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Previous research has shown that constraining the gradient of loss function with respect to model-predicted probabilities can enhance the model robustness against noisy labels. These methods typically specify a fixed optimal threshold for gradient clipping through validation data to obtain the desired robustness against noise. However, this common practice overlooks the dynamic distribution of gradients from both clean and noisy-labeled samples at different stages of training, significantly limiting the model capability to adapt to the variable nature of gradients throughout the training process. To address this issue, we propose a simple yet effective approach called Optimized Gradient Clipping (OGC), which dynamically adjusts the clipping threshold based on the ratio of noise gradients to clean gradients after clipping, estimated by modeling the distributions of clean and noisy samples. This approach allows us to modify the clipping threshold at each training step, effectively controlling the influence of noise gradients. Additionally, we provide statistical analysis to certify the noise-tolerance ability of OGC. Our extensive experiments across various types of label noise, including symmetric, asymmetric, instance-dependent, and real-world noise, demonstrate the effectiveness of our approach. The code and a technical appendix for better digital viewing are included as supplementary materials and scheduled to be open-sourced upon publication., Comment: Accepted by AAAI2025

We provide the formula of motivic zeta function for semi-quasihomogeneous singularities and in dimension two, we determine the poles of zeta functions. We also give another formula for stringy E-function using embedded $\mathbb{Q}$-resolution, and we utilize it to calculate the stringy E-function for semi-quasihomogeneous polynomials and non-degenerate polynomials., Comment: 19 pages

Numerous theories have postulated the existence of exotic spin-dependent interactions beyond the Standard Model of particle physics. Spin-based quantum sensors, which utilize the quantum properties of spins to enhance measurement precision, emerge as powerful tools for probing these exotic interactions. These sensors encompass a wide range of technologies, such as optically pumped magnetometers, atomic comagnetometers, spin masers, nuclear magnetic resonance, spin amplifiers, and nitrogen-vacancy centers. These technologies stand out for their ultrahigh sensitivity, compact tabletop design, and cost-effectiveness, offering complementary approaches to the large-scale particle colliders and astrophysical observations. This article reviews the underlying physical principles of various spin sensors and highlights the recent theoretical and experimental progress in the searches for exotic spin-dependent interactions with these quantum sensors. Investigations covered include the exotic interactions of spins with ultralight dark matter, exotic spin-dependent forces, electric dipole moment, spin-gravity interactions, and among others. Ongoing and forthcoming experiments using advanced spin-based sensors to investigate exotic spin-dependent interactions are discussed., Comment: 32 pages, 13 figures, accepted for publication in Reports on Progress in Physics

Out-of-distribution (OOD) detection is an essential approach to robustifying deep learning models, enabling them to identify inputs that fall outside of their trained distribution. Existing OOD detection methods usually depend on crafted data, such as specific outlier datasets or elaborate data augmentations. While this is reasonable, the frequent mismatch between crafted data and OOD data limits model robustness and generalizability. In response to this issue, we introduce Outlier Exposure by Simple Transformations (OEST), a framework that enhances OOD detection by leveraging "peripheral-distribution" (PD) data. Specifically, PD data are samples generated through simple data transformations, thus providing an efficient alternative to manually curated outliers. We adopt energy-based models (EBMs) to study PD data. We recognize the "energy barrier" in OOD detection, which characterizes the energy difference between in-distribution (ID) and OOD samples and eases detection. PD data are introduced to establish the energy barrier during training. Furthermore, this energy barrier concept motivates a theoretically grounded energy-barrier loss to replace the classical energy-bounded loss, leading to an improved paradigm, OEST*, which achieves a more effective and theoretically sound separation between ID and OOD samples. We perform empirical validation of our proposal, and extensive experiments across various benchmarks demonstrate that OEST* achieves better or similar accuracy compared with state-of-the-art methods., Comment: This work has been submitted to the IEEE for possible publication

