Daily Papers

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.

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of `flows' -- one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time R^3times R, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towards general vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of initial conditions. The network training considers two constraints. A data term is responsible for fitting the initial condition to the corresponding time instant, usually R^3 times {0}. Then, a LSE term forces the network to approximate the underlying geometric evolution given by the LSE, without any supervision. The network can also be initialized based on previously trained initial conditions, resulting in faster convergence compared to the standard approach.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion.

Large language models (LLMs) show excellent performance but are compute- and memory-intensive. Quantization can reduce memory and accelerate inference. However, existing methods cannot maintain accuracy and hardware efficiency at the same time. We propose SmoothQuant, a training-free, accuracy-preserving, and general-purpose post-training quantization (PTQ) solution to enable 8-bit weight, 8-bit activation (W8A8) quantization for LLMs. Based on the fact that weights are easy to quantize while activations are not, SmoothQuant smooths the activation outliers by offline migrating the quantization difficulty from activations to weights with a mathematically equivalent transformation. SmoothQuant enables an INT8 quantization of both weights and activations for all the matrix multiplications in LLMs, including OPT, BLOOM, GLM, MT-NLG, and LLaMA family. We demonstrate up to 1.56x speedup and 2x memory reduction for LLMs with negligible loss in accuracy. SmoothQuant enables serving 530B LLM within a single node. Our work offers a turn-key solution that reduces hardware costs and democratizes LLMs. Code is available at https://github.com/mit-han-lab/smoothquant.

Well-known activation functions like ReLU or Leaky ReLU are non-differentiable at the origin. Over the years, many smooth approximations of ReLU have been proposed using various smoothing techniques. We propose new smooth approximations of a non-differentiable activation function by convolving it with approximate identities. In particular, we present smooth approximations of Leaky ReLU and show that they outperform several well-known activation functions in various datasets and models. We call this function Smooth Activation Unit (SAU). Replacing ReLU by SAU, we get 5.12% improvement with ShuffleNet V2 (2.0x) model on CIFAR100 dataset.

Explaining the output of a deep network remains a challenge. In the case of an image classifier, one type of explanation is to identify pixels that strongly influence the final decision. A starting point for this strategy is the gradient of the class score function with respect to the input image. This gradient can be interpreted as a sensitivity map, and there are several techniques that elaborate on this basic idea. This paper makes two contributions: it introduces SmoothGrad, a simple method that can help visually sharpen gradient-based sensitivity maps, and it discusses lessons in the visualization of these maps. We publish the code for our experiments and a website with our results.

This paper introduces a new learning paradigm termed Neural Metamorphosis (NeuMeta), which aims to build self-morphable neural networks. Contrary to crafting separate models for different architectures or sizes, NeuMeta directly learns the continuous weight manifold of neural networks. Once trained, we can sample weights for any-sized network directly from the manifold, even for previously unseen configurations, without retraining. To achieve this ambitious goal, NeuMeta trains neural implicit functions as hypernetworks. They accept coordinates within the model space as input, and generate corresponding weight values on the manifold. In other words, the implicit function is learned in a way, that the predicted weights is well-performed across various models sizes. In training those models, we notice that, the final performance closely relates on smoothness of the learned manifold. In pursuit of enhancing this smoothness, we employ two strategies. First, we permute weight matrices to achieve intra-model smoothness, by solving the Shortest Hamiltonian Path problem. Besides, we add a noise on the input coordinates when training the implicit function, ensuring models with various sizes shows consistent outputs. As such, NeuMeta shows promising results in synthesizing parameters for various network configurations. Our extensive tests in image classification, semantic segmentation, and image generation reveal that NeuMeta sustains full-size performance even at a 75% compression rate.

We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal point iterations on the proxy combined with relatively few stochastic gradients from the objective. When the difference between the objective and the proxy is delta-smooth, our algorithm guarantees convergence at a rate matching stochastic gradient descent on a delta-smooth objective, which can lead to substantially better sample efficiency. Our algorithm has many potential applications in machine learning, and provides a principled means of leveraging synthetic data, physics simulators, mixed public and private data, and more.

Learning spatial-temporal correspondences in cardiac motion from images is important for understanding the underlying dynamics of cardiac anatomical structures. Many methods explicitly impose smoothness constraints such as the L_2 norm on the displacement vector field (DVF), while usually ignoring biomechanical feasibility in the transformation. Other geometric constraints either regularize specific regions of interest such as imposing incompressibility on the myocardium or introduce additional steps such as training a separate network-based regularizer on physically simulated datasets. In this work, we propose an explicit biomechanics-informed prior as regularization on the predicted DVF in modeling a more generic biomechanically plausible transformation within all cardiac structures without introducing additional training complexity. We validate our methods on two publicly available datasets in the context of 2D MRI data and perform extensive experiments to illustrate the effectiveness and robustness of our proposed methods compared to other competing regularization schemes. Our proposed methods better preserve biomechanical properties by visual assessment and show advantages in segmentation performance using quantitative evaluation metrics. The code is publicly available at https://github.com/Voldemort108X/bioinformed_reg.

In this paper, we adopt the Universal Manifold Embedding (UME) framework for the estimation of rigid transformations and extend it, so that it can accommodate scenarios involving partial overlap and differently sampled point clouds. UME is a methodology designed for mapping observations of the same object, related by rigid transformations, into a single low-dimensional linear subspace. This process yields a transformation-invariant representation of the observations, with its matrix form representation being covariant (i.e. equivariant) with the transformation. We extend the UME framework by introducing a UME-compatible feature extraction method augmented with a unique UME contrastive loss and a sampling equalizer. These components are integrated into a comprehensive and robust registration pipeline, named UMERegRobust. We propose the RotKITTI registration benchmark, specifically tailored to evaluate registration methods for scenarios involving large rotations. UMERegRobust achieves better than state-of-the-art performance on the KITTI benchmark, especially when strict precision of (1{\deg}, 10cm) is considered (with an average gain of +9%), and notably outperform SOTA methods on the RotKITTI benchmark (with +45% gain compared the most recent SOTA method).

Trustworthy interpretation of deep learning models is critical for neuroimaging applications, yet commonly used Explainable AI (XAI) methods lack rigorous validation, risking misinterpretation. We performed the first large-scale, systematic comparison of XAI methods on ~45,000 structural brain MRIs using a novel XAI validation framework. This framework establishes verifiable ground truth by constructing prediction tasks with known signal sources - from localized anatomical features to subject-specific clinical lesions - without artificially altering input images. Our analysis reveals systematic failures in two of the most widely used methods: GradCAM consistently failed to localize predictive features, while Layer-wise Relevance Propagation generated extensive, artifactual explanations that suggest incompatibility with neuroimaging data characteristics. Our results indicate that these failures stem from a domain mismatch, where methods with design principles tailored to natural images require substantial adaptation for neuroimaging data. In contrast, the simpler, gradient-based method SmoothGrad, which makes fewer assumptions about data structure, proved consistently accurate, suggesting its conceptual simplicity makes it more robust to this domain shift. These findings highlight the need for domain-specific adaptation and validation of XAI methods, suggest that interpretations from prior neuroimaging studies using standard XAI methodology warrant re-evaluation, and provide urgent guidance for practical application of XAI in neuroimaging.

Diffusion models have achieved remarkable image generation quality surpassing previous generative models. However, a notable limitation of diffusion models, in comparison to GANs, is their difficulty in smoothly interpolating between two image samples, due to their highly unstructured latent space. Such a smooth interpolation is intriguing as it naturally serves as a solution for the image morphing task with many applications. In this work, we present DiffMorpher, the first approach enabling smooth and natural image interpolation using diffusion models. Our key idea is to capture the semantics of the two images by fitting two LoRAs to them respectively, and interpolate between both the LoRA parameters and the latent noises to ensure a smooth semantic transition, where correspondence automatically emerges without the need for annotation. In addition, we propose an attention interpolation and injection technique and a new sampling schedule to further enhance the smoothness between consecutive images. Extensive experiments demonstrate that DiffMorpher achieves starkly better image morphing effects than previous methods across a variety of object categories, bridging a critical functional gap that distinguished diffusion models from GANs.

Randomized smoothing is the state-of-the-art approach to construct image classifiers that are provably robust against additive adversarial perturbations of bounded magnitude. However, it is more complicated to construct reasonable certificates against semantic transformation (e.g., image blurring, translation, gamma correction) and their compositions. In this work, we propose General Lipschitz (GL), a new framework to certify neural networks against composable resolvable semantic perturbations. Within the framework, we analyze transformation-dependent Lipschitz-continuity of smoothed classifiers w.r.t. transformation parameters and derive corresponding robustness certificates. Our method performs comparably to state-of-the-art approaches on the ImageNet dataset.

The equivalence of realizable and agnostic learnability is a fundamental phenomenon in learning theory. With variants ranging from classical settings like PAC learning and regression to recent trends such as adversarially robust learning, it's surprising that we still lack a unified theory; traditional proofs of the equivalence tend to be disparate, and rely on strong model-specific assumptions like uniform convergence and sample compression. In this work, we give the first model-independent framework explaining the equivalence of realizable and agnostic learnability: a three-line blackbox reduction that simplifies, unifies, and extends our understanding across a wide variety of settings. This includes models with no known characterization of learnability such as learning with arbitrary distributional assumptions and more general loss functions, as well as a host of other popular settings such as robust learning, partial learning, fair learning, and the statistical query model. More generally, we argue that the equivalence of realizable and agnostic learning is actually a special case of a broader phenomenon we call property generalization: any desirable property of a learning algorithm (e.g. noise tolerance, privacy, stability) that can be satisfied over finite hypothesis classes extends (possibly in some variation) to any learnable hypothesis class.

Developing equivariant neural networks for the E(3) group plays an important role in modeling 3D data across real-world applications. Enforcing this equivariance primarily involves the tensor products of irreducible representations (irreps). However, the computational complexity of such operations increases significantly as higher-order tensors are used. In this work, we propose a systematic approach to substantially accelerate the computation of the tensor products of irreps. We mathematically connect the commonly used Clebsch-Gordan coefficients to the Gaunt coefficients, which are integrals of products of three spherical harmonics. Through Gaunt coefficients, the tensor product of irreps becomes equivalent to the multiplication between spherical functions represented by spherical harmonics. This perspective further allows us to change the basis for the equivariant operations from spherical harmonics to a 2D Fourier basis. Consequently, the multiplication between spherical functions represented by a 2D Fourier basis can be efficiently computed via the convolution theorem and Fast Fourier Transforms. This transformation reduces the complexity of full tensor products of irreps from O(L^6) to O(L^3), where L is the max degree of irreps. Leveraging this approach, we introduce the Gaunt Tensor Product, which serves as a new method to construct efficient equivariant operations across different model architectures. Our experiments on the Open Catalyst Project and 3BPA datasets demonstrate both the increased efficiency and improved performance of our approach.

Deep networks are gradually penetrating almost every domain in our lives due to their amazing success. However, with substantive performance accuracy improvements comes the price of irreproducibility. Two identical models, trained on the exact same training dataset may exhibit large differences in predictions on individual examples even when average accuracy is similar, especially when trained on highly distributed parallel systems. The popular Rectified Linear Unit (ReLU) activation has been key to recent success of deep networks. We demonstrate, however, that ReLU is also a catalyzer to irreproducibility in deep networks. We show that not only can activations smoother than ReLU provide better accuracy, but they can also provide better accuracy-reproducibility tradeoffs. We propose a new family of activations; Smooth ReLU (SmeLU), designed to give such better tradeoffs, while also keeping the mathematical expression simple, and thus implementation cheap. SmeLU is monotonic, mimics ReLU, while providing continuous gradients, yielding better reproducibility. We generalize SmeLU to give even more flexibility and then demonstrate that SmeLU and its generalized form are special cases of a more general methodology of REctified Smooth Continuous Unit (RESCU) activations. Empirical results demonstrate the superior accuracy-reproducibility tradeoffs with smooth activations, SmeLU in particular.

