Daily Papers

Most 3D generation research focuses on up-projecting 2D foundation models into the 3D space, either by minimizing 2D Score Distillation Sampling (SDS) loss or fine-tuning on multi-view datasets. Without explicit 3D priors, these methods often lead to geometric anomalies and multi-view inconsistency. Recently, researchers have attempted to improve the genuineness of 3D objects by directly training on 3D datasets, albeit at the cost of low-quality texture generation due to the limited texture diversity in 3D datasets. To harness the advantages of both approaches, we propose Bidirectional Diffusion(BiDiff), a unified framework that incorporates both a 3D and a 2D diffusion process, to preserve both 3D fidelity and 2D texture richness, respectively. Moreover, as a simple combination may yield inconsistent generation results, we further bridge them with novel bidirectional guidance. In addition, our method can be used as an initialization of optimization-based models to further improve the quality of 3D model and efficiency of optimization, reducing the generation process from 3.4 hours to 20 minutes. Experimental results have shown that our model achieves high-quality, diverse, and scalable 3D generation. Project website: https://bidiff.github.io/.

Despite significant advances in image anomaly detection and segmentation, few methods use 3D information. We utilize a recently introduced 3D anomaly detection dataset to evaluate whether or not using 3D information is a lost opportunity. First, we present a surprising finding: standard color-only methods outperform all current methods that are explicitly designed to exploit 3D information. This is counter-intuitive as even a simple inspection of the dataset shows that color-only methods are insufficient for images containing geometric anomalies. This motivates the question: how can anomaly detection methods effectively use 3D information? We investigate a range of shape representations including hand-crafted and deep-learning-based; we demonstrate that rotation invariance plays the leading role in the performance. We uncover a simple 3D-only method that beats all recent approaches while not using deep learning, external pre-training datasets, or color information. As the 3D-only method cannot detect color and texture anomalies, we combine it with color-based features, significantly outperforming previous state-of-the-art. Our method, dubbed BTF (Back to the Feature) achieves pixel-wise ROCAUC: 99.3% and PRO: 96.4% on MVTec 3D-AD.

Industrial anomaly detection is generally addressed as an unsupervised task that aims at locating defects with only normal training samples. Recently, numerous 2D anomaly detection methods have been proposed and have achieved promising results, however, using only the 2D RGB data as input is not sufficient to identify imperceptible geometric surface anomalies. Hence, in this work, we focus on multi-modal anomaly detection. Specifically, we investigate early multi-modal approaches that attempted to utilize models pre-trained on large-scale visual datasets, i.e., ImageNet, to construct feature databases. And we empirically find that directly using these pre-trained models is not optimal, it can either fail to detect subtle defects or mistake abnormal features as normal ones. This may be attributed to the domain gap between target industrial data and source data.Towards this problem, we propose a Local-to-global Self-supervised Feature Adaptation (LSFA) method to finetune the adaptors and learn task-oriented representation toward anomaly detection.Both intra-modal adaptation and cross-modal alignment are optimized from a local-to-global perspective in LSFA to ensure the representation quality and consistency in the inference stage.Extensive experiments demonstrate that our method not only brings a significant performance boost to feature embedding based approaches, but also outperforms previous State-of-The-Art (SoTA) methods prominently on both MVTec-3D AD and Eyecandies datasets, e.g., LSFA achieves 97.1% I-AUROC on MVTec-3D, surpass previous SoTA by +3.4%.

Anomalies in transverse Ward--Takahashi identities are studied, allowing discussion of the feasibility of anomalies arising in general non-symmetry Ward--Takahashi identities. We adopt the popular Fujikawa's method and rigorous dimensional renormalization to verify the existence of transverse anomalies to one-loop order and any loop order, respectively. The arbitrariness of coefficients of transverse anomalies is revealed, and a way out is also proposed after relating transverse anomalies to Schwinger terms and comparing symmetry and non-symmetry anomalies. Papers that claim the non-existence of transverse anomalies are reviewed to find anomalies hidden in their approaches. The role played by transverse anomalies is discussed.

