Daily Papers

Error Feedback (EF) is a highly popular and immensely effective mechanism for fixing convergence issues which arise in distributed training methods (such as distributed GD or SGD) when these are enhanced with greedy communication compression techniques such as TopK. While EF was proposed almost a decade ago (Seide et al., 2014), and despite concentrated effort by the community to advance the theoretical understanding of this mechanism, there is still a lot to explore. In this work we study a modern form of error feedback called EF21 (Richtarik et al., 2021) which offers the currently best-known theoretical guarantees, under the weakest assumptions, and also works well in practice. In particular, while the theoretical communication complexity of EF21 depends on the quadratic mean of certain smoothness parameters, we improve this dependence to their arithmetic mean, which is always smaller, and can be substantially smaller, especially in heterogeneous data regimes. We take the reader on a journey of our discovery process. Starting with the idea of applying EF21 to an equivalent reformulation of the underlying problem which (unfortunately) requires (often impractical) machine cloning, we continue to the discovery of a new weighted version of EF21 which can (fortunately) be executed without any cloning, and finally circle back to an improved analysis of the original EF21 method. While this development applies to the simplest form of EF21, our approach naturally extends to more elaborate variants involving stochastic gradients and partial participation. Further, our technique improves the best-known theory of EF21 in the rare features regime (Richtarik et al., 2023). Finally, we validate our theoretical findings with suitable experiments.

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.

Generalized self-concordance is a key property present in the objective function of many important learning problems. We establish the convergence rate of a simple Frank-Wolfe variant that uses the open-loop step size strategy gamma_t = 2/(t+2), obtaining a O(1/t) convergence rate for this class of functions in terms of primal gap and Frank-Wolfe gap, where t is the iteration count. This avoids the use of second-order information or the need to estimate local smoothness parameters of previous work. We also show improved convergence rates for various common cases, e.g., when the feasible region under consideration is uniformly convex or polyhedral.

ML-augmented algorithms utilize predictions to achieve performance beyond their worst-case bounds. Producing these predictions might be a costly operation -- this motivated Im et al. '22 to introduce the study of algorithms which use predictions parsimoniously. We design parsimonious algorithms for caching and MTS with action predictions, proposed by Antoniadis et al. '20, focusing on the parameters of consistency (performance with perfect predictions) and smoothness (dependence of their performance on the prediction error). Our algorithm for caching is 1-consistent, robust, and its smoothness deteriorates with the decreasing number of available predictions. We propose an algorithm for general MTS whose consistency and smoothness both scale linearly with the decreasing number of predictions. Without the restriction on the number of available predictions, both algorithms match the earlier guarantees achieved by Antoniadis et al. '20.

3D Gaussian Splatting has recently emerged as a highly promising technique for modeling of static 3D scenes. In contrast to Neural Radiance Fields, it utilizes efficient rasterization allowing for very fast rendering at high-quality. However, the storage size is significantly higher, which hinders practical deployment, e.g.~on resource constrained devices. In this paper, we introduce a compact scene representation organizing the parameters of 3D Gaussian Splatting (3DGS) into a 2D grid with local homogeneity, ensuring a drastic reduction in storage requirements without compromising visual quality during rendering. Central to our idea is the explicit exploitation of perceptual redundancies present in natural scenes. In essence, the inherent nature of a scene allows for numerous permutations of Gaussian parameters to equivalently represent it. To this end, we propose a novel highly parallel algorithm that regularly arranges the high-dimensional Gaussian parameters into a 2D grid while preserving their neighborhood structure. During training, we further enforce local smoothness between the sorted parameters in the grid. The uncompressed Gaussians use the same structure as 3DGS, ensuring a seamless integration with established renderers. Our method achieves a reduction factor of 8x to 26x in size for complex scenes with no increase in training time, marking a substantial leap forward in the domain of 3D scene distribution and consumption. Additional information can be found on our project page: https://fraunhoferhhi.github.io/Self-Organizing-Gaussians/

In this paper, we propose LEURN: a neural network architecture that learns univariate decision rules. LEURN is a white-box algorithm that results into univariate trees and makes explainable decisions in every stage. In each layer, LEURN finds a set of univariate rules based on an embedding of the previously checked rules and their corresponding responses. Both rule finding and final decision mechanisms are weighted linear combinations of these embeddings, hence contribution of all rules are clearly formulated and explainable. LEURN can select features, extract feature importance, provide semantic similarity between a pair of samples, be used in a generative manner and can give a confidence score. Thanks to a smoothness parameter, LEURN can also controllably behave like decision trees or vanilla neural networks. Besides these advantages, LEURN achieves comparable performance to state-of-the-art methods across 30 tabular datasets for classification and regression problems.

In the misspecified kernel ridge regression problem, researchers usually assume the underground true function f_{rho}^{*} in [H]^{s}, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) H for some sin (0,1). The existing minimax optimal results require |f_{rho}^{*}|_{L^{infty}}<infty which implicitly requires s > alpha_{0} where alpha_{0}in (0,1) is the embedding index, a constant depending on H. Whether the KRR is optimal for all sin (0,1) is an outstanding problem lasting for years. In this paper, we show that KRR is minimax optimal for any sin (0,1) when the H is a Sobolev RKHS.

Integral reinforcement learning (IntRL) demands the precise computation of the utility function's integral at its policy evaluation (PEV) stage. This is achieved through quadrature rules, which are weighted sums of utility functions evaluated from state samples obtained in discrete time. Our research reveals a critical yet underexplored phenomenon: the choice of the computational method -- in this case, the quadrature rule -- can significantly impact control performance. This impact is traced back to the fact that computational errors introduced in the PEV stage can affect the policy iteration's convergence behavior, which in turn affects the learned controller. To elucidate how computation impacts control, we draw a parallel between IntRL's policy iteration and Newton's method applied to the Hamilton-Jacobi-Bellman equation. In this light, computational error in PEV manifests as an extra error term in each iteration of Newton's method, with its upper bound proportional to the computational error. Further, we demonstrate that when the utility function resides in a reproducing kernel Hilbert space (RKHS), the optimal quadrature is achievable by employing Bayesian quadrature with the RKHS-inducing kernel function. We prove that the local convergence rates for IntRL using the trapezoidal rule and Bayesian quadrature with a Mat\'ern kernel to be O(N^{-2}) and O(N^{-b}), where N is the number of evenly-spaced samples and b is the Mat\'ern kernel's smoothness parameter. These theoretical findings are finally validated by two canonical control tasks.

In machine learning applications, it is well known that carefully designed learning rate (step size) schedules can significantly improve the convergence of commonly used first-order optimization algorithms. Therefore how to set step size adaptively becomes an important research question. A popular and effective method is the Polyak step size, which sets step size adaptively for gradient descent or stochastic gradient descent without the need to estimate the smoothness parameter of the objective function. However, there has not been a principled way to generalize the Polyak step size for algorithms with momentum accelerations. This paper presents a general framework to set the learning rate adaptively for first-order optimization methods with momentum, motivated by the derivation of Polyak step size. It is shown that the resulting methods are much less sensitive to the choice of momentum parameter and may avoid the oscillation of the heavy-ball method on ill-conditioned problems. These adaptive step sizes are further extended to the stochastic settings, which are attractive choices for stochastic gradient descent with momentum. Our methods are demonstrated to be more effective for stochastic gradient methods than prior adaptive step size algorithms in large-scale machine learning tasks.

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.

We analyze surface patches with a corner that is rounded in the sense that the partial derivatives at that point are antiparallel. Sufficient conditions for G^1 smoothness are given, which, up to a certain degenerate case, are also necessary. Further, we investigate curvature integrability and present examples

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/.

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.

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}.

In this work, we introduce a single parameter omega, to effectively control granularity in diffusion-based synthesis. This parameter is incorporated during the denoising steps of the diffusion model's reverse process. Our approach does not require model retraining, architectural modifications, or additional computational overhead during inference, yet enables precise control over the level of details in the generated outputs. Moreover, spatial masks or denoising schedules with varying omega values can be applied to achieve region-specific or timestep-specific granularity control. Prior knowledge of image composition from control signals or reference images further facilitates the creation of precise omega masks for granularity control on specific objects. To highlight the parameter's role in controlling subtle detail variations, the technique is named Omegance, combining "omega" and "nuance". Our method demonstrates impressive performance across various image and video synthesis tasks and is adaptable to advanced diffusion models. The code is available at https://github.com/itsmag11/Omegance.

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.

We show how to transform a non-differentiable rasterizer into a differentiable one with minimal engineering efforts and no external dependencies (no Pytorch/Tensorflow). We rely on Stochastic Gradient Estimation, a technique that consists of rasterizing after randomly perturbing the scene's parameters such that their gradient can be stochastically estimated and descended. This method is simple and robust but does not scale in dimensionality (number of scene parameters). Our insight is that the number of parameters contributing to a given rasterized pixel is bounded. Estimating and averaging gradients on a per-pixel basis hence bounds the dimensionality of the underlying optimization problem and makes the method scalable. Furthermore, it is simple to track per-pixel contributing parameters by rasterizing ID- and UV-buffers, which are trivial additions to a rasterization engine if not already available. With these minor modifications, we obtain an in-engine optimizer for 3D assets with millions of geometry and texture parameters.

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.

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.

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.

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.

