Daily Papers

E. T. Whittaker produced two papers in 1903 and 1904 that, although sometimes considered mere mathematical statements (Barrett, 1993), held important implications for physical theory. The Whittaker 1903 paper united electrostatic and gravitational attraction as resulting from longitudinal waves - waves whose wavefronts propagate parallel to their direction. The Whittaker 1904 paper showed that electromagnetic waves resulted from the interference of two such longitudinal waves or scalar potential functions. Although unexplored, the implications of these papers are profound: gravitational lensing, gravitational waves, the Aharonov-Bohm effect, the existence of a hyperspace above or behind normal space, the elimination of gravitational and point charge singularities, MOND, and the expansion of the universe. This last implication can be related to the recent finding that black holes with posited vacuum energy interior solutions alongside cosmological boundaries have a cosmological coupling constant of k=3, meaning that black holes gain mass-proportional to a3 in a parameterization equation within a Robertson-Walker cosmology and are a cosmological accelerated expansion species (Farrah et al., 2023). This expansion and many features of General Relativity can be explained by the mass-proportionality and preferred direction of the longitudinal waves within the two underlying non-local Whittaker potentials (Titleman, 2022). Whittaker potential theory also offers a simple explanation for expansion of the universe - it is produced as longitudinal motion within the Whittaker potentials only when dynamic electromagnetism is separate from time-static gravity in intergalactic space.

Diffusion models usher a new era of video editing, flexibly manipulating the video contents with text prompts. Despite the widespread application demand in editing human-centered videos, these models face significant challenges in handling complex objects like humans. In this paper, we introduce DeCo, a novel video editing framework specifically designed to treat humans and the background as separate editable targets, ensuring global spatial-temporal consistency by maintaining the coherence of each individual component. Specifically, we propose a decoupled dynamic human representation that utilizes a parametric human body prior to generate tailored humans while preserving the consistent motions as the original video. In addition, we consider the background as a layered atlas to apply text-guided image editing approaches on it. To further enhance the geometry and texture of humans during the optimization, we extend the calculation of score distillation sampling into normal space and image space. Moreover, we tackle inconsistent lighting between the edited targets by leveraging a lighting-aware video harmonizer, a problem previously overlooked in decompose-edit-combine approaches. Extensive qualitative and numerical experiments demonstrate that DeCo outperforms prior video editing methods in human-centered videos, especially in longer videos.

Anomalies in the domain of autonomous driving are a major hindrance to the large-scale deployment of autonomous vehicles. In this work, we focus on high-resolution camera data from urban scenes that include anomalies of various types and sizes. Based on a Variational Autoencoder, we condition its latent space to classify samples as either normal data or anomalies. In order to emphasize especially small anomalies, we perform experiments where we provide the VAE with a discrepancy map as an additional input, evaluating its impact on the detection performance. Our method separates normal data and anomalies into isolated clusters while still reconstructing high-quality images, leading to meaningful latent representations.

We introduce Metric3D v2, a geometric foundation model for zero-shot metric depth and surface normal estimation from a single image, which is crucial for metric 3D recovery. While depth and normal are geometrically related and highly complimentary, they present distinct challenges. SoTA monocular depth methods achieve zero-shot generalization by learning affine-invariant depths, which cannot recover real-world metrics. Meanwhile, SoTA normal estimation methods have limited zero-shot performance due to the lack of large-scale labeled data. To tackle these issues, we propose solutions for both metric depth estimation and surface normal estimation. For metric depth estimation, we show that the key to a zero-shot single-view model lies in resolving the metric ambiguity from various camera models and large-scale data training. We propose a canonical camera space transformation module, which explicitly addresses the ambiguity problem and can be effortlessly plugged into existing monocular models. For surface normal estimation, we propose a joint depth-normal optimization module to distill diverse data knowledge from metric depth, enabling normal estimators to learn beyond normal labels. Equipped with these modules, our depth-normal models can be stably trained with over 16 million of images from thousands of camera models with different-type annotations, resulting in zero-shot generalization to in-the-wild images with unseen camera settings. Our method enables the accurate recovery of metric 3D structures on randomly collected internet images, paving the way for plausible single-image metrology. Our project page is at https://JUGGHM.github.io/Metric3Dv2.

