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Let $\Lambda_X(s)=\det(I-sX^{\dagger})$ be the characteristic polynomial of the unitary matrix $X$. It is believed that the distribution of values of $\Lambda_X(s)$ model the distribution of values of the Riemann zeta-function $\zeta(s)$. This principle motivates many avenues of study. Of particular interest is the behavior of $\Lambda_X'(s)$ and the distribution of its zeros (all of which lie inside or on the unit circle). In this article we present several identities for the moments of $\Lambda_X'(s)$ averaged over $U(N)$, for $x \in \mathbb{C}$ as well as specialized to $|x|=1$. Additionally, we prove, for positive integer $k$, that the polynomial $\int_{U(N)} |\Lambda_X(1)|^{2k} dX$ of degree $k^2$ in $N$ divides the polynomial $\int_{U(N)} |\Lambda_X'(1)|^{2k} dX$ which is of degree $k^2+2k$ in $N$ and that the ratio, $f(N,k)$, of these moments factors into linear factors modulo $4k-1$ if $4k-1$ is prime. We also discuss the relationship of these moments to a solution of a second order non-linear Painl\'{e}ve differential equation. Finally we give some formulas in terms of the $_3F_2$ hypergeometric series for the moments in the simplest case when $N=2$, and also study the radial distribution of the zeros of $\Lambda_X'(s)$ in that case.

Customizing text-to-image (T2I) models has seen tremendous progress recently, particularly in areas such as personalization, stylization, and conditional generation. However, expanding this progress to video generation is still in its infancy, primarily due to the lack of customized video data. In this work, we introduce Still-Moving, a novel generic framework for customizing a text-to-video (T2V) model, without requiring any customized video data. The framework applies to the prominent T2V design where the video model is built over a text-to-image (T2I) model (e.g., via inflation). We assume access to a customized version of the T2I model, trained only on still image data (e.g., using DreamBooth or StyleDrop). Naively plugging in the weights of the customized T2I model into the T2V model often leads to significant artifacts or insufficient adherence to the customization data. To overcome this issue, we train lightweight $\textit{Spatial Adapters}$ that adjust the features produced by the injected T2I layers. Importantly, our adapters are trained on $\textit{"frozen videos"}$ (i.e., repeated images), constructed from image samples generated by the customized T2I model. This training is facilitated by a novel $\textit{Motion Adapter}$ module, which allows us to train on such static videos while preserving the motion prior of the video model. At test time, we remove the Motion Adapter modules and leave in only the trained Spatial Adapters. This restores the motion prior of the T2V model while adhering to the spatial prior of the customized T2I model. We demonstrate the effectiveness of our approach on diverse tasks including personalized, stylized, and conditional generation. In all evaluated scenarios, our method seamlessly integrates the spatial prior of the customized T2I model with a motion prior supplied by the T2V model., Comment: Webpage: https://still-moving.github.io/ | Video: https://www.youtube.com/watch?v=U7UuV_VIjnA

We present Magic Insert, a method for dragging-and-dropping subjects from a user-provided image into a target image of a different style in a physically plausible manner while matching the style of the target image. This work formalizes the problem of style-aware drag-and-drop and presents a method for tackling it by addressing two sub-problems: style-aware personalization and realistic object insertion in stylized images. For style-aware personalization, our method first fine-tunes a pretrained text-to-image diffusion model using LoRA and learned text tokens on the subject image, and then infuses it with a CLIP representation of the target style. For object insertion, we use Bootstrapped Domain Adaption to adapt a domain-specific photorealistic object insertion model to the domain of diverse artistic styles. Overall, the method significantly outperforms traditional approaches such as inpainting. Finally, we present a dataset, SubjectPlop, to facilitate evaluation and future progress in this area. Project page: https://magicinsert.github.io/, Comment: Project page: https://magicinsert.github.io/