Deep supervised learning has achieved remarkable success across a wide range of tasks, yet it remains susceptible to overfitting when confronted with noisy labels. To address this issue, noise-robust loss functions offer an effective solution for enhancing learning in the presence of label noise. In this work, we systematically investigate the limitation of the recently proposed Active Passive Loss (APL), which employs Mean Absolute Error (MAE) as its passive loss function. Despite the robustness brought by MAE, one of its key drawbacks is that it pays equal attention to clean and noisy samples; this feature slows down convergence and potentially makes training difficult, particularly in large-scale datasets. To overcome these challenges, we introduce a novel loss function class, termed Normalized Negative Loss Functions (NNLFs), which serve as passive loss functions within the APL framework. NNLFs effectively address the limitations of MAE by concentrating more on memorized clean samples. By replacing MAE in APL with our proposed NNLFs, we enhance APL and present a new framework called Active Negative Loss (ANL). Moreover, in non-symmetric noise scenarios, we propose an entropy-based regularization technique to mitigate the vulnerability to the label imbalance. Extensive experiments demonstrate that the new loss functions adopted by our ANL framework can achieve better or comparable performance to state-of-the-art methods across various label noise types and in image segmentation tasks. The source code is available at: https://github.com/Virusdoll/Active-Negative-Loss., Comment: This work has been submitted to the IEEE for possible publication

The inherent non-linearity of intensity correlation functions can be used to spatially distinguish identical emitters beyond the diffraction limit, for example, achieved in Super-Resolution Optical Fluctuation Imaging (SOFI). Here, we propose a complementary concept based on spectral correlation functions, termed Spectral Fluctuation Super-Resolution (SFSR) imaging. Through theoretical and computational analysis, we show that spatially resolving time-domain spectral correlation functions using second-order correlation analysis can improve resolution by up to twofold for two emitters. This enhancement is achieved by quantifying the correlated to uncorrelated spectral fluctuations on different time scales at different positions. Experimentally, SFSR can be implemented using a combination of interferometry and photon-correlation measurements. The method works for non-blinking emitters and stochastic spectral fluctuations of arbitrary temporal statistics. This suggests its utility in super-resolution microscopy of quantum emitters at low temperatures, for which spectral diffusion is often more pronounced than emitter blinking.

Video action recognition has made significant strides, but challenges remain in effectively using both spatial and temporal information. While existing methods often focus on either spatial features (e.g., object appearance) or temporal dynamics (e.g., motion), they rarely address the need for a comprehensive integration of both. Capturing the rich temporal evolution of video frames, while preserving their spatial details, is crucial for improving accuracy. In this paper, we introduce the Temporal Integration and Motion Enhancement (TIME) layer, a novel preprocessing technique designed to incorporate temporal information. The TIME layer generates new video frames by rearranging the original sequence, preserving temporal order while embedding $N^2$ temporally evolving frames into a single spatial grid of size $N \times N$. This transformation creates new frames that balance both spatial and temporal information, making them compatible with existing video models. When $N=1$, the layer captures rich spatial details, similar to existing methods. As $N$ increases ($N\geq2$), temporal information becomes more prominent, while the spatial information decreases to ensure compatibility with model inputs. We demonstrate the effectiveness of the TIME layer by integrating it into popular action recognition models, such as ResNet-50, Vision Transformer, and Video Masked Autoencoders, for both RGB and depth video data. Our experiments show that the TIME layer enhances recognition accuracy, offering valuable insights for video processing tasks., Comment: Research report

The detection of a stochastic gravitational wave background by pulsar timing arrays suggests the presence of a supermassive black hole binary population. Although the observed spectrum generally aligns with predictions from orbital evolution driven by gravitational wave emission in circular orbits, there is a discernible preference for a turnover at the lowest observed frequencies. This turnover could indicate a significant hardening phase, transitioning from early environmental influences to later stages predominantly influenced by gravitational wave emission. In the vicinity of these binaries, the ejection of stars or dark matter particles through gravitational three-body slingshots efficiently extracts orbital energy, leading to a low-frequency turnover in the spectrum. By analyzing the NANOGrav 15-year data, we assess how the gravitational wave spectrum depends on the initial inner galactic profile prior to disruption by binary ejections, accounting for a range of initial binary eccentricities. Our findings suggest a parsec-scale galactic center density around $10^6\,M_\odot/\textrm{pc}^3$ across most of the parameter space, offering insights into the environmental effects on black hole evolution and combined matter density near galaxy centers., Comment: 15 pages, 5 figures