We review the method NAV (New Algol Variable) first introduced in 2012Ap.....55..536A, which uses the locally-dependent shapes of eclipses in an addition to the trigonometric polynomial of the second order (which typically describes the "out-of-eclipse" part of the light curve with effects of reflection, ellipticity and O'Connell). Eclipsing binary stars are believed to show distinct eclipses only if belonging to the EA type. With a decreasing eclipse width, the statistically optimal value of the trigonometric polynomial s (2003ASPC..292..391A) drastically increases from ~2 for elliptic (EL) variables without eclipses, ~6-8 for EW and up to ~30-50 for some EA with narrow eclipses. In this case of large number of parameters, the smoothing curve becomes very noisy and apparent waves (the Gibbs phenomenon) may be seen. The NAV set of the parameters may be used for classification in the GCVS, VSX and similar catalogs. The maximal number of parameters is m=12, which corresponds to s=5, if correcting both the period and the initial epoch. We have applied the method to few stars, also in a case of multi-color photometry (2015JASS...32..127A), when it is possible to use the phenomenological parameters from the NAV fit to estimate physical parameters using statistical dependencies. We conclude that the NAV approximation is better than the TP one even for the case of EW-type stars with much wider eclipses. It may also be used to determine timings (see 2005ASPC..335...37A for a review of methods) or to determine parameters in the case of variable period, using a complete light curve modeling the phase variations. The method is illustrated on 2MASS J11080447-6143290 (EA-type), USNO-B1.0 1265-0306001 and USNO-B1.0 1266-0313413 (EW-type) and compared to various other methods from the literature.

Loss landscape is a useful tool to characterize and compare neural network models. The main challenge for analysis of loss landscape for the deep neural networks is that they are generally highly non-convex in very high dimensional space. In this paper, we develop "the roughness"concept for understanding such landscapes in high dimensions and apply this technique to study two neural network models arising from solving differential equations. Our main innovation is the proposal of a well-defined and easy-to-compute roughness index (RI) which is based on the mean and variance of the (normalized) total variation for one-dimensional functions projected on randomly sampled directions. A large RI at the local minimizer hints an oscillatory landscape profile and indicates a severe challenge for the first-order optimization method. Particularly, we observe the increasing-then-decreasing pattern for RI along the gradient descent path in most models. We apply our method to two types of loss functions used to solve partial differential equations (PDEs) when the solution of PDE is parametrized by neural networks. Our empirical results on these PDE problems reveal important and consistent observations that the landscapes from the deep Galerkin method around its local minimizers are less rough than the deep Ritz method.

This work addresses the challenge of high-quality surface normal estimation from monocular colored inputs (i.e., images and videos), a field which has recently been revolutionized by repurposing diffusion priors. However, previous attempts still struggle with stochastic inference, conflicting with the deterministic nature of the Image2Normal task, and costly ensembling step, which slows down the estimation process. Our method, StableNormal, mitigates the stochasticity of the diffusion process by reducing inference variance, thus producing "Stable-and-Sharp" normal estimates without any additional ensembling process. StableNormal works robustly under challenging imaging conditions, such as extreme lighting, blurring, and low quality. It is also robust against transparent and reflective surfaces, as well as cluttered scenes with numerous objects. Specifically, StableNormal employs a coarse-to-fine strategy, which starts with a one-step normal estimator (YOSO) to derive an initial normal guess, that is relatively coarse but reliable, then followed by a semantic-guided refinement process (SG-DRN) that refines the normals to recover geometric details. The effectiveness of StableNormal is demonstrated through competitive performance in standard datasets such as DIODE-indoor, iBims, ScannetV2 and NYUv2, and also in various downstream tasks, such as surface reconstruction and normal enhancement. These results evidence that StableNormal retains both the "stability" and "sharpness" for accurate normal estimation. StableNormal represents a baby attempt to repurpose diffusion priors for deterministic estimation. To democratize this, code and models have been publicly available in hf.co/Stable-X

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.

We made a comparative analysis of numerical methods for multidimensional optimization. The main parameter is a number of computations of the test function to reach necessary accuracy, as it is computationally "slow". For complex functions, analytic differentiation by many parameters can cause problems associated with a significant complication of the program and thus slowing its operation. For comparison, we used the methods: "brute force" (or minimization on a regular grid), Monte Carlo, steepest descent, conjugate gradients, Brent's method (golden section search), parabolic interpolation etc. The Monte-Carlo method was applied to the eclipsing binary system AM Leo.

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.

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory. We consider here the classic regression setup, where a real valued square integrable r.v. Y is to be predicted upon observing a (possibly high dimensional) random vector X by means of a predictive function f(X) as accurately as possible in the mean-squared sense and study a nearest-neighbour-based pointwise estimate of the gradient of the optimal predictive function, the regression function m(x)=E[Ymid X=x]. Under classic smoothness conditions combined with the assumption that the tails of Y-m(X) are sub-Gaussian, we prove nonasymptotic bounds improving upon those obtained for alternative estimation methods. Beyond the novel theoretical results established, several illustrative numerical experiments have been carried out. The latter provide strong empirical evidence that the estimation method proposed works very well for various statistical problems involving gradient estimation, namely dimensionality reduction, stochastic gradient descent optimization and quantifying disentanglement.

This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayes-optimal test error for classification while obtaining (nearly) zero-training error under the lazy training regime. For this purpose, we unify three interrelated concepts of overparameterization, benign overfitting, and the Lipschitz constant of DNNs. Our results indicate that interpolating with smoother functions leads to better generalization. Furthermore, we investigate the special case where interpolating smooth ground-truth functions is performed by DNNs under the Neural Tangent Kernel (NTK) regime for generalization. Our result demonstrates that the generalization error converges to a constant order that only depends on label noise and initialization noise, which theoretically verifies benign overfitting. Our analysis provides a tight lower bound on the normalized margin under non-smooth activation functions, as well as the minimum eigenvalue of NTK under high-dimensional settings, which has its own interest in learning theory.

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.

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently, diffusion models have been successfully employed for randomized smoothing to purify noise-perturbed samples before making predictions with a standard classifier. While these methods excel at small perturbation radii, they struggle with larger perturbations and incur a significant computational overhead during inference compared to classical methods. To address this, we reformulate the generative modeling task along the diffusion trajectories in pixel space as a discriminative task in the latent space. Specifically, we use instance discrimination to achieve consistent representations along the trajectories by aligning temporally adjacent points. After fine-tuning based on the learned representations, our model enables implicit denoising-then-classification via a single prediction, substantially reducing inference costs. We conduct extensive experiments on various datasets and achieve state-of-the-art performance with minimal computation budget during inference. For example, our method outperforms the certified accuracy of diffusion-based methods on ImageNet across all perturbation radii by 5.3% on average, with up to 11.6% at larger radii, while reducing inference costs by 85times on average. Codes are available at: https://github.com/jiachenlei/rRCM.

Diffusion models have emerged as a powerful class of generative models, capable of producing high-quality images by mapping noise to a data distribution. However, recent findings suggest that image likelihood does not align with perceptual quality: high-likelihood samples tend to be smooth, while lower-likelihood ones are more detailed. Controlling sample density is thus crucial for balancing realism and detail. In this paper, we analyze an existing technique, Prior Guidance, which scales the latent code to influence image detail. We introduce score alignment, a condition that explains why this method works and show that it can be tractably checked for any continuous normalizing flow model. We then propose Density Guidance, a principled modification of the generative ODE that enables exact log-density control during sampling. Finally, we extend Density Guidance to stochastic sampling, ensuring precise log-density control while allowing controlled variation in structure or fine details. Our experiments demonstrate that these techniques provide fine-grained control over image detail without compromising sample quality.

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.

We introduce Gravity, another algorithm for gradient-based optimization. In this paper, we explain how our novel idea change parameters to reduce the deep learning model's loss. It has three intuitive hyper-parameters that the best values for them are proposed. Also, we propose an alternative to moving average. To compare the performance of the Gravity optimizer with two common optimizers, Adam and RMSProp, five standard datasets were trained on two VGGNet models with a batch size of 128 for 100 epochs. Gravity hyper-parameters did not need to be tuned for different models. As will be explained more in the paper, to investigate the direct impact of the optimizer itself on loss reduction no overfitting prevention technique was used. The obtained results show that the Gravity optimizer has more stable performance than Adam and RMSProp and gives greater values of validation accuracy for datasets with more output classes like CIFAR-100 (Fine).

In this article, we consider a newly proposed parameterization of the viscosity coefficient zeta, specifically zeta=zeta_0 {Omega^s_m} H , where zeta_0 = zeta_0{{Omega^s_{m_0}}} within the coincident f(Q) gravity formalism. We consider a non-linear function f(Q)= -Q +alpha Q^n, where alpha and n are arbitrary model parameters, which is a power-law correction to the STEGR scenario. We find an autonomous system by invoking the dimensionless density parameters as the governing phase-space variables. We discuss the physical significance of the model corresponding to the parameter choices n=-1 and n=2 along with the exponent choices s=0, 0.5, and 1.05. We find that model I shows the stable de-Sitter type or stable phantom type (depending on the choice of exponent s) behavior with no transition epoch, whereas model II shows the evolutionary phase from the radiation epoch to the accelerated de-Sitter epoch via passing through the matter-dominated epoch. Hence, we conclude that model I provides a good description of the late-time cosmology but fails to describe the transition epoch, whereas model II modifies the description in the context of the early universe and provides a good description of the matter and radiation era along with the transition phase.

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.

Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting the hyper-parameters remains a black art that requires years of experience to acquire. This report proposes several efficient ways to set the hyper-parameters that significantly reduce training time and improves performance. Specifically, this report shows how to examine the training validation/test loss function for subtle clues of underfitting and overfitting and suggests guidelines for moving toward the optimal balance point. Then it discusses how to increase/decrease the learning rate/momentum to speed up training. Our experiments show that it is crucial to balance every manner of regularization for each dataset and architecture. Weight decay is used as a sample regularizer to show how its optimal value is tightly coupled with the learning rates and momentums. Files to help replicate the results reported here are available.

Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the curse of dimensionality on RS. Specifically, the upper bound of {ell_2} certified robustness radius provided by RS exhibits a diminishing trend with the expansion of the input dimension d, proportionally decreasing at a rate of 1/d. This paper explores the feasibility of providing {ell_2} certified robustness for high-dimensional input through the utilization of dual smoothing in the lower-dimensional space. The proposed Dual Randomized Smoothing (DRS) down-samples the input image into two sub-images and smooths the two sub-images in lower dimensions. Theoretically, we prove that DRS guarantees a tight {ell_2} certified robustness radius for the original input and reveal that DRS attains a superior upper bound on the {ell_2} robustness radius, which decreases proportionally at a rate of (1/sqrt m + 1/sqrt n ) with m+n=d. Extensive experiments demonstrate the generalizability and effectiveness of DRS, which exhibits a notable capability to integrate with established methodologies, yielding substantial improvements in both accuracy and {ell_2} certified robustness baselines of RS on the CIFAR-10 and ImageNet datasets. Code is available at https://github.com/xiasong0501/DRS.

Calibration measures and reliability diagrams are two fundamental tools for measuring and interpreting the calibration of probabilistic predictors. Calibration measures quantify the degree of miscalibration, and reliability diagrams visualize the structure of this miscalibration. However, the most common constructions of reliability diagrams and calibration measures -- binning and ECE -- both suffer from well-known flaws (e.g. discontinuity). We show that a simple modification fixes both constructions: first smooth the observations using an RBF kernel, then compute the Expected Calibration Error (ECE) of this smoothed function. We prove that with a careful choice of bandwidth, this method yields a calibration measure that is well-behaved in the sense of (B{\l}asiok, Gopalan, Hu, and Nakkiran 2023a) -- a consistent calibration measure. We call this measure the SmoothECE. Moreover, the reliability diagram obtained from this smoothed function visually encodes the SmoothECE, just as binned reliability diagrams encode the BinnedECE. We also provide a Python package with simple, hyperparameter-free methods for measuring and plotting calibration: `pip install relplot\`.

In recent years, the development of diffusion models has led to significant progress in image and video generation tasks, with pre-trained models like the Stable Diffusion series playing a crucial role. Inspired by model pruning which lightens large pre-trained models by removing unimportant parameters, we propose a novel model fine-tuning method to make full use of these ineffective parameters and enable the pre-trained model with new task-specified capabilities. In this work, we first investigate the importance of parameters in pre-trained diffusion models, and discover that the smallest 10% to 20% of parameters by absolute values do not contribute to the generation process. Based on this observation, we propose a method termed SaRA that re-utilizes these temporarily ineffective parameters, equating to optimizing a sparse weight matrix to learn the task-specific knowledge. To mitigate overfitting, we propose a nuclear-norm-based low-rank sparse training scheme for efficient fine-tuning. Furthermore, we design a new progressive parameter adjustment strategy to make full use of the re-trained/finetuned parameters. Finally, we propose a novel unstructural backpropagation strategy, which significantly reduces memory costs during fine-tuning. Our method enhances the generative capabilities of pre-trained models in downstream applications and outperforms traditional fine-tuning methods like LoRA in maintaining model's generalization ability. We validate our approach through fine-tuning experiments on SD models, demonstrating significant improvements. SaRA also offers a practical advantage that requires only a single line of code modification for efficient implementation and is seamlessly compatible with existing methods.

Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However how to design an efficient classifier with an associated certified radius? Randomized smoothing provides a promising framework by relying on noise injection into the inputs to obtain a smoothed and robust classifier. In this paper, we first show that the variance introduced by the Monte-Carlo sampling in the randomized smoothing procedure estimate closely interacts with two other important properties of the classifier, i.e. its Lipschitz constant and margin. More precisely, our work emphasizes the dual impact of the Lipschitz constant of the base classifier, on both the smoothed classifier and the empirical variance. To increase the certified robust radius, we introduce a different way to convert logits to probability vectors for the base classifier to leverage the variance-margin trade-off. We leverage the use of Bernstein's concentration inequality along with enhanced Lipschitz bounds for randomized smoothing. Experimental results show a significant improvement in certified accuracy compared to current state-of-the-art methods. Our novel certification procedure allows us to use pre-trained models with randomized smoothing, effectively improving the current certification radius in a zero-shot manner.

We propose a novel parameterized skill-learning algorithm that aims to learn transferable parameterized skills and synthesize them into a new action space that supports efficient learning in long-horizon tasks. We propose to leverage off-policy Meta-RL combined with a trajectory-centric smoothness term to learn a set of parameterized skills. Our agent can use these learned skills to construct a three-level hierarchical framework that models a Temporally-extended Parameterized Action Markov Decision Process. We empirically demonstrate that the proposed algorithms enable an agent to solve a set of difficult long-horizon (obstacle-course and robot manipulation) tasks.

Phenomenological modeling of variable stars allows determination of a set of the parameters, which are needed for classification in the "General Catalogue of Variable Stars" and similar catalogs. We apply a recent method NAV ("New Algol Variable") to eclipsing binary stars of different types. Although all periodic functions may be represented as Fourier series with an infinite number of coefficients, this is impossible for a finite number of the observations. Thus one may use a restricted Fourier series, i.e. a trigonometric polynomial (TP) of order s either for fitting the light curve, or to make a periodogram analysis. However, the number of parameters needed drastically increases with decreasing width of minimum. In the NAV algorithm, the special shape of minimum is used, so the number of parameters is limited to 10 (if the period and initial epoch are fixed) or 12 (not fixed). We illustrate the NAV method by application to a recently discovered Algol-type eclipsing variable 2MASS J11080308-6145589 (in the field of previously known variable star RS Car) and compare results to that obtained using the TP fits. For this system, the statistically optimal number of parameters is 44, but the fit is still worse than that of the NAV fit. Application to the system GSC 3692-00624 argues that the NAV fit is better than the TP one even for the case of EW-type stars with much wider eclipses. Model parameters are listed.

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its practical efficacy: the implicit regularization it instigates. Several studies have investigated the linear stability property of SGD in the vicinity of a stationary point as a predictive proxy for sharpness and generalization error in overparameterized neural networks (Wu et al., 2022; Jastrzebski et al., 2019; Cohen et al., 2021). In this paper, we delve deeper into the relationship between linear stability and sharpness. More specifically, we meticulously delineate the necessary and sufficient conditions for linear stability, contingent on hyperparameters of SGD and the sharpness at the optimum. Towards this end, we introduce a novel coherence measure of the loss Hessian that encapsulates pertinent geometric properties of the loss function that are relevant to the linear stability of SGD. It enables us to provide a simplified sufficient condition for identifying linear instability at an optimum. Notably, compared to previous works, our analysis relies on significantly milder assumptions and is applicable for a broader class of loss functions than known before, encompassing not only mean-squared error but also cross-entropy loss.

Quantization scale and bit-width are the most important parameters when considering how to quantize a neural network. Prior work focuses on optimizing quantization scales in a global manner through gradient methods (gradient descent \& Hessian analysis). Yet, when applying perturbations to quantization scales, we observe a very jagged, highly non-smooth test loss landscape. In fact, small perturbations in quantization scale can greatly affect accuracy, yielding a 0.5-0.8% accuracy boost in 4-bit quantized vision transformers (ViTs). In this regime, gradient methods break down, since they cannot reliably reach local minima. In our work, dubbed Evol-Q, we use evolutionary search to effectively traverse the non-smooth landscape. Additionally, we propose using an infoNCE loss, which not only helps combat overfitting on the small calibration dataset (1,000 images) but also makes traversing such a highly non-smooth surface easier. Evol-Q improves the top-1 accuracy of a fully quantized ViT-Base by 10.30%, 0.78%, and 0.15% for 3-bit, 4-bit, and 8-bit weight quantization levels. Extensive experiments on a variety of CNN and ViT architectures further demonstrate its robustness in extreme quantization scenarios. Our code is available at https://github.com/enyac-group/evol-q

Automatic 3D content creation has gained increasing attention recently, due to its potential in various applications such as video games, film industry, and AR/VR. Recent advancements in diffusion models and multimodal models have notably improved the quality and efficiency of 3D object generation given a single RGB image. However, 3D objects generated even by state-of-the-art methods are still unsatisfactory compared to human-created assets. Considering only textures instead of materials makes these methods encounter challenges in photo-realistic rendering, relighting, and flexible appearance editing. And they also suffer from severe misalignment between geometry and high-frequency texture details. In this work, we propose a novel approach to boost the quality of generated 3D objects from the perspective of Physics-Based Rendering (PBR) materials. By analyzing the components of PBR materials, we choose to consider albedo, roughness, metalness, and bump maps. For albedo and bump maps, we leverage Stable Diffusion fine-tuned on synthetic data to extract these values, with novel usages of these fine-tuned models to obtain 3D consistent albedo UV and bump UV for generated objects. In terms of roughness and metalness maps, we adopt a semi-automatic process to provide room for interactive adjustment, which we believe is more practical. Extensive experiments demonstrate that our model is generally beneficial for various state-of-the-art generation methods, significantly boosting the quality and realism of their generated 3D objects, with natural relighting effects and substantially improved geometry.

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.

Knowledge distillation (KD) has been extensively employed to transfer the knowledge from a large teacher model to the smaller students, where the parameters of the teacher are fixed (or partially) during training. Recent studies show that this mode may cause difficulties in knowledge transfer due to the mismatched model capacities. To alleviate the mismatch problem, teacher-student joint training methods, e.g., online distillation, have been proposed, but it always requires expensive computational cost. In this paper, we present a parameter-efficient and student-friendly knowledge distillation method, namely PESF-KD, to achieve efficient and sufficient knowledge transfer by updating relatively few partial parameters. Technically, we first mathematically formulate the mismatch as the sharpness gap between their predictive distributions, where we show such a gap can be narrowed with the appropriate smoothness of the soft label. Then, we introduce an adapter module for the teacher and only update the adapter to obtain soft labels with appropriate smoothness. Experiments on a variety of benchmarks show that PESF-KD can significantly reduce the training cost while obtaining competitive results compared to advanced online distillation methods. Code will be released upon acceptance.