Using parts of existing models to rebuild new models, commonly termed as example-based modeling, is a classical methodology in the realm of computer graphics. Previous works mostly focus on shape composition, making them very hard to use for realistic composition of 3D objects captured from real-world scenes. This leads to combining multiple NeRFs into a single 3D scene to achieve seamless appearance blending. However, the current SeamlessNeRF method struggles to achieve interactive editing and harmonious stitching for real-world scenes due to its gradient-based strategy and grid-based representation. To this end, we present an example-based modeling method that combines multiple Gaussian fields in a point-based representation using sample-guided synthesis. Specifically, as for composition, we create a GUI to segment and transform multiple fields in real time, easily obtaining a semantically meaningful composition of models represented by 3D Gaussian Splatting (3DGS). For texture blending, due to the discrete and irregular nature of 3DGS, straightforwardly applying gradient propagation as SeamlssNeRF is not supported. Thus, a novel sampling-based cloning method is proposed to harmonize the blending while preserving the original rich texture and content. Our workflow consists of three steps: 1) real-time segmentation and transformation of a Gaussian model using a well-tailored GUI, 2) KNN analysis to identify boundary points in the intersecting area between the source and target models, and 3) two-phase optimization of the target model using sampling-based cloning and gradient constraints. Extensive experimental results validate that our approach significantly outperforms previous works in terms of realistic synthesis, demonstrating its practicality. More demos are available at https://ingra14m.github.io/gs_stitching_website.

Textured 3D morphing creates smooth and plausible interpolation sequences between two 3D objects, focusing on transitions in both shape and texture. This is important for creative applications like visual effects in filmmaking. Previous methods rely on establishing point-to-point correspondences and determining smooth deformation trajectories, which inherently restrict them to shape-only morphing on untextured, topologically aligned datasets. This restriction leads to labor-intensive preprocessing and poor generalization. To overcome these challenges, we propose a method for 3D regenerative morphing using a 3D diffusion prior. Unlike previous methods that depend on explicit correspondences and deformations, our method eliminates the additional need for obtaining correspondence and uses the 3D diffusion prior to generate morphing. Specifically, we introduce a 3D diffusion model and interpolate the source and target information at three levels: initial noise, model parameters, and condition features. We then explore an Attention Fusion strategy to generate more smooth morphing sequences. To further improve the plausibility of semantic interpolation and the generated 3D surfaces, we propose two strategies: (a) Token Reordering, where we match approximate tokens based on semantic analysis to guide implicit correspondences in the denoising process of the diffusion model, and (b) Low-Frequency Enhancement, where we enhance low-frequency signals in the tokens to improve the quality of generated surfaces. Experimental results show that our method achieves superior smoothness and plausibility in 3D morphing across diverse cross-category object pairs, offering a novel regenerative method for 3D morphing with textured representations.

Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn representations that are globally smooth on a manifold. To do so, it shows that under typical conditions the problem of learning a Lipschitz continuous function on a manifold is equivalent to a dynamically weighted manifold regularization problem. This observation leads to a practical algorithm based on a weighted Laplacian penalty whose weights are adapted using stochastic gradient techniques. It is shown that under mild conditions, this method estimates the Lipschitz constant of the solution, learning a globally smooth solution as a byproduct. Experiments on real world data illustrate the advantages of the proposed method relative to existing alternatives.

Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization (muP) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern scale-invariant architectures, training quickly enters an optimizer-governed steady state where normalization layers create backward scale sensitivity and the effective learning rate becomes width dependent, degrading muP transfer. We address this by introducing a weight-decay scaling rule for AdamW that preserves sublayer gain across widths. Empirically, the singular-value spectrum of each matrix parameter scales in norm as eta/lambda with an approximately invariant shape; under width scaling d, we observe that the top singular value scales approximately as eta/lambdacdot d^{0.75}. Combining this observation with the muP learning-rate rule eta_2propto d^{-1} for matrix-like parameters implies an empirical weight-decay scaling rule lambda_2propto d that approximately keeps sublayer gains width invariant. Together with vector-like parameters trained at eta_1=Theta_d(1) and lambda_1=0, this yields zero-shot transfer of both learning rate and weight decay from proxy to target widths, removing per-width sweeps. We validate the rule on LLaMA-style Transformers and in a minimal synthetic setting, and we provide a simple diagnostic, matching top singular values, to check sublayer-gain invariance. Our results extend muP beyond the near-init regime by explicitly controlling steady-state scales set by the optimizer, offering a practical recipe for width-robust hyperparameter transfer under AdamW.

We provide a mapping between past null and future null infinity in three-dimensional flat space, using symmetry considerations. From this we derive a mapping between the corresponding asymptotic symmetry groups. By studying the metric at asymptotic regions, we find that the mapping is energy preserving and yields an infinite number of conservation laws.

In this paper, we study the implicit regularization of stochastic gradient descent (SGD) through the lens of {\em dynamical stability} (Wu et al., 2018). We start by revising existing stability analyses of SGD, showing how the Frobenius norm and trace of Hessian relate to different notions of stability. Notably, if a global minimum is linearly stable for SGD, then the trace of Hessian must be less than or equal to 2/eta, where eta denotes the learning rate. By contrast, for gradient descent (GD), the stability imposes a similar constraint but only on the largest eigenvalue of Hessian. We then turn to analyze the generalization properties of these stable minima, focusing specifically on two-layer ReLU networks and diagonal linear networks. Notably, we establish the {\em equivalence} between these metrics of sharpness and certain parameter norms for the two models, which allows us to show that the stable minima of SGD provably generalize well. By contrast, the stability-induced regularization of GD is provably too weak to ensure satisfactory generalization. This discrepancy provides an explanation of why SGD often generalizes better than GD. Note that the learning rate (LR) plays a pivotal role in the strength of stability-induced regularization. As the LR increases, the regularization effect becomes more pronounced, elucidating why SGD with a larger LR consistently demonstrates superior generalization capabilities. Additionally, numerical experiments are provided to support our theoretical findings.

This work provides a smooth and everywhere well-defined extension of Bondi-Metzner-Sachs (BMS) supertranslations into the bulk of Minkowski space. The supertranslations lead to physically distinct spacetimes, all isometric to Minkowski space. This construction is in contrast to the often used, non-smooth BMS transformations that appear in a gauge-fixed description of the theory.

In studies of transferable learning, scaling laws are obtained for various important foundation models to predict their properties and performance at larger scales. We show here how scaling law derivation can also be used for model and dataset comparison, allowing to decide which procedure is to be preferred for pre-training. For the first time, full scaling laws based on dense measurements across a wide span of model and samples seen scales are derived for two important language-vision learning procedures, CLIP and MaMMUT, that use either contrastive only or contrastive and captioning text generative loss. Ensuring sufficient prediction accuracy for held out points, we use derived scaling laws to compare both models, obtaining evidence for MaMMUT's stronger improvement with scale and better sample efficiency than standard CLIP. To strengthen validity of the comparison, we show scaling laws for various downstream tasks, classification, retrieval, and segmentation, and for different open datasets, DataComp, DFN and Re-LAION, observing consistently the same trends. We show that comparison can also be performed when deriving scaling laws with a constant learning rate schedule, reducing compute cost. Accurate derivation of scaling laws provides thus means to perform model and dataset comparison across scale spans, avoiding misleading conclusions based on measurements from single reference scales only, paving the road for systematic comparison and improvement of open foundation models and datasets for their creation. We release all the pre-trained models with their intermediate checkpoints, including openMaMMUT-L/14, which achieves 80.3% zero-shot ImageNet-1k accuracy, trained on 12.8B samples from DataComp-1.4B. Code for reproducing experiments in the paper and raw experiments data can be found at https://github.com/LAION-AI/scaling-laws-for-comparison.

The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms -- often variants of stochastic gradient descent -- exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. 2021. We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we identify intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory.

Datasets often have their intrinsic symmetries, and particular deep-learning models called equivariant or invariant models have been developed to exploit these symmetries. However, if some or all of these symmetries are only approximate, which frequently happens in practice, these models may be suboptimal due to the architectural restrictions imposed on them. We tackle this issue of approximate symmetries in a setup where symmetries are mixed, i.e., they are symmetries of not single but multiple different types and the degree of approximation varies across these types. Instead of proposing a new architectural restriction as in most of the previous approaches, we present a regularizer-based method for building a model for a dataset with mixed approximate symmetries. The key component of our method is what we call equivariance regularizer for a given type of symmetries, which measures how much a model is equivariant with respect to the symmetries of the type. Our method is trained with these regularizers, one per each symmetry type, and the strength of the regularizers is automatically tuned during training, leading to the discovery of the approximation levels of some candidate symmetry types without explicit supervision. Using synthetic function approximation and motion forecasting tasks, we demonstrate that our method achieves better accuracy than prior approaches while discovering the approximate symmetry levels correctly.

We tackle the task of geometric image editing, where an object within an image is repositioned, reoriented, or reshaped while preserving overall scene coherence. Previous diffusion-based editing methods often attempt to handle all relevant subtasks in a single step, proving difficult when transformations become large or structurally complex. We address this by proposing a decoupled pipeline that separates object transformation, source region inpainting, and target region refinement. Both inpainting and refinement are implemented using a training-free diffusion approach, FreeFine. In experiments on our new GeoBench benchmark, which contains both 2D and 3D editing scenarios, FreeFine outperforms state-of-the-art alternatives in image fidelity, and edit precision, especially under demanding transformations. Code and benchmark are available at: https://github.com/CIawevy/FreeFine

This study explores the concept of equivariance in vision-language foundation models (VLMs), focusing specifically on the multimodal similarity function that is not only the major training objective but also the core delivery to support downstream tasks. Unlike the existing image-text similarity objective which only categorizes matched pairs as similar and unmatched pairs as dissimilar, equivariance also requires similarity to vary faithfully according to the semantic changes. This allows VLMs to generalize better to nuanced and unseen multimodal compositions. However, modeling equivariance is challenging as the ground truth of semantic change is difficult to collect. For example, given an image-text pair about a dog, it is unclear to what extent the similarity changes when the pixel is changed from dog to cat? To this end, we propose EqSim, a regularization loss that can be efficiently calculated from any two matched training pairs and easily pluggable into existing image-text retrieval fine-tuning. Meanwhile, to further diagnose the equivariance of VLMs, we present a new challenging benchmark EqBen. Compared to the existing evaluation sets, EqBen is the first to focus on "visual-minimal change". Extensive experiments show the lack of equivariance in current VLMs and validate the effectiveness of EqSim. Code is available at https://github.com/Wangt-CN/EqBen.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

Video generators are increasingly evaluated as potential world models, which requires them to encode and understand physical laws. We investigate their representation of a fundamental law: gravity. Out-of-the-box video generators consistently generate objects falling at an effectively slower acceleration. However, these physical tests are often confounded by ambiguous metric scale. We first investigate if observed physical errors are artifacts of these ambiguities (e.g., incorrect frame rate assumptions). We find that even temporal rescaling cannot correct the high-variance gravity artifacts. To rigorously isolate the underlying physical representation from these confounds, we introduce a unit-free, two-object protocol that tests the timing ratio t_1^2/t_2^2 = h_1/h_2, a relationship independent of g, focal length, and scale. This relative test reveals violations of Galileo's equivalence principle. We then demonstrate that this physical gap can be partially mitigated with targeted specialization. A lightweight low-rank adaptor fine-tuned on only 100 single-ball clips raises g_{eff} from 1.81,m/s^2 to 6.43,m/s^2 (reaching 65% of terrestrial gravity). This specialist adaptor also generalizes zero-shot to two-ball drops and inclined planes, offering initial evidence that specific physical laws can be corrected with minimal data.

We introduce a novel method for representation learning that uses an artificial supervision signal based on counting visual primitives. This supervision signal is obtained from an equivariance relation, which does not require any manual annotation. We relate transformations of images to transformations of the representations. More specifically, we look for the representation that satisfies such relation rather than the transformations that match a given representation. In this paper, we use two image transformations in the context of counting: scaling and tiling. The first transformation exploits the fact that the number of visual primitives should be invariant to scale. The second transformation allows us to equate the total number of visual primitives in each tile to that in the whole image. These two transformations are combined in one constraint and used to train a neural network with a contrastive loss. The proposed task produces representations that perform on par or exceed the state of the art in transfer learning benchmarks.

Geometric deep learning, i.e., designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, have achieved great successes in the last decade. One critical inductive bias is that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. The existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. To solve this problem, we revisit why the existing neural networks cannot maintain transformation invariance when handling geometric data. Our findings show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNN), a straightforward and general framework for geometric data. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling before feeding the representations into neural networks. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our proposed method. Based on the experimental results, we advocate that TinvNN should be considered a new starting point and an essential baseline for further studies of transformation-invariant geometric deep learning.