We report the discovery of a peculiar X-ray transient, EP240408a, by Einstein Probe (EP) and follow-up studies made with EP, Swift, NICER, GROND, ATCA and other ground-based multi-wavelength telescopes. The new transient was first detected with Wide-field X-ray Telescope (WXT) on board EP on April 8th, 2024, manifested in an intense yet brief X-ray flare lasting for 12 seconds. The flare reached a peak flux of 3.9x10^(-9) erg/cm2/s in 0.5-4 keV, about 300 times brighter than the underlying X-ray emission detected throughout the observation. Rapid and more precise follow-up observations by EP/FXT, Swift and NICER confirmed the finding of this new transient. Its X-ray spectrum is non-thermal in 0.5-10 keV, with a power-law photon index varying within 1.8-2.5. The X-ray light curve shows a plateau lasting for about 4 days, followed by a steep decay till becoming undetectable about 10 days after the initial detection. Based on its temporal property and constraints from previous EP observations, an unusual timescale in the range of 7-23 days is found for EP240408a, which is intermediate between the commonly found fast and long-term transients. No counterparts have been found in optical and near-infrared, with the earliest observation at 17 hours after the initial X-ray detection, suggestive of intrinsically weak emission in these bands. We demonstrate that the remarkable properties of EP240408a are inconsistent with any of the transient types known so far, by comparison with, in particular, jetted tidal disruption events, gamma-ray bursts, X-ray binaries and fast blue optical transients. The nature of EP240408a thus remains an enigma. We suggest that EP240408a may represent a new type of transients with intermediate timescales of the order of about 10 days. The detection and follow-ups of more of such objects are essential for revealing their origin., Comment: 25 pages, 11 figures

The stochastic gravitational wave background (SGWB) consists of an incoherent collection of waves from both astrophysical and cosmological sources. To distinguish the SGWB from noise, it is essential to verify its quadrupolar nature, exemplified by the cross-correlations among pairs of pulsars within a pulsar timing array, commonly referred to as the Hellings-Downs curve. We extend the concept of quadrupolar correlations to pairs of general gravitational wave detectors, classified by their antenna responses. This study involves space-based missions such as the laser interferometers LISA, Taiji, and TianQin, along with atom interferometers like AEDGE/MAGIS. We calculate modulations in their correlations due to orbital motions and relative orientations, which are characteristic markers for identifying the quadrupolar nature of the SGWB. Our findings identify optimal configurations for these missions, offer forecasts for the time needed to identify the quadrupolar nature of the SGWB, and are applicable to both space-space and space-terrestrial correlations., Comment: 19 pages, 6 figures

Music is essential in daily life, fulfilling emotional and entertainment needs, and connecting us personally, socially, and culturally. A better understanding of music can enhance our emotions, cognitive skills, and cultural connections. The rapid advancement of artificial intelligence (AI) has introduced new ways to analyze music, aiming to replicate human understanding of music and provide related services. While the traditional models focused on audio features and simple tasks, the recent development of large language models (LLMs) and foundation models (FMs), which excel in various fields by integrating semantic information and demonstrating strong reasoning abilities, could capture complex musical features and patterns, integrate music with language and incorporate rich musical, emotional and psychological knowledge. Therefore, they have the potential in handling complex music understanding tasks from a semantic perspective, producing outputs closer to human perception. This work, to our best knowledge, is one of the early reviews of the intersection of AI techniques and music understanding. We investigated, analyzed, and tested recent large-scale music foundation models in respect of their music comprehension abilities. We also discussed their limitations and proposed possible future directions, offering insights for researchers in this field., Comment: 20 pages, 2 figures

