method faces prohibitive computational costs as the mass ratio increases due to the need to resolve vastly different thermal velocities. Unlike [I. M. Gamba, S. Jin, and L. Liu, Commun. Math. Sci., 17 (2019), pp. 1257-1289], we propose an alternative approach based on proper truncation of asymptotic expansions of the collision operators, which significantly reduces the computational complexity and works well for small varepsilon. By incorporating the separation of three time scales in the model's relaxation process [P. Degond and B. Lucquin-Desreux, Math. Models Methods Appl. Sci., 6 (1996), pp. 405-436], we design an AP scheme that captures the specific dynamics of the disparate mass model while maintaining computational efficiency. Numerical experiments demonstrate the effectiveness of the proposed scheme in handling large mass ratios of heavy and light species, as well as capturing the epochal relaxation phenomenon.

Updating a truncated Singular Value Decomposition (SVD) is crucial in representation learning, especially when dealing with large-scale data matrices that continuously evolve in practical scenarios. Aligning SVD-based models with fast-paced updates becomes increasingly important. Existing methods for updating truncated SVDs employ Rayleigh-Ritz projection procedures, where projection matrices are augmented based on original singular vectors. However, these methods suffer from inefficiency due to the densification of the update matrix and the application of the projection to all singular vectors. To address these limitations, we introduce a novel method for dynamically approximating the truncated SVD of a sparse and temporally evolving matrix. Our approach leverages sparsity in the orthogonalization process of augmented matrices and utilizes an extended decomposition to independently store projections in the column space of singular vectors. Numerical experiments demonstrate a remarkable efficiency improvement of an order of magnitude compared to previous methods. Remarkably, this improvement is achieved while maintaining a comparable precision to existing approaches.

Interactive 3D scene generation from a single image has gained significant attention due to its potential to create immersive virtual worlds. However, a key challenge in current 3D generation methods is the limited explorability, which cannot render high-quality images during larger maneuvers beyond the original viewpoint, particularly when attempting to move forward into unseen areas. To address this challenge, we propose WonderFree, the first model that enables users to interactively generate 3D worlds with the freedom to explore from arbitrary angles and directions. Specifically, we decouple this challenge into two key subproblems: novel view quality, which addresses visual artifacts and floating issues in novel views, and cross-view consistency, which ensures spatial consistency across different viewpoints. To enhance rendering quality in novel views, we introduce WorldRestorer, a data-driven video restoration model designed to eliminate floaters and artifacts. In addition, a data collection pipeline is presented to automatically gather training data for WorldRestorer, ensuring it can handle scenes with varying styles needed for 3D scene generation. Furthermore, to improve cross-view consistency, we propose ConsistView, a multi-view joint restoration mechanism that simultaneously restores multiple perspectives while maintaining spatiotemporal coherence. Experimental results demonstrate that WonderFree not only enhances rendering quality across diverse viewpoints but also significantly improves global coherence and consistency. These improvements are confirmed by CLIP-based metrics and a user study showing a 77.20% preference for WonderFree over WonderWorld enabling a seamless and immersive 3D exploration experience. The code, model, and data will be publicly available.

Novel view synthesis (NVS) enables to generate new images of a scene or convert a set of 2D images into a comprehensive 3D model. In the context of Space Domain Awareness, since space is becoming increasingly congested, NVS can accurately map space objects and debris, improving the safety and efficiency of space operations. Similarly, in Rendezvous and Proximity Operations missions, 3D models can provide details about a target object's shape, size, and orientation, allowing for better planning and prediction of the target's behavior. In this work, we explore the generalization abilities of these reconstruction techniques, aiming to avoid the necessity of retraining for each new scene, by presenting a novel approach to 3D spacecraft reconstruction from single-view images, DreamSat, by fine-tuning the Zero123 XL, a state-of-the-art single-view reconstruction model, on a high-quality dataset of 190 high-quality spacecraft models and integrating it into the DreamGaussian framework. We demonstrate consistent improvements in reconstruction quality across multiple metrics, including Contrastive Language-Image Pretraining (CLIP) score (+0.33%), Peak Signal-to-Noise Ratio (PSNR) (+2.53%), Structural Similarity Index (SSIM) (+2.38%), and Learned Perceptual Image Patch Similarity (LPIPS) (+0.16%) on a test set of 30 previously unseen spacecraft images. Our method addresses the lack of domain-specific 3D reconstruction tools in the space industry by leveraging state-of-the-art diffusion models and 3D Gaussian splatting techniques. This approach maintains the efficiency of the DreamGaussian framework while enhancing the accuracy and detail of spacecraft reconstructions. The code for this work can be accessed on GitHub (https://github.com/ARCLab-MIT/space-nvs).