We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small L^2 error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order moment, by either employing early stopping or assuming smoothness condition on the score function of the data distribution. Our result does not rely on any log-concavity or functional inequality assumption and has a logarithmic dependence on the smoothness. In particular, we show that under only a finite second moment condition, approximating the following in reverse KL divergence in epsilon-accuracy can be done in tilde Oleft(d log (1/delta){epsilon}right) steps: 1) the variance-delta Gaussian perturbation of any data distribution; 2) data distributions with 1/delta-smooth score functions. Our analysis also provides a quantitative comparison between different discrete approximations and may guide the choice of discretization points in practice.

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.

This work proposes aesthetic gradients, a method to personalize a CLIP-conditioned diffusion model by guiding the generative process towards custom aesthetics defined by the user from a set of images. The approach is validated with qualitative and quantitative experiments, using the recent stable diffusion model and several aesthetically-filtered datasets. Code is released at https://github.com/vicgalle/stable-diffusion-aesthetic-gradients

Robustness remains a paramount concern in deep reinforcement learning (DRL), with randomized smoothing emerging as a key technique for enhancing this attribute. However, a notable gap exists in the performance of current smoothed DRL agents, often characterized by significantly low clean rewards and weak robustness. In response to this challenge, our study introduces innovative algorithms aimed at training effective smoothed robust DRL agents. We propose S-DQN and S-PPO, novel approaches that demonstrate remarkable improvements in clean rewards, empirical robustness, and robustness guarantee across standard RL benchmarks. Notably, our S-DQN and S-PPO agents not only significantly outperform existing smoothed agents by an average factor of 2.16times under the strongest attack, but also surpass previous robustly-trained agents by an average factor of 2.13times. This represents a significant leap forward in the field. Furthermore, we introduce Smoothed Attack, which is 1.89times more effective in decreasing the rewards of smoothed agents than existing adversarial attacks.

In the artificial neuron, I replace the dot product with the weighted Lehmer mean, which may emulate different cases of a generalized mean. The single neuron instance is replaced by a multiplet of neurons which have the same averaging weights. A group of outputs feed forward, in lieu of the single scalar. The generalization parameter is typically set to a different value for each neuron in the multiplet. I further extend the concept to a multiplet taken from the Gini mean. Derivatives with respect to the weight parameters and with respect to the two generalization parameters are given. Some properties of the network are investigated, showing the capacity to emulate the classical exclusive-or problem organically in two layers and perform some multiplication and division. The network can instantiate truncated power series and variants, which can be used to approximate different functions, provided that parameters are constrained. Moreover, a mean case slope score is derived that can facilitate a learning-rate novelty based on homogeneity of the selected elements. The multiplet neuron equation provides a way to segment regularization timeframes and approaches.

This study introduces a novel and interpretable model, DiffVox, for matching vocal effects in music production. DiffVox, short for ``Differentiable Vocal Fx", integrates parametric equalisation, dynamic range control, delay, and reverb with efficient differentiable implementations to enable gradient-based optimisation for parameter estimation. Vocal presets are retrieved from two datasets, comprising 70 tracks from MedleyDB and 365 tracks from a private collection. Analysis of parameter correlations highlights strong relationships between effects and parameters, such as the high-pass and low-shelf filters often behaving together to shape the low end, and the delay time correlates with the intensity of the delayed signals. Principal component analysis reveals connections to McAdams' timbre dimensions, where the most crucial component modulates the perceived spaciousness while the secondary components influence spectral brightness. Statistical testing confirms the non-Gaussian nature of the parameter distribution, highlighting the complexity of the vocal effects space. These initial findings on the parameter distributions set the foundation for future research in vocal effects modelling and automatic mixing. Our source code and datasets are accessible at https://github.com/SonyResearch/diffvox.

The aim of the present work is to investigate the influence of the realistic model parameters on the equipartition of energy in a vibrofluidized system. To achieve this, a three-dimensional vertically vibrated granular system consisting of spherical particles is simulated using the discrete element method (DEM) using the open-source software LAMMPS. Interparticle and wall-particle interactions are determined using the linear-spring dashpot model. Simulations are performed for nearly perfectly smooth to nearly perfectly rough particles. Two different values for the ratio of the tangential to normal spring stiffness coefficient kappa (2/7 and 3/4) are chosen. Non-equipartition of energy between the translational and rotational modes is observed for all realistic values in the parametric range.

In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation ability of idealised denoising diffusion models for high-dimensional target data, implementations introduce thresholding procedures for the generating process to overcome issues arising from the unbounded state space of such models. This mismatch between theoretical design and implementation of diffusion models has been addressed empirically by using a reflected diffusion process as the driver of noise instead. In this paper, we study statistical guarantees of these denoising reflected diffusion models. In particular, we establish minimax optimal rates of convergence in total variation, up to a polylogarithmic factor, under Sobolev smoothness assumptions. Our main contributions include the statistical analysis of this novel class of denoising reflected diffusion models and a refined score approximation method in both time and space, leveraging spectral decomposition and rigorous neural network analysis.

We report on analysis of the two-color VR CCD observations of the newly discovered variable 2MASS J18024395+4003309=VSX J180243.9+400331 obtained using the 1-m telescope of the Mt. Lemmon Observatory (LOAO) in the field of the intermediate polar V1323 Her. The extended version of this conference talk we published in 2015JASS...32..127A. The variability was reported in 2012OAP....25..150A, and the object was monitored. The two-color observations covered all phase interval. The object is classified as an Algol-type variable with tidally distorted components, and shows an asymmetry of the maxima (the O\'Connell effect). For phenomenological modeling, we used the trigonometric polynomial approximation of statistically optimal degree, and a recent method "NAV" (New Algol Variable) using local specific shapes for the eclipse. Methodological aspects are described, especially for the case of few color observations. Estimates of the physical parameters based on analysis of phenomenological parameters, are presented.

This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed ell^2 Lipschitz bounds, i.e. limited sensitivity to input perturbations. The Lipschitz guarantees are equivalent to the tightest-known bounds based on certification via a semidefinite program (SDP). We provide a ``direct'' parameterization, i.e., a smooth mapping from mathbb R^N onto the set of weights satisfying the SDP-based bound. Moreover, our parameterization is complete, i.e. a neural network satisfies the SDP bound if and only if it can be represented via our parameterization. This enables training using standard gradient methods, without any inner approximation or computationally intensive tasks (e.g. projections or barrier terms) for the SDP constraint. The new parameterization can equivalently be thought of as either a new layer type (the sandwich layer), or a novel parameterization of standard feedforward networks with parameter sharing between neighbouring layers. A comprehensive set of experiments on image classification shows that sandwich layers outperform previous approaches on both empirical and certified robust accuracy. Code is available at https://github.com/acfr/LBDN.

Automatic analysis of the enormous sets of images is a critical task in life sciences. This faces many challenges such as: algorithms are highly parameterized, significant human input is intertwined, and lacking a standard meta-visualization approach. This paper proposes an alternative iterative approach for optimizing input parameters, saving time by minimizing the user involvement, and allowing for understanding the workflow of algorithms and discovering new ones. The main focus is on developing an interactive visualization technique that enables users to analyze the relationships between sampled input parameters and corresponding output. This technique is implemented as a prototype called Veni Vidi Vici, or "I came, I saw, I conquered." This strategy is inspired by the mathematical formulas of numbering computable functions and is developed atop ImageJ, a scientific image processing program. A case study is presented to investigate the proposed framework. Finally, the paper explores some potential future issues in the application of the proposed approach in parameter space analysis in visualization.

We study the robust interpolation problem of arbitrary data distributions supported on a bounded space and propose a two-fold law of robustness. Robust interpolation refers to the problem of interpolating n noisy training data points in R^d by a Lipschitz function. Although this problem has been well understood when the samples are drawn from an isoperimetry distribution, much remains unknown concerning its performance under generic or even the worst-case distributions. We prove a Lipschitzness lower bound Omega(n/p) of the interpolating neural network with p parameters on arbitrary data distributions. With this result, we validate the law of robustness conjecture in prior work by Bubeck, Li, and Nagaraj on two-layer neural networks with polynomial weights. We then extend our result to arbitrary interpolating approximators and prove a Lipschitzness lower bound Omega(n^{1/d}) for robust interpolation. Our results demonstrate a two-fold law of robustness: i) we show the potential benefit of overparametrization for smooth data interpolation when n=poly(d), and ii) we disprove the potential existence of an O(1)-Lipschitz robust interpolating function when n=exp(omega(d)).

With the growing size of pre-trained models, full fine-tuning and storing all the parameters for various downstream tasks is costly and infeasible. In this paper, we propose a new parameter-efficient fine-tuning method, Gradient-based Parameter Selection (GPS), demonstrating that only tuning a few selected parameters from the pre-trained model while keeping the remainder of the model frozen can generate similar or better performance compared with the full model fine-tuning method. Different from the existing popular and state-of-the-art parameter-efficient fine-tuning approaches, our method does not introduce any additional parameters and computational costs during both the training and inference stages. Another advantage is the model-agnostic and non-destructive property, which eliminates the need for any other design specific to a particular model. Compared with the full fine-tuning, GPS achieves 3.33% (91.78% vs. 88.45%, FGVC) and 9.61% (73.1% vs. 65.57%, VTAB) improvement of the accuracy with tuning only 0.36% parameters of the pre-trained model on average over 24 image classification tasks; it also demonstrates a significant improvement of 17% and 16.8% in mDice and mIoU, respectively, on medical image segmentation task. Moreover, GPS achieves state-of-the-art performance compared with existing PEFT methods.

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.