Gaining insight into how deep convolutional neural network models perform image classification and how to explain their outputs have been a concern to computer vision researchers and decision makers. These deep models are often referred to as black box due to low comprehension of their internal workings. As an effort to developing explainable deep learning models, several methods have been proposed such as finding gradients of class output with respect to input image (sensitivity maps), class activation map (CAM), and Gradient based Class Activation Maps (Grad-CAM). These methods under perform when localizing multiple occurrences of the same class and do not work for all CNNs. In addition, Grad-CAM does not capture the entire object in completeness when used on single object images, this affect performance on recognition tasks. With the intention to create an enhanced visual explanation in terms of visual sharpness, object localization and explaining multiple occurrences of objects in a single image, we present Smooth Grad-CAM++ Simple demo: http://35.238.22.135:5000/, a technique that combines methods from two other recent techniques---SMOOTHGRAD and Grad-CAM++. Our Smooth Grad-CAM++ technique provides the capability of either visualizing a layer, subset of feature maps, or subset of neurons within a feature map at each instance at the inference level (model prediction process). After experimenting with few images, Smooth Grad-CAM++ produced more visually sharp maps with better localization of objects in the given input images when compared with other methods.

Backdoor inversion, the process of finding a backdoor trigger inserted into a machine learning model, has become the pillar of many backdoor detection and defense methods. Previous works on backdoor inversion often recover the backdoor through an optimization process to flip a support set of clean images into the target class. However, it is rarely studied and understood how large this support set should be to recover a successful backdoor. In this work, we show that one can reliably recover the backdoor trigger with as few as a single image. Specifically, we propose the SmoothInv method, which first constructs a robust smoothed version of the backdoored classifier and then performs guided image synthesis towards the target class to reveal the backdoor pattern. SmoothInv requires neither an explicit modeling of the backdoor via a mask variable, nor any complex regularization schemes, which has become the standard practice in backdoor inversion methods. We perform both quantitaive and qualitative study on backdoored classifiers from previous published backdoor attacks. We demonstrate that compared to existing methods, SmoothInv is able to recover successful backdoors from single images, while maintaining high fidelity to the original backdoor. We also show how we identify the target backdoored class from the backdoored classifier. Last, we propose and analyze two countermeasures to our approach and show that SmoothInv remains robust in the face of an adaptive attacker. Our code is available at https://github.com/locuslab/smoothinv .

Diffusion models have achieved state-of-the-art performance in generating images, audio, and video, but their adaptation to text remains challenging due to its discrete nature. Prior approaches either apply Gaussian diffusion in continuous latent spaces, which inherits semantic structure but struggles with token decoding, or operate in categorical simplex space, which respect discreteness but disregard semantic relation between tokens. In this paper, we propose Smoothing Diffusion on Token Embeddings (Smoothie), a novel diffusion method that combines the strengths of both approaches by progressively smoothing token embeddings based on semantic similarity. This technique enables gradual information removal while maintaining a natural decoding process. Experimental results on several sequence-to-sequence generation tasks demonstrate that Smoothie outperforms existing diffusion-based models in generation quality. Furthermore, ablation studies show that our proposed diffusion space yields better performance than both the standard embedding space and the categorical simplex. Our code is available at https://github.com/ashaba1in/smoothie.

Text-guided non-rigid editing involves complex edits for input images, such as changing motion or compositions within their surroundings. Since it requires manipulating the input structure, existing methods often struggle with preserving object identity and background, particularly when combined with Stable Diffusion. In this work, we propose a training-free approach for non-rigid editing with Stable Diffusion, aimed at improving the identity preservation quality without compromising editability. Our approach comprises three stages: text optimization, latent inversion, and timestep-aware text injection sampling. Inspired by the recent success of Imagic, we employ their text optimization for smooth editing. Then, we introduce latent inversion to preserve the input image's identity without additional model fine-tuning. To fully utilize the input reconstruction ability of latent inversion, we suggest timestep-aware text inject sampling. This effectively retains the structure of the input image by injecting the source text prompt in early sampling steps and then transitioning to the target prompt in subsequent sampling steps. This strategic approach seamlessly harmonizes with text optimization, facilitating complex non-rigid edits to the input without losing the original identity. We demonstrate the effectiveness of our method in terms of identity preservation, editability, and aesthetic quality through extensive experiments.

In an unbounded plane, straight lines are used extensively for mathematical analysis. They are tools of convenience. However, those with high slope values become unbounded at a faster rate than the independent variable. So, straight lines, in this work, are made to be bounded by introducing a parametric nonlinear term that is positive. The straight lines are transformed into bounded nonlinear curves that become unbounded at a much slower rate than the independent variable. This transforming equation can be expressed as a continued fraction of straight lines. The continued fraction is real-valued and converges to the solutions of the transforming equation. Following Euler's method, the continued fraction has been reduced into an infinite series. The usefulness of the bounding nature of continued fraction is demonstrated by solving the problem of image classification. Parameters estimated on the Fashion-MNIST dataset of greyscale images using continued fraction of regression lines have less variance, converge quickly and are more accurate than the linear counterpart. Moreover, this multi-dimensional parametric estimation problem can be expressed on xy- plane using the parameters of the continued fraction and patterns emerge on planar plots.

Recent one-shot video tuning methods, which fine-tune the network on a specific video based on pre-trained text-to-image models (e.g., Stable Diffusion), are popular in the community because of the flexibility. However, these methods often produce videos marred by incoherence and inconsistency. To address these limitations, this paper introduces a simple yet effective noise constraint across video frames. This constraint aims to regulate noise predictions across their temporal neighbors, resulting in smooth latents. It can be simply included as a loss term during the training phase. By applying the loss to existing one-shot video tuning methods, we significantly improve the overall consistency and smoothness of the generated videos. Furthermore, we argue that current video evaluation metrics inadequately capture smoothness. To address this, we introduce a novel metric that considers detailed features and their temporal dynamics. Experimental results validate the effectiveness of our approach in producing smoother videos on various one-shot video tuning baselines. The source codes and video demos are available at https://github.com/SPengLiang/SmoothVideo{https://github.com/SPengLiang/SmoothVideo}.

Large language models (LLMs) have shown remarkable capabilities in various tasks. However their huge model size and the consequent demand for computational and memory resources also pose challenges to model deployment. Currently, 4-bit post-training quantization (PTQ) has achieved some success in LLMs, reducing the memory footprint by approximately 75% compared to FP16 models, albeit with some accuracy loss. In this paper, we propose SmoothQuant+, an accurate and efficient 4-bit weight-only PTQ that requires no additional training, which enables lossless in accuracy for LLMs for the first time. Based on the fact that the loss of weight quantization is amplified by the activation outliers, SmoothQuant+ smoothes the activation outliers by channel before quantization, while adjusting the corresponding weights for mathematical equivalence, and then performs group-wise 4-bit weight quantization for linear layers. We have integrated SmoothQuant+ into the vLLM framework, an advanced high-throughput inference engine specially developed for LLMs, and equipped it with an efficient W4A16 CUDA kernels, so that vLLM can seamlessly support SmoothQuant+ 4-bit weight quantization. Our results show that, with SmoothQuant+, the Code Llama-34B model can be quantized and deployed on a A100 40GB GPU, achieving lossless accuracy and a throughput increase of 1.9 to 4.0 times compared to the FP16 model deployed on two A100 40GB GPUs. Moreover, the latency per token is only 68% of the FP16 model deployed on two A100 40GB GPUs. This is the state-of-the-art 4-bit weight quantization for LLMs as we know.

Linear transformation of the inputs alters the training performance of feed-forward networks that are otherwise equivalent. However, most linear transforms are viewed as a pre-processing operation separate from the actual training. Starting from equivalent networks, it is shown that pre-processing inputs using linear transformation are equivalent to multiplying the negative gradient matrix with an autocorrelation matrix per training iteration. Second order method is proposed to find the autocorrelation matrix that maximizes learning in a given iteration. When the autocorrelation matrix is diagonal, the method optimizes input gains. This optimal input gain (OIG) approach is used to improve two first-order two-stage training algorithms, namely back-propagation (BP) and hidden weight optimization (HWO), which alternately update the input weights and solve linear equations for output weights. Results show that the proposed OIG approach greatly enhances the performance of the first-order algorithms, often allowing them to rival the popular Levenberg-Marquardt approach with far less computation. It is shown that HWO is equivalent to BP with Whitening transformation applied to the inputs. HWO effectively combines Whitening transformation with learning. Thus, OIG improved HWO could be a significant building block to more complex deep learning architectures.

Averaging the parameters of models that have the same architecture and initialization can provide a means of combining their respective capabilities. In this paper, we take the perspective that this "merging" operation can be seen as choosing parameters that approximately maximize the joint likelihood of the posteriors of the models' parameters. Computing a simple average of the models' parameters therefore corresponds to making an isotropic Gaussian approximation to their posteriors. We develop an alternative merging procedure based on the Laplace approximation where we approximate each model's posterior as a Gaussian distribution whose precision matrix corresponds to its Fisher information. We first show that our "Fisher merging" technique provides a performance boost in settings where simple parameter averaging is currently used -- specifically, robust fine-tuning and model ensembling. Then, we compare merging to standard gradient-based transfer learning and demonstrate that merging enables a fundamentally different method for transferring capabilities across models. Specifically, we show that Fisher merging is competitive with gradient-based transfer learning approaches (while being significantly cheaper) in intermediate-task training and domain-adaptive pre-training. We also show that our merging procedure makes it possible to combine models in previously unexplored ways. We release our code to facilitate future research into methods for merging models.

In this paper, by introducing Generalized Bernstein condition, we propose the first Obig(sqrt{p}{nepsilon}big) high probability excess population risk bound for differentially private algorithms under the assumptions G-Lipschitz, L-smooth, and Polyak-{\L}ojasiewicz condition, based on gradient perturbation method. If we replace the properties G-Lipschitz and L-smooth by alpha-H{\"o}lder smoothness (which can be used in non-smooth setting), the high probability bound comes to Obig(n^{-alpha{1+2alpha}}big) w.r.t n, which cannot achieve Oleft(1/nright) when alphain(0,1]. To solve this problem, we propose a variant of gradient perturbation method, max{1,g-Normalized Gradient Perturbation} (m-NGP). We further show that by normalization, the high probability excess population risk bound under assumptions alpha-H{\"o}lder smooth and Polyak-{\L}ojasiewicz condition can achieve Obig(sqrt{p}{nepsilon}big), which is the first Oleft(1/nright) high probability excess population risk bound w.r.t n for differentially private algorithms under non-smooth conditions. Moreover, we evaluate the performance of the new proposed algorithm m-NGP, the experimental results show that m-NGP improves the performance of the differentially private model over real datasets. It demonstrates that m-NGP improves the utility bound and the accuracy of the DP model on real datasets simultaneously.

Imitation Learning has become a fundamental approach in robotic manipulation. However, collecting large-scale real-world robot demonstrations is prohibitively expensive. Simulators offer a cost-effective alternative, but the sim-to-real gap make it extremely challenging to scale. Therefore, we introduce RoboTransfer, a diffusion-based video generation framework for robotic data synthesis. Unlike previous methods, RoboTransfer integrates multi-view geometry with explicit control over scene components, such as background and object attributes. By incorporating cross-view feature interactions and global depth/normal conditions, RoboTransfer ensures geometry consistency across views. This framework allows fine-grained control, including background edits and object swaps. Experiments demonstrate that RoboTransfer is capable of generating multi-view videos with enhanced geometric consistency and visual fidelity. In addition, policies trained on the data generated by RoboTransfer achieve a 33.3% relative improvement in the success rate in the DIFF-OBJ setting and a substantial 251% relative improvement in the more challenging DIFF-ALL scenario. Explore more demos on our project page: https://horizonrobotics.github.io/robot_lab/robotransfer

Post-training quantization (PTQ) has emerged as a widely adopted technique for compressing and accelerating Large Language Models (LLMs). The major challenge in LLM quantization is that uneven and heavy-tailed data distributions can expand the quantization range, thereby reducing bit precision for most values. Recent methods attempt to eliminate outliers and balance inter-channel differences by employing linear transformations; however, they remain heuristic and are often overlook optimizing the data distribution across the entire quantization space.In this paper, we introduce Quantization Space Utilization Rate (QSUR), a novel metric that effectively assesses the quantizability of transformed data by measuring the space utilization of the data in the quantization space. We complement QSUR with mathematical derivations that examine the effects and limitations of various transformations, guiding our development of Orthogonal and Scaling Transformation-based Quantization (OSTQuant). OSQuant employs a learnable equivalent transformation, consisting of an orthogonal transformation and a scaling transformation, to optimize the distributions of weights and activations across the entire quantization space. Futhermore, we propose the KL-Top loss function, designed to mitigate noise during optimization while retaining richer semantic information within the limited calibration data imposed by PTQ. OSTQuant outperforms existing work on various LLMs and benchmarks. In the W4-only setting, it retains 99.5\% of the floating-point accuracy. In the more challenging W4A4KV4 configuration, OSTQuant reduces the performance gap by 32\% on the LLaMA-3-8B model compared to state-of-the-art methods. https://github.com/BrotherHappy/OSTQuant{https://github.com/BrotherHappy/OSTQuant}.