Multiobjective optimization problems (MOPs) are prevalent in machine learning, with applications in multi-task learning, learning under fairness or robustness constraints, etc. Instead of reducing multiple objective functions into a scalar objective, MOPs aim to optimize for the so-called Pareto optimality or Pareto set learning, which involves optimizing more than one objective function simultaneously, over models with thousands / millions of parameters. Existing benchmark libraries for MOPs mainly focus on evolutionary algorithms, most of which are zeroth-order / meta-heuristic methods that do not effectively utilize higher-order information from objectives and cannot scale to large-scale models with thousands / millions of parameters. In light of the above gap, this paper introduces LibMOON, the first multiobjective optimization library that supports state-of-the-art gradient-based methods, provides a fair benchmark, and is open-sourced for the community., Comment: NeurIPS 2024

Hotspots, often characterized as point-like emissions, frequently manifest near black holes, displaying significantly increased luminosity compared to the surrounding accretion flow. It is noteworthy that these hotspots regularly occur outside the black hole at the center of the Milky Way. Light rays emitted from these sources follow complex trajectories around the black hole, ultimately arriving at distinct locations on the observer's image plane. To extract precise spacetime information, including the black hole mass, spin, and inclination angle, it is crucial to accurately resolve both the direct emission and its higher-order images, despite the latter's intensity suppression. To enhance the accuracy and efficiency of modeling and analyzing these hotspots, we introduce a forward ray tracing method, a departure from the traditional backward ray tracing approach. By utilizing conserved quantities in Kerr spacetime, this method initiates geodesics from a specified emission point near the black hole and terminates them at a distant observer, effectively capturing multiple images. By introducing perturbations to these geodesics, we map finite-size emissions to distinct regions on the image plane, allowing for the quantification of image shapes and amplification rates. This approach facilitates efficient spacetime tomography and hotspot localization, leveraging observations from the Event Horizon Telescope and its next-generation upgrades., Comment: 26 pages, 11 figures

The unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings. However, existing analyses of the algorithm for strongly log-concave distributions suggest that, as the dimension $d$ of the problem increases, the number of iterations required to ensure convergence within a desired error in the $W_2$ metric scales in proportion to $d$ or $\sqrt{d}$. In this paper, we argue that, despite this poor scaling of the $W_2$ error for the full set of variables, the behavior for a small number of variables can be significantly better: a number of iterations proportional to $K$, up to logarithmic terms in $d$, often suffices for the algorithm to converge to within a desired $W_2$ error for all $K$-marginals. We refer to this effect as delocalization of bias. We show that the delocalization effect does not hold universally and prove its validity for Gaussian distributions and strongly log-concave distributions with certain sparse interactions. Our analysis relies on a novel $W_{2,\ell^\infty}$ metric to measure convergence. A key technical challenge we address is the lack of a one-step contraction property in this metric. Finally, we use asymptotic arguments to explore potential generalizations of the delocalization effect beyond the Gaussian and sparse interactions setting.

Strong gravitational lensing occurs when photons pass through the vicinity of a black hole. We investigate this phenomenon in the context of a gravitational-wave event, specifically when a black hole is settling into its final state. The deflection angle of photons mimics the ringdown pattern of the gravitational wave at intermediate times. At late times it has an inverse cubic dependence on observation time. The deviation angle increases exponentially as photons approach the photon ring orbit, reflecting its unstable nature. Our findings are directly applicable to imaging scenarios involving stars against the background of compact binaries, or circumbinary accretion disks, particularly during the merger of two black holes., Comment: 16 pages, 4 figures