Despite the popularity of guitar effects, there is very little existing research on classification and parameter estimation of specific plugins or effect units from guitar recordings. In this paper, convolutional neural networks were used for classification and parameter estimation for 13 overdrive, distortion and fuzz guitar effects. A novel dataset of processed electric guitar samples was assembled, with four sub-datasets consisting of monophonic or polyphonic samples and discrete or continuous settings values, for a total of about 250 hours of processed samples. Results were compared for networks trained and tested on the same or on a different sub-dataset. We found that discrete datasets could lead to equally high performance as continuous ones, whilst being easier to design, analyse and modify. Classification accuracy was above 80\%, with confusion matrices reflecting similarities in the effects timbre and circuits design. With parameter values between 0.0 and 1.0, the mean absolute error is in most cases below 0.05, while the root mean square error is below 0.1 in all cases but one.

Averaging neural network parameters is an intuitive method for fusing the knowledge of two independent models. It is most prominently used in federated learning. If models are averaged at the end of training, this can only lead to a good performing model if the loss surface of interest is very particular, i.e., the loss in the midpoint between the two models needs to be sufficiently low. This is impossible to guarantee for the non-convex losses of state-of-the-art networks. For averaging models trained on vastly different datasets, it was proposed to average only the parameters of particular layers or combinations of layers, resulting in better performing models. To get a better understanding of the effect of layer-wise averaging, we analyse the performance of the models that result from averaging single layers, or groups of layers. Based on our empirical and theoretical investigation, we introduce a novel notion of the layer-wise linear connectivity, and show that deep networks do not have layer-wise barriers between them.

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.

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel classifiers. With some mild assumptions on the conditional probability eta(x)=P(Y=1mid X=x), we derive an upper bound on the classification excess risk of a kernel classifier using recent advances in the theory of kernel regression. We also obtain a minimax lower bound for Sobolev spaces, which shows the optimality of the proposed classifier. Our theoretical results can be extended to the generalization error of overparameterized neural network classifiers. To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of 2eta(x)-1 and apply the method to real datasets.

We introduce the framework of performative reinforcement learning where the policy chosen by the learner affects the underlying reward and transition dynamics of the environment. Following the recent literature on performative prediction~Perdomo et. al., 2020, we introduce the concept of performatively stable policy. We then consider a regularized version of the reinforcement learning problem and show that repeatedly optimizing this objective converges to a performatively stable policy under reasonable assumptions on the transition dynamics. Our proof utilizes the dual perspective of the reinforcement learning problem and may be of independent interest in analyzing the convergence of other algorithms with decision-dependent environments. We then extend our results for the setting where the learner just performs gradient ascent steps instead of fully optimizing the objective, and for the setting where the learner has access to a finite number of trajectories from the changed environment. For both settings, we leverage the dual formulation of performative reinforcement learning and establish convergence to a stable solution. Finally, through extensive experiments on a grid-world environment, we demonstrate the dependence of convergence on various parameters e.g. regularization, smoothness, and the number of samples.

Post-training has emerged as a crucial paradigm for adapting large-scale pre-trained models to various tasks, whose effects are fully reflected by delta parameters (i.e., the disparity between post-trained and pre-trained parameters). While numerous studies have explored delta parameter properties via operations like pruning, quantization, low-rank approximation, and extrapolation, a unified framework for systematically examining these characteristics has been lacking. In this paper, we propose a novel perspective based on Riemann sum approximation of the loss function to elucidate delta parameter editing operations. Our analysis categorizes existing methods into three classes based on their post-editing performance: competitive, decreased, and improved, explaining how they are expressed by the Riemann sum approximation term and how they alter the model performance. Extensive experiments on both visual and language models, including ViT, LLaMA 3, Qwen 2, and Mistral, corroborate our theoretical findings. Furthermore, we introduce extensions to existing techniques like DARE and BitDelta, highlighting their limitations in leveraging the properties of delta parameters and reorganizing them into general expressions to enhance the applicability and effectiveness of delta parameter editing in post-trained models.

Second-order optimization has been developed to accelerate the training of deep neural networks and it is being applied to increasingly larger-scale models. In this study, towards training on further larger scales, we identify a specific parameterization for second-order optimization that promotes feature learning in a stable manner even if the network width increases significantly. Inspired by a maximal update parameterization, we consider a one-step update of the gradient and reveal the appropriate scales of hyperparameters including random initialization, learning rates, and damping terms. Our approach covers two major second-order optimization algorithms, K-FAC and Shampoo, and we demonstrate that our parameterization achieves higher generalization performance in feature learning. In particular, it enables us to transfer the hyperparameters across models with different widths.

Compliance is a useful parametrization of tactile information that humans often utilize in manipulation tasks. It can be used to inform low-level contact-rich actions or characterize objects at a high-level. In robotic manipulation, existing approaches to estimate compliance have struggled to generalize across object shape and material. Using camera-based tactile sensors, we present a novel approach to parametrize compliance through Young's modulus E. We evaluate our method over a novel dataset of 285 common objects, including a wide array of shapes and materials with Young's moduli ranging from 5.0 kPa to 250 GPa. Data is collected over automated parallel grasps of each object. Combining analytical and data-driven approaches, we develop a hybrid system using a multi-tower neural network to analyze a sequence of tactile images from grasping. This system is shown to estimate the Young's modulus of unseen objects within an order of magnitude at 74.2% accuracy across our dataset. This is a drastic improvement over a purely analytical baseline, which exhibits only 28.9% accuracy. Importantly, this estimation system performs irrespective of object geometry and demonstrates robustness across object materials. Thus, it could be applied in a general robotic manipulation setting to characterize unknown objects and inform decision-making, for instance to sort produce by ripeness.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

Recent work has highlighted the complex influence training hyperparameters, e.g., the number of training epochs, can have on the prunability of machine learning models. Perhaps surprisingly, a systematic approach to predict precisely how adjusting a specific hyperparameter will affect prunability remains elusive. To address this gap, we introduce a phenomenological model grounded in the statistical mechanics of learning. Our approach uses temperature-like and load-like parameters to model the impact of neural network (NN) training hyperparameters on pruning performance. A key empirical result we identify is a sharp transition phenomenon: depending on the value of a load-like parameter in the pruned model, increasing the value of a temperature-like parameter in the pre-pruned model may either enhance or impair subsequent pruning performance. Based on this transition, we build a three-regime model by taxonomizing the global structure of the pruned NN loss landscape. Our model reveals that the dichotomous effect of high temperature is associated with transitions between distinct types of global structures in the post-pruned model. Based on our results, we present three case-studies: 1) determining whether to increase or decrease a hyperparameter for improved pruning; 2) selecting the best model to prune from a family of models; and 3) tuning the hyperparameter of the Sharpness Aware Minimization method for better pruning performance.

Transfer learning has fundamentally changed the landscape of natural language processing (NLP) research. Many existing state-of-the-art models are first pre-trained on a large text corpus and then fine-tuned on downstream tasks. However, due to limited data resources from downstream tasks and the extremely large capacity of pre-trained models, aggressive fine-tuning often causes the adapted model to overfit the data of downstream tasks and forget the knowledge of the pre-trained model. To address the above issue in a more principled manner, we propose a new computational framework for robust and efficient fine-tuning for pre-trained language models. Specifically, our proposed framework contains two important ingredients: 1. Smoothness-inducing regularization, which effectively manages the capacity of the model; 2. Bregman proximal point optimization, which is a class of trust-region methods and can prevent knowledge forgetting. Our experiments demonstrate that our proposed method achieves the state-of-the-art performance on multiple NLP benchmarks.

As hyperparameter tuning becomes increasingly costly at scale, efficient tuning methods are essential. Yet principles for guiding hyperparameter tuning remain limited. In this work, we seek to establish such principles by considering a broad range of hyperparameters, including batch size, learning rate, and weight decay. We identify a phenomenon we call trajectory invariance, where pre-training loss curves, gradient noise, and gradient norm exhibit invariance--closely overlapping--with respect to a quantity that combines learning rate and weight decay. This phenomenon effectively reduces the original two-dimensional hyperparameter space to one dimension, yielding an efficient tuning rule: follow the salient direction revealed by trajectory invariance. Furthermore, we refine previous scaling laws and challenge several existing viewpoints. Overall, our work proposes new principles for efficient tuning and inspires future research on scaling laws.

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.

Recent studies have shown that CLIP has achieved remarkable success in performing zero-shot inference while its fine-tuning performance is not satisfactory. In this paper, we identify that fine-tuning performance is significantly impacted by hyper-parameter choices. We examine various key hyper-parameters and empirically evaluate their impact in fine-tuning CLIP for classification tasks through a comprehensive study. We find that the fine-tuning performance of CLIP is substantially underestimated. Equipped with hyper-parameter refinement, we demonstrate CLIP itself is better or at least competitive in fine-tuning compared with large-scale supervised pre-training approaches or latest works that use CLIP as prediction targets in Masked Image Modeling. Specifically, CLIP ViT-Base/16 and CLIP ViT-Large/14 can achieve 85.7%,88.0% finetuning Top-1 accuracy on the ImageNet-1K dataset . These observations challenge the conventional conclusion that CLIP is not suitable for fine-tuning, and motivate us to rethink recently proposed improvements based on CLIP. We will release our code publicly at https://github.com/LightDXY/FT-CLIP.

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.

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.

Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new insights on deep neural networks for estimating smooth functions in usual settings such as nonparametric regression. In this paper, we show that variational inference for sparse deep learning retains the same generalization properties than exact Bayesian inference. In particular, we highlight the connection between estimation and approximation theories via the classical bias-variance trade-off and show that it leads to near-minimax rates of convergence for H\"older smooth functions. Additionally, we show that the model selection framework over the neural network architecture via ELBO maximization does not overfit and adaptively achieves the optimal rate of convergence.