Autoencoders have been proposed as a powerful tool for model-independent anomaly detection in high-energy physics. The operating principle is that events which do not belong to the space of training data will be reconstructed poorly, thus flagging them as anomalies. We point out that in a variety of examples of interest, the connection between large reconstruction error and anomalies is not so clear. In particular, for data sets with nontrivial topology, there will always be points that erroneously seem anomalous due to global issues. Conversely, neural networks typically have an inductive bias or prior to locally interpolate such that undersampled or rare events may be reconstructed with small error, despite actually being the desired anomalies. Taken together, these facts are in tension with the simple picture of the autoencoder as an anomaly detector. Using a series of illustrative low-dimensional examples, we show explicitly how the intrinsic and extrinsic topology of the dataset affects the behavior of an autoencoder and how this topology is manifested in the latent space representation during training. We ground this analysis in the discussion of a mock "bump hunt" in which the autoencoder fails to identify an anomalous "signal" for reasons tied to the intrinsic topology of n-particle phase space.

3D anomaly detection plays a crucial role in monitoring parts for localized inherent defects in precision manufacturing. Embedding-based and reconstruction-based approaches are among the most popular and successful methods. However, there are two major challenges to the practical application of the current approaches: 1) the embedded models suffer the prohibitive computational and storage due to the memory bank structure; 2) the reconstructive models based on the MAE mechanism fail to detect anomalies in the unmasked regions. In this paper, we propose R3D-AD, reconstructing anomalous point clouds by diffusion model for precise 3D anomaly detection. Our approach capitalizes on the data distribution conversion of the diffusion process to entirely obscure the input's anomalous geometry. It step-wisely learns a strict point-level displacement behavior, which methodically corrects the aberrant points. To increase the generalization of the model, we further present a novel 3D anomaly simulation strategy named Patch-Gen to generate realistic and diverse defect shapes, which narrows the domain gap between training and testing. Our R3D-AD ensures a uniform spatial transformation, which allows straightforwardly generating anomaly results by distance comparison. Extensive experiments show that our R3D-AD outperforms previous state-of-the-art methods, achieving 73.4% Image-level AUROC on the Real3D-AD dataset and 74.9% Image-level AUROC on the Anomaly-ShapeNet dataset with an exceptional efficiency.

Problems involving geometric data arise in a variety of fields, including computer vision, robotics, chemistry, and physics. Such data can take numerous forms, such as points, direction vectors, planes, or transformations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric algebra, which offers an efficient 16-dimensional vector space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a transformer, GATr is scalable, expressive, and versatile. In experiments with n-body modeling and robotic planning, GATr shows strong improvements over non-geometric baselines.

Anomaly detection is the task of identifying examples that do not behave as expected. Because anomalies are rare and unexpected events, collecting real anomalous examples is often challenging in several applications. In addition, learning an anomaly detector with limited (or no) anomalies often yields poor prediction performance. One option is to employ auxiliary synthetic anomalies to improve the model training. However, synthetic anomalies may be of poor quality: anomalies that are unrealistic or indistinguishable from normal samples may deteriorate the detector's performance. Unfortunately, no existing methods quantify the quality of auxiliary anomalies. We fill in this gap and propose the expected anomaly posterior (EAP), an uncertainty-based score function that measures the quality of auxiliary anomalies by quantifying the total uncertainty of an anomaly detector. Experimentally on 40 benchmark datasets of images and tabular data, we show that EAP outperforms 12 adapted data quality estimators in the majority of cases.

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects--the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra--which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. In this paper we initiate an exploration of "positive geometries" and "canonical forms" as objects of study in their own right in a more general mathematical setting. We give a precise definition of positive geometries and canonical forms, introduce general methods for finding forms for more complicated positive geometries from simpler ones, and present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties. We also illustrate a number of strategies for computing canonical forms which yield interesting representations for the forms associated with wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex polytopes.