Recent advances in neural reconstruction using posed image sequences have made remarkable progress. However, due to the lack of depth information, existing volumetric-based techniques simply duplicate 2D image features of the object surface along the entire camera ray. We contend this duplication introduces noise in empty and occluded spaces, posing challenges for producing high-quality 3D geometry. Drawing inspiration from traditional multi-view stereo methods, we propose an end-to-end 3D neural reconstruction framework CVRecon, designed to exploit the rich geometric embedding in the cost volumes to facilitate 3D geometric feature learning. Furthermore, we present Ray-contextual Compensated Cost Volume (RCCV), a novel 3D geometric feature representation that encodes view-dependent information with improved integrity and robustness. Through comprehensive experiments, we demonstrate that our approach significantly improves the reconstruction quality in various metrics and recovers clear fine details of the 3D geometries. Our extensive ablation studies provide insights into the development of effective 3D geometric feature learning schemes. Project page: https://cvrecon.ziyue.cool/

The sliced Wasserstein (SW) distances between two probability measures are defined as the expectation of the Wasserstein distance between two one-dimensional projections of the two measures. The randomness comes from a projecting direction that is used to project the two input measures to one dimension. Due to the intractability of the expectation, Monte Carlo integration is performed to estimate the value of the SW distance. Despite having various variants, there has been no prior work that improves the Monte Carlo estimation scheme for the SW distance in terms of controlling its variance. To bridge the literature on variance reduction and the literature on the SW distance, we propose computationally efficient control variates to reduce the variance of the empirical estimation of the SW distance. The key idea is to first find Gaussian approximations of projected one-dimensional measures, then we utilize the closed-form of the Wasserstein-2 distance between two Gaussian distributions to design the control variates. In particular, we propose using a lower bound and an upper bound of the Wasserstein-2 distance between two fitted Gaussians as two computationally efficient control variates. We empirically show that the proposed control variate estimators can help to reduce the variance considerably when comparing measures over images and point-clouds. Finally, we demonstrate the favorable performance of the proposed control variate estimators in gradient flows to interpolate between two point-clouds and in deep generative modeling on standard image datasets, such as CIFAR10 and CelebA.

We present GSD, a diffusion model approach based on Gaussian Splatting (GS) representation for 3D object reconstruction from a single view. Prior works suffer from inconsistent 3D geometry or mediocre rendering quality due to improper representations. We take a step towards resolving these shortcomings by utilizing the recent state-of-the-art 3D explicit representation, Gaussian Splatting, and an unconditional diffusion model. This model learns to generate 3D objects represented by sets of GS ellipsoids. With these strong generative 3D priors, though learning unconditionally, the diffusion model is ready for view-guided reconstruction without further model fine-tuning. This is achieved by propagating fine-grained 2D features through the efficient yet flexible splatting function and the guided denoising sampling process. In addition, a 2D diffusion model is further employed to enhance rendering fidelity, and improve reconstructed GS quality by polishing and re-using the rendered images. The final reconstructed objects explicitly come with high-quality 3D structure and texture, and can be efficiently rendered in arbitrary views. Experiments on the challenging real-world CO3D dataset demonstrate the superiority of our approach. Project page: https://yxmu.foo/GSD/{this https URL}

Current deep learning models for Multispectral and Hyperspectral Image Fusion (MS/HS fusion) are typically designed for fixed spectral bands and spatial scales, which limits their transferability across diverse sensors. To address this, we propose SSA, a universal framework for MS/HS fusion with spectral-band and fusion-scale agnosticism. Specifically, we introduce Matryoshka Kernel (MK), a novel operator that enables a single model to adapt to arbitrary numbers of spectral channels. Meanwhile, we build SSA upon an Implicit Neural Representation (INR) backbone that models the HS signal as a continuous function, enabling reconstruction at arbitrary spatial resolutions. Together, these two forms of agnosticism enable a single MS/HS fusion model that generalizes effectively to unseen sensors and spatial scales. Extensive experiments demonstrate that our single model achieves state-of-the-art performance while generalizing well to unseen sensors and scales, paving the way toward future HS foundation models.

The adoption of Foundation Models in resource-constrained environments remains challenging due to their large size and inference costs. A promising way to overcome these limitations is post-training compression, which aims to balance reduced model size against performance degradation. This work presents Any Compression via Iterative Pruning (ACIP), a novel algorithmic approach to determine a compression-performance trade-off from a single stochastic gradient descent run. To ensure parameter efficiency, we use an SVD-reparametrization of linear layers and iteratively prune their singular values with a sparsity-inducing penalty. The resulting pruning order gives rise to a global parameter ranking that allows us to materialize models of any target size. Importantly, the compressed models exhibit strong predictive downstream performance without the need for costly fine-tuning. We evaluate ACIP on a large selection of open-weight LLMs and tasks, and demonstrate state-of-the-art results compared to existing factorisation-based compression methods. We also show that ACIP seamlessly complements common quantization-based compression techniques.