Dataset distillation synthesizes a small set of images from a large-scale real dataset such that synthetic and real images share similar behavioral properties (e.g, distributions of gradients or features) during a training process. Through extensive analyses on current methods and real datasets, together with empirical observations, we provide in this paper two important things to share for dataset distillation. First, object parts that appear on one side of a real image are highly likely to appear on the opposite side of another image within a dataset, which we call the bilateral equivalence. Second, the bilateral equivalence enforces synthetic images to duplicate discriminative parts of objects on both the left and right sides of the images, limiting the recognition of subtle differences between objects. To address this problem, we introduce a surprisingly simple yet effective technique for dataset distillation, dubbed FYI, that enables distilling rich semantics of real images into synthetic ones. To this end, FYI embeds a horizontal flipping technique into distillation processes, mitigating the influence of the bilateral equivalence, while capturing more details of objects. Experiments on CIFAR-10/100, Tiny-ImageNet, and ImageNet demonstrate that FYI can be seamlessly integrated into several state-of-the-art methods, without modifying training objectives and network architectures, and it improves the performance remarkably.

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural implicit surfaces to simple parametric domains like spheres and polycubes. Our method allows users to specify the number of cubes in the parametric domain, learning a configuration that closely resembles the target 3D object's geometry. It computes bi-directional deformation between the object and the domain using a forward mapping from the object's zero level set and an inverse deformation for backward mapping. We ensure nearly bijective mapping with a cycle loss and optimize deformation smoothness. The parameterization quality, assessed by angle and area distortions, is guaranteed using a Laplacian regularizer and an optimized learned parametric domain. Our framework integrates with existing neural rendering pipelines, using multi-view images of a single object or multiple objects of similar geometries to reconstruct 3D geometry and compute texture maps automatically, eliminating the need for any prior information. We demonstrate the method's effectiveness on images of human heads and man-made objects.

Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are sub-optimal. Instead, these problems have been shown to satisfy certain generalized-smooth conditions, which have not been well understood in the existing literature. In this paper, we propose a notion of alpha-symmetric generalized-smoothness that extends the existing notions and covers many important functions such as high-order polynomials and exponential functions. We study the fundamental properties and establish descent lemmas for the functions in this class. Then, to solve such a large class of nonconvex problems, we design a special deterministic normalized gradient descent algorithm that achieves the optimal iteration complexity O(epsilon^{-2}), and also prove that the popular SPIDER variance reduction algorithm achieves the optimal sample complexity O(epsilon^{-3}) in the stochastic setting. Our results show that solving generalized-smooth nonconvex problems is as efficient as solving smooth nonconvex problems.

Parameter-efficient finetuning (PEFT) has become ubiquitous to adapt foundation models to downstream task requirements while retaining their generalization ability. However, the amount of additionally introduced parameters and compute for successful adaptation and hyperparameter searches can explode quickly, especially when deployed at scale to serve numerous individual requests. To ensure effective, parameter-efficient, and hyperparameter-robust adaptation, we propose the ETHER transformation family, which performs Efficient fineTuning via HypErplane Reflections. By design, ETHER transformations require a minimal number of parameters, are less likely to deteriorate model performance, and exhibit robustness to hyperparameter and learning rate choices. In particular, we introduce ETHER and its relaxation ETHER+, which match or outperform existing PEFT methods with significantly fewer parameters (sim10-100 times lower than LoRA or OFT) across multiple image synthesis and natural language tasks without exhaustive hyperparameter tuning. Finally, we investigate the recent emphasis on Hyperspherical Energy retention for adaptation and raise questions on its practical utility. The code is available at https://github.com/mwbini/ether.

The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. This morphing is obtained by deforming a reference shape, through the resolution of a sequence of linear elasticity equations, onto the target shape. In particular, our approach does not assume any knowledge of a boundary parametrization. Furthermore, we demonstrate how constraints can be imposed on specific points, lines and surfaces in the reference domain to ensure alignment with their counterparts in the target domain after morphing. Additionally, we show how the proposed methodology can be integrated in an offline and online paradigm, which is useful in reduced-order modeling scenarii involving variable shapes. This framework facilitates the efficient computation of the morphings in various geometric configurations, thus improving the versatility and applicability of the approach. The methodology is illustrated on the regression problem of the drag and lift coefficients of airfoils of non-parameterized variable shapes.

In state-of-the-art self-supervised learning (SSL) pre-training produces semantically good representations by encouraging them to be invariant under meaningful transformations prescribed from human knowledge. In fact, the property of invariance is a trivial instance of a broader class called equivariance, which can be intuitively understood as the property that representations transform according to the way the inputs transform. Here, we show that rather than using only invariance, pre-training that encourages non-trivial equivariance to some transformations, while maintaining invariance to other transformations, can be used to improve the semantic quality of representations. Specifically, we extend popular SSL methods to a more general framework which we name Equivariant Self-Supervised Learning (E-SSL). In E-SSL, a simple additional pre-training objective encourages equivariance by predicting the transformations applied to the input. We demonstrate E-SSL's effectiveness empirically on several popular computer vision benchmarks, e.g. improving SimCLR to 72.5% linear probe accuracy on ImageNet. Furthermore, we demonstrate usefulness of E-SSL for applications beyond computer vision; in particular, we show its utility on regression problems in photonics science. Our code, datasets and pre-trained models are available at https://github.com/rdangovs/essl to aid further research in E-SSL.

Recent advances in image editing, driven by image diffusion models, have shown remarkable progress. However, significant challenges remain, as these models often struggle to follow complex edit instructions accurately and frequently compromise fidelity by altering key elements of the original image. Simultaneously, video generation has made remarkable strides, with models that effectively function as consistent and continuous world simulators. In this paper, we propose merging these two fields by utilizing image-to-video models for image editing. We reformulate image editing as a temporal process, using pretrained video models to create smooth transitions from the original image to the desired edit. This approach traverses the image manifold continuously, ensuring consistent edits while preserving the original image's key aspects. Our approach achieves state-of-the-art results on text-based image editing, demonstrating significant improvements in both edit accuracy and image preservation.

Whitening loss offers a theoretical guarantee against feature collapse in self-supervised learning (SSL) with joint embedding architectures. Typically, it involves a hard whitening approach, transforming the embedding and applying loss to the whitened output. In this work, we introduce Spectral Transformation (ST), a framework to modulate the spectrum of embedding and to seek for functions beyond whitening that can avoid dimensional collapse. We show that whitening is a special instance of ST by definition, and our empirical investigations unveil other ST instances capable of preventing collapse. Additionally, we propose a novel ST instance named IterNorm with trace loss (INTL). Theoretical analysis confirms INTL's efficacy in preventing collapse and modulating the spectrum of embedding toward equal-eigenvalues during optimization. Our experiments on ImageNet classification and COCO object detection demonstrate INTL's potential in learning superior representations. The code is available at https://github.com/winci-ai/INTL.

This paper presents a new approach and algorithm for solving a class of constrained Bi-Level Optimization (BLO) problems in which the lower-level problem involves constraints coupling both upper-level and lower-level variables. Such problems have recently gained significant attention due to their broad applicability in machine learning. However, conventional gradient-based methods unavoidably rely on computationally intensive calculations related to the Hessian matrix. To address this challenge, we begin by devising a smooth proximal Lagrangian value function to handle the constrained lower-level problem. Utilizing this construct, we introduce a single-level reformulation for constrained BLOs that transforms the original BLO problem into an equivalent optimization problem with smooth constraints. Enabled by this reformulation, we develop a Hessian-free gradient-based algorithm-termed proximal Lagrangian Value function-based Hessian-free Bi-level Algorithm (LV-HBA)-that is straightforward to implement in a single loop manner. Consequently, LV-HBA is especially well-suited for machine learning applications. Furthermore, we offer non-asymptotic convergence analysis for LV-HBA, eliminating the need for traditional strong convexity assumptions for the lower-level problem while also being capable of accommodating non-singleton scenarios. Empirical results substantiate the algorithm's superior practical performance.

In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The key innovation of our analysis is a novel notion called Gradient-Normalized Smoothness, which characterizes the maximum radius of a ball around the current point that yields a good relative approximation of the gradient field. Our theory establishes a natural intrinsic connection between Hessian approximation and the linearization of the gradient. Importantly, Gradient-Normalized Smoothness does not depend on the specific problem class of the objective functions, while effectively translating local information about the gradient field and Hessian approximation into the global behavior of the method. This new concept equips approximate second-order algorithms with universal global convergence guarantees, recovering state-of-the-art rates for functions with H\"older-continuous Hessians and third derivatives, quasi-self-concordant functions, as well as smooth classes in first-order optimization. These rates are achieved automatically and extend to broader classes, such as generalized self-concordant functions. We demonstrate direct applications of our results for global linear rates in logistic regression and softmax problems with approximate Hessians, as well as in non-convex optimization using Fisher and Gauss-Newton approximations.

Strategies for the generation of periodic discrete structures with identical two-point correlation are developed. Starting from a pair of root structures, which are not related by translation, phase inversion or axis reflections, child structures of arbitrary resolution (i.e., pixel or voxel numbers) and number of phases (i.e., material phases/species) can be generated by means of trivial embedding based phase extension, application of kernels and/or phase coalescence, such that the generated structures inherit the two-point-correlation equivalence. Proofs of the inheritance property are provided by means of the Discrete Fourier Transform theory. A Python 3 implementation of the results is offered by the authors through the Github repository https://github.com/DataAnalyticsEngineering/EQ2PC in order to make the provided results reproducible and useful for all interested readers. Examples for the generation of structures are demonstrated, together with applications in the homogenization theory of periodic media.

Given a composite image, image harmonization aims to adjust the foreground illumination to be consistent with background. Previous methods have explored transforming foreground features to achieve competitive performance. In this work, we show that using global information to guide foreground feature transformation could achieve significant improvement. Besides, we propose to transfer the foreground-background relation from real images to composite images, which can provide intermediate supervision for the transformed encoder features. Additionally, considering the drawbacks of existing harmonization datasets, we also contribute a ccHarmony dataset which simulates the natural illumination variation. Extensive experiments on iHarmony4 and our contributed dataset demonstrate the superiority of our method. Our ccHarmony dataset is released at https://github.com/bcmi/Image-Harmonization-Dataset-ccHarmony.

The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.

We present SmoothRot, a novel post-training quantization technique to enhance the efficiency of 4-bit quantization in Large Language Models (LLMs). SmoothRot addresses the critical challenge of massive activation outliers, by integrating channel-wise scaling with Hadamard transformations. Our technique effectively transforms extreme outliers into quantization-friendly activations, significantly improving quantization accuracy. Experiments conducted on popular LLMs (LLaMA2 7B, LLaMA3.1 8B, and Mistral 7B) demonstrate that SmoothRot consistently reduces the performance gap between quantized and FP16 models by approximately 10-30\% across language generation and zero-shot reasoning tasks, without introducing additional inference latency. Code is available at https://github.com/czakop/smoothrot.