State-of-the-art space science missions increasingly rely on automation due to spacecraft complexity and the costs of human oversight. The high volume of data, including scientific and telemetry data, makes manual inspection challenging. Machine learning offers significant potential to meet these demands. The Euclid space telescope, in its survey phase since February 2024, exemplifies this shift. Euclid's success depends on accurate monitoring and interpretation of housekeeping telemetry and science-derived data. Thousands of telemetry parameters, monitored as time series, may or may not impact the quality of scientific data. These parameters have complex interdependencies, often due to physical relationships (e.g., proximity of temperature sensors). Optimising science operations requires careful anomaly detection and identification of hidden parameter states. Moreover, understanding the interactions between known anomalies and physical quantities is crucial yet complex, as related parameters may display anomalies with varied timing and intensity. We address these challenges by analysing temperature anomalies in Euclid's telemetry from February to August 2024, focusing on eleven temperature parameters and 35 covariates. We use a predictive XGBoost model to forecast temperatures based on historical values, detecting anomalies as deviations from predictions. A second XGBoost model predicts anomalies from covariates, capturing their relationships to temperature anomalies. We identify the top three anomalies per parameter and analyse their interactions with covariates using SHAP (Shapley Additive Explanations), enabling rapid, automated analysis of complex parameter relationships. Our method demonstrates how machine learning can enhance telemetry monitoring, offering scalable solutions for other missions with similar data challenges.

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the 'manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.

Industrial anomaly detection achieves progress thanks to datasets such as MVTec-AD and VisA. However, they suf- fer from limitations in terms of the number of defect sam- ples, types of defects, and availability of real-world scenes. These constraints inhibit researchers from further exploring the performance of industrial detection with higher accuracy. To this end, we propose a new large-scale anomaly detection dataset called 3CAD, which is derived from real 3C produc- tion lines. Specifically, the proposed 3CAD includes eight different types of manufactured parts, totaling 27,039 high- resolution images labeled with pixel-level anomalies. The key features of 3CAD are that it covers anomalous regions of different sizes, multiple anomaly types, and the possibility of multiple anomalous regions and multiple anomaly types per anomaly image. This is the largest and first anomaly de- tection dataset dedicated to 3C product quality control for community exploration and development. Meanwhile, we in- troduce a simple yet effective framework for unsupervised anomaly detection: a Coarse-to-Fine detection paradigm with Recovery Guidance (CFRG). To detect small defect anoma- lies, the proposed CFRG utilizes a coarse-to-fine detection paradigm. Specifically, we utilize a heterogeneous distilla- tion model for coarse localization and then fine localiza- tion through a segmentation model. In addition, to better capture normal patterns, we introduce recovery features as guidance. Finally, we report the results of our CFRG frame- work and popular anomaly detection methods on the 3CAD dataset, demonstrating strong competitiveness and providing a highly challenging benchmark to promote the development of the anomaly detection field. Data and code are available: https://github.com/EnquanYang2022/3CAD.

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the Pin(p,q,r) group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable geometric templates that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.

We introduce a classification conjecture for kappa-solutions in 4d Ricci flow. Our conjectured list includes known examples from the literature, but also a new 1-parameter family of Z_2^2times O_3-symmetric bubble-sheet ovals that we construct. We observe that some special cases of the conjecture follow from recent results in the literature. We also introduce a stronger variant of the classification conjecture for ancient asymptotically cylindrical 4d Ricci flows, which does not assume smoothness and nonnegative curvature operator a priori. Assuming this stronger variant holds true, we establish a canonical neighborhood theorem for 4d Ricci flow through cylindrical singularities, which shares some elements in common with Perelman's canonical neighborhood theorem for 3d Ricci flow as well as the mean-convex neighborhood theorem for mean curvature flow through neck-singularities. Finally, we argue that quotient-necks lead to new phenomena, and sketch an example of non-uniqueness for 4d Ricci flow through singularities.

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of geometric deep learning. Often problems in the physical sciences deal with relatively small sets of points in two- or three-dimensional space wherein translation, rotation, and permutation equivariance are important or even vital for models to be useful in practice. In this work, we present rotation- and permutation-equivariant architectures for deep learning on these small point clouds, composed of a set of products of terms from the geometric algebra and reductions over those products using an attention mechanism. The geometric algebra provides valuable mathematical structure by which to combine vector, scalar, and other types of geometric inputs in a systematic way to account for rotation invariance or covariance, while attention yields a powerful way to impose permutation equivariance. We demonstrate the usefulness of these architectures by training models to solve sample problems relevant to physics, chemistry, and biology.