We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is that despite operating in high-dimensional parameter spaces (d=128), transformer training trajectories rapidly collapse onto low-dimensional execution manifolds of dimension 3--4. This dimensional collapse is robust across random seeds and moderate task difficulties, though the orientation of the manifold in parameter space varies between runs. We demonstrate that this geometric structure underlies several empirically observed phenomena: (1) sharp attention concentration emerges as saturation along routing coordinates within the execution manifold, (2) SGD commutators are preferentially aligned with the execution subspace (up to 10times random baseline) early in training, with >92% of non-commutativity confined to orthogonal staging directions and this alignment decreasing as training converges, and (3) sparse autoencoders capture auxiliary routing structure but fail to isolate execution itself, which remains distributed across the low-dimensional manifold. Our results suggest a unifying geometric framework for understanding transformer learning, where the vast majority of parameters serve to absorb optimization interference while core computation occurs in a dramatically reduced subspace. These findings have implications for interpretability, training curriculum design, and understanding the role of overparameterization in neural network learning.

Dimensionality reduction is critical for deploying dense retrieval systems at scale, yet mainstream post-hoc methods face a fundamental trade-off: principal component analysis (PCA) preserves dominant variance but underutilizes representational capacity, while whitening enforces isotropy at the cost of amplifying noise in the heavy-tailed eigenspectrum of retrieval embeddings. Intermediate spectral scaling methods unify these extremes by reweighting dimensions with a power coefficient γ, but treat γ as a fixed hyperparameter that requires task-specific tuning. We show that the optimal scaling strength γ is not a global constant: it varies systematically with target dimensionality k and is governed by the signal-to-noise ratio (SNR) of the retained subspace. Based on this insight, we propose Spectral Tempering (SpecTemp), a learning-free method that derives an adaptive γ(k) directly from the corpus eigenspectrum using local SNR analysis and knee-point normalization, requiring no labeled data or validation-based search. Extensive experiments demonstrate that Spectral Tempering consistently achieves near-oracle performance relative to grid-searched γ^*(k) while remaining fully learning-free and model-agnostic. Our code is publicly available at https://anonymous.4open.science/r/SpecTemp-0D37.

Diffusion models suffer from substantial computational overhead due to their inherently iterative inference process. While feature caching offers a promising acceleration strategy by reusing intermediate outputs across timesteps, naive reuse often incurs noticeable quality degradation. In this work, we formally analyze the cumulative error introduced by caching and decompose it into two principal components: feature shift error, caused by inaccuracies in cached outputs, and step amplification error, which arises from error propagation under fixed timestep schedules. To address these issues, we propose ERTACache, a principled caching framework that jointly rectifies both error types. Our method employs an offline residual profiling stage to identify reusable steps, dynamically adjusts integration intervals via a trajectory-aware correction coefficient, and analytically approximates cache-induced errors through a closed-form residual linearization model. Together, these components enable accurate and efficient sampling under aggressive cache reuse. Extensive experiments across standard image and video generation benchmarks show that ERTACache achieves up to 2x inference speedup while consistently preserving or even improving visual quality. Notably, on the state-of-the-art Wan2.1 video diffusion model, ERTACache delivers 2x acceleration with minimal VBench degradation, effectively maintaining baseline fidelity while significantly improving efficiency. The code is available at https://github.com/bytedance/ERTACache.

Image Super-Resolution is a fundamental problem in computer vision with broad applications spacing from medical imaging to satellite analysis. The ability to reconstruct high-resolution images from low-resolution inputs is crucial for enhancing downstream tasks such as object detection and segmentation. While deep learning has significantly advanced SR, achieving high-quality reconstructions with fine-grained details and realistic textures remains challenging, particularly at high upscaling factors. Recent approaches leveraging diffusion models have demonstrated promising results, yet they often struggle to balance perceptual quality with structural fidelity. In this work, we introduce ResQu a novel SR framework that integrates a quaternion wavelet preprocessing framework with latent diffusion models, incorporating a new quaternion wavelet- and time-aware encoder. Unlike prior methods that simply apply wavelet transforms within diffusion models, our approach enhances the conditioning process by exploiting quaternion wavelet embeddings, which are dynamically integrated at different stages of denoising. Furthermore, we also leverage the generative priors of foundation models such as Stable Diffusion. Extensive experiments on domain-specific datasets demonstrate that our method achieves outstanding SR results, outperforming in many cases existing approaches in perceptual quality and standard evaluation metrics. The code will be available after the revision process.