Polymers are an effective test-bed for studying topological constraints in condensed matter due to a wide array of synthetically-available chain topologies. When linear and ring polymers are blended together, emergent rheological properties are observed as the blend can be more viscous than either of the individual components. This emergent behavior arises since ring-linear blends can form long-lived topological constraints as the linear polymers thread the ring polymers. Here, we demonstrate how the Gauss linking integral can be used to efficiently evaluate the relaxation of topological constraints in ring-linear polymer blends. For majority-linear blends, the relaxation rate of topological constraints depends primarily on reptation of the linear polymers, resulting in the diffusive time $\tau_{d,R}$ for rings of length $N_R$ blended with linear chains of length $N_l$ to scale as $\tau_{d,R}\sim N_R^2N_L^{3.4}$., Comment: 6 pages, 6 figures

Recent advances in large-scale pretraining have yielded visual foundation models with strong capabilities. Not only can recent models generalize to arbitrary images for their training task, their intermediate representations are useful for other visual tasks such as detection and segmentation. Given that such models can classify, delineate, and localize objects in 2D, we ask whether they also represent their 3D structure? In this work, we analyze the 3D awareness of visual foundation models. We posit that 3D awareness implies that representations (1) encode the 3D structure of the scene and (2) consistently represent the surface across views. We conduct a series of experiments using task-specific probes and zero-shot inference procedures on frozen features. Our experiments reveal several limitations of the current models. Our code and analysis can be found at https://github.com/mbanani/probe3d., Comment: Accepted to CVPR 2024. Project page: https://github.com/mbanani/probe3d

We introduce Lumiere -- a text-to-video diffusion model designed for synthesizing videos that portray realistic, diverse and coherent motion -- a pivotal challenge in video synthesis. To this end, we introduce a Space-Time U-Net architecture that generates the entire temporal duration of the video at once, through a single pass in the model. This is in contrast to existing video models which synthesize distant keyframes followed by temporal super-resolution -- an approach that inherently makes global temporal consistency difficult to achieve. By deploying both spatial and (importantly) temporal down- and up-sampling and leveraging a pre-trained text-to-image diffusion model, our model learns to directly generate a full-frame-rate, low-resolution video by processing it in multiple space-time scales. We demonstrate state-of-the-art text-to-video generation results, and show that our design easily facilitates a wide range of content creation tasks and video editing applications, including image-to-video, video inpainting, and stylized generation., Comment: Webpage: https://lumiere-video.github.io/ | Video: https://www.youtube.com/watch?v=wxLr02Dz2Sc

We introduce WonderJourney, a modularized framework for perpetual 3D scene generation. Unlike prior work on view generation that focuses on a single type of scenes, we start at any user-provided location (by a text description or an image) and generate a journey through a long sequence of diverse yet coherently connected 3D scenes. We leverage an LLM to generate textual descriptions of the scenes in this journey, a text-driven point cloud generation pipeline to make a compelling and coherent sequence of 3D scenes, and a large VLM to verify the generated scenes. We show compelling, diverse visual results across various scene types and styles, forming imaginary "wonderjourneys". Project website: https://kovenyu.com/WonderJourney/, Comment: Project website with video results: https://kovenyu.com/WonderJourney/

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely $f(f(z))=f(z)$. The proposed model $f$ is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely $f(x)=x$. We define the target manifold as the set of all instances that $f$ maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, $f(f(z))=f(z)$ which encourages the range of $f(z)$ to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

Recent advances in generative imagery have brought forth outpainting and inpainting models that can produce high-quality, plausible image content in unknown regions. However, the content these models hallucinate is necessarily inauthentic, since they are unaware of the true scene. In this work, we propose RealFill, a novel generative approach for image completion that fills in missing regions of an image with the content that should have been there. RealFill is a generative inpainting model that is personalized using only a few reference images of a scene. These reference images do not have to be aligned with the target image, and can be taken with drastically varying viewpoints, lighting conditions, camera apertures, or image styles. Once personalized, RealFill is able to complete a target image with visually compelling contents that are faithful to the original scene. We evaluate RealFill on a new image completion benchmark that covers a set of diverse and challenging scenarios, and find that it outperforms existing approaches by a large margin. Project page: https://realfill.github.io, Comment: SIGGRAPH 2024 (Journal Track). Project page: https://realfill.github.io