Type IIB supergravity enjoys a discrete non-Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F-theory. Remarkably, a subtle modification of the standard 10d Chern-Simons term cancels these anomalies, a fact which relies on the ***specific*** field content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green-Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls.

We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance varepsilon, using tools from variational analysis. In particular, we describe necessary conditions associated with the optimal classifier subject to such an adversary. Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as varepsilon varies. This evolution equation may be described as an uncoupled system of differential equations in one dimension, or as a mean curvature type equation in higher dimension. In one dimension, and under mild assumptions on the data distribution, we rigorously prove that one can use the initial value problem starting from varepsilon=0, which is simply the Bayes classifier, in order to solve for the global minimizer of the adversarial problem for small values of varepsilon. In higher dimensions we provide a similar result, albeit conditional to the existence of regular solutions of the initial value problem. In the process of proving our main results we obtain a result of independent interest connecting the original adversarial problem with an optimal transport problem under no assumptions on whether classes are balanced or not. Numerical examples illustrating these ideas are also presented.

Modifying the fundamental commutation relation of quantum mechanics to reflect the influence of gravity is an important approach to reconcile the contradiction between quantum field theory and general relativity. In the past two decades, researchers have conducted extensive research on geometric phase problems in non-commutative spaces, but few have mentioned the correction of geometric phase problems using the Generalized Uncertainty Principle (GUP). This paper is the first to study the phase correction of Aharonov-Bohm (AB) effect by GUP.

Detecting the anomaly of human behavior is paramount to timely recognizing endangering situations, such as street fights or elderly falls. However, anomaly detection is complex since anomalous events are rare and because it is an open set recognition task, i.e., what is anomalous at inference has not been observed at training. We propose COSKAD, a novel model that encodes skeletal human motion by a graph convolutional network and learns to COntract SKeletal kinematic embeddings onto a latent hypersphere of minimum volume for Video Anomaly Detection. We propose three latent spaces: the commonly-adopted Euclidean and the novel spherical and hyperbolic. All variants outperform the state-of-the-art on the most recent UBnormal dataset, for which we contribute a human-related version with annotated skeletons. COSKAD sets a new state-of-the-art on the human-related versions of ShanghaiTech Campus and CUHK Avenue, with performance comparable to video-based methods. Source code and dataset will be released upon acceptance.

Graph-level anomaly detection aims to identify anomalous graphs from a collection of graphs in an unsupervised manner. A common assumption of anomaly detection is that a reasonable decision boundary has a hypersphere shape, but may appear some non-conforming phenomena in high dimensions. Towards this end, we firstly propose a novel deep graph-level anomaly detection model, which learns the graph representation with maximum mutual information between substructure and global structure features while exploring a hypersphere anomaly decision boundary. The idea is to ensure the training data distribution consistent with the decision hypersphere via an orthogonal projection layer. Moreover, we further perform the bi-hypersphere compression to emphasize the discrimination of anomalous graphs from normal graphs. Note that our method is not confined to graph data and is applicable to anomaly detection of other data such as images. The numerical and visualization results on benchmark datasets demonstrate the effectiveness and superiority of our methods in comparison to many baselines and state-of-the-arts.

Visual surface anomaly detection aims to detect local image regions that significantly deviate from normal appearance. Recent surface anomaly detection methods rely on generative models to accurately reconstruct the normal areas and to fail on anomalies. These methods are trained only on anomaly-free images, and often require hand-crafted post-processing steps to localize the anomalies, which prohibits optimizing the feature extraction for maximal detection capability. In addition to reconstructive approach, we cast surface anomaly detection primarily as a discriminative problem and propose a discriminatively trained reconstruction anomaly embedding model (DRAEM). The proposed method learns a joint representation of an anomalous image and its anomaly-free reconstruction, while simultaneously learning a decision boundary between normal and anomalous examples. The method enables direct anomaly localization without the need for additional complicated post-processing of the network output and can be trained using simple and general anomaly simulations. On the challenging MVTec anomaly detection dataset, DRAEM outperforms the current state-of-the-art unsupervised methods by a large margin and even delivers detection performance close to the fully-supervised methods on the widely used DAGM surface-defect detection dataset, while substantially outperforming them in localization accuracy.