Contrastive Language-Image Pre-training (CLIP) models excel in integrating semantic information between images and text through contrastive learning techniques. It has achieved remarkable performance in various multimodal tasks. However, the deployment of large CLIP models is hindered in resource-limited environments, while smaller models frequently fail to meet the performance benchmarks required for practical applications. In this paper, we propose a novel approach, ComKD-CLIP: Comprehensive Knowledge Distillation for Contrastive Language-Image Pre-traning Model, which aims to comprehensively distill the knowledge from a large teacher CLIP model into a smaller student model, ensuring comparable performance with significantly reduced parameters. ComKD-CLIP is composed of two key mechanisms: Image Feature Alignment (IFAlign) and Educational Attention (EduAttention). IFAlign makes the image features extracted by the student model closely match those extracted by the teacher model, enabling the student to learn teacher's knowledge of extracting image features. EduAttention explores the cross-relationships between text features extracted by the teacher model and image features extracted by the student model, enabling the student model to learn how the teacher model integrates text-image features. In addition, ComKD-CLIP can refine the knowledge distilled from IFAlign and EduAttention by leveraging the text-image feature fusion results of the teacher model, ensuring the student model accurately absorbs the teacher's knowledge. Extensive experiments conducted on 11 datasets have demonstrated the superiority of the proposed method., Comment: update

Current large language models (LLMs) primarily utilize next-token prediction method for inference, which significantly impedes their processing speed. In this paper, we introduce a novel inference methodology termed next-sentence prediction, aiming at enhancing the inference efficiency of LLMs. We present Sentence Variational Autoencoder (SentenceVAE), which includes a Sentence Encoder to compress multiple tokens in a sentence into a single token, and a Sentence Decoder to reconstruct it. By integrating SentenceVAE into the input and output layers of LLMs, we develop Sentence-level LLMs (SLLMs) that employ a sentence-by-sentence inference method. In addition, the SentenceVAE module of SLLMs can maintain the integrity of the original semantic content by segmenting the context into sentences, thereby improving accuracy while boosting inference speed. Moreover, compared to previous LLMs, SLLMs process fewer tokens over equivalent context length, significantly reducing memory demands for self-attention computation and facilitating the handling of longer context. Extensive experiments on Wanjuan dataset have revealed that the proposed method can accelerate inference speed by 204~365%, reduce perplexity (PPL) to 46~75% of its original metric, and decrease memory overhead by 86~91% for the equivalent context length, compared to previous token-by-token methods., Comment: update the article

The dynamics of probability density functions has been extensively studied in science and engineering to understand physical phenomena and facilitate algorithmic design. Of particular interest are dynamics that can be formulated as gradient flows of energy functionals under the Wasserstein metric. The development of functional inequalities, such as the log-Sobolev inequality, plays a pivotal role in analyzing the convergence of these dynamics. The goal of this paper is to parallel the success of techniques using functional inequalities, for dynamics that are gradient flows under the Fisher-Rao metric, with various $f$-divergences as energy functionals. Such dynamics take the form of a nonlocal differential equation, for which existing analysis critically relies on using the explicit solution formula in special cases. We provide a comprehensive study on functional inequalities and the relevant geodesic convexity for Fisher-Rao gradient flows under minimal assumptions. A notable feature of the obtained functional inequalities is that they do not depend on the log-concavity or log-Sobolev constants of the target distribution. Consequently, the convergence rate of the dynamics (assuming well-posed) is uniform across general target distributions, making them potentially desirable dynamics for posterior sampling applications in Bayesian inference., Comment: 38 pages

Layout generation is a foundation task of graphic design, which requires the integration of visual aesthetics and harmonious expression of content delivery. However, existing methods still face challenges in generating precise and visually appealing layouts, including blocking, overlapping, small-sized, or spatial misalignment. We found that these methods overlook the crucial balance between learning content-aware and graphic-aware features. This oversight results in their limited ability to model the graphic structure of layouts and generate reasonable layout arrangements. To address these challenges, we introduce LayoutDiT, an effective framework that balances content and graphic features to generate high-quality, visually appealing layouts. Specifically, we first design an adaptive factor that optimizes the model's awareness of the layout generation space, balancing the model's performance in both content and graphic aspects. Secondly, we introduce a graphic condition, the saliency bounding box, to bridge the modality difference between images in the visual domain and layouts in the geometric parameter domain. In addition, we adapt a diffusion transformer model as the backbone, whose powerful generative capability ensures the quality of layout generation. Benefiting from the properties of diffusion models, our method excels in constrained settings without introducing additional constraint modules. Extensive experimental results demonstrate that our method achieves superior performance in both constrained and unconstrained settings, significantly outperforming existing methods.