Motion magnification helps us visualize subtle, imperceptible motion. However, prior methods only work for 2D videos captured with a fixed camera. We present a 3D motion magnification method that can magnify subtle motions from scenes captured by a moving camera, while supporting novel view rendering. We represent the scene with time-varying radiance fields and leverage the Eulerian principle for motion magnification to extract and amplify the variation of the embedding of a fixed point over time. We study and validate our proposed principle for 3D motion magnification using both implicit and tri-plane-based radiance fields as our underlying 3D scene representation. We evaluate the effectiveness of our method on both synthetic and real-world scenes captured under various camera setups., Comment: ICCV 2023. See the project page at https://3d-motion-magnification.github.io

Personalization has emerged as a prominent aspect within the field of generative AI, enabling the synthesis of individuals in diverse contexts and styles, while retaining high-fidelity to their identities. However, the process of personalization presents inherent challenges in terms of time and memory requirements. Fine-tuning each personalized model needs considerable GPU time investment, and storing a personalized model per subject can be demanding in terms of storage capacity. To overcome these challenges, we propose HyperDreamBooth-a hypernetwork capable of efficiently generating a small set of personalized weights from a single image of a person. By composing these weights into the diffusion model, coupled with fast finetuning, HyperDreamBooth can generate a person's face in various contexts and styles, with high subject details while also preserving the model's crucial knowledge of diverse styles and semantic modifications. Our method achieves personalization on faces in roughly 20 seconds, 25x faster than DreamBooth and 125x faster than Textual Inversion, using as few as one reference image, with the same quality and style diversity as DreamBooth. Also our method yields a model that is 10000x smaller than a normal DreamBooth model. Project page: https://hyperdreambooth.github.io, Comment: project page: https://hyperdreambooth.github.io

Estimating the depth of objects from a single image is a valuable task for many vision, robotics, and graphics applications. However, current methods often fail to produce accurate depth for objects in diverse scenes. In this work, we propose a simple yet effective Background Prompting strategy that adapts the input object image with a learned background. We learn the background prompts only using small-scale synthetic object datasets. To infer object depth on a real image, we place the segmented object into the learned background prompt and run off-the-shelf depth networks. Background Prompting helps the depth networks focus on the foreground object, as they are made invariant to background variations. Moreover, Background Prompting minimizes the domain gap between synthetic and real object images, leading to better sim2real generalization than simple finetuning. Results on multiple synthetic and real datasets demonstrate consistent improvements in real object depths for a variety of existing depth networks. Code and optimized background prompts can be found at: https://mbaradad.github.io/depth_prompt.

Estimating 3D articulated shapes like animal bodies from monocular images is inherently challenging due to the ambiguities of camera viewpoint, pose, texture, lighting, etc. We propose ARTIC3D, a self-supervised framework to reconstruct per-instance 3D shapes from a sparse image collection in-the-wild. Specifically, ARTIC3D is built upon a skeleton-based surface representation and is further guided by 2D diffusion priors from Stable Diffusion. First, we enhance the input images with occlusions/truncation via 2D diffusion to obtain cleaner mask estimates and semantic features. Second, we perform diffusion-guided 3D optimization to estimate shape and texture that are of high-fidelity and faithful to input images. We also propose a novel technique to calculate more stable image-level gradients via diffusion models compared to existing alternatives. Finally, we produce realistic animations by fine-tuning the rendered shape and texture under rigid part transformations. Extensive evaluations on multiple existing datasets as well as newly introduced noisy web image collections with occlusions and truncation demonstrate that ARTIC3D outputs are more robust to noisy images, higher quality in terms of shape and texture details, and more realistic when animated. Project page: https://chhankyao.github.io/artic3d/, Comment: Project page: https://chhankyao.github.io/artic3d/