We introduce POP3D, a novel framework that creates a full 360^circ-view 3D model from a single image. POP3D resolves two prominent issues that limit the single-view reconstruction. Firstly, POP3D offers substantial generalizability to arbitrary categories, a trait that previous methods struggle to achieve. Secondly, POP3D further improves reconstruction fidelity and naturalness, a crucial aspect that concurrent works fall short of. Our approach marries the strengths of four primary components: (1) a monocular depth and normal predictor that serves to predict crucial geometric cues, (2) a space carving method capable of demarcating the potentially unseen portions of the target object, (3) a generative model pre-trained on a large-scale image dataset that can complete unseen regions of the target, and (4) a neural implicit surface reconstruction method tailored in reconstructing objects using RGB images along with monocular geometric cues. The combination of these components enables POP3D to readily generalize across various in-the-wild images and generate state-of-the-art reconstructions, outperforming similar works by a significant margin. Project page: http://cg.postech.ac.kr/research/POP3D

Diffusion models have achieved state-of-the-art synthesis quality on both visual and audio tasks, and recent works further adapt them to textual data by diffusing on the embedding space. In this paper, we conduct systematic studies and analyze the challenges between the continuous data space and the embedding space which have not been carefully explored. Firstly, the data distribution is learnable for embeddings, which may lead to the collapse of the loss function. Secondly, as the norm of embeddings varies between popular and rare words, adding the same noise scale will lead to sub-optimal results. In addition, we find the normal level of noise causes insufficient training of the model. To address the above challenges, we propose Difformer, an embedding diffusion model based on Transformer, which consists of three essential modules including an additional anchor loss function, a layer normalization module for embeddings, and a noise factor to the Gaussian noise. Experiments on two seminal text generation tasks including machine translation and text summarization show the superiority of Difformer over compared embedding diffusion baselines.

Modeling the time-dependent evolution of electron density is essential for understanding quantum mechanical behaviors of condensed matter and enabling predictive simulations in spectroscopy, photochemistry, and ultrafast science. Yet, while machine learning methods have advanced static density prediction, modeling its spatiotemporal dynamics remains largely unexplored. In this work, we introduce a generative framework that combines a 3D convolutional autoencoder with a latent diffusion model (LDM) to learn electron density trajectories from ab-initio molecular dynamics (AIMD) simulations. Our method encodes electron densities into a compact latent space and predicts their future states by sampling from the learned conditional distribution, enabling stable long-horizon rollouts without drift or collapse. To preserve statistical fidelity, we incorporate a scaled Jensen-Shannon divergence regularization that aligns generated and reference density distributions. On AIMD trajectories of liquid lithium at 800 K, our model accurately captures both the spatial correlations and the log-normal-like statistical structure of the density. The proposed framework has the potential to accelerate the simulation of quantum dynamics and overcome key challenges faced by current spatiotemporal machine learning methods as surrogates of quantum mechanical simulators.

State-space models (SSMs) have recently emerged as a framework for learning long-range sequence tasks. An example is the structured state-space sequence (S4) layer, which uses the diagonal-plus-low-rank structure of the HiPPO initialization framework. However, the complicated structure of the S4 layer poses challenges; and, in an effort to address these challenges, models such as S4D and S5 have considered a purely diagonal structure. This choice simplifies the implementation, improves computational efficiency, and allows channel communication. However, diagonalizing the HiPPO framework is itself an ill-posed problem. In this paper, we propose a general solution for this and related ill-posed diagonalization problems in machine learning. We introduce a generic, backward-stable "perturb-then-diagonalize" (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences. As a result, our new models show resilience to Fourier-mode noise-perturbed inputs, a crucial property not achieved by the S4D/S5 models. In addition to improved robustness, our S5-PTD model averages 87.6% accuracy on the Long-Range Arena benchmark, demonstrating that the PTD methodology helps to improve the accuracy of deep learning models.

We propose a novel method called SHS-Net for oriented normal estimation of point clouds by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our SHS-Net outperforms the state-of-the-art methods in both unoriented and oriented normal estimation on the widely used benchmarks. The code, data and pretrained models are publicly available.

Denoising diffusion probabilistic models (DDPMs) employ a sequence of white Gaussian noise samples to generate an image. In analogy with GANs, those noise maps could be considered as the latent code associated with the generated image. However, this native noise space does not possess a convenient structure, and is thus challenging to work with in editing tasks. Here, we propose an alternative latent noise space for DDPM that enables a wide range of editing operations via simple means, and present an inversion method for extracting these edit-friendly noise maps for any given image (real or synthetically generated). As opposed to the native DDPM noise space, the edit-friendly noise maps do not have a standard normal distribution and are not statistically independent across timesteps. However, they allow perfect reconstruction of any desired image, and simple transformations on them translate into meaningful manipulations of the output image (e.g., shifting, color edits). Moreover, in text-conditional models, fixing those noise maps while changing the text prompt, modifies semantics while retaining structure. We illustrate how this property enables text-based editing of real images via the diverse DDPM sampling scheme (in contrast to the popular non-diverse DDIM inversion). We also show how it can be used within existing diffusion-based editing methods to improve their quality and diversity.