The emergence of the large language model~(LLM) poses an exponential growth of demand for computation throughput, memory capacity, and communication bandwidth. Such a demand growth has significantly surpassed the improvement of corresponding chip designs. With the advancement of fabrication and integration technologies, designers have been developing Wafer-Scale Chips~(WSCs) to scale up and exploit the limits of computation density, memory capacity, and communication bandwidth at the level of a single chip. Existing solutions have demonstrated the significant advantages of WSCs over traditional designs, showing potential to effectively support LLM workloads. Despite the benefits, exploring the early-stage design space of WSCs for LLMs is a crucial yet challenging task due to the enormous and complicated design space, time-consuming evaluation methods, and inefficient exploration strategies. To address these challenges, we propose Theseus, an efficient WSC design space exploration framework for LLMs. We construct the design space of WSCs with various constraints considering the unique characteristics of WSCs. We propose efficient evaluation methodologies for large-scale NoC-based WSCs and introduce multi-fidelity Bayesian optimization to efficiently explore the design space. Evaluation results demonstrate the efficiency of Theseus that the searched Pareto optimal results outperform GPU cluster and existing WSC designs by up to 62.8\%/73.7\% in performance and 38.6\%/42.4\% in power consumption for LLM training, while improving up to 23.2$\times$ and 15.7$\times$ for the performance and power of inference tasks. Furthermore, we conduct case studies to address the design tradeoffs in WSCs and provide insights to facilitate WSC designs for LLMs.

In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and engineering applications. The computational challenges we address with the proposed methodology are: (i) the need for repeated evaluations of expensive forward models; (ii) the potential existence of multiple modes; and (iii) the fact that gradient of, or adjoint solver for, the forward model might not be feasible. While existing Bayesian inference methods meet some of these challenges individually, we propose a framework that tackles all three systematically. Our approach builds upon the Fisher-Rao gradient flow in probability space, yielding a dynamical system for probability densities that converges towards the target distribution at a uniform exponential rate. This rapid convergence is advantageous for the computational burden outlined in (i). We apply Gaussian mixture approximations with operator splitting techniques to simulate the flow numerically; the resulting approximation can capture multiple modes thus addressing (ii). Furthermore, we employ the Kalman methodology to facilitate a derivative-free update of these Gaussian components and their respective weights, addressing the issue in (iii). The proposed methodology results in an efficient derivative-free sampler flexible enough to handle multi-modal distributions: Gaussian Mixture Kalman Inversion (GMKI). The effectiveness of GMKI is demonstrated both theoretically and numerically in several experiments with multimodal target distributions, including proof-of-concept and two-dimensional examples, as well as a large-scale application: recovering the Navier-Stokes initial condition from solution data at positive times., Comment: 42 pages, 10 figures

Previous foundation models for retinal images were pre-trained with limited disease categories and knowledge base. Here we introduce RetiZero, a vision-language foundation model that leverages knowledge from over 400 fundus diseases. To RetiZero's pre-training, we compiled 341,896 fundus images paired with text descriptions, sourced from public datasets, ophthalmic literature, and online resources, encompassing a diverse range of diseases across multiple ethnicities and countries. RetiZero exhibits superior performance in several downstream tasks, including zero-shot disease recognition, image-to-image retrieval, and internal- and cross-domain disease identification. In zero-shot scenarios, RetiZero achieves Top5 accuracy scores of 0.8430 for 15 fundus diseases and 0.7561 for 52 fundus diseases. For image retrieval, it achieves Top5 scores of 0.9500 and 0.8860 for the same disease sets, respectively. Clinical evaluations show that RetiZero's Top3 zero-shot performance surpasses the average of 19 ophthalmologists from Singapore, China and the United States. Furthermore, RetiZero significantly enhances clinicians' accuracy in diagnosing fundus disease. These findings underscore the value of integrating the RetiZero foundation model into clinical settings, where a variety of fundus diseases are encountered.