Phenomenological characteristics of the sample of the Algol-type stars are revised using a recently developed NAV ("New Algol Variable") algorithm (2012Ap.....55..536A, 2012arXiv 1212.6707A) and compared to that obtained using common methods of Trigonometric Polynomial Fit (TP) or local Algebraic Polynomial (A) fit of a fixed or (alternately) statistically optimal degree (1994OAP.....7...49A, 2003ASPC..292..391A). The computer program NAV is introduced, which allows to determine the best fit with 7 "linear" and 5 "non-linear" parameters and their error estimates. The number of parameters is much smaller than for the TP fit (typically 20-40, depending on the width of the eclipse, and is much smaller (5-20) for the W UMa and beta Lyrae - type stars. This causes more smooth approximation taking into account the reflection and ellipsoidal effects (TP2) and generally different shapes of the primary and secondary eclipses. An application of the method to two-color CCD photometry to the recently discovered eclipsing variable 2MASS J18024395 + 4003309 = VSX J180243.9 +400331 (2015JASS...32..101A) allowed to make estimates of the physical parameters of the binary system based on the phenomenological parameters of the light curve. The phenomenological parameters of the light curves were determined for the sample of newly discovered EA and EW - type stars (VSX J223429.3+552903, VSX J223421.4+553013, VSX J223416.2+553424, US-NO-B1.0 1347-0483658, UCAC3-191-085589, VSX J180755.6+074711= UCAC3 196-166827). Despite we have used original observations published by the discoverers, the accuracy estimates of the period using the NAV method are typically better than the original ones.

Creating plausible surfaces is an essential component in achieving a high degree of realism in rendering. To relieve artists, who create these surfaces in a time-consuming, manual process, automated retrieval of the spatially-varying Bidirectional Reflectance Distribution Function (SVBRDF) from a single mobile phone image is desirable. By leveraging a deep neural network, this casual capturing method can be achieved. The trained network can estimate per pixel normal, base color, metallic and roughness parameters from the Disney BRDF. The input image is taken with a mobile phone lit by the camera flash. The network is trained to compensate for environment lighting and thus learned to reduce artifacts introduced by other light sources. These losses contain a multi-scale discriminator with an additional perceptual loss, a rendering loss using a differentiable renderer, and a parameter loss. Besides the local precision, this loss formulation generates material texture maps which are globally more consistent. The network is set up as a generator network trained in an adversarial fashion to ensure that only plausible maps are produced. The estimated parameters not only reproduce the material faithfully in rendering but capture the style of hand-authored materials due to the more global loss terms compared to previous works without requiring additional post-processing. Both the resolution and the quality is improved.

Bilevel optimization is an important formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain neural networks such as recurrent neural networks (RNNs) and long-short-term memory networks (LSTMs) exhibit potential unbounded smoothness, rendering conventional bilevel optimization algorithms unsuitable. In this paper, we design a new bilevel optimization algorithm, namely BO-REP, to address this challenge. This algorithm updates the upper-level variable using normalized momentum and incorporates two novel techniques for updating the lower-level variable: initialization refinement and periodic updates. Specifically, once the upper-level variable is initialized, a subroutine is invoked to obtain a refined estimate of the corresponding optimal lower-level variable, and the lower-level variable is updated only after every specific period instead of each iteration. When the upper-level problem is nonconvex and unbounded smooth, and the lower-level problem is strongly convex, we prove that our algorithm requires mathcal{O}(1/epsilon^4) iterations to find an epsilon-stationary point in the stochastic setting, where each iteration involves calling a stochastic gradient or Hessian-vector product oracle. Notably, this result matches the state-of-the-art complexity results under the bounded smoothness setting and without mean-squared smoothness of the stochastic gradient, up to logarithmic factors. Our proof relies on novel technical lemmas for the periodically updated lower-level variable, which are of independent interest. Our experiments on hyper-representation learning, hyperparameter optimization, and data hyper-cleaning for text classification tasks demonstrate the effectiveness of our proposed algorithm.

We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter sigma describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it, if needed. They are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected. This exhibits the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data.

We apply augmentations to our dataset to enhance the quality of our predictions and make our final models more resilient to noisy data and domain drifts. Yet the question remains, how are these augmentations going to perform with different hyper-parameters? In this study we evaluate the sensitivity of augmentations with regards to the model's hyper parameters along with their consistency and influence by performing a Local Surrogate (LIME) interpretation on the impact of hyper-parameters when different augmentations are applied to a machine learning model. We have utilized Linear regression coefficients for weighing each augmentation. Our research has proved that there are some augmentations which are highly sensitive to hyper-parameters and others which are more resilient and reliable.

Robust and effective scaling of models from small to large width typically requires the precise adjustment of many algorithmic and architectural details, such as parameterization and optimizer choices. In this work, we propose a new perspective on parameterization by investigating a key assumption in prior work about the alignment between parameters and data and derive new theoretical results under weaker assumptions and a broader set of optimizers. Our extensive empirical investigation includes tens of thousands of models trained with all combinations of three optimizers, four parameterizations, several alignment assumptions, more than a dozen learning rates, and fourteen model sizes up to 26.8B parameters. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work. Our results show that all parameterizations, not just maximal update parameterization (muP), can achieve hyperparameter transfer; moreover, our novel per-layer learning rate prescription for standard parameterization outperforms muP. Finally, we demonstrate that an overlooked aspect of parameterization, the epsilon parameter in Adam, must be scaled correctly to avoid gradient underflow and propose Adam-atan2, a new numerically stable, scale-invariant version of Adam that eliminates the epsilon hyperparameter entirely.

Large pre-trained language models have recently gained significant traction due to their improved performance on various down-stream tasks like text classification and question answering, requiring only few epochs of fine-tuning. However, their large model sizes often prohibit their applications on resource-constrained edge devices. Existing solutions of yielding parameter-efficient BERT models largely rely on compute-exhaustive training and fine-tuning. Moreover, they often rely on additional compute heavy models to mitigate the performance gap. In this paper, we present Sensi-BERT, a sensitivity driven efficient fine-tuning of BERT models that can take an off-the-shelf pre-trained BERT model and yield highly parameter-efficient models for downstream tasks. In particular, we perform sensitivity analysis to rank each individual parameter tensor, that then is used to trim them accordingly during fine-tuning for a given parameter or FLOPs budget. Our experiments show the efficacy of Sensi-BERT across different downstream tasks including MNLI, QQP, QNLI, SST-2 and SQuAD, showing better performance at similar or smaller parameter budget compared to various alternatives.

Sharpness of minima is a promising quantity that can correlate with generalization in deep networks and, when optimized during training, can improve generalization. However, standard sharpness is not invariant under reparametrizations of neural networks, and, to fix this, reparametrization-invariant sharpness definitions have been proposed, most prominently adaptive sharpness (Kwon et al., 2021). But does it really capture generalization in modern practical settings? We comprehensively explore this question in a detailed study of various definitions of adaptive sharpness in settings ranging from training from scratch on ImageNet and CIFAR-10 to fine-tuning CLIP on ImageNet and BERT on MNLI. We focus mostly on transformers for which little is known in terms of sharpness despite their widespread usage. Overall, we observe that sharpness does not correlate well with generalization but rather with some training parameters like the learning rate that can be positively or negatively correlated with generalization depending on the setup. Interestingly, in multiple cases, we observe a consistent negative correlation of sharpness with out-of-distribution error implying that sharper minima can generalize better. Finally, we illustrate on a simple model that the right sharpness measure is highly data-dependent, and that we do not understand well this aspect for realistic data distributions. The code of our experiments is available at https://github.com/tml-epfl/sharpness-vs-generalization.

We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural network parameterizations and normalizations during stochastic optimization, which impedes fast convergence and hurts generalization performance. Addressing this, we propose Geometric Parameterization (GmP), a novel neural network parameterization technique that effectively separates the radial and angular components of weights in the hyperspherical coordinate system. We show theoretically that GmP resolves the aforementioned instability issue. We report empirical results on various models and benchmarks to verify GmP's theoretical advantages of optimization stability, convergence speed and generalization performance.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

In today's heavily overparameterized models, the value of the training loss provides few guarantees on model generalization ability. Indeed, optimizing only the training loss value, as is commonly done, can easily lead to suboptimal model quality. Motivated by prior work connecting the geometry of the loss landscape and generalization, we introduce a novel, effective procedure for instead simultaneously minimizing loss value and loss sharpness. In particular, our procedure, Sharpness-Aware Minimization (SAM), seeks parameters that lie in neighborhoods having uniformly low loss; this formulation results in a min-max optimization problem on which gradient descent can be performed efficiently. We present empirical results showing that SAM improves model generalization across a variety of benchmark datasets (e.g., CIFAR-10, CIFAR-100, ImageNet, finetuning tasks) and models, yielding novel state-of-the-art performance for several. Additionally, we find that SAM natively provides robustness to label noise on par with that provided by state-of-the-art procedures that specifically target learning with noisy labels. We open source our code at https://github.com/google-research/sam.

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization".

We introduce CADE 2.5 (Comfy Adaptive Detail Enhancer), a sampler-level guidance stack for SD/SDXL latent diffusion models. The central module, ZeResFDG, unifies (i) frequency-decoupled guidance that reweights low- and high-frequency components of the guidance signal, (ii) energy rescaling that matches the per-sample magnitude of the guided prediction to the positive branch, and (iii) zero-projection that removes the component parallel to the unconditional direction. A lightweight spectral EMA with hysteresis switches between a conservative and a detail-seeking mode as structure crystallizes during sampling. Across SD/SDXL samplers, ZeResFDG improves sharpness, prompt adherence, and artifact control at moderate guidance scales without any retraining. In addition, we employ a training-free inference-time stabilizer, QSilk Micrograin Stabilizer (quantile clamp + depth/edge-gated micro-detail injection), which improves robustness and yields natural high-frequency micro-texture at high resolutions with negligible overhead. For completeness we note that the same rule is compatible with alternative parameterizations (e.g., velocity), which we briefly discuss in the Appendix; however, this paper focuses on SD/SDXL latent diffusion models.