We introduce a simple and intuitive self-supervision task, Natural Synthetic Anomalies (NSA), for training an end-to-end model for anomaly detection and localization using only normal training data. NSA integrates Poisson image editing to seamlessly blend scaled patches of various sizes from separate images. This creates a wide range of synthetic anomalies which are more similar to natural sub-image irregularities than previous data-augmentation strategies for self-supervised anomaly detection. We evaluate the proposed method using natural and medical images. Our experiments with the MVTec AD dataset show that a model trained to localize NSA anomalies generalizes well to detecting real-world a priori unknown types of manufacturing defects. Our method achieves an overall detection AUROC of 97.2 outperforming all previous methods that learn without the use of additional datasets. Code available at https://github.com/hmsch/natural-synthetic-anomalies.

For several classes of BPS vacua, we find a procedure to modify the PDEs that imply preserved supersymmetry and the equations of motion so that they still imply the latter but not the former. In each case we trace back this supersymmetry-breaking deformation to a distinct modification of the pure spinor equations that provide a geometrical interpretation of supersymmetry. We give some concrete examples: first we generalize the Imamura class of Mink6 solutions by removing a symmetry requirement, and then derive some local and global solutions both before and after breaking supersymmetry.

Detecting anomalies in images is an important task, especially in real-time computer vision applications. In this work, we focus on computational efficiency and propose a lightweight feature extractor that processes an image in less than a millisecond on a modern GPU. We then use a student-teacher approach to detect anomalous features. We train a student network to predict the extracted features of normal, i.e., anomaly-free training images. The detection of anomalies at test time is enabled by the student failing to predict their features. We propose a training loss that hinders the student from imitating the teacher feature extractor beyond the normal images. It allows us to drastically reduce the computational cost of the student-teacher model, while improving the detection of anomalous features. We furthermore address the detection of challenging logical anomalies that involve invalid combinations of normal local features, for example, a wrong ordering of objects. We detect these anomalies by efficiently incorporating an autoencoder that analyzes images globally. We evaluate our method, called EfficientAD, on 32 datasets from three industrial anomaly detection dataset collections. EfficientAD sets new standards for both the detection and the localization of anomalies. At a latency of two milliseconds and a throughput of six hundred images per second, it enables a fast handling of anomalies. Together with its low error rate, this makes it an economical solution for real-world applications and a fruitful basis for future research.

Anomaly detection is critical in surveillance systems and patrol robots by identifying anomalous regions in images for early warning. Depending on whether reference data are utilized, anomaly detection can be categorized into anomaly detection with reference and anomaly detection without reference. Currently, anomaly detection without reference, which is closely related to out-of-distribution (OoD) object detection, struggles with learning anomalous patterns due to the difficulty of collecting sufficiently large and diverse anomaly datasets with the inherent rarity and novelty of anomalies. Alternatively, anomaly detection with reference employs the scheme of change detection to identify anomalies by comparing semantic changes between a reference image and a query one. However, there are very few ADr works due to the scarcity of public datasets in this domain. In this paper, we aim to address this gap by introducing the UMAD Benchmark Dataset. To our best knowledge, this is the first benchmark dataset designed specifically for anomaly detection with reference in robotic patrolling scenarios, e.g., where an autonomous robot is employed to detect anomalous objects by comparing a reference and a query video sequences. The reference sequences can be taken by the robot along a specified route when there are no anomalous objects in the scene. The query sequences are captured online by the robot when it is patrolling in the same scene following the same route. Our benchmark dataset is elaborated such that each query image can find a corresponding reference based on accurate robot localization along the same route in the prebuilt 3D map, with which the reference and query images can be geometrically aligned using adaptive warping. Besides the proposed benchmark dataset, we evaluate the baseline models of ADr on this dataset.