Automatic 3D facial texture generation has gained significant interest recently. Existing approaches may not support the traditional physically based rendering pipeline or rely on 3D data captured by Light Stage. Our key contribution is a progressive latent space refinement approach that can bootstrap from 3D Morphable Models (3DMMs)-based texture maps generated from facial images to generate high-quality and diverse PBR textures, including albedo, normal, and roughness. It starts with enhancing Generative Adversarial Networks (GANs) for text-guided and diverse texture generation. To this end, we design a self-supervised paradigm to overcome the reliance on ground truth 3D textures and train the generative model with only entangled texture maps. Besides, we foster mutual enhancement between GANs and Score Distillation Sampling (SDS). SDS boosts GANs with more generative modes, while GANs promote more efficient optimization of SDS. Furthermore, we introduce an edge-aware SDS for multi-view consistent facial structure. Experiments demonstrate that our method outperforms existing 3D texture generation methods regarding photo-realistic quality, diversity, and efficiency.

Unsupervised reconstruction networks using self-attention transformers have achieved state-of-the-art performance for multi-class (unified) anomaly detection with a single model. However, these self-attention reconstruction models primarily operate on target features, which may result in perfect reconstruction for both normal and anomaly features due to high consistency with context, leading to failure in detecting anomalies. Additionally, these models often produce inaccurate anomaly segmentation due to performing reconstruction in a low spatial resolution latent space. To enable reconstruction models enjoying high efficiency while enhancing their generalization for unified anomaly detection, we propose a simple yet effective method that reconstructs normal features and restores anomaly features with just One Normal Image Prompt (OneNIP). In contrast to previous work, OneNIP allows for the first time to reconstruct or restore anomalies with just one normal image prompt, effectively boosting unified anomaly detection performance. Furthermore, we propose a supervised refiner that regresses reconstruction errors by using both real normal and synthesized anomalous images, which significantly improves pixel-level anomaly segmentation. OneNIP outperforms previous methods on three industry anomaly detection benchmarks: MVTec, BTAD, and VisA. The code and pre-trained models are available at https://github.com/gaobb/OneNIP.

Recent years have witnessed a surge of interests of using neural topic models for automatic topic extraction from text, since they avoid the complicated mathematical derivations for model inference as in traditional topic models such as Latent Dirichlet Allocation (LDA). However, these models either typically assume improper prior (e.g. Gaussian or Logistic Normal) over latent topic space or could not infer topic distribution for a given document. To address these limitations, we propose a neural topic modeling approach, called Bidirectional Adversarial Topic (BAT) model, which represents the first attempt of applying bidirectional adversarial training for neural topic modeling. The proposed BAT builds a two-way projection between the document-topic distribution and the document-word distribution. It uses a generator to capture the semantic patterns from texts and an encoder for topic inference. Furthermore, to incorporate word relatedness information, the Bidirectional Adversarial Topic model with Gaussian (Gaussian-BAT) is extended from BAT. To verify the effectiveness of BAT and Gaussian-BAT, three benchmark corpora are used in our experiments. The experimental results show that BAT and Gaussian-BAT obtain more coherent topics, outperforming several competitive baselines. Moreover, when performing text clustering based on the extracted topics, our models outperform all the baselines, with more significant improvements achieved by Gaussian-BAT where an increase of near 6\% is observed in accuracy.

Motivation: Ab initio protein docking represents a major challenge for optimizing a noisy and costly "black box"-like function in a high-dimensional space. Despite progress in this field, there is no docking method available for rigorous uncertainty quantification (UQ) of its solution quality (e.g. interface RMSD or iRMSD). Results: We introduce a novel algorithm, Bayesian Active Learning (BAL), for optimization and UQ of such black-box functions and flexible protein docking. BAL directly models the posterior distribution of the global optimum (or native structures for protein docking) with active sampling and posterior estimation iteratively feeding each other. Furthermore, we use complex normal modes to represent a homogeneous Euclidean conformation space suitable for high-dimension optimization and construct funnel-like energy models for encounter complexes. Over a protein docking benchmark set and a CAPRI set including homology docking, we establish that BAL significantly improve against both starting points by rigid docking and refinements by particle swarm optimization, providing for one third targets a top-3 near-native prediction. BAL also generates tight confidence intervals with half range around 25% of iRMSD and confidence level at 85%. Its estimated probability of a prediction being native or not achieves binary classification AUROC at 0.93 and AUPRC over 0.60 (compared to 0.14 by chance); and also found to help ranking predictions. To the best of our knowledge, this study represents the first uncertainty quantification solution for protein docking, with theoretical rigor and comprehensive assessment. Source codes are available at https://github.com/Shen-Lab/BAL.