The goal of this article is to provide an introduction to the desirability function approach to multi-objective optimization (direct and surrogate model-based), and multi-objective hyperparameter tuning. This work is based on the paper by Kuhn (2016). It presents a `Python` implementation of Kuhn's `R` package `desirability`. The `Python` package `spotdesirability` is available as part of the `sequential parameter optimization` framework. After a brief introduction to the desirability function approach is presented, three examples are given that demonstrate how to use the desirability functions for classical optimization, surrogate-model based optimization, and hyperparameter tuning.

We develop regularity theory for critical points of variational integrals defined on Hessian spaces of functions on open, bounded subdomains of R^n, under compactly supported variations. The critical point solves a fourth order nonlinear equation in double divergence form. We show that for smooth convex functionals, a W^{2,infty} critical point with bounded Hessian is smooth provided that its Hessian has a small bounded mean oscillation (BMO). We deduce that the interior singular set of a critical point has Hausdorff dimension at most n-p_0, for some p_0 in (2,3). We state some applications of our results to variational problems in Lagrangian geometry. Finally, we use the Hamiltonian stationary equation to demonstrate the importance of our assumption on the a priori regularity of the critical point.

Despite the growing demand for accurate surface normal estimation models, existing methods use general-purpose dense prediction models, adopting the same inductive biases as other tasks. In this paper, we discuss the inductive biases needed for surface normal estimation and propose to (1) utilize the per-pixel ray direction and (2) encode the relationship between neighboring surface normals by learning their relative rotation. The proposed method can generate crisp - yet, piecewise smooth - predictions for challenging in-the-wild images of arbitrary resolution and aspect ratio. Compared to a recent ViT-based state-of-the-art model, our method shows a stronger generalization ability, despite being trained on an orders of magnitude smaller dataset. The code is available at https://github.com/baegwangbin/DSINE.

We study the bi-parameter local linearization of the one-dimensional nonlinear stochastic wave equation driven by a Gaussian noise, which is white in time and has a spatially homogeneous covariance structure of Riesz-kernel type. We establish that the second-order increments of the solution can be approximated by those of the corresponding linearized wave equation, modulated by the diffusion coefficient. These findings extend the previous results of Huang et al. HOO2024, which addressed the case of space-time white noise. As applications, we analyze the quadratic variation of the solution and construct a consistent estimator for the diffusion parameter.

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.

Most models in machine learning contain at least one hyperparameter to control for model complexity. Choosing an appropriate set of hyperparameters is both crucial in terms of model accuracy and computationally challenging. In this work we propose an algorithm for the optimization of continuous hyperparameters using inexact gradient information. An advantage of this method is that hyperparameters can be updated before model parameters have fully converged. We also give sufficient conditions for the global convergence of this method, based on regularity conditions of the involved functions and summability of errors. Finally, we validate the empirical performance of this method on the estimation of regularization constants of L2-regularized logistic regression and kernel Ridge regression. Empirical benchmarks indicate that our approach is highly competitive with respect to state of the art methods.

We present Paint-it, a text-driven high-fidelity texture map synthesis method for 3D meshes via neural re-parameterized texture optimization. Paint-it synthesizes texture maps from a text description by synthesis-through-optimization, exploiting the Score-Distillation Sampling (SDS). We observe that directly applying SDS yields undesirable texture quality due to its noisy gradients. We reveal the importance of texture parameterization when using SDS. Specifically, we propose Deep Convolutional Physically-Based Rendering (DC-PBR) parameterization, which re-parameterizes the physically-based rendering (PBR) texture maps with randomly initialized convolution-based neural kernels, instead of a standard pixel-based parameterization. We show that DC-PBR inherently schedules the optimization curriculum according to texture frequency and naturally filters out the noisy signals from SDS. In experiments, Paint-it obtains remarkable quality PBR texture maps within 15 min., given only a text description. We demonstrate the generalizability and practicality of Paint-it by synthesizing high-quality texture maps for large-scale mesh datasets and showing test-time applications such as relighting and material control using a popular graphics engine. Project page: https://kim-youwang.github.io/paint-it

In reinforcement learning from human feedback, it is common to optimize against a reward model trained to predict human preferences. Because the reward model is an imperfect proxy, optimizing its value too much can hinder ground truth performance, in accordance with Goodhart's law. This effect has been frequently observed, but not carefully measured due to the expense of collecting human preference data. In this work, we use a synthetic setup in which a fixed "gold-standard" reward model plays the role of humans, providing labels used to train a proxy reward model. We study how the gold reward model score changes as we optimize against the proxy reward model using either reinforcement learning or best-of-n sampling. We find that this relationship follows a different functional form depending on the method of optimization, and that in both cases its coefficients scale smoothly with the number of reward model parameters. We also study the effect on this relationship of the size of the reward model dataset, the number of reward model and policy parameters, and the coefficient of the KL penalty added to the reward in the reinforcement learning setup. We explore the implications of these empirical results for theoretical considerations in AI alignment.

We propose to study and promote the robustness of a model as per its performance through the interpolation of training data distributions. Specifically, (1) we augment the data by finding the worst-case Wasserstein barycenter on the geodesic connecting subpopulation distributions of different categories. (2) We regularize the model for smoother performance on the continuous geodesic path connecting subpopulation distributions. (3) Additionally, we provide a theoretical guarantee of robustness improvement and investigate how the geodesic location and the sample size contribute, respectively. Experimental validations of the proposed strategy on four datasets, including CIFAR-100 and ImageNet, establish the efficacy of our method, e.g., our method improves the baselines' certifiable robustness on CIFAR10 up to 7.7%, with 16.8% on empirical robustness on CIFAR-100. Our work provides a new perspective of model robustness through the lens of Wasserstein geodesic-based interpolation with a practical off-the-shelf strategy that can be combined with existing robust training methods.

We present AI-SARAH, a practical variant of SARAH. As a variant of SARAH, this algorithm employs the stochastic recursive gradient yet adjusts step-size based on local geometry. AI-SARAH implicitly computes step-size and efficiently estimates local Lipschitz smoothness of stochastic functions. It is fully adaptive, tune-free, straightforward to implement, and computationally efficient. We provide technical insight and intuitive illustrations on its design and convergence. We conduct extensive empirical analysis and demonstrate its strong performance compared with its classical counterparts and other state-of-the-art first-order methods in solving convex machine learning problems.

We study uncertainty quantification for partial differential equations subject to domain uncertainty. We parameterize the random domain using the model recently considered by Chernov and Le (2024) as well as Harbrecht, Schmidlin, and Schwab (2024) in which the input random field is assumed to belong to a Gevrey smoothness class. This approach has the advantage of being substantially more general than models which assume a particular parametric representation of the input random field such as a Karhunen-Loeve series expansion. We consider both the Poisson equation as well as the heat equation and design randomly shifted lattice quasi-Monte Carlo (QMC) cubature rules for the computation of the expected solution under domain uncertainty. We show that these QMC rules exhibit dimension-independent, essentially linear cubature convergence rates in this framework. In addition, we complete the error analysis by taking into account the approximation errors incurred by dimension truncation of the random input field and finite element discretization. Numerical experiments are presented to confirm the theoretical rates.

It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of neural networks that are shift invariant and preserve smoothness of the data: functional neural networks (FNNs). For this, we use methods from functional data analysis (FDA) to extend multi-layer perceptrons and convolutional neural networks to functional data. We propose different model architectures, show that the models outperform a benchmark model from FDA in terms of accuracy and successfully use FNNs to classify electroencephalography (EEG) data.

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.

Generative AI raises many societal concerns such as boosting disinformation and propaganda campaigns. Watermarking AI-generated content is a key technology to address these concerns and has been widely deployed in industry. However, watermarking is vulnerable to removal attacks and forgery attacks. In this work, we propose the first image watermarks with certified robustness guarantees against removal and forgery attacks. Our method leverages randomized smoothing, a popular technique to build certifiably robust classifiers and regression models. Our major technical contributions include extending randomized smoothing to watermarking by considering its unique characteristics, deriving the certified robustness guarantees, and designing algorithms to estimate them. Moreover, we extensively evaluate our image watermarks in terms of both certified and empirical robustness. Our code is available at https://github.com/zhengyuan-jiang/Watermark-Library.

Editing materials of objects in images based on exemplar images is an active area of research in computer vision and graphics. We propose MARBLE, a method for performing material blending and recomposing fine-grained material properties by finding material embeddings in CLIP-space and using that to control pre-trained text-to-image models. We improve exemplar-based material editing by finding a block in the denoising UNet responsible for material attribution. Given two material exemplar-images, we find directions in the CLIP-space for blending the materials. Further, we can achieve parametric control over fine-grained material attributes such as roughness, metallic, transparency, and glow using a shallow network to predict the direction for the desired material attribute change. We perform qualitative and quantitative analysis to demonstrate the efficacy of our proposed method. We also present the ability of our method to perform multiple edits in a single forward pass and applicability to painting. Project Page: https://marblecontrol.github.io/

Image interpolation based on diffusion models is promising in creating fresh and interesting images. Advanced interpolation methods mainly focus on spherical linear interpolation, where images are encoded into the noise space and then interpolated for denoising to images. However, existing methods face challenges in effectively interpolating natural images (not generated by diffusion models), thereby restricting their practical applicability. Our experimental investigations reveal that these challenges stem from the invalidity of the encoding noise, which may no longer obey the expected noise distribution, e.g., a normal distribution. To address these challenges, we propose a novel approach to correct noise for image interpolation, NoiseDiffusion. Specifically, NoiseDiffusion approaches the invalid noise to the expected distribution by introducing subtle Gaussian noise and introduces a constraint to suppress noise with extreme values. In this context, promoting noise validity contributes to mitigating image artifacts, but the constraint and introduced exogenous noise typically lead to a reduction in signal-to-noise ratio, i.e., loss of original image information. Hence, NoiseDiffusion performs interpolation within the noisy image space and injects raw images into these noisy counterparts to address the challenge of information loss. Consequently, NoiseDiffusion enables us to interpolate natural images without causing artifacts or information loss, thus achieving the best interpolation results.