Pre-trained large text-to-image models synthesize impressive images with an appropriate use of text prompts. However, ambiguities inherent in natural language and out-of-distribution effects make it hard to synthesize image styles, that leverage a specific design pattern, texture or material. In this paper, we introduce StyleDrop, a method that enables the synthesis of images that faithfully follow a specific style using a text-to-image model. The proposed method is extremely versatile and captures nuances and details of a user-provided style, such as color schemes, shading, design patterns, and local and global effects. It efficiently learns a new style by fine-tuning very few trainable parameters (less than $1\%$ of total model parameters) and improving the quality via iterative training with either human or automated feedback. Better yet, StyleDrop is able to deliver impressive results even when the user supplies only a single image that specifies the desired style. An extensive study shows that, for the task of style tuning text-to-image models, StyleDrop implemented on Muse convincingly outperforms other methods, including DreamBooth and textual inversion on Imagen or Stable Diffusion. More results are available at our project website: https://styledrop.github.io, Comment: Preprint. Project page at https://styledrop.github.io

Priors are essential for reconstructing images from noisy and/or incomplete measurements. The choice of the prior determines both the quality and uncertainty of recovered images. We propose turning score-based diffusion models into principled image priors ("score-based priors") for analyzing a posterior of images given measurements. Previously, probabilistic priors were limited to handcrafted regularizers and simple distributions. In this work, we empirically validate the theoretically-proven probability function of a score-based diffusion model. We show how to sample from resulting posteriors by using this probability function for variational inference. Our results, including experiments on denoising, deblurring, and interferometric imaging, suggest that score-based priors enable principled inference with a sophisticated, data-driven image prior., Comment: ICCV 2023

We present DreamBooth3D, an approach to personalize text-to-3D generative models from as few as 3-6 casually captured images of a subject. Our approach combines recent advances in personalizing text-to-image models (DreamBooth) with text-to-3D generation (DreamFusion). We find that naively combining these methods fails to yield satisfactory subject-specific 3D assets due to personalized text-to-image models overfitting to the input viewpoints of the subject. We overcome this through a 3-stage optimization strategy where we jointly leverage the 3D consistency of neural radiance fields together with the personalization capability of text-to-image models. Our method can produce high-quality, subject-specific 3D assets with text-driven modifications such as novel poses, colors and attributes that are not seen in any of the input images of the subject., Comment: Project page at https://dreambooth3d.github.io/ Video Summary at https://youtu.be/kKVDrbfvOoA

We present Muse, a text-to-image Transformer model that achieves state-of-the-art image generation performance while being significantly more efficient than diffusion or autoregressive models. Muse is trained on a masked modeling task in discrete token space: given the text embedding extracted from a pre-trained large language model (LLM), Muse is trained to predict randomly masked image tokens. Compared to pixel-space diffusion models, such as Imagen and DALL-E 2, Muse is significantly more efficient due to the use of discrete tokens and requiring fewer sampling iterations; compared to autoregressive models, such as Parti, Muse is more efficient due to the use of parallel decoding. The use of a pre-trained LLM enables fine-grained language understanding, translating to high-fidelity image generation and the understanding of visual concepts such as objects, their spatial relationships, pose, cardinality etc. Our 900M parameter model achieves a new SOTA on CC3M, with an FID score of 6.06. The Muse 3B parameter model achieves an FID of 7.88 on zero-shot COCO evaluation, along with a CLIP score of 0.32. Muse also directly enables a number of image editing applications without the need to fine-tune or invert the model: inpainting, outpainting, and mask-free editing. More results are available at https://muse-model.github.io