Finding an initial noise vector that produces an input image when fed into the diffusion process (known as inversion) is an important problem in denoising diffusion models (DDMs), with applications for real image editing. The state-of-the-art approach for real image editing with inversion uses denoising diffusion implicit models (DDIMs) to deterministically noise the image to the intermediate state along the path that the denoising would follow given the original conditioning. However, DDIM inversion for real images is unstable as it relies on local linearization assumptions, which result in the propagation of errors, leading to incorrect image reconstruction and loss of content. To alleviate these problems, we propose Exact Diffusion Inversion via Coupled Transformations (EDICT), an inversion method that draws inspiration from affine coupling layers. EDICT enables mathematically exact inversion of real and model-generated images by maintaining two coupled noise vectors which are used to invert each other in an alternating fashion. Using Stable Diffusion, a state-of-the-art latent diffusion model, we demonstrate that EDICT successfully reconstructs real images with high fidelity. On complex image datasets like MS-COCO, EDICT reconstruction significantly outperforms DDIM, improving the mean square error of reconstruction by a factor of two. Using noise vectors inverted from real images, EDICT enables a wide range of image edits--from local and global semantic edits to image stylization--while maintaining fidelity to the original image structure. EDICT requires no model training/finetuning, prompt tuning, or extra data and can be combined with any pretrained DDM. Code is available at https://github.com/salesforce/EDICT.

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant attention in measuring the similarity between features learned by distinct networks. However, feature similarity could be vague in describing the same feature since equivalent features hardly exist. In this paper, we expand the concept of equivalent feature and provide the definition of what we call functionally equivalent features. These features produce equivalent output under certain transformations. Using this definition, we aim to derive a more intrinsic metric for the so-called feature complexity regarding the redundancy of features learned by a neural network at each layer. We offer a formal interpretation of our approach through the lens of category theory, a well-developed area in mathematics. To quantify the feature complexity, we further propose an efficient algorithm named Iterative Feature Merging. Our experimental results validate our ideas and theories from various perspectives. We empirically demonstrate that the functionally equivalence widely exists among different features learned by the same neural network and we could reduce the number of parameters of the network without affecting the performance.The IFM shows great potential as a data-agnostic model prune method. We have also drawn several interesting empirical findings regarding the defined feature complexity.

Mamba is an efficient sequence model that rivals Transformers and demonstrates significant potential as a foundational architecture for various tasks. Quantization is commonly used in neural networks to reduce model size and computational latency. However, applying quantization to Mamba remains underexplored, and existing quantization methods, which have been effective for CNN and Transformer models, appear inadequate for Mamba models (e.g., Quarot suffers a 21% accuracy drop on Vim-T^dagger even under W8A8). We have pioneered the exploration of this issue and identified several key challenges. First, significant outliers are present in gate projections, output projections, and matrix multiplications. Second, Mamba's unique parallel scan further amplifies these outliers, leading to uneven and heavy-tailed data distributions. Third, even with the application of the Hadamard transform, the variance across channels in weights and activations still remains inconsistent. To these ends, we propose MambaQuant, a post-training quantization (PTQ) framework consisting of: 1) Karhunen-Loeve Transformation (KLT) enhanced rotation, rendering the rotation matrix adaptable to diverse channel distributions. 2) Smooth-Fused rotation, which equalizes channel variances and can merge additional parameters into model weights. Experiments show that MambaQuant can quantize both weights and activations into 8-bit with less than 1% accuracy loss for Mamba-based vision and language tasks. To the best of our knowledge, MambaQuant is the first comprehensive PTQ design for the Mamba family, paving the way for further advancements in its application.

Leveraging text, images, structure maps, or motion trajectories as conditional guidance, diffusion models have achieved great success in automated and high-quality video generation. However, generating smooth and rational transition videos given the first and last video frames as well as descriptive text prompts is far underexplored. We present VTG, a Versatile Transition video Generation framework that can generate smooth, high-fidelity, and semantically coherent video transitions. VTG introduces interpolation-based initialization that helps preserve object identity and handle abrupt content changes effectively. In addition, it incorporates dual-directional motion fine-tuning and representation alignment regularization to mitigate the limitations of pre-trained image-to-video diffusion models in motion smoothness and generation fidelity, respectively. To evaluate VTG and facilitate future studies on unified transition generation, we collected TransitBench, a comprehensive benchmark for transition generation covering two representative transition tasks: concept blending and scene transition. Extensive experiments show that VTG achieves superior transition performance consistently across all four tasks.

We study the problem of (learning) algorithm comparison, where the goal is to find differences between models trained with two different learning algorithms. We begin by formalizing this goal as one of finding distinguishing feature transformations, i.e., input transformations that change the predictions of models trained with one learning algorithm but not the other. We then present ModelDiff, a method that leverages the datamodels framework (Ilyas et al., 2022) to compare learning algorithms based on how they use their training data. We demonstrate ModelDiff through three case studies, comparing models trained with/without data augmentation, with/without pre-training, and with different SGD hyperparameters. Our code is available at https://github.com/MadryLab/modeldiff .

We present WUKONG, a novel training-free framework for high-fidelity textured 3D morphing that takes a pair of source and target prompts (image or text) as input. Unlike conventional methods -- which rely on manual correspondence matching and deformation trajectory estimation (limiting generalization and requiring costly preprocessing) -- WUKONG leverages the generative prior of flow-based transformers to produce high-fidelity 3D transitions with rich texture details. To ensure smooth shape transitions, we exploit the inherent continuity of flow-based generative processes and formulate morphing as an optimal transport barycenter problem. We further introduce a sequential initialization strategy to prevent abrupt geometric distortions and preserve identity coherence. For faithful texture preservation, we propose a similarity-guided semantic consistency mechanism that selectively retains high-frequency details and enables precise control over blending dynamics. This avoids common artifacts like oversmoothing while maintaining semantic fidelity. Extensive quantitative and qualitative evaluations demonstrate that WUKONG significantly outperforms state-of-the-art methods, achieving superior results across diverse geometry and texture variations.

Class incremental learning (CIL) trains a network on sequential tasks with separated categories but suffers from catastrophic forgetting, where models quickly lose previously learned knowledge when acquiring new tasks. The generalized CIL (GCIL) aims to address the CIL problem in a more real-world scenario, where incoming data have mixed data categories and unknown sample size distribution, leading to intensified forgetting. Existing attempts for the GCIL either have poor performance, or invade data privacy by saving historical exemplars. To address this, in this paper, we propose an exemplar-free generalized analytic class incremental learning (G-ACIL). The G-ACIL adopts analytic learning (a gradient-free training technique), and delivers an analytical solution (i.e., closed-form) to the GCIL scenario. This solution is derived via decomposing the incoming data into exposed and unexposed classes, allowing an equivalence between the incremental learning and its joint training, i.e., the weight-invariant property. Such an equivalence is theoretically validated through matrix analysis tools, and hence contributes interpretability in GCIL. It is also empirically evidenced by experiments on various datasets and settings of GCIL. The results show that the G-ACIL exhibits leading performance with high robustness compared with existing competitive GCIL methods. Codes will be ready at https://github.com/ZHUANGHP/Analytic-continual-learning.

We investigate a construction providing pairs of Calabi-Yau varieties described as zero loci of pushforwards of a hyperplane section on a roof as described by Kanemitsu. We discuss the implications of such construction at the level of Hodge equivalence, derived equivalence and mathbb L-equivalence. For the case of K3 surfaces, we provide alternative interpretations for the Fourier-Mukai duality in the family of K3 surfaces of degree 12 of Mukai. In all these constructions the derived equivalence lifts to an equivalence of matrix factorizations categories.

Recent advancements in neural representations, such as Neural Radiance Fields and 3D Gaussian Splatting, have increased interest in applying style transfer to 3D scenes. While existing methods can transfer style patterns onto 3D-consistent neural representations, they struggle to effectively extract and transfer high-level style semantics from the reference style image. Additionally, the stylized results often lack structural clarity and separation, making it difficult to distinguish between different instances or objects within the 3D scene. To address these limitations, we propose a novel 3D style transfer pipeline that effectively integrates prior knowledge from pretrained 2D diffusion models. Our pipeline consists of two key stages: First, we leverage diffusion priors to generate stylized renderings of key viewpoints. Then, we transfer the stylized key views onto the 3D representation. This process incorporates two innovative designs. The first is cross-view style alignment, which inserts cross-view attention into the last upsampling block of the UNet, allowing feature interactions across multiple key views. This ensures that the diffusion model generates stylized key views that maintain both style fidelity and instance-level consistency. The second is instance-level style transfer, which effectively leverages instance-level consistency across stylized key views and transfers it onto the 3D representation. This results in a more structured, visually coherent, and artistically enriched stylization. Extensive qualitative and quantitative experiments demonstrate that our 3D style transfer pipeline significantly outperforms state-of-the-art methods across a wide range of scenes, from forward-facing to challenging 360-degree environments. Visit our project page https://jm-xu.github.io/SSGaussian for immersive visualization.

Yes. SE data can have "smoother" boundaries between classes (compared to traditional AI data sets). To be more precise, the magnitude of the second derivative of the loss function found in SE data is typically much smaller. A new hyper-parameter optimizer, called SMOOTHIE, can exploit this idiosyncrasy of SE data. We compare SMOOTHIE and a state-of-the-art AI hyper-parameter optimizer on three tasks: (a) GitHub issue lifetime prediction (b) detecting static code warnings false alarm; (c) defect prediction. For completeness, we also show experiments on some standard AI datasets. SMOOTHIE runs faster and predicts better on the SE data--but ties on non-SE data with the AI tool. Hence we conclude that SE data can be different to other kinds of data; and those differences mean that we should use different kinds of algorithms for our data. To support open science and other researchers working in this area, all our scripts and datasets are available on-line at https://github.com/yrahul3910/smoothness-hpo/.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric structure to the embedding space by enforcing transformations of input space to correspond to simple (i.e., linear) transformations of embedding space. Specifically, in the contrastive learning setting, we introduce an equivariance objective and theoretically prove that its minima forces augmentations on input space to correspond to rotations on the spherical embedding space. We show that merely combining our equivariant loss with a non-collapse term results in non-trivial representations, without requiring invariance to data augmentations. Optimal performance is achieved by also encouraging approximate invariance, where input augmentations correspond to small rotations. Our method, CARE: Contrastive Augmentation-induced Rotational Equivariance, leads to improved performance on downstream tasks, and ensures sensitivity in embedding space to important variations in data (e.g., color) that standard contrastive methods do not achieve. Code is available at https://github.com/Sharut/CARE.

Training deep neural networks (DNNs) is computationally expensive, which is problematic especially when performing duplicated or similar training runs in model ensemble or fine-tuning pre-trained models, for example. Once we have trained one DNN on some dataset, we have its learning trajectory (i.e., a sequence of intermediate parameters during training) which may potentially contain useful information for learning the dataset. However, there has been no attempt to utilize such information of a given learning trajectory for another training. In this paper, we formulate the problem of "transferring" a given learning trajectory from one initial parameter to another one (learning transfer problem) and derive the first algorithm to approximately solve it by matching gradients successively along the trajectory via permutation symmetry. We empirically show that the transferred parameters achieve non-trivial accuracy before any direct training, and can be trained significantly faster than training from scratch.

Stable Diffusion XL (SDXL) has become the best open source text-to-image model (T2I) for its versatility and top-notch image quality. Efficiently addressing the computational demands of SDXL models is crucial for wider reach and applicability. In this work, we introduce two scaled-down variants, Segmind Stable Diffusion (SSD-1B) and Segmind-Vega, with 1.3B and 0.74B parameter UNets, respectively, achieved through progressive removal using layer-level losses focusing on reducing the model size while preserving generative quality. We release these models weights at https://hf.co/Segmind. Our methodology involves the elimination of residual networks and transformer blocks from the U-Net structure of SDXL, resulting in significant reductions in parameters, and latency. Our compact models effectively emulate the original SDXL by capitalizing on transferred knowledge, achieving competitive results against larger multi-billion parameter SDXL. Our work underscores the efficacy of knowledge distillation coupled with layer-level losses in reducing model size while preserving the high-quality generative capabilities of SDXL, thus facilitating more accessible deployment in resource-constrained environments.