Unsupervised anomaly detection in brain images is crucial for identifying injuries and pathologies without access to labels. However, the accurate localization of anomalies in medical images remains challenging due to the inherent complexity and variability of brain structures and the scarcity of annotated abnormal data. To address this challenge, we propose a novel approach that incorporates masking within diffusion models, leveraging their generative capabilities to learn robust representations of normal brain anatomy. During training, our model processes only normal brain MRI scans and performs a forward diffusion process in the latent space that adds noise to the features of randomly-selected patches. Following a dual objective, the model learns to identify which patches are noisy and recover their original features. This strategy ensures that the model captures intricate patterns of normal brain structures while isolating potential anomalies as noise in the latent space. At inference, the model identifies noisy patches corresponding to anomalies and generates a normal counterpart for these patches by applying a reverse diffusion process. Our method surpasses existing unsupervised anomaly detection techniques, demonstrating superior performance in generating accurate normal counterparts and localizing anomalies. The code is available at hhttps://github.com/farzad-bz/MAD-AD.

Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties for a class of structured symmetric positive-definite matrices with the affine-invariant metric. We do so by proposing a generalized version of the Riemannian normal coordinates that dynamically orthonormalizes the metric and locally converts the problem into an unconstrained problem in the Euclidean space. We use our approach to simplify existing approaches for structured covariances and develop matrix-inverse-free 2^nd-order optimizers for deep learning in low precision settings. Code: https://github.com/yorkerlin/StructuredNGD-DL

Likelihood approximations for images are not trivial to compute and can be useful in many applications. We examine the use of Contrastive Language-Image Pre-training (CLIP) to assess the likelihood of images and captions. We introduce Whitened CLIP, a novel transformation of the CLIP latent space via an invertible linear operation. This transformation ensures that each feature in the embedding space has zero mean, unit standard deviation, and no correlation with all other features, resulting in an identity covariance matrix. We show that the whitened embeddings statistics can be well approximated as a standard normal distribution, thus, the log-likelihood is estimated simply by the square Euclidean norm in the whitened embedding space. The whitening procedure is completely training-free and performed using a pre-computed whitening matrix, hence, is very fast. We present several preliminary experiments demonstrating the properties and applicability of these likelihood scores to images and captions.

In this paper, we introduce Latent Bridge Matching (LBM), a new, versatile and scalable method that relies on Bridge Matching in a latent space to achieve fast image-to-image translation. We show that the method can reach state-of-the-art results for various image-to-image tasks using only a single inference step. In addition to its efficiency, we also demonstrate the versatility of the method across different image translation tasks such as object removal, normal and depth estimation, and object relighting. We also derive a conditional framework of LBM and demonstrate its effectiveness by tackling the tasks of controllable image relighting and shadow generation. We provide an open-source implementation of the method at https://github.com/gojasper/LBM.

An approach to the construction of classifiers from imbalanced datasets is described. A dataset is imbalanced if the classification categories are not approximately equally represented. Often real-world data sets are predominately composed of "normal" examples with only a small percentage of "abnormal" or "interesting" examples. It is also the case that the cost of misclassifying an abnormal (interesting) example as a normal example is often much higher than the cost of the reverse error. Under-sampling of the majority (normal) class has been proposed as a good means of increasing the sensitivity of a classifier to the minority class. This paper shows that a combination of our method of over-sampling the minority (abnormal) class and under-sampling the majority (normal) class can achieve better classifier performance (in ROC space) than only under-sampling the majority class. This paper also shows that a combination of our method of over-sampling the minority class and under-sampling the majority class can achieve better classifier performance (in ROC space) than varying the loss ratios in Ripper or class priors in Naive Bayes. Our method of over-sampling the minority class involves creating synthetic minority class examples. Experiments are performed using C4.5, Ripper and a Naive Bayes classifier. The method is evaluated using the area under the Receiver Operating Characteristic curve (AUC) and the ROC convex hull strategy.