Recorrupted-to-Recorrupted (R2R) has emerged as a methodology for training deep networks for image restoration in a self-supervised manner from noisy measurement data alone, demonstrating equivalence in expectation to the supervised squared loss in the case of Gaussian noise. However, its effectiveness with non-Gaussian noise remains unexplored. In this paper, we propose Generalized R2R (GR2R), extending the R2R framework to handle a broader class of noise distribution as additive noise like log-Rayleigh and address the natural exponential family including Poisson and Gamma noise distributions, which play a key role in many applications including low-photon imaging and synthetic aperture radar. We show that the GR2R loss is an unbiased estimator of the supervised loss and that the popular Stein's unbiased risk estimator can be seen as a special case. A series of experiments with Gaussian, Poisson, and Gamma noise validate GR2R's performance, showing its effectiveness compared to other self-supervised methods.

We show that in a variety of large-scale deep learning scenarios the gradient dynamically converges to a very small subspace after a short period of training. The subspace is spanned by a few top eigenvectors of the Hessian (equal to the number of classes in the dataset), and is mostly preserved over long periods of training. A simple argument then suggests that gradient descent may happen mostly in this subspace. We give an example of this effect in a solvable model of classification, and we comment on possible implications for optimization and learning.

Image restoration problems are typically ill-posed in the sense that each degraded image can be restored in infinitely many valid ways. To accommodate this, many works generate a diverse set of outputs by attempting to randomly sample from the posterior distribution of natural images given the degraded input. Here we argue that this strategy is commonly of limited practical value because of the heavy tail of the posterior distribution. Consider for example inpainting a missing region of the sky in an image. Since there is a high probability that the missing region contains no object but clouds, any set of samples from the posterior would be entirely dominated by (practically identical) completions of sky. However, arguably, presenting users with only one clear sky completion, along with several alternative solutions such as airships, birds, and balloons, would better outline the set of possibilities. In this paper, we initiate the study of meaningfully diverse image restoration. We explore several post-processing approaches that can be combined with any diverse image restoration method to yield semantically meaningful diversity. Moreover, we propose a practical approach for allowing diffusion based image restoration methods to generate meaningfully diverse outputs, while incurring only negligent computational overhead. We conduct extensive user studies to analyze the proposed techniques, and find the strategy of reducing similarity between outputs to be significantly favorable over posterior sampling. Code and examples are available at https://noa-cohen.github.io/MeaningfulDiversityInIR.

The sufficiently scattered condition (SSC) is a key condition in the study of identifiability of various matrix factorization problems, including nonnegative, minimum-volume, symmetric, simplex-structured, and polytopic matrix factorizations. The SSC allows one to guarantee that the computed matrix factorization is unique/identifiable, up to trivial ambiguities. However, this condition is NP-hard to check in general. In this paper, we show that it can however be checked in a reasonable amount of time in realistic scenarios, when the factorization rank is not too large. This is achieved by formulating the problem as a non-convex quadratic optimization problem over a bounded set. We use the global non-convex optimization software Gurobi, and showcase the usefulness of this code on synthetic data sets and on real-world hyperspectral images.

The space of unitary C_{0}-semigroups on separable infinite dimensional Hilbert space, when viewed under the topology of uniform weak convergence on compact subsets of R_{+}, is known to admit various interesting residual subspaces. Before treating the contractive case, the problem of the complete metrisability of this space was raised in [Eisner, 2010]. Utilising Borel complexity computations and automatic continuity results for semigroups, we obtain a general result, which in particular implies that the one-/multiparameter contractive C_{0}-semigroups constitute Polish spaces and thus positively addresses the open problem.

Off-resonance artifacts in magnetic resonance imaging (MRI) are visual distortions that occur when the actual resonant frequencies of spins within the imaging volume differ from the expected frequencies used to encode spatial information. These discrepancies can be caused by a variety of factors, including magnetic field inhomogeneities, chemical shifts, or susceptibility differences within the tissues. Such artifacts can manifest as blurring, ghosting, or misregistration of the reconstructed image, and they often compromise its diagnostic quality. We propose to resolve these artifacts by lifting the 2D MRI reconstruction problem to 3D, introducing an additional "spectral" dimension to model this off-resonance. Our approach is inspired by recent progress in modeling radiance fields, and is capable of reconstructing both static and dynamic MR images as well as separating fat and water, which is of independent clinical interest. We demonstrate our approach in the context of PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction) MRI acquisitions, which are popular for their robustness to motion artifacts. Our method operates in a few minutes on a single GPU, and to our knowledge is the first to correct for chemical shift in gradient echo PROPELLER MRI reconstruction without additional measurements or pretraining data.