Domain adversarial training has been ubiquitous for achieving invariant representations and is used widely for various domain adaptation tasks. In recent times, methods converging to smooth optima have shown improved generalization for supervised learning tasks like classification. In this work, we analyze the effect of smoothness enhancing formulations on domain adversarial training, the objective of which is a combination of task loss (eg. classification, regression, etc.) and adversarial terms. We find that converging to a smooth minima with respect to (w.r.t.) task loss stabilizes the adversarial training leading to better performance on target domain. In contrast to task loss, our analysis shows that converging to smooth minima w.r.t. adversarial loss leads to sub-optimal generalization on the target domain. Based on the analysis, we introduce the Smooth Domain Adversarial Training (SDAT) procedure, which effectively enhances the performance of existing domain adversarial methods for both classification and object detection tasks. Our analysis also provides insight into the extensive usage of SGD over Adam in the community for domain adversarial training.

We introduce UniGraspTransformer, a universal Transformer-based network for dexterous robotic grasping that simplifies training while enhancing scalability and performance. Unlike prior methods such as UniDexGrasp++, which require complex, multi-step training pipelines, UniGraspTransformer follows a streamlined process: first, dedicated policy networks are trained for individual objects using reinforcement learning to generate successful grasp trajectories; then, these trajectories are distilled into a single, universal network. Our approach enables UniGraspTransformer to scale effectively, incorporating up to 12 self-attention blocks for handling thousands of objects with diverse poses. Additionally, it generalizes well to both idealized and real-world inputs, evaluated in state-based and vision-based settings. Notably, UniGraspTransformer generates a broader range of grasping poses for objects in various shapes and orientations, resulting in more diverse grasp strategies. Experimental results demonstrate significant improvements over state-of-the-art, UniDexGrasp++, across various object categories, achieving success rate gains of 3.5%, 7.7%, and 10.1% on seen objects, unseen objects within seen categories, and completely unseen objects, respectively, in the vision-based setting. Project page: https://dexhand.github.io/UniGraspTransformer.

Diffusion models have demonstrated remarkable and robust abilities in both image and video generation. To achieve greater control over generated results, researchers introduce additional architectures, such as ControlNet, Adapters and ReferenceNet, to integrate conditioning controls. However, current controllable generation methods often require substantial additional computational resources, especially for video generation, and face challenges in training or exhibit weak control. In this paper, we propose ControlNeXt: a powerful and efficient method for controllable image and video generation. We first design a more straightforward and efficient architecture, replacing heavy additional branches with minimal additional cost compared to the base model. Such a concise structure also allows our method to seamlessly integrate with other LoRA weights, enabling style alteration without the need for additional training. As for training, we reduce up to 90% of learnable parameters compared to the alternatives. Furthermore, we propose another method called Cross Normalization (CN) as a replacement for Zero-Convolution' to achieve fast and stable training convergence. We have conducted various experiments with different base models across images and videos, demonstrating the robustness of our method.

Image-to-image translation is a class of vision and graphics problems where the goal is to learn the mapping between an input image and an output image using a training set of aligned image pairs. However, for many tasks, paired training data will not be available. We present an approach for learning to translate an image from a source domain X to a target domain Y in the absence of paired examples. Our goal is to learn a mapping G: X rightarrow Y such that the distribution of images from G(X) is indistinguishable from the distribution Y using an adversarial loss. Because this mapping is highly under-constrained, we couple it with an inverse mapping F: Y rightarrow X and introduce a cycle consistency loss to push F(G(X)) approx X (and vice versa). Qualitative results are presented on several tasks where paired training data does not exist, including collection style transfer, object transfiguration, season transfer, photo enhancement, etc. Quantitative comparisons against several prior methods demonstrate the superiority of our approach.

The capability to transfer mastered skills to accomplish a range of similar yet novel tasks is crucial for intelligent robots. In this work, we introduce Diff-Transfer, a novel framework leveraging differentiable physics simulation to efficiently transfer robotic skills. Specifically, Diff-Transfer discovers a feasible path within the task space that brings the source task to the target task. At each pair of adjacent points along this task path, which is two sub-tasks, Diff-Transfer adapts known actions from one sub-task to tackle the other sub-task successfully. The adaptation is guided by the gradient information from differentiable physics simulations. We propose a novel path-planning method to generate sub-tasks, leveraging Q-learning with a task-level state and reward. We implement our framework in simulation experiments and execute four challenging transfer tasks on robotic manipulation, demonstrating the efficacy of Diff-Transfer through comprehensive experiments. Supplementary and Videos are on the website https://sites.google.com/view/difftransfer

Transition videos play a crucial role in media production, enhancing the flow and coherence of visual narratives. Traditional methods like morphing often lack artistic appeal and require specialized skills, limiting their effectiveness. Recent advances in diffusion model-based video generation offer new possibilities for creating transitions but face challenges such as poor inter-frame relationship modeling and abrupt content changes. We propose a novel training-free Transition Video Generation (TVG) approach using video-level diffusion models that addresses these limitations without additional training. Our method leverages Gaussian Process Regression (GPR) to model latent representations, ensuring smooth and dynamic transitions between frames. Additionally, we introduce interpolation-based conditional controls and a Frequency-aware Bidirectional Fusion (FBiF) architecture to enhance temporal control and transition reliability. Evaluations of benchmark datasets and custom image pairs demonstrate the effectiveness of our approach in generating high-quality smooth transition videos. The code are provided in https://sobeymil.github.io/tvg.com.

Photorealistic style transfer aims to transfer the artistic style of an image onto an input image or video while keeping photorealism. In this paper, we think it's the summary statistics matching scheme in existing algorithms that leads to unrealistic stylization. To avoid employing the popular Gram loss, we propose a self-supervised style transfer framework, which contains a style removal part and a style restoration part. The style removal network removes the original image styles, and the style restoration network recovers image styles in a supervised manner. Meanwhile, to address the problems in current feature transformation methods, we propose decoupled instance normalization to decompose feature transformation into style whitening and restylization. It works quite well in ColoristaNet and can transfer image styles efficiently while keeping photorealism. To ensure temporal coherency, we also incorporate optical flow methods and ConvLSTM to embed contextual information. Experiments demonstrates that ColoristaNet can achieve better stylization effects when compared with state-of-the-art algorithms.

Video-to-video editing involves editing a source video along with additional control (such as text prompts, subjects, or styles) to generate a new video that aligns with the source video and the provided control. Traditional methods have been constrained to certain editing types, limiting their ability to meet the wide range of user demands. In this paper, we introduce AnyV2V, a novel training-free framework designed to simplify video editing into two primary steps: (1) employing an off-the-shelf image editing model (e.g. InstructPix2Pix, InstantID, etc) to modify the first frame, (2) utilizing an existing image-to-video generation model (e.g. I2VGen-XL) for DDIM inversion and feature injection. In the first stage, AnyV2V can plug in any existing image editing tools to support an extensive array of video editing tasks. Beyond the traditional prompt-based editing methods, AnyV2V also can support novel video editing tasks, including reference-based style transfer, subject-driven editing, and identity manipulation, which were unattainable by previous methods. In the second stage, AnyV2V can plug in any existing image-to-video models to perform DDIM inversion and intermediate feature injection to maintain the appearance and motion consistency with the source video. On the prompt-based editing, we show that AnyV2V can outperform the previous best approach by 35\% on prompt alignment, and 25\% on human preference. On the three novel tasks, we show that AnyV2V also achieves a high success rate. We believe AnyV2V will continue to thrive due to its ability to seamlessly integrate the fast-evolving image editing methods. Such compatibility can help AnyV2V to increase its versatility to cater to diverse user demands.

We present a complete formalization in Isabelle/HOL of the object part of an equivalence between L-mosaics and bounded join-semilattices, employing an AI-assisted methodology that integrates large language models as reasoning assistants throughout the proof development process. The equivalence was originally established by Cangiotti, Linzi, and Talotti in their study of hypercompositional structures related to orthomodular lattices and quantum logic. Our formalization rigorously verifies the main theoretical result and demonstrates the mutual inverse property of the transformations establishing this equivalence. The development showcases both the mathematical depth of multivalued algebraic operations and the potential for AI-enhanced interactive theorem proving in tackling complex formalization projects.

The neural tangent kernel is a kernel function defined over the parameter distribution of an infinite width neural network. Despite the impracticality of this limit, the neural tangent kernel has allowed for a more direct study of neural networks and a gaze through the veil of their black box. More recently, it has been shown theoretically that the Laplace kernel and neural tangent kernel share the same reproducing kernel Hilbert space in the space of S^{d-1} alluding to their equivalence. In this work, we analyze the practical equivalence of the two kernels. We first do so by matching the kernels exactly and then by matching posteriors of a Gaussian process. Moreover, we analyze the kernels in R^d and experiment with them in the task of regression.

In computer vision, models must be able to adapt to changes in image resolution to effectively carry out tasks such as image segmentation; This is known as scale-equivariance. Recent works have made progress in developing scale-equivariant convolutional neural networks, e.g., through weight-sharing and kernel resizing. However, these networks are not truly scale-equivariant in practice. Specifically, they do not consider anti-aliasing as they formulate the down-scaling operation in the continuous domain. To address this shortcoming, we directly formulate down-scaling in the discrete domain with consideration of anti-aliasing. We then propose a novel architecture based on Fourier layers to achieve truly scale-equivariant deep nets, i.e., absolute zero equivariance-error. Following prior works, we test this model on MNIST-scale and STL-10 datasets. Our proposed model achieves competitive classification performance while maintaining zero equivariance-error.

Human motion generation is a long-standing problem, and scene-aware motion synthesis has been widely researched recently due to its numerous applications. Prevailing methods rely heavily on paired motion-scene data whose quantity is limited. Meanwhile, it is difficult to generalize to diverse scenes when trained only on a few specific ones. Thus, we propose a unified framework, termed Diffusion Implicit Policy (DIP), for scene-aware motion synthesis, where paired motion-scene data are no longer necessary. In this framework, we disentangle human-scene interaction from motion synthesis during training and then introduce an interaction-based implicit policy into motion diffusion during inference. Synthesized motion can be derived through iterative diffusion denoising and implicit policy optimization, thus motion naturalness and interaction plausibility can be maintained simultaneously. The proposed implicit policy optimizes the intermediate noised motion in a GAN Inversion manner to maintain motion continuity and control keyframe poses though the ControlNet branch and motion inpainting. For long-term motion synthesis, we introduce motion blending for stable transitions between multiple sub-tasks, where motions are fused in rotation power space and translation linear space. The proposed method is evaluated on synthesized scenes with ShapeNet furniture, and real scenes from PROX and Replica. Results show that our framework presents better motion naturalness and interaction plausibility than cutting-edge methods. This also indicates the feasibility of utilizing the DIP for motion synthesis in more general tasks and versatile scenes. https://jingyugong.github.io/DiffusionImplicitPolicy/

With the increasingly powerful performances and enormous scales of Pretrained Language Models (PLMs), promoting parameter efficiency in fine-tuning has become a crucial need for effective and efficient adaptation to various downstream tasks. One representative line of fine-tuning methods is Orthogonal Fine-tuning (OFT), which rigorously preserves the angular distances within the parameter space to preserve the pretrained knowledge. Despite the empirical effectiveness, OFT still suffers low parameter efficiency at O(d^2) and limited capability of downstream adaptation. Inspired by Givens rotation, in this paper, we proposed quasi-Givens Orthogonal Fine-Tuning (qGOFT) to address the problems. We first use O(d) Givens rotations to accomplish arbitrary orthogonal transformation in SO(d) with provable equivalence, reducing parameter complexity from O(d^2) to O(d). Then we introduce flexible norm and relative angular adjustments under soft orthogonality regularization to enhance the adaptation capability of downstream semantic deviations. Extensive experiments on various tasks and PLMs validate the effectiveness of our methods.

Large language models have demonstrated promising capabilities upon scaling up parameters. However, serving large language models incurs substantial computation and memory movement costs due to their large scale. Quantization methods have been employed to reduce service costs and latency. Nevertheless, outliers in activations hinder the development of INT4 weight-activation quantization. Existing approaches separate outliers and normal values into two matrices or migrate outliers from activations to weights, suffering from high latency or accuracy degradation. Based on observing activations from large language models, outliers can be classified into channel-wise and spike outliers. In this work, we propose Rotated Runtime Smooth (RRS), a plug-and-play activation smoother for quantization, consisting of Runtime Smooth and the Rotation operation. Runtime Smooth (RS) is introduced to eliminate channel-wise outliers by smoothing activations with channel-wise maximums during runtime. The rotation operation can narrow the gap between spike outliers and normal values, alleviating the effect of victims caused by channel-wise smoothing. The proposed method outperforms the state-of-the-art method in the LLaMA and Qwen families and improves WikiText-2 perplexity from 57.33 to 6.66 for INT4 inference.