Deep neural networks are prone to adversarial examples that maliciously alter the network's outcome. Due to the increasing popularity of 3D sensors in safety-critical systems and the vast deployment of deep learning models for 3D point sets, there is a growing interest in adversarial attacks and defenses for such models. So far, the research has focused on the semantic level, namely, deep point cloud classifiers. However, point clouds are also widely used in a geometric-related form that includes encoding and reconstructing the geometry. In this work, we are the first to consider the problem of adversarial examples at a geometric level. In this setting, the question is how to craft a small change to a clean source point cloud that leads, after passing through an autoencoder model, to the reconstruction of a different target shape. Our attack is in sharp contrast to existing semantic attacks on 3D point clouds. While such works aim to modify the predicted label by a classifier, we alter the entire reconstructed geometry. Additionally, we demonstrate the robustness of our attack in the case of defense, where we show that remnant characteristics of the target shape are still present at the output after applying the defense to the adversarial input. Our code is publicly available at https://github.com/itailang/geometric_adv.

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.

A single unexpected object on the road can cause an accident or may lead to injuries. To prevent this, we need a reliable mechanism for finding anomalous objects on the road. This task, called anomaly segmentation, can be a stepping stone to safe and reliable autonomous driving. Current approaches tackle anomaly segmentation by assigning an anomaly score to each pixel and by grouping anomalous regions using simple heuristics. However, pixel grouping is a limiting factor when it comes to evaluating the segmentation performance of individual anomalous objects. To address the issue of grouping multiple anomaly instances into one, we propose an approach that produces accurate anomaly instance masks. Our approach centers on an out-of-distribution segmentation model for identifying uncertain regions and a strong generalist segmentation model for anomaly instances segmentation. We investigate ways to use uncertain regions to guide such a segmentation model to perform segmentation of anomalous instances. By incorporating strong object priors from a generalist model we additionally improve the per-pixel anomaly segmentation performance. Our approach outperforms current pixel-level anomaly segmentation methods, achieving an AP of 80.08% and 88.98% on the Fishyscapes Lost and Found and the RoadAnomaly validation sets respectively. Project page: https://vision.rwth-aachen.de/ugains

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

We discuss relevant scalar deformations of a holographic theory with a compact boundary. An example of such a theory would be the global AdS_4 with its spatially compact boundary S^2. To introduce a relevant deformation, we choose to turn on a time-independent and spatially homogeneous non-normalizable scalar operator with m^2 = -2. The finite size of a compact boundary cuts down the RG flow at a finite length scale leading to an incomplete RG flow to IR. We discuss a version of {\it incomplete} C-theorem and an {\it incomplete} attractor like mechanism. We discuss the implication of our results for entanglement entropy and geometric quantities like scalar curvature, volume and mass scale of fundamental excitation of the how these quantities increase or decrease (often monotonically) with the strength of the deformation. Thermal physics of a holographic theory defined on a compact boundary is more interesting than its non-compact counterpart. It is well known that with a compact boundary, there is a possibility of a first order Hawking-Page transition dual to a de-confinement phase transition. From a gravity perspective, a relevant deformation dumps negative energy inside the bulk, increasing the effective cosmological constant (Lambda) of the AdS. Dumping more negative energy in the bulk would make the HP transition harder and the corresponding HP transition temperature would increase. However, we have found the size of the BH at the transition temperature decreases.

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.

Geometry problem solving is a well-recognized testbed for evaluating the high-level multi-modal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two specific tasks, hindering a deep model to unify its reasoning capability on multiple math tasks. However, in essence, these two tasks have similar problem representations and overlapped math knowledge which can improve the understanding and reasoning ability of a deep model on both two tasks. Therefore, we construct a large-scale Unified Geometry problem benchmark, UniGeo, which contains 4,998 calculation problems and 9,543 proving problems. Each proving problem is annotated with a multi-step proof with reasons and mathematical expressions. The proof can be easily reformulated as a proving sequence that shares the same formats with the annotated program sequence for calculation problems. Naturally, we also present a unified multi-task Geometric Transformer framework, Geoformer, to tackle calculation and proving problems simultaneously in the form of sequence generation, which finally shows the reasoning ability can be improved on both two tasks by unifying formulation. Furthermore, we propose a Mathematical Expression Pretraining (MEP) method that aims to predict the mathematical expressions in the problem solution, thus improving the Geoformer model. Experiments on the UniGeo demonstrate that our proposed Geoformer obtains state-of-the-art performance by outperforming task-specific model NGS with over 5.6% and 3.2% accuracies on calculation and proving problems, respectively.