Recent advances in diffusion models have revolutionized text-guided image editing, yet existing editing methods face critical challenges in hyperparameter identification. To get the reasonable editing performance, these methods often require the user to brute-force tune multiple interdependent hyperparameters, such as inversion timesteps and attention modification, etc. This process incurs high computational costs due to the huge hyperparameter search space. We consider searching optimal editing's hyperparameters as a sequential decision-making task within the diffusion denoising process. Specifically, we propose a reinforcement learning framework, which establishes a Markov Decision Process that dynamically adjusts hyperparameters across denoising steps, integrating editing objectives into a reward function. The method achieves time efficiency through proximal policy optimization while maintaining optimal hyperparameter configurations. Experiments demonstrate significant reduction in search time and computational overhead compared to existing brute-force approaches, advancing the practical deployment of a diffusion-based image editing framework in the real world.

We investigate the effects of the sharpness of the phase transition between hadronic matter and quark matter on various properties of neutron stars. We construct hybrid equations of state by combining a hadronic model with a quark model using a Gaussian function. This approach introduces a smooth transition characterized by two parameters: one representing the overpressure relative to the first-order phase transition point, and the other related to the range over which the hybrid region extends in baryon chemical potential. We find that the sharpness of the phase transition significantly influences the equation of state, which can deviate by several tens of MeV fm^{-3} from the one with a sharp first-order transition. The speed of sound exhibits diverse behaviors, including drastic drops, pronounced peaks, and oscillatory patterns, depending on the sharpness parameters. In terms of stellar structure, while the maximum neutron star mass remains largely unaffected by the sharpness of the phase transition, the stellar radii can vary significantly. Smoother transitions lead to a leftward shift (up to 1 km) of the mass-radius curve segment corresponding to hybrid stars. The tidal deformability decreases with smoother transitions, especially for higher-mass stars. Our results are quite general and do not qualitatively depend on the specific hadronic and quark matter models employed. In fact, the hybrid equation of state and stellar properties derived from microscopic models of quark-hadron pasta phases display the same behavior as described above.

Although randomized smoothing has demonstrated high certified robustness and superior scalability to other certified defenses, the high computational overhead of the robustness certification bottlenecks the practical applicability, as it depends heavily on the large sample approximation for estimating the confidence interval. In existing works, the sample size for the confidence interval is universally set and agnostic to the input for prediction. This Input-Agnostic Sampling (IAS) scheme may yield a poor Average Certified Radius (ACR)-runtime trade-off which calls for improvement. In this paper, we propose Input-Specific Sampling (ISS) acceleration to achieve the cost-effectiveness for robustness certification, in an adaptive way of reducing the sampling size based on the input characteristic. Furthermore, our method universally controls the certified radius decline from the ISS sample size reduction. The empirical results on CIFAR-10 and ImageNet show that ISS can speed up the certification by more than three times at a limited cost of 0.05 certified radius. Meanwhile, ISS surpasses IAS on the average certified radius across the extensive hyperparameter settings. Specifically, ISS achieves ACR=0.958 on ImageNet (sigma=1.0) in 250 minutes, compared to ACR=0.917 by IAS under the same condition. We release our code in https://github.com/roy-ch/Input-Specific-Certification.

Despite the great success of Transformer networks in various applications such as natural language processing and computer vision, their theoretical aspects are not well understood. In this paper, we study the approximation and estimation ability of Transformers as sequence-to-sequence functions with infinite dimensional inputs. Although inputs and outputs are both infinite dimensional, we show that when the target function has anisotropic smoothness, Transformers can avoid the curse of dimensionality due to their feature extraction ability and parameter sharing property. In addition, we show that even if the smoothness changes depending on each input, Transformers can estimate the importance of features for each input and extract important features dynamically. Then, we proved that Transformers achieve similar convergence rate as in the case of the fixed smoothness. Our theoretical results support the practical success of Transformers for high dimensional data.

LOBSTER (LOss-Based SensiTivity rEgulaRization) is a method for training neural networks having a sparse topology. Let the sensitivity of a network parameter be the variation of the loss function with respect to the variation of the parameter. Parameters with low sensitivity, i.e. having little impact on the loss when perturbed, are shrunk and then pruned to sparsify the network. Our method allows to train a network from scratch, i.e. without preliminary learning or rewinding. Experiments on multiple architectures and datasets show competitive compression ratios with minimal computational overhead.

Various tasks in data science are modeled utilizing the variational regularization approach, where manually selecting regularization parameters presents a challenge. The difficulty gets exacerbated when employing regularizers involving a large number of hyperparameters. To overcome this challenge, bilevel learning can be employed to learn such parameters from data. However, neither exact function values nor exact gradients with respect to the hyperparameters are attainable, necessitating methods that only rely on inexact evaluation of such quantities. State-of-the-art inexact gradient-based methods a priori select a sequence of the required accuracies and cannot identify an appropriate step size since the Lipschitz constant of the hypergradient is unknown. In this work, we propose an algorithm with backtracking line search that only relies on inexact function evaluations and hypergradients and show convergence to a stationary point. Furthermore, the proposed algorithm determines the required accuracy dynamically rather than manually selected before running it. Our numerical experiments demonstrate the efficiency and feasibility of our approach for hyperparameter estimation on a range of relevant problems in imaging and data science such as total variation and field of experts denoising and multinomial logistic regression. Particularly, the results show that the algorithm is robust to its own hyperparameters such as the initial accuracies and step size.

Zero-shot models like CLIP are often fine-tuned on a target dataset to improve its accuracy further, but this can compromise out-of-distribution (OOD) robustness. Robust Fine-Tuning (RFT )~wortsman2021robust, which interpolates between the zero-shot and fine-tuned models, has been proposed to address this issue. However, understanding when RFT actually improves OOD error remains limited. In this work, we empirically investigate the robustness of RFT in CLIP models, with a focus on the sharpness of the CLIP model during interpolation. First, we demonstrate that while sharpness may not serve as a reliable indicator for predicting the generalization of modern architectures like CLIP on OOD data, this challenges the conventional belief in the generalization benefits of flat minima in foundation models. However, by examining the role of the straggler layer phenomenon, we show that, unlike overall sharpness, the layer-wise sharpness of straggler layers can reliably capture the generalization performance of interpolated CLIP models on OOD data. Our extensive experiments reveal that layer-wise sharpness correlates with generalization in OOD accuracy for RFT. Furthermore, we demonstrate that by inducing sparsity in the straggler layers, we can mitigate the failure mode phenomenon in RFT. To the best of our knowledge, this is the first work to study the role of sharpness in the success of interpolation in the weight space of CLIP foundation models. Our code is available at https://github.com/alirezaabdollahpour/CLIP_Mode_Connectivity.

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.

This paper rigorously shows how over-parameterization changes the convergence behaviors of gradient descent (GD) for the matrix sensing problem, where the goal is to recover an unknown low-rank ground-truth matrix from near-isotropic linear measurements. First, we consider the symmetric setting with the symmetric parameterization where M^* in R^{n times n} is a positive semi-definite unknown matrix of rank r ll n, and one uses a symmetric parameterization XX^top to learn M^*. Here X in R^{n times k} with k > r is the factor matrix. We give a novel Omega (1/T^2) lower bound of randomly initialized GD for the over-parameterized case (k >r) where T is the number of iterations. This is in stark contrast to the exact-parameterization scenario (k=r) where the convergence rate is exp (-Omega (T)). Next, we study asymmetric setting where M^* in R^{n_1 times n_2} is the unknown matrix of rank r ll min{n_1,n_2}, and one uses an asymmetric parameterization FG^top to learn M^* where F in R^{n_1 times k} and G in R^{n_2 times k}. Building on prior work, we give a global exact convergence result of randomly initialized GD for the exact-parameterization case (k=r) with an exp (-Omega(T)) rate. Furthermore, we give the first global exact convergence result for the over-parameterization case (k>r) with an exp(-Omega(alpha^2 T)) rate where alpha is the initialization scale. This linear convergence result in the over-parameterization case is especially significant because one can apply the asymmetric parameterization to the symmetric setting to speed up from Omega (1/T^2) to linear convergence. On the other hand, we propose a novel method that only modifies one step of GD and obtains a convergence rate independent of alpha, recovering the rate in the exact-parameterization case.

In this work, we focus on a fractional differential equation in Riesz form discretized by a polynomial B-spline collocation method. For an arbitrary polynomial degree p, we show that the resulting coefficient matrices possess a Toeplitz-like structure. We investigate their spectral properties via their symbol and we prove that, like for second order differential problems, also in this case the given matrices are ill-conditioned both in the low and high frequencies for large p. More precisely, in the fractional scenario the symbol has a single zero at 0 of order α, with α the fractional derivative order that ranges from 1 to 2, and it presents an exponential decay to zero at π for increasing p that becomes faster as α approaches 1. This translates in a mitigated conditioning in the low frequencies and in a deterioration in the high frequencies when compared to second order problems. Furthermore, the derivation of the symbol reveals another similarity of our problem with a classical diffusion problem. Since the entries of the coefficient matrices are defined as evaluations of fractional derivatives of the B-spline basis at the collocation points, we are able to express the central entries of the coefficient matrix as inner products of two fractional derivatives of cardinal B-splines. Finally, we perform a numerical study of the approximation behavior of polynomial B-spline collocation. This study suggests that, in line with non-fractional diffusion problems, the approximation order for smooth solutions in the fractional case is p+2-α for even p, and p+1-α for odd p.

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/