Recent advances in deep generative modeling have unlocked unprecedented opportunities for video synthesis. In real-world applications, however, users often seek tools to faithfully realize their creative editing intentions with precise and consistent control. Despite the progress achieved by existing methods, ensuring fine-grained alignment with user intentions remains an open and challenging problem. In this work, we present Shape-for-Motion, a novel framework that incorporates a 3D proxy for precise and consistent video editing. Shape-for-Motion achieves this by converting the target object in the input video to a time-consistent mesh, i.e., a 3D proxy, allowing edits to be performed directly on the proxy and then inferred back to the video frames. To simplify the editing process, we design a novel Dual-Propagation Strategy that allows users to perform edits on the 3D mesh of a single frame, and the edits are then automatically propagated to the 3D meshes of the other frames. The 3D meshes for different frames are further projected onto the 2D space to produce the edited geometry and texture renderings, which serve as inputs to a decoupled video diffusion model for generating edited results. Our framework supports various precise and physically-consistent manipulations across the video frames, including pose editing, rotation, scaling, translation, texture modification, and object composition. Our approach marks a key step toward high-quality, controllable video editing workflows. Extensive experiments demonstrate the superiority and effectiveness of our approach. Project page: https://shapeformotion.github.io/

Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets. Therefore, in order to expand the transfer learning scheme to regression tasks, we propose a novel transfer technique based on differential geometry, namely the Geometrically Aligned Transfer Encoder (GATE). In this method, we interpret the latent vectors from the model to exist on a Riemannian curved manifold. We find a proper diffeomorphism between pairs of tasks to ensure that every arbitrary point maps to a locally flat coordinate in the overlapping region, allowing the transfer of knowledge from the source to the target data. This also serves as an effective regularizer for the model to behave in extrapolation regions. In this article, we demonstrate that GATE outperforms conventional methods and exhibits stable behavior in both the latent space and extrapolation regions for various molecular graph datasets.

Face morphing is a problem in computer graphics with numerous artistic and forensic applications. It is challenging due to variations in pose, lighting, gender, and ethnicity. This task consists of a warping for feature alignment and a blending for a seamless transition between the warped images. We propose to leverage coord-based neural networks to represent such warpings and blendings of face images. During training, we exploit the smoothness and flexibility of such networks by combining energy functionals employed in classical approaches without discretizations. Additionally, our method is time-dependent, allowing a continuous warping/blending of the images. During morphing inference, we need both direct and inverse transformations of the time-dependent warping. The first (second) is responsible for warping the target (source) image into the source (target) image. Our neural warping stores those maps in a single network dismissing the need for inverting them. The results of our experiments indicate that our method is competitive with both classical and generative models under the lens of image quality and face-morphing detectors. Aesthetically, the resulting images present a seamless blending of diverse faces not yet usual in the literature.

Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation speed by straightening the ODE path. Its key components include: 1) using the diffusion form of flow-matching, 2) employing boldsymbol v-prediction, and 3) performing rectification (a.k.a. reflow). In this paper, we argue that the success of rectification primarily lies in using a pretrained diffusion model to obtain matched pairs of noise and samples, followed by retraining with these matched noise-sample pairs. Based on this, components 1) and 2) are unnecessary. Furthermore, we highlight that straightness is not an essential training target for rectification; rather, it is a specific case of flow-matching models. The more critical training target is to achieve a first-order approximate ODE path, which is inherently curved for models like DDPM and Sub-VP. Building on this insight, we propose Rectified Diffusion, which generalizes the design space and application scope of rectification to encompass the broader category of diffusion models, rather than being restricted to flow-matching models. We validate our method on Stable Diffusion v1-5 and Stable Diffusion XL. Our method not only greatly simplifies the training procedure of rectified flow-based previous works (e.g., InstaFlow) but also achieves superior performance with even lower training cost. Our code is available at https://github.com/G-U-N/Rectified-Diffusion.

Contrastive representation learning has been outstandingly successful in practice. In this work, we identify two key properties related to the contrastive loss: (1) alignment (closeness) of features from positive pairs, and (2) uniformity of the induced distribution of the (normalized) features on the hypersphere. We prove that, asymptotically, the contrastive loss optimizes these properties, and analyze their positive effects on downstream tasks. Empirically, we introduce an optimizable metric to quantify each property. Extensive experiments on standard vision and language datasets confirm the strong agreement between both metrics and downstream task performance. Remarkably, directly optimizing for these two metrics leads to representations with comparable or better performance at downstream tasks than contrastive learning. Project Page: https://tongzhouwang.info/hypersphere Code: https://github.com/SsnL/align_uniform , https://github.com/SsnL/moco_align_uniform

Text-driven style transfer aims to merge the style of a reference image with content described by a text prompt. Recent advancements in text-to-image models have improved the nuance of style transformations, yet significant challenges remain, particularly with overfitting to reference styles, limiting stylistic control, and misaligning with textual content. In this paper, we propose three complementary strategies to address these issues. First, we introduce a cross-modal Adaptive Instance Normalization (AdaIN) mechanism for better integration of style and text features, enhancing alignment. Second, we develop a Style-based Classifier-Free Guidance (SCFG) approach that enables selective control over stylistic elements, reducing irrelevant influences. Finally, we incorporate a teacher model during early generation stages to stabilize spatial layouts and mitigate artifacts. Our extensive evaluations demonstrate significant improvements in style transfer quality and alignment with textual prompts. Furthermore, our approach can be integrated into existing style transfer frameworks without fine-tuning.

This work investigates the compatibility between label smoothing (LS) and knowledge distillation (KD). Contemporary findings addressing this thesis statement take dichotomous standpoints: Muller et al. (2019) and Shen et al. (2021b). Critically, there is no effort to understand and resolve these contradictory findings, leaving the primal question -- to smooth or not to smooth a teacher network? -- unanswered. The main contributions of our work are the discovery, analysis and validation of systematic diffusion as the missing concept which is instrumental in understanding and resolving these contradictory findings. This systematic diffusion essentially curtails the benefits of distilling from an LS-trained teacher, thereby rendering KD at increased temperatures ineffective. Our discovery is comprehensively supported by large-scale experiments, analyses and case studies including image classification, neural machine translation and compact student distillation tasks spanning across multiple datasets and teacher-student architectures. Based on our analysis, we suggest practitioners to use an LS-trained teacher with a low-temperature transfer to achieve high performance students. Code and models are available at https://keshik6.github.io/revisiting-ls-kd-compatibility/

Effective out-of-distribution (OOD) detection is crucial for reliable machine learning models, yet most current methods are limited in practical use due to requirements like access to training data or intervention in training. We present a novel method for detecting OOD data in Transformers based on transformation smoothness between intermediate layers of a network (BLOOD), which is applicable to pre-trained models without access to training data. BLOOD utilizes the tendency of between-layer representation transformations of in-distribution (ID) data to be smoother than the corresponding transformations of OOD data, a property that we also demonstrate empirically. We evaluate BLOOD on several text classification tasks with Transformer networks and demonstrate that it outperforms methods with comparable resource requirements. Our analysis also suggests that when learning simpler tasks, OOD data transformations maintain their original sharpness, whereas sharpness increases with more complex tasks.

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.

We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Throughout, we show how the analysis extends to AD methods for computing higher order derivatives using a Taylor approximation.

The Stable Diffusion model is a prominent text-to-image generation model that relies on a text prompt as its input, which is encoded using the Contrastive Language-Image Pre-Training (CLIP). However, text prompts have limitations when it comes to incorporating implicit information from reference images. Existing methods have attempted to address this limitation by employing expensive training procedures involving millions of training samples for image-to-image generation. In contrast, this paper demonstrates that the CLIP model, as utilized in Stable Diffusion, inherently possesses the ability to instantaneously convert images into text prompts. Such an image-to-prompt conversion can be achieved by utilizing a linear projection matrix that is calculated in a closed form. Moreover, the paper showcases that this capability can be further enhanced by either utilizing a small amount of similar-domain training data (approximately 100 images) or incorporating several online training steps (around 30 iterations) on the reference images. By leveraging these approaches, the proposed method offers a simple and flexible solution to bridge the gap between images and text prompts. This methodology can be applied to various tasks such as image variation and image editing, facilitating more effective and seamless interaction between images and textual prompts.

Automatic differentiation (autodiff) has revolutionized machine learning. It allows to express complex computations by composing elementary ones in creative ways and removes the burden of computing their derivatives by hand. More recently, differentiation of optimization problem solutions has attracted widespread attention with applications such as optimization layers, and in bi-level problems such as hyper-parameter optimization and meta-learning. However, so far, implicit differentiation remained difficult to use for practitioners, as it often required case-by-case tedious mathematical derivations and implementations. In this paper, we propose automatic implicit differentiation, an efficient and modular approach for implicit differentiation of optimization problems. In our approach, the user defines directly in Python a function F capturing the optimality conditions of the problem to be differentiated. Once this is done, we leverage autodiff of F and the implicit function theorem to automatically differentiate the optimization problem. Our approach thus combines the benefits of implicit differentiation and autodiff. It is efficient as it can be added on top of any state-of-the-art solver and modular as the optimality condition specification is decoupled from the implicit differentiation mechanism. We show that seemingly simple principles allow to recover many existing implicit differentiation methods and create new ones easily. We demonstrate the ease of formulating and solving bi-level optimization problems using our framework. We also showcase an application to the sensitivity analysis of molecular dynamics.

In many neural networks, different values of the parameters may result in the same loss value. Parameter space symmetries are loss-invariant transformations that change the model parameters. Teleportation applies such transformations to accelerate optimization. However, the exact mechanism behind this algorithm's success is not well understood. In this paper, we show that teleportation not only speeds up optimization in the short-term, but gives overall faster time to convergence. Additionally, teleporting to minima with different curvatures improves generalization, which suggests a connection between the curvature of the minimum and generalization ability. Finally, we show that integrating teleportation into a wide range of optimization algorithms and optimization-based meta-learning improves convergence. Our results showcase the versatility of teleportation and demonstrate the potential of incorporating symmetry in optimization.

Photorealistic image stylization concerns transferring style of a reference photo to a content photo with the constraint that the stylized photo should remain photorealistic. While several photorealistic image stylization methods exist, they tend to generate spatially inconsistent stylizations with noticeable artifacts. In this paper, we propose a method to address these issues. The proposed method consists of a stylization step and a smoothing step. While the stylization step transfers the style of the reference photo to the content photo, the smoothing step ensures spatially consistent stylizations. Each of the steps has a closed-form solution and can be computed efficiently. We conduct extensive experimental validations. The results show that the proposed method generates photorealistic stylization outputs that are more preferred by human subjects as compared to those by the competing methods while running much faster. Source code and additional results are available at https://github.com/NVIDIA/FastPhotoStyle .

Unlabeled data is a key component of modern machine learning. In general, the role of unlabeled data is to impose a form of smoothness, usually from the similarity information encoded in a base kernel, such as the epsilon-neighbor kernel or the adjacency matrix of a graph. This work revisits the classical idea of spectrally transformed kernel regression (STKR), and provides a new class of general and scalable STKR estimators able to leverage unlabeled data. Intuitively, via spectral transformation, STKR exploits the data distribution for which unlabeled data can provide additional information. First, we show that STKR is a principled and general approach, by characterizing a universal type of "target smoothness", and proving that any sufficiently smooth function can be learned by STKR. Second, we provide scalable STKR implementations for the inductive setting and a general transformation function, while prior work is mostly limited to the transductive setting. Third, we derive statistical guarantees for two scenarios: STKR with a known polynomial transformation, and STKR with kernel PCA when the transformation is unknown. Overall, we believe that this work helps deepen our understanding of how to work with unlabeled data, and its generality makes it easier to inspire new methods.