Automatically estimating 3D skeleton, shape, camera viewpoints, and part articulation from sparse in-the-wild image ensembles is a severely under-constrained and challenging problem. Most prior methods rely on large-scale image datasets, dense temporal correspondence, or human annotations like camera pose, 2D keypoints, and shape templates. We propose Hi-LASSIE, which performs 3D articulated reconstruction from only 20-30 online images in the wild without any user-defined shape or skeleton templates. We follow the recent work of LASSIE that tackles a similar problem setting and make two significant advances. First, instead of relying on a manually annotated 3D skeleton, we automatically estimate a class-specific skeleton from the selected reference image. Second, we improve the shape reconstructions with novel instance-specific optimization strategies that allow reconstructions to faithful fit on each instance while preserving the class-specific priors learned across all images. Experiments on in-the-wild image ensembles show that Hi-LASSIE obtains higher fidelity state-of-the-art 3D reconstructions despite requiring minimum user input., Comment: Project page: https://chhankyao.github.io/hi-lassie/

Scene flow estimation is a long-standing problem in computer vision, where the goal is to find the 3D motion of a scene from its consecutive observations. Recently, there have been efforts to compute the scene flow from 3D point clouds. A common approach is to train a regression model that consumes source and target point clouds and outputs the per-point translation vector. An alternative is to learn point matches between the point clouds concurrently with regressing a refinement of the initial correspondence flow. In both cases, the learning task is very challenging since the flow regression is done in the free 3D space, and a typical solution is to resort to a large annotated synthetic dataset. We introduce SCOOP, a new method for scene flow estimation that can be learned on a small amount of data without employing ground-truth flow supervision. In contrast to previous work, we train a pure correspondence model focused on learning point feature representation and initialize the flow as the difference between a source point and its softly corresponding target point. Then, in the run-time phase, we directly optimize a flow refinement component with a self-supervised objective, which leads to a coherent and accurate flow field between the point clouds. Experiments on widespread datasets demonstrate the performance gains achieved by our method compared to existing leading techniques while using a fraction of the training data. Our code is publicly available at https://github.com/itailang/SCOOP., Comment: CVPR 2023. Project page: https://itailang.github.io/SCOOP/

Large text-to-image models achieved a remarkable leap in the evolution of AI, enabling high-quality and diverse synthesis of images from a given text prompt. However, these models lack the ability to mimic the appearance of subjects in a given reference set and synthesize novel renditions of them in different contexts. In this work, we present a new approach for "personalization" of text-to-image diffusion models. Given as input just a few images of a subject, we fine-tune a pretrained text-to-image model such that it learns to bind a unique identifier with that specific subject. Once the subject is embedded in the output domain of the model, the unique identifier can be used to synthesize novel photorealistic images of the subject contextualized in different scenes. By leveraging the semantic prior embedded in the model with a new autogenous class-specific prior preservation loss, our technique enables synthesizing the subject in diverse scenes, poses, views and lighting conditions that do not appear in the reference images. We apply our technique to several previously-unassailable tasks, including subject recontextualization, text-guided view synthesis, and artistic rendering, all while preserving the subject's key features. We also provide a new dataset and evaluation protocol for this new task of subject-driven generation. Project page: https://dreambooth.github.io/, Comment: Published at CVPR 2023. Project page: https://dreambooth.github.io/

YouTube users looking for instructions for a specific task may spend a long time browsing content trying to find the right video that matches their needs. Creating a visual summary (abridged version of a video) provides viewers with a quick overview and massively reduces search time. In this work, we focus on summarizing instructional videos, an under-explored area of video summarization. In comparison to generic videos, instructional videos can be parsed into semantically meaningful segments that correspond to important steps of the demonstrated task. Existing video summarization datasets rely on manual frame-level annotations, making them subjective and limited in size. To overcome this, we first automatically generate pseudo summaries for a corpus of instructional videos by exploiting two key assumptions: (i) relevant steps are likely to appear in multiple videos of the same task (Task Relevance), and (ii) they are more likely to be described by the demonstrator verbally (Cross-Modal Saliency). We propose an instructional video summarization network that combines a context-aware temporal video encoder and a segment scoring transformer. Using pseudo summaries as weak supervision, our network constructs a visual summary for an instructional video given only video and transcribed speech. To evaluate our model, we collect a high-quality test set, WikiHow Summaries, by scraping WikiHow articles that contain video demonstrations and visual depictions of steps allowing us to obtain the ground-truth summaries. We outperform several baselines and a state-of-the-art video summarization model on this new benchmark., Comment: Accepted to ECCV 2022. Website: https://medhini.github.io/ivsum/