Although Retrieval-Augmented Large Language Models (RALMs) demonstrate their superiority in terms of factuality, they do not consistently outperform the original retrieval-free Language Models (LMs). Our experiments reveal that this example-level performance inconsistency exists not only between retrieval-augmented and retrieval-free LM but also among different retrievers. To understand this phenomenon, we investigate the degeneration behavior of RALMs and theoretically decompose it into four categories. Further analysis based on our decomposition reveals that the innate difference in knowledge sources and the unpredictable degeneration of the reader model contribute most to the inconsistency. Drawing from our analysis, we introduce Ensemble of Retrievers (EoR), a trainable framework that can adaptively retrieve from different knowledge sources and effectively decrease unpredictable reader errors. Our experiments on Open Domain Question Answering show that EoR substantially improves performance over the RALM with a single retriever by considerably reducing inconsistent behaviors., Comment: ACL 2024 (findings)

Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on approximations in the generative process to be generic to different inverse problems, leading to inaccurate sample distributions that deviate from the target posterior defined within the Bayesian framework. To harness the generative power of DMs while avoiding such approximations, we propose a Markov chain Monte Carlo algorithm that performs posterior sampling for general inverse problems by reducing it to sampling the posterior of a Gaussian denoising problem. Crucially, we leverage a general DM formulation as a unified interface that allows for rigorously solving the denoising problem with a range of state-of-the-art DMs. We demonstrate the effectiveness of the proposed method on six inverse problems (three linear and three nonlinear), including a real-world black hole imaging problem. Experimental results indicate that our proposed method offers more accurate reconstructions and posterior estimation compared to existing DM-based imaging inverse methods., Comment: Accepted to NeurIPS 2024

The article presents a systematic study of the problem of conditioning a Gaussian random variable $\xi$ on nonlinear observations of the form $F \circ \phi(\xi)$ where $\phi: \mathcal{X} \to \mathbb{R}^N$ is a bounded linear operator and $F$ is nonlinear. Such problems arise in the context of Bayesian inference and recent machine learning-inspired PDE solvers. We give a representer theorem for the conditioned random variable $\xi \mid F\circ \phi(\xi)$, stating that it decomposes as the sum of an infinite-dimensional Gaussian (which is identified analytically) as well as a finite-dimensional non-Gaussian measure. We also introduce a novel notion of the mode of a conditional measure by taking the limit of the natural relaxation of the problem, to which we can apply the existing notion of maximum a posteriori estimators of posterior measures. Finally, we introduce a variant of the Laplace approximation for the efficient simulation of the aforementioned conditioned Gaussian random variables towards uncertainty quantification.

We present new complete Calabi-Yau metrics defined on the complement of a smooth anticanonical divisor with ample normal bundle, approaching the Calabi model space at a polynomial rate. Moreover, we establish the uniqueness of this type of Calabi-Yau metric within a fixed cohomology class.

The Event Horizon Telescope (EHT) has revolutionized our ability to study black holes by providing unprecedented spatial resolution and unveiling horizon-scale details. With advancements leading to the next-generation EHT, there is potential to probe even deeper into the black hole's dark region, especially the inner shadow characterized by low-intensity foreground emissions from the jet, thanks to a significant enhancement in dynamic range by two orders of magnitude. We demonstrate how such enhanced observations could transform supermassive black holes into powerful probes for detecting annihilating dark matter, which can form a dense profile in the vicinity of supermassive black holes, by examining the morphology of the black hole image., Comment: 19 pages, 6 figures, references updated