In this paper, we propose a diffusion-based unsupervised framework that incorporates physically explainable Retinex theory with diffusion models for low-light image enhancement, named LightenDiffusion. Specifically, we present a content-transfer decomposition network that performs Retinex decomposition within the latent space instead of image space as in previous approaches, enabling the encoded features of unpaired low-light and normal-light images to be decomposed into content-rich reflectance maps and content-free illumination maps. Subsequently, the reflectance map of the low-light image and the illumination map of the normal-light image are taken as input to the diffusion model for unsupervised restoration with the guidance of the low-light feature, where a self-constrained consistency loss is further proposed to eliminate the interference of normal-light content on the restored results to improve overall visual quality. Extensive experiments on publicly available real-world benchmarks show that the proposed LightenDiffusion outperforms state-of-the-art unsupervised competitors and is comparable to supervised methods while being more generalizable to various scenes. Our code is available at https://github.com/JianghaiSCU/LightenDiffusion.

In human learning, it is common to use multiple sources of information jointly. However, most existing feature learning approaches learn from only a single task. In this paper, we propose a novel multi-task deep network to learn generalizable high-level visual representations. Since multi-task learning requires annotations for multiple properties of the same training instance, we look to synthetic images to train our network. To overcome the domain difference between real and synthetic data, we employ an unsupervised feature space domain adaptation method based on adversarial learning. Given an input synthetic RGB image, our network simultaneously predicts its surface normal, depth, and instance contour, while also minimizing the feature space domain differences between real and synthetic data. Through extensive experiments, we demonstrate that our network learns more transferable representations compared to single-task baselines. Our learned representation produces state-of-the-art transfer learning results on PASCAL VOC 2007 classification and 2012 detection.

Surface normal estimation serves as a cornerstone for a spectrum of computer vision applications. While numerous efforts have been devoted to static image scenarios, ensuring temporal coherence in video-based normal estimation remains a formidable challenge. Instead of merely augmenting existing methods with temporal components, we present NormalCrafter to leverage the inherent temporal priors of video diffusion models. To secure high-fidelity normal estimation across sequences, we propose Semantic Feature Regularization (SFR), which aligns diffusion features with semantic cues, encouraging the model to concentrate on the intrinsic semantics of the scene. Moreover, we introduce a two-stage training protocol that leverages both latent and pixel space learning to preserve spatial accuracy while maintaining long temporal context. Extensive evaluations demonstrate the efficacy of our method, showcasing a superior performance in generating temporally consistent normal sequences with intricate details from diverse videos.

In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an n-sample in a space M can be considered as an element of the quotient space of M^n modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces. We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. These results are non-trivial even when M is Euclidean. We show that the infinite sample space exists in a Gromov-Hausdorff type sense and coincides with the Wasserstein space of probability distributions on M. We exhibit Fr\'echet means and k-means as metric projections onto 1-skeleta or k-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.

Given the exponential growth of the volume of the ball w.r.t. its radius, the hyperbolic space is capable of embedding trees with arbitrarily small distortion and hence has received wide attention for representing hierarchical datasets. However, this exponential growth property comes at a price of numerical instability such that training hyperbolic learning models will sometimes lead to catastrophic NaN problems, encountering unrepresentable values in floating point arithmetic. In this work, we carefully analyze the limitation of two popular models for the hyperbolic space, namely, the Poincar\'e ball and the Lorentz model. We first show that, under the 64 bit arithmetic system, the Poincar\'e ball has a relatively larger capacity than the Lorentz model for correctly representing points. Then, we theoretically validate the superiority of the Lorentz model over the Poincar\'e ball from the perspective of optimization. Given the numerical limitations of both models, we identify one Euclidean parametrization of the hyperbolic space which can alleviate these limitations. We further extend this Euclidean parametrization to hyperbolic hyperplanes and exhibits its ability in improving the performance of hyperbolic SVM.

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset, regardless of whether they belong to known or unknown classes. In GCD, the common practice typically involves applying a spherical projection operator at the end of the self-supervised pretrained backbone, operating within Euclidean or spherical space. However, both of these spaces have been shown to be suboptimal for encoding samples that possesses hierarchical structures. In contrast, hyperbolic space exhibits exponential volume growth relative to radius, making it inherently strong at capturing the hierarchical structure of samples from both seen and unseen categories. Therefore, we propose to tackle the category discovery challenge in the hyperbolic space. We introduce HypCD, a simple Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery. HypCD first transforms the Euclidean embedding space of the backbone network into hyperbolic space, facilitating subsequent representation and classification learning by considering both hyperbolic distance and the angle between samples. This approach is particularly helpful for knowledge transfer from known to unknown categories in GCD. We thoroughly evaluate HypCD on public GCD benchmarks, by applying it to various baseline and state-of-the-art methods, consistently achieving significant improvements.