Score distillation sampling (SDS), the methodology in which the score from pretrained 2D diffusion models is distilled into 3D representation, has recently brought significant advancements in text-to-3D generation task. However, this approach is still confronted with critical geometric inconsistency problems such as the Janus problem. Starting from a hypothesis that such inconsistency problems may be induced by multiview inconsistencies between 2D scores predicted from various viewpoints, we introduce GSD, a simple and general plug-and-play framework for incorporating 3D consistency and therefore geometry awareness into the SDS process. Our methodology is composed of three components: 3D consistent noising, designed to produce 3D consistent noise maps that perfectly follow the standard Gaussian distribution, geometry-based gradient warping for identifying correspondences between predicted gradients of different viewpoints, and novel gradient consistency loss to optimize the scene geometry toward producing more consistent gradients. We demonstrate that our method significantly improves performance, successfully addressing the geometric inconsistency problems in text-to-3D generation task with minimal computation cost and being compatible with existing score distillation-based models. Our project page is available at https://ku-cvlab.github.io/GSD/.

We present a dataset for investigating the impact of stellar activity on astrometric measurements using NASA's Solar Dynamics Observatory (SDO) images of the Sun. The sensitivity of astrometry for detecting exoplanets is limited by stellar activity (e.g. starspots), which causes the measured "center of flux" of the star to deviate from the true, geometric, center, producing false positive detections. We analyze Helioseismic and Magnetic Imager continuum image data obtained from SDO between July 2015 and December 2022 to examine this "astrometric jitter" phenomenon for the Sun. We employ data processing procedures to clean the images and compute the time series of the sunspot-induced shift between the center of flux and the geometric center. The resulting time series show quasiperiodic variations up to 0.05% of the Sun's radius at its rotation period.

Proving geometric theorems constitutes a hallmark of visual reasoning combining both intuitive and logical skills. Therefore, automated theorem proving of Olympiad-level geometry problems is considered a notable milestone in human-level automated reasoning. The introduction of AlphaGeometry, a neuro-symbolic model trained with 100 million synthetic samples, marked a major breakthrough. It solved 25 of 30 International Mathematical Olympiad (IMO) problems whereas the reported baseline based on Wu's method solved only ten. In this note, we revisit the IMO-AG-30 Challenge introduced with AlphaGeometry, and find that Wu's method is surprisingly strong. Wu's method alone can solve 15 problems, and some of them are not solved by any of the other methods. This leads to two key findings: (i) Combining Wu's method with the classic synthetic methods of deductive databases and angle, ratio, and distance chasing solves 21 out of 30 methods by just using a CPU-only laptop with a time limit of 5 minutes per problem. Essentially, this classic method solves just 4 problems less than AlphaGeometry and establishes the first fully symbolic baseline strong enough to rival the performance of an IMO silver medalist. (ii) Wu's method even solves 2 of the 5 problems that AlphaGeometry failed to solve. Thus, by combining AlphaGeometry with Wu's method we set a new state-of-the-art for automated theorem proving on IMO-AG-30, solving 27 out of 30 problems, the first AI method which outperforms an IMO gold medalist.

A triangular mesh is one of the most popular 3D data representations. As such, the deployment of deep neural networks for mesh processing is widely spread and is increasingly attracting more attention. However, neural networks are prone to adversarial attacks, where carefully crafted inputs impair the model's functionality. The need to explore these vulnerabilities is a fundamental factor in the future development of 3D-based applications. Recently, mesh attacks were studied on the semantic level, where classifiers are misled to produce wrong predictions. Nevertheless, mesh surfaces possess complex geometric attributes beyond their semantic meaning, and their analysis often includes the need to encode and reconstruct the geometry of the shape. We propose a novel framework for a geometric adversarial attack on a 3D mesh autoencoder. In this setting, an adversarial input mesh deceives the autoencoder by forcing it to reconstruct a different geometric shape at its output. The malicious input is produced by perturbing a clean shape in the spectral domain. Our method leverages the spectral decomposition of the mesh along with additional mesh-related properties to obtain visually credible results that consider the delicacy of surface distortions. Our code is publicly available at https://github.com/StolikTomer/SAGA.