The task of few-shot GAN adaptation aims to adapt a pre-trained GAN model to a small dataset with very few training images. While existing methods perform well when the dataset for pre-training is structurally similar to the target dataset, the approaches suffer from training instabilities or memorization issues when the objects in the two domains have a very different structure. To mitigate this limitation, we propose a new smoothness similarity regularization that transfers the inherently learned smoothness of the pre-trained GAN to the few-shot target domain even if the two domains are very different. We evaluate our approach by adapting an unconditional and a class-conditional GAN to diverse few-shot target domains. Our proposed method significantly outperforms prior few-shot GAN adaptation methods in the challenging case of structurally dissimilar source-target domains, while performing on par with the state of the art for similar source-target domains.

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a (delta,epsilon)-stationary point from O(epsilon^{-4}delta^{-1}) stochastic gradient queries to O(epsilon^{-3}delta^{-1}), which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to online learning, after which our results follow from standard regret bounds in online learning. For deterministic and second-order smooth objectives, applying more advanced optimistic online learning techniques enables a new complexity of O(epsilon^{-1.5}delta^{-0.5}). Our techniques also recover all optimal or best-known results for finding epsilon stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings.

Rectified flow and reflow procedures have significantly advanced fast generation by progressively straightening ordinary differential equation (ODE) flows. They operate under the assumption that image and noise pairs, known as couplings, can be approximated by straight trajectories with constant velocity. However, we observe that modeling with constant velocity and using reflow procedures have limitations in accurately learning straight trajectories between pairs, resulting in suboptimal performance in few-step generation. To address these limitations, we introduce Constant Acceleration Flow (CAF), a novel framework based on a simple constant acceleration equation. CAF introduces acceleration as an additional learnable variable, allowing for more expressive and accurate estimation of the ODE flow. Moreover, we propose two techniques to further improve estimation accuracy: initial velocity conditioning for the acceleration model and a reflow process for the initial velocity. Our comprehensive studies on toy datasets, CIFAR-10, and ImageNet 64x64 demonstrate that CAF outperforms state-of-the-art baselines for one-step generation. We also show that CAF dramatically improves few-step coupling preservation and inversion over Rectified flow. Code is available at https://github.com/mlvlab/CAF{https://github.com/mlvlab/CAF}.

We introduce Equilibrium Matching (EqM), a generative modeling framework built from an equilibrium dynamics perspective. EqM discards the non-equilibrium, time-conditional dynamics in traditional diffusion and flow-based generative models and instead learns the equilibrium gradient of an implicit energy landscape. Through this approach, we can adopt an optimization-based sampling process at inference time, where samples are obtained by gradient descent on the learned landscape with adjustable step sizes, adaptive optimizers, and adaptive compute. EqM surpasses the generation performance of diffusion/flow models empirically, achieving an FID of 1.90 on ImageNet 256times256. EqM is also theoretically justified to learn and sample from the data manifold. Beyond generation, EqM is a flexible framework that naturally handles tasks including partially noised image denoising, OOD detection, and image composition. By replacing time-conditional velocities with a unified equilibrium landscape, EqM offers a tighter bridge between flow and energy-based models and a simple route to optimization-driven inference.

This paper investigates the global convergence of stepsized Newton methods for convex functions. We propose several simple stepsize schedules with fast global convergence guarantees, up to O (k^{-3}), nearly matching lower complexity bounds Omega (k^{-3.5}) of second-order methods. For cases with multiple plausible smoothness parameterizations or an unknown smoothness constant, we introduce a stepsize backtracking procedure that ensures convergence as if the optimal smoothness parameters were known.

The recovery of time-varying graph signals is a fundamental problem with numerous applications in sensor networks and forecasting in time series. Effectively capturing the spatio-temporal information in these signals is essential for the downstream tasks. Previous studies have used the smoothness of the temporal differences of such graph signals as an initial assumption. Nevertheless, this smoothness assumption could result in a degradation of performance in the corresponding application when the prior does not hold. In this work, we relax the requirement of this hypothesis by including a learning module. We propose a Time Graph Neural Network (TimeGNN) for the recovery of time-varying graph signals. Our algorithm uses an encoder-decoder architecture with a specialized loss composed of a mean squared error function and a Sobolev smoothness operator.TimeGNN shows competitive performance against previous methods in real datasets.

Balancing fidelity and editability is essential in text-based image editing (TIE), where failures commonly lead to over- or under-editing issues. Existing methods typically rely on attention injections for structure preservation and leverage the inherent text alignment capabilities of pre-trained text-to-image (T2I) models for editability, but they lack explicit and unified mechanisms to properly balance these two objectives. In this work, we introduce UnifyEdit, a tuning-free method that performs diffusion latent optimization to enable a balanced integration of fidelity and editability within a unified framework. Unlike direct attention injections, we develop two attention-based constraints: a self-attention (SA) preservation constraint for structural fidelity, and a cross-attention (CA) alignment constraint to enhance text alignment for improved editability. However, simultaneously applying both constraints can lead to gradient conflicts, where the dominance of one constraint results in over- or under-editing. To address this challenge, we introduce an adaptive time-step scheduler that dynamically adjusts the influence of these constraints, guiding the diffusion latent toward an optimal balance. Extensive quantitative and qualitative experiments validate the effectiveness of our approach, demonstrating its superiority in achieving a robust balance between structure preservation and text alignment across various editing tasks, outperforming other state-of-the-art methods. The source code will be available at https://github.com/CUC-MIPG/UnifyEdit.

We propose using Normalizing Flows as a trainable kernel within the molecular dynamics update of Hamiltonian Monte Carlo (HMC). By learning (invertible) transformations that simplify our dynamics, we can outperform traditional methods at generating independent configurations. We show that, using a carefully constructed network architecture, our approach can be easily scaled to large lattice volumes with minimal retraining effort. The source code for our implementation is publicly available online at https://github.com/nftqcd/fthmc.

A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choice determines the flexibility of these models. Building upon recent work, we propose a fully-differentiable module based on monotonic rational-quadratic splines, which enhances the flexibility of both coupling and autoregressive transforms while retaining analytic invertibility. We demonstrate that neural spline flows improve density estimation, variational inference, and generative modeling of images.

While style transfer techniques have been well-developed for 2D image stylization, the extension of these methods to 3D scenes remains relatively unexplored. Existing approaches demonstrate proficiency in transferring colors and textures but often struggle with replicating the geometry of the scenes. In our work, we leverage an explicit Gaussian Splatting (GS) representation and directly match the distributions of Gaussians between style and content scenes using the Earth Mover's Distance (EMD). By employing the entropy-regularized Wasserstein-2 distance, we ensure that the transformation maintains spatial smoothness. Additionally, we decompose the scene stylization problem into smaller chunks to enhance efficiency. This paradigm shift reframes stylization from a pure generative process driven by latent space losses to an explicit matching of distributions between two Gaussian representations. Our method achieves high-resolution 3D stylization by faithfully transferring details from 3D style scenes onto the content scene. Furthermore, WaSt-3D consistently delivers results across diverse content and style scenes without necessitating any training, as it relies solely on optimization-based techniques. See our project page for additional results and source code: https://compvis.github.io/wast3d/{https://compvis.github.io/wast3d/}.

The diffusion-based text-to-image model harbors immense potential in transferring reference style. However, current encoder-based approaches significantly impair the text controllability of text-to-image models while transferring styles. In this paper, we introduce DEADiff to address this issue using the following two strategies: 1) a mechanism to decouple the style and semantics of reference images. The decoupled feature representations are first extracted by Q-Formers which are instructed by different text descriptions. Then they are injected into mutually exclusive subsets of cross-attention layers for better disentanglement. 2) A non-reconstructive learning method. The Q-Formers are trained using paired images rather than the identical target, in which the reference image and the ground-truth image are with the same style or semantics. We show that DEADiff attains the best visual stylization results and optimal balance between the text controllability inherent in the text-to-image model and style similarity to the reference image, as demonstrated both quantitatively and qualitatively. Our project page is https://tianhao-qi.github.io/DEADiff/.

Recently, unsupervised exemplar-based image-to-image translation, conditioned on a given exemplar without the paired data, has accomplished substantial advancements. In order to transfer the information from an exemplar to an input image, existing methods often use a normalization technique, e.g., adaptive instance normalization, that controls the channel-wise statistics of an input activation map at a particular layer, such as the mean and the variance. Meanwhile, style transfer approaches similar task to image translation by nature, demonstrated superior performance by using the higher-order statistics such as covariance among channels in representing a style. In detail, it works via whitening (given a zero-mean input feature, transforming its covariance matrix into the identity). followed by coloring (changing the covariance matrix of the whitened feature to those of the style feature). However, applying this approach in image translation is computationally intensive and error-prone due to the expensive time complexity and its non-trivial backpropagation. In response, this paper proposes an end-to-end approach tailored for image translation that efficiently approximates this transformation with our novel regularization methods. We further extend our approach to a group-wise form for memory and time efficiency as well as image quality. Extensive qualitative and quantitative experiments demonstrate that our proposed method is fast, both in training and inference, and highly effective in reflecting the style of an exemplar. Finally, our code is available at https://github.com/WonwoongCho/GDWCT.

Text-to-image diffusion models offer powerful image editing capabilities. To edit real images, many methods rely on the inversion of the image into Gaussian noise. A common approach to invert an image is to gradually add noise to the image, where the noise is determined by reversing the sampling equation. This process has an inherent tradeoff between reconstruction and editability, limiting the editing of challenging images such as highly-detailed ones. Recognizing the reliance of text-to-image models inversion on a text condition, this work explores the importance of the condition choice. We show that a condition that precisely aligns with the input image significantly improves the inversion quality. Based on our findings, we introduce Tight Inversion, an inversion method that utilizes the most possible precise condition -- the input image itself. This tight condition narrows the distribution of the model's output and enhances both reconstruction and editability. We demonstrate the effectiveness of our approach when combined with existing inversion methods through extensive experiments, evaluating the reconstruction accuracy as well as the integration with various editing methods.

Diffusion models exhibit remarkable generative ability, yet achieving smooth and semantically consistent image morphing remains a challenge. Existing approaches often yield abrupt transitions or over-saturated appearances due to the lack of adaptive structural and semantic alignments. We propose CHIMERA, a zero-shot diffusion-based framework that formulates morphing as a cached inversion-guided denoising process. To handle large semantic and appearance disparities, we propose Adaptive Cache Injection and Semantic Anchor Prompting. Adaptive Cache Injection (ACI) caches down, mid, and up blocks features from both inputs during DDIM inversion and re-injects them adaptively during denoising, enabling spatial and semantic alignment in depth- and time-adaptive manners and enabling natural feature fusion and smooth transitions. Semantic Anchor Prompting (SAP) leverages a vision-language model to generate a shared anchor prompt that serves as a semantic anchor, bridging dissimilar inputs and guiding the denoising process toward coherent results. Finally, we introduce the Global-Local Consistency Score (GLCS), a morphing-oriented metric that simultaneously evaluates the global harmonization of the two inputs and the smoothness of the local morphing transition. Extensive experiments and user studies show that CHIMERA achieves smoother and more semantically aligned transitions than existing methods, establishing a new state of the art in image morphing. The code and project page will be publicly released.

Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid, resulting in a learnable parameterization that is unlimited in resolution. Unfortunately, these methods are often unsuitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Implicit Fields. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define DeepMesh - an end-to-end differentiable mesh representation that can vary its topology. We validate our theoretical insight through several applications: Single view 3D Reconstruction via Differentiable Rendering, Physically-Driven Shape Optimization, Full Scene 3D Reconstruction from Scans and End-to-End Training. In all cases our end-to-end differentiable parameterization gives us an edge over state-of-the-art algorithms.

Arbitrary image style transfer is a challenging task which aims to stylize a content image conditioned on arbitrary style images. In this task the feature-level content-style transformation plays a vital role for proper fusion of features. Existing feature transformation algorithms often suffer from loss of content or style details, non-natural stroke patterns, and unstable training. To mitigate these issues, this paper proposes a new feature-level style transformation technique, named Style Projection, for parameter-free, fast, and effective content-style transformation. This paper further presents a real-time feed-forward model to leverage Style Projection for arbitrary image style transfer, which includes a regularization term for matching the semantics between input contents and stylized outputs. Extensive qualitative analysis, quantitative evaluation, and user study have demonstrated the effectiveness and efficiency of the proposed methods.