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fr\'echet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some scenarios where stronger results are needed in order to establish an asymptotic normal approximation uniformly over a family of probability measures. In this note we collect some results in this direction. We restrict ourselves to weak convergence in mathbb R^d with continuous limit measures.

Recent text-to-3D methods employing diffusion models have made significant advancements in 3D human generation. However, these approaches face challenges due to the limitations of the text-to-image diffusion model, which lacks an understanding of 3D structures. Consequently, these methods struggle to achieve high-quality human generation, resulting in smooth geometry and cartoon-like appearances. In this paper, we observed that fine-tuning text-to-image diffusion models with normal maps enables their adaptation into text-to-normal diffusion models, which enhances the 2D perception of 3D geometry while preserving the priors learned from large-scale datasets. Therefore, we propose HumanNorm, a novel approach for high-quality and realistic 3D human generation by learning the normal diffusion model including a normal-adapted diffusion model and a normal-aligned diffusion model. The normal-adapted diffusion model can generate high-fidelity normal maps corresponding to prompts with view-dependent text. The normal-aligned diffusion model learns to generate color images aligned with the normal maps, thereby transforming physical geometry details into realistic appearance. Leveraging the proposed normal diffusion model, we devise a progressive geometry generation strategy and coarse-to-fine texture generation strategy to enhance the efficiency and robustness of 3D human generation. Comprehensive experiments substantiate our method's ability to generate 3D humans with intricate geometry and realistic appearances, significantly outperforming existing text-to-3D methods in both geometry and texture quality. The project page of HumanNorm is https://humannorm.github.io/.

Recovering a 3D surface from its surface normal map, a problem known as normal integration, is a key component for photometric shape reconstruction techniques such as shape-from-shading and photometric stereo. The vast majority of existing approaches for normal integration handle only implicitly the presence of depth discontinuities and are limited to orthographic or ideal pinhole cameras. In this paper, we propose a novel formulation that allows modeling discontinuities explicitly and handling generic central cameras. Our key idea is based on a local planarity assumption, that we model through constraints between surface normals and ray directions. Compared to existing methods, our approach more accurately approximates the relation between depth and surface normals, achieves state-of-the-art results on the standard normal integration benchmark, and is the first to directly handle generic central camera models.

As its width tends to infinity, a deep neural network's behavior under gradient descent can become simplified and predictable (e.g. given by the Neural Tangent Kernel (NTK)), if it is parametrized appropriately (e.g. the NTK parametrization). However, we show that the standard and NTK parametrizations of a neural network do not admit infinite-width limits that can learn features, which is crucial for pretraining and transfer learning such as with BERT. We propose simple modifications to the standard parametrization to allow for feature learning in the limit. Using the *Tensor Programs* technique, we derive explicit formulas for such limits. On Word2Vec and few-shot learning on Omniglot via MAML, two canonical tasks that rely crucially on feature learning, we compute these limits exactly. We find that they outperform both NTK baselines and finite-width networks, with the latter approaching the infinite-width feature learning performance as width increases. More generally, we classify a natural space of neural network parametrizations that generalizes standard, NTK, and Mean Field parametrizations. We show 1) any parametrization in this space either admits feature learning or has an infinite-width training dynamics given by kernel gradient descent, but not both; 2) any such infinite-width limit can be computed using the Tensor Programs technique. Code for our experiments can be found at github.com/edwardjhu/TP4.

We introduce a new functional space U designed to contain all classical arithmetic functions (Mobius, von Mangoldt, Euler phi, divisor functions, Dirichlet characters, etc.). The norm of U combines a Hilbert-type component, based on square summability of Dirichlet coefficients for every s > 1, with a Banach component controlling logarithmic averages of partial sums. We prove that U is a complete Banach space which embeds continuously all standard Hilbert spaces of Dirichlet series and allows natural actions of Dirichlet convolution and shift operators. This framework provides a unified analytic setting for classical and modern problems in multiplicative number theory.

We propose a novel neural network architecture, the normalized Transformer (nGPT) with representation learning on the hypersphere. In nGPT, all vectors forming the embeddings, MLP, attention matrices and hidden states are unit norm normalized. The input stream of tokens travels on the surface of a hypersphere, with each layer contributing a displacement towards the target output predictions. These displacements are defined by the MLP and attention blocks, whose vector components also reside on the same hypersphere. Experiments show that nGPT learns much faster, reducing the number of training steps required to achieve the same accuracy by a factor of 4 to 20, depending on the sequence length.