Creating high-quality articulated 3D models of animals is challenging either via manual creation or using 3D scanning tools. Therefore, techniques to reconstruct articulated 3D objects from 2D images are crucial and highly useful. In this work, we propose a practical problem setting to estimate 3D pose and shape of animals given only a few (10-30) in-the-wild images of a particular animal species (say, horse). Contrary to existing works that rely on pre-defined template shapes, we do not assume any form of 2D or 3D ground-truth annotations, nor do we leverage any multi-view or temporal information. Moreover, each input image ensemble can contain animal instances with varying poses, backgrounds, illuminations, and textures. Our key insight is that 3D parts have much simpler shape compared to the overall animal and that they are robust w.r.t. animal pose articulations. Following these insights, we propose LASSIE, a novel optimization framework which discovers 3D parts in a self-supervised manner with minimal user intervention. A key driving force behind LASSIE is the enforcing of 2D-3D part consistency using self-supervisory deep features. Experiments on Pascal-Part and self-collected in-the-wild animal datasets demonstrate considerably better 3D reconstructions as well as both 2D and 3D part discovery compared to prior arts. Project page: chhankyao.github.io/lassie/

How important are training details and datasets to recent optical flow models like RAFT? And do they generalize? To explore these questions, rather than develop a new model, we revisit three prominent models, PWC-Net, IRR-PWC and RAFT, with a common set of modern training techniques and datasets, and observe significant performance gains, demonstrating the importance and generality of these training details. Our newly trained PWC-Net and IRR-PWC models show surprisingly large improvements, up to 30% versus original published results on Sintel and KITTI 2015 benchmarks. They outperform the more recent Flow1D on KITTI 2015 while being 3x faster during inference. Our newly trained RAFT achieves an Fl-all score of 4.31% on KITTI 2015, more accurate than all published optical flow methods at the time of writing. Our results demonstrate the benefits of separating the contributions of models, training techniques and datasets when analyzing performance gains of optical flow methods. Our source code will be publicly available., Comment: Accepted to ECCV22. 33 pages, including supplementals. Website at: https://autoflow-google.github.io/

Using only a model that was trained to predict where people look at images, and no additional training data, we can produce a range of powerful editing effects for reducing distraction in images. Given an image and a mask specifying the region to edit, we backpropagate through a state-of-the-art saliency model to parameterize a differentiable editing operator, such that the saliency within the masked region is reduced. We demonstrate several operators, including: a recoloring operator, which learns to apply a color transform that camouflages and blends distractors into their surroundings; a warping operator, which warps less salient image regions to cover distractors, gradually collapsing objects into themselves and effectively removing them (an effect akin to inpainting); a GAN operator, which uses a semantic prior to fully replace image regions with plausible, less salient alternatives. The resulting effects are consistent with cognitive research on the human visual system (e.g., since color mismatch is salient, the recoloring operator learns to harmonize objects' colors with their surrounding to reduce their saliency), and, importantly, are all achieved solely through the guidance of the pretrained saliency model, with no additional supervision. We present results on a variety of natural images and conduct a perceptual study to evaluate and validate the changes in viewers' eye-gaze between the original images and our edited results., Comment: https://deep-saliency-prior.github.io/