Large garages are ubiquitous yet intricate scenes that present unique challenges due to their monotonous colors, repetitive patterns, reflective surfaces, and transparent vehicle glass. Conventional Structure from Motion (SfM) methods for camera pose estimation and 3D reconstruction often fail in these environments due to poor correspondence construction. To address these challenges, we introduce LetsGo, a LiDAR-assisted Gaussian splatting framework for large-scale garage modeling and rendering. We develop a handheld scanner, Polar, equipped with IMU, LiDAR, and a fisheye camera, to facilitate accurate data acquisition. Using this Polar device, we present the GarageWorld dataset, consisting of eight expansive garage scenes with diverse geometric structures, which will be made publicly available for further research. Our approach demonstrates that LiDAR point clouds collected by the Polar device significantly enhance a suite of 3D Gaussian splatting algorithms for garage scene modeling and rendering. We introduce a novel depth regularizer that effectively eliminates floating artifacts in rendered images. Additionally, we propose a multi-resolution 3D Gaussian representation designed for Level-of-Detail (LOD) rendering. This includes adapted scaling factors for individual levels and a random-resolution-level training scheme to optimize the Gaussians across different resolutions. This representation enables efficient rendering of large-scale garage scenes on lightweight devices via a web-based renderer. Experimental results on our GarageWorld dataset, as well as on ScanNet++ and KITTI-360, demonstrate the superiority of our method in terms of rendering quality and resource efficiency., Comment: Project Page: https://zhaofuq.github.io/LetsGo/

Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial differential equations over time. This work shows that sequential-in-time training methods can be understood broadly as either optimize-then-discretize (OtD) or discretize-then-optimize (DtO) schemes, which are well known concepts in numerical analysis. The unifying perspective leads to novel stability and a posteriori error analysis results that provide insights into theoretical and numerical aspects that are inherent to either OtD or DtO schemes such as the tangent space collapse phenomenon, which is a form of over-fitting. Additionally, the unified perspective facilitates establishing connections between variants of sequential-in-time training methods, which is demonstrated by identifying natural gradient descent methods on energy functionals as OtD schemes applied to the corresponding gradient flows.

We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling. Given observations of the system state over time, we formulate the forecasting problem as sampling from the conditional distribution of the future system state given its current state. To this end, we leverage the framework of stochastic interpolants, which facilitates the construction of a generative model between an arbitrary base distribution and the target. We design a fictitious, non-physical stochastic dynamics that takes as initial condition the current system state and produces as output a sample from the target conditional distribution in finite time and without bias. This process therefore maps a point mass centered at the current state onto a probabilistic ensemble of forecasts. We prove that the drift coefficient entering the stochastic differential equation (SDE) achieving this task is non-singular, and that it can be learned efficiently by square loss regression over the time-series data. We show that the drift and the diffusion coefficients of this SDE can be adjusted after training, and that a specific choice that minimizes the impact of the estimation error gives a F\"ollmer process. We highlight the utility of our approach on several complex, high-dimensional forecasting problems, including stochastically forced Navier-Stokes and video prediction on the KTH and CLEVRER datasets.

Multiobjective optimization (MOO) is prevalent in numerous applications, in which a Pareto front (PF) is constructed to display optima under various preferences. Previous methods commonly utilize the set of Pareto objectives (particles on the PF) to represent the entire PF. However, the empirical distribution of the Pareto objectives on the PF is rarely studied, which implicitly impedes the generation of diverse and representative Pareto objectives in previous methods. To bridge the gap, we suggest in this paper constructing \emph{uniformly distributed} Pareto objectives on the PF, so as to alleviate the limited diversity found in previous MOO approaches. We are the first to formally define the concept of ``uniformity" for an MOO problem. We optimize the maximal minimal distances on the Pareto front using a neural network, resulting in both asymptotically and non-asymptotically uniform Pareto objectives. Our proposed method is validated through experiments on real-world and synthetic problems, which demonstrates the efficacy in generating high-quality uniform Pareto objectives and the encouraging performance exceeding existing state-of-the-art methods. The detailed model implementation and the code are scheduled to be open-sourced upon publication.