Surface normal integration is a fundamental problem in computer vision, dealing with the objective of reconstructing a surface from its corresponding normal map. Existing approaches require an iterative global optimization to jointly estimate the depth of each pixel, which scales poorly to larger normal maps. In this paper, we address this problem by recasting normal integration as the estimation of relative scales of continuous components. By constraining pixels belonging to the same component to jointly vary their scale, we drastically reduce the number of optimization variables. Our framework includes a heuristic to accurately estimate continuous components from the start, a strategy to rebalance optimization terms, and a technique to iteratively merge components to further reduce the size of the problem. Our method achieves state-of-the-art results on the standard normal integration benchmark in as little as a few seconds and achieves one-order-of-magnitude speedup over pixel-level approaches on large-resolution normal maps.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

We consider fermions in a zero-temperature superconducting anti-de Sitter domain wall solution and find continuous bands of normal modes. These bands can be either partially filled or totally empty and gapped. We present a semi-classical argument which approximately captures the main features of the normal mode spectrum.

Existing works have extensively studied adversarial examples, which are minimal perturbations that can mislead the output of deep neural networks (DNNs) while remaining imperceptible to humans. However, in this work, we reveal the existence of a harmless perturbation space, in which perturbations drawn from this space, regardless of their magnitudes, leave the network output unchanged when applied to inputs. Essentially, the harmless perturbation space emerges from the usage of non-injective functions (linear or non-linear layers) within DNNs, enabling multiple distinct inputs to be mapped to the same output. For linear layers with input dimensions exceeding output dimensions, any linear combination of the orthogonal bases of the nullspace of the parameter consistently yields no change in their output. For non-linear layers, the harmless perturbation space may expand, depending on the properties of the layers and input samples. Inspired by this property of DNNs, we solve for a family of general perturbation spaces that are redundant for the DNN's decision, and can be used to hide sensitive data and serve as a means of model identification. Our work highlights the distinctive robustness of DNNs (i.e., consistency under large magnitude perturbations) in contrast to adversarial examples (vulnerability for small imperceptible noises).

Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep generative models. A key issue with these models is their tendency to output samples outside of the support of the target distribution when learning disconnected distributions. We investigate the relationship between the performance of these models and the geometry of their latent space. Building on recent developments in geometric measure theory, we prove a sufficient condition for optimality in the case where the dimension of the latent space is larger than the number of modes. Through experiments on GANs, we demonstrate the validity of our theoretical results and gain new insights into the latent space geometry of these models. Additionally, we propose a truncation method that enforces a simplicial cluster structure in the latent space and improves the performance of GANs.

Magnitude of a finite metric space and the related notion of magnitude functions on metric spaces is an active area of research in algebraic topology. Magnitude originally arose in the context of biology, where it represents the number of effective species in an environment; when applied to a one-parameter family of metric spaces tX with scale parameter t, the magnitude captures much of the underlying geometry of the space. Prior work has mostly focussed on properties of magnitude in a global sense; in this paper we restrict the sets to finite subsets of Euclidean space and investigate its individual components. We give an explicit formula for the corrected inclusion-exclusion principle, and define a quantity associated with each point, called the moment which gives an intrinsic ordering to the points. We exploit this in order to form an algorithm which approximates the convex hull.

In deep learning, performance is strongly affected by the choice of architecture and hyperparameters. While there has been extensive work on automatic hyperparameter optimization for simple spaces, complex spaces such as the space of deep architectures remain largely unexplored. As a result, the choice of architecture is done manually by the human expert through a slow trial and error process guided mainly by intuition. In this paper we describe a framework for automatically designing and training deep models. We propose an extensible and modular language that allows the human expert to compactly represent complex search spaces over architectures and their hyperparameters. The resulting search spaces are tree-structured and therefore easy to traverse. Models can be automatically compiled to computational graphs once values for all hyperparameters have been chosen. We can leverage the structure of the search space to introduce different model search algorithms, such as random search, Monte Carlo tree search (MCTS), and sequential model-based optimization (SMBO). We present experiments comparing the different algorithms on CIFAR-10 and show that MCTS and SMBO outperform random search. In addition, these experiments show that our framework can be used effectively for model discovery, as it is possible to describe expressive search spaces and discover competitive models without much effort from the human expert. Code for our framework and experiments has been made publicly available.

Let E be the HNN-extension of a group B with subgroups H and K associated according to an isomorphism varphicolon H to K. Suppose that H and K are normal in B and (H cap K)varphi = H cap K. Under these assumptions, we prove necessary and sufficient conditions for E to be residually a C-group, where C is a class of groups closed under taking subgroups, quotient groups, and unrestricted wreath products. Among other things, these conditions give new facts on the residual finiteness and the residual p-finiteness of the group E.