Computer vision is increasingly effective at segmenting objects in images and videos; however, scene effects related to the objects -- shadows, reflections, generated smoke, etc -- are typically overlooked. Identifying such scene effects and associating them with the objects producing them is important for improving our fundamental understanding of visual scenes, and can also assist a variety of applications such as removing, duplicating, or enhancing objects in video. In this work, we take a step towards solving this novel problem of automatically associating objects with their effects in video. Given an ordinary video and a rough segmentation mask over time of one or more subjects of interest, we estimate an omnimatte for each subject -- an alpha matte and color image that includes the subject along with all its related time-varying scene elements. Our model is trained only on the input video in a self-supervised manner, without any manual labels, and is generic -- it produces omnimattes automatically for arbitrary objects and a variety of effects. We show results on real-world videos containing interactions between different types of subjects (cars, animals, people) and complex effects, ranging from semi-transparent elements such as smoke and reflections, to fully opaque effects such as objects attached to the subject., Comment: CVPR 2021 Oral. Project webpage: https://omnimatte.github.io/. Added references

We classify all sets of nonzero vectors in $\mathbb{R}^3$ such that the angle formed by each pair is a rational multiple of $\pi$. The special case of four-element subsets lets us classify all tetrahedra whose dihedral angles are multiples of $\pi$, solving a 1976 problem of Conway and Jones: there are $2$ one-parameter families and $59$ sporadic tetrahedra, all but three of which are related to either the icosidodecahedron or the $B_3$ root lattice. The proof requires the solution in roots of unity of a $W(D_6)$-symmetric polynomial equation with $105$ monomials (the previous record was $12$ monomials)., Comment: 30 pages. Associated code at https://github.com/kedlaya/tetrahedra

We present a method for retiming people in an ordinary, natural video -- manipulating and editing the time in which different motions of individuals in the video occur. We can temporally align different motions, change the speed of certain actions (speeding up/slowing down, or entirely "freezing" people), or "erase" selected people from the video altogether. We achieve these effects computationally via a dedicated learning-based layered video representation, where each frame in the video is decomposed into separate RGBA layers, representing the appearance of different people in the video. A key property of our model is that it not only disentangles the direct motions of each person in the input video, but also correlates each person automatically with the scene changes they generate -- e.g., shadows, reflections, and motion of loose clothing. The layers can be individually retimed and recombined into a new video, allowing us to achieve realistic, high-quality renderings of retiming effects for real-world videos depicting complex actions and involving multiple individuals, including dancing, trampoline jumping, or group running., Comment: In SIGGRAPH Asia 2020. Project webpage: https://retiming.github.io/. Added references

Let $N=UV$, where $U,V$ are integers, with $1< U,V

We wish to automatically predict the "speediness" of moving objects in videos---whether they move faster, at, or slower than their "natural" speed. The core component in our approach is SpeedNet---a novel deep network trained to detect if a video is playing at normal rate, or if it is sped up. SpeedNet is trained on a large corpus of natural videos in a self-supervised manner, without requiring any manual annotations. We show how this single, binary classification network can be used to detect arbitrary rates of speediness of objects. We demonstrate prediction results by SpeedNet on a wide range of videos containing complex natural motions, and examine the visual cues it utilizes for making those predictions. Importantly, we show that through predicting the speed of videos, the model learns a powerful and meaningful space-time representation that goes beyond simple motion cues. We demonstrate how those learned features can boost the performance of self-supervised action recognition, and can be used for video retrieval. Furthermore, we also apply SpeedNet for generating time-varying, adaptive video speedups, which can allow viewers to watch videos faster, but with less of the jittery, unnatural motions typical to videos that are sped up uniformly., Comment: Accepted to CVPR 2020 (oral). Project webpage: http://speednet-cvpr20.github.io

Molecular dynamics simulations confirm recent extensional flow experiments showing ring polymer melts exhibit strong extension-rate thickening of the viscosity at Weissenberg numbers $Wi<<1$. Thickening coincides with the extreme elongation of a minority population of rings that grows with $Wi$. The large susceptibility of some rings to extend is due to a flow-driven formation of topological links that connect multiple rings into supramolecular chains. Links form spontaneously with a longer delay at lower $Wi$ and are pulled tight and stabilized by the flow. Once linked, these composite objects experience larger drag forces than individual rings, driving their strong elongation. The fraction of linked rings generated by flow depends non-monotonically on $Wi$, increasing to a maximum when $Wi\sim1$ before rapidly decreasing when the strain rate approaches the relaxation rate of the smallest ring loops $\sim 1/\tau_e$., Comment: 5 Pages, 5 Figures