Anomalies are rare and anomaly detection is often therefore framed as One-Class Classification (OCC), i.e. trained solely on normalcy. Leading OCC techniques constrain the latent representations of normal motions to limited volumes and detect as abnormal anything outside, which accounts satisfactorily for the openset'ness of anomalies. But normalcy shares the same openset'ness property since humans can perform the same action in several ways, which the leading techniques neglect. We propose a novel generative model for video anomaly detection (VAD), which assumes that both normality and abnormality are multimodal. We consider skeletal representations and leverage state-of-the-art diffusion probabilistic models to generate multimodal future human poses. We contribute a novel conditioning on the past motion of people and exploit the improved mode coverage capabilities of diffusion processes to generate different-but-plausible future motions. Upon the statistical aggregation of future modes, an anomaly is detected when the generated set of motions is not pertinent to the actual future. We validate our model on 4 established benchmarks: UBnormal, HR-UBnormal, HR-STC, and HR-Avenue, with extensive experiments surpassing state-of-the-art results.

Deep learning optimizers are often motivated through a mix of convex and approximate second-order theory. We select three such methods -- Adam, Shampoo and Prodigy -- and argue that each method can instead be understood as a squarely first-order method without convexity assumptions. In fact, after switching off exponential moving averages, each method is equivalent to steepest descent under a particular norm. By generalizing this observation, we chart a new design space for training algorithms. Different operator norms should be assigned to different tensors based on the role that the tensor plays within the network. For example, while linear and embedding layers may have the same weight space of R^{mtimes n}, these layers play different roles and should be assigned different norms. We hope that this idea of carefully metrizing the neural architecture might lead to more stable, scalable and indeed faster training.

Laboratory test results are an important and generally high dimensional component of a patient's Electronic Health Record (EHR). We train embedding representations (via Word2Vec and GloVe) for LOINC codes of laboratory tests from the EHRs of about 80,000 patients at a cancer center. To include information about lab test outcomes, we also train embeddings on the concatenation of a LOINC code with a symbol indicating normality or abnormality of the result. We observe several clinically meaningful similarities among LOINC embeddings trained over our data. For the embeddings of the concatenation of LOINCs with abnormality codes, we evaluate the performance for mortality prediction tasks and the ability to preserve ordinality properties: i.e. a lab test with normal outcome should be more similar to an abnormal one than to the a very abnormal one.

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a compositional model of meaning for distributional semantics, in which each word in a sentence has a meaning vector and the distributional meaning of the sentence is a function of the tensor products of the word vectors. Abstractly speaking, this function is the morphism corresponding to the grammatical structure of the sentence in the category of finite dimensional vector spaces. In this paper, we provide a concrete method for implementing this linear meaning map, by constructing a corpus-based vector space for the type of sentence. Our construction method is based on structured vector spaces whereby meaning vectors of all sentences, regardless of their grammatical structure, live in the same vector space. Our proposed sentence space is the tensor product of two noun spaces, in which the basis vectors are pairs of words each augmented with a grammatical role. This enables us to compare meanings of sentences by simply taking the inner product of their vectors.

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

Anomaly Detection (AD) in images is a fundamental computer vision problem and refers to identifying images and image substructures that deviate significantly from the norm. Popular AD algorithms commonly try to learn a model of normality from scratch using task specific datasets, but are limited to semi-supervised approaches employing mostly normal data due to the inaccessibility of anomalies on a large scale combined with the ambiguous nature of anomaly appearance. We follow an alternative approach and demonstrate that deep feature representations learned by discriminative models on large natural image datasets are well suited to describe normality and detect even subtle anomalies in a transfer learning setting. Our model of normality is established by fitting a multivariate Gaussian (MVG) to deep feature representations of classification networks trained on ImageNet using normal data only. By subsequently applying the Mahalanobis distance as the anomaly score we outperform the current state of the art on the public MVTec AD dataset, achieving an AUROC value of 95.8 pm 1.2 (mean pm SEM) over all 15 classes. We further investigate why the learned representations are discriminative to the AD task using Principal Component Analysis. We find that the principal components containing little variance in normal data are the ones crucial for discriminating between normal and anomalous instances. This gives a possible explanation to the often sub-par performance of AD approaches trained from scratch using normal data only. By selectively fitting a MVG to these most relevant components only, we are able to further reduce model complexity while retaining AD performance. We also investigate setting the working point by selecting acceptable False Positive Rate thresholds based on the MVG assumption. Code available at https://github.com/ORippler/gaussian-ad-mvtec