How much can we infer about a person's looks from the way they speak? In this paper, we study the task of reconstructing a facial image of a person from a short audio recording of that person speaking. We design and train a deep neural network to perform this task using millions of natural Internet/YouTube videos of people speaking. During training, our model learns voice-face correlations that allow it to produce images that capture various physical attributes of the speakers such as age, gender and ethnicity. This is done in a self-supervised manner, by utilizing the natural co-occurrence of faces and speech in Internet videos, without the need to model attributes explicitly. We evaluate and numerically quantify how--and in what manner--our Speech2Face reconstructions, obtained directly from audio, resemble the true face images of the speakers., Comment: To appear in CVPR2019. Project page: http://speech2face.github.io

Following the work of Conrey, Rubinstein and Snaith and Forrester and Witte we examine a mixed moment of the characteristic polynomial and its derivative for matrices from the unitary group U(N) (also known as the CUE) and relate the moment to the solution of a Painleve differential equation. We also calculate a simple form for the asymptotic behaviour of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle.

We study piecewise polynomial functions $\gamma_k(c)$ that appear in the asymptotics of averages of the divisor sum in short intervals. Specifically, we express these polynomials as the inverse Fourier transform of a Hankel determinant that satisfies a Painlev\'e V equation. We prove that $\gamma_k(c)$ is very smooth at its transition points, and also determine the asymptotics of $\gamma_k(c)$ in a large neighbourhood of $k=c/2$. Finally, we consider the coefficients that appear in the asymptotics of elliptic Aliquot cycles.

We present a joint audio-visual model for isolating a single speech signal from a mixture of sounds such as other speakers and background noise. Solving this task using only audio as input is extremely challenging and does not provide an association of the separated speech signals with speakers in the video. In this paper, we present a deep network-based model that incorporates both visual and auditory signals to solve this task. The visual features are used to "focus" the audio on desired speakers in a scene and to improve the speech separation quality. To train our joint audio-visual model, we introduce AVSpeech, a new dataset comprised of thousands of hours of video segments from the Web. We demonstrate the applicability of our method to classic speech separation tasks, as well as real-world scenarios involving heated interviews, noisy bars, and screaming children, only requiring the user to specify the face of the person in the video whose speech they want to isolate. Our method shows clear advantage over state-of-the-art audio-only speech separation in cases of mixed speech. In addition, our model, which is speaker-independent (trained once, applicable to any speaker), produces better results than recent audio-visual speech separation methods that are speaker-dependent (require training a separate model for each speaker of interest)., Comment: Accepted to SIGGRAPH 2018. Project webpage: https://looking-to-listen.github.io

Let $q$ be an odd prime power, and $H_{d,q}$ denote the set of square-free monic polynomials $D(x) \in F_q[x]$ of degree $d$. Katz and Sarnak showed that the moments, over $H_{d,q}$, of the zeta functions associated to the curves $y^2=D(x)$, evaluated at the central point, tend, as $q \to \infty$, to the moments of characteristic polynomials, evaluated at the central point, of matrices in $USp(2\lfloor (d-1)/2 \rfloor)$. Using techniques that were originally developed for studying moments of $L$-functions over number fields, Andrade and Keating conjectured an asymptotic formula for the moments for $q$ fixed and $d \to \infty$. We provide theoretical and numerical evidence in favour of their conjecture. In some cases we are able to work out exact formulas for the moments and use these to precisely determine the size of the remainder term in the predicted moments., Comment: 32 pages

We describe some experiments that show a connection between elliptic curves of high rank and the Riemann zeta function on the one line. We also discuss a couple of statistics involving $L$-functions where the zeta function on the one line plays a prominent role., Comment: 21 pages, lots of figures, very cool