arXiv subjects
Publications and source records attributed to Yuanyuan Li.
In this paper, we investigate the optimal transport problem when the source is a non-convex polygonal domain in $\mathbb{R}^2$. We show a global $W^{2,1+ε}$ estimate for potentials of optimal transport. Our method applies to a more general class of domains.
Visual Generative AI models have demonstrated remarkable capability in generating high-quality images from user inputs like text prompts. However, because these models have billions of parameters, they risk memorizing certain parts of the training data and reproducing the memorized content. Memorization often raises concerns about safety of such models -- usually involving intellectual property (IP) infringement risk -- and deters their large scale adoption. In this paper, we evaluate the effectiveness of prompt engineering techniques in reducing memorization risk in image generation. Our findings demonstrate the effectiveness of prompt engineering in reducing the similarity between generated images and the training data of diffusion models, while maintaining relevance and aestheticity of the generated output.
Large scale text-to-image generation models can memorize and reproduce their training dataset. Since the training dataset often contains copyrighted material, reproduction of training dataset poses a copyright infringement risk, which could result in legal liabilities and financial losses for both the AI user and the developer. The current works explores the potential of chain-of-thought and task instruction prompting in reducing copyrighted content generation. To this end, we present a formulation that combines these two techniques with two other copyright mitigation strategies: a) negative prompting, and b) prompt re-writing. We study the generated images in terms their similarity to a copyrighted image and their relevance of the user input. We present numerical experiments on a variety of models and provide insights on the effectiveness of the aforementioned techniques for varying model complexity.
We carry out a post-election analysis of the 2024 U.S. Presidential Election (USPE) using a prediction model derived from the Small Area Estimation (SAE) methodology. With pollster data obtained one week prior to the election day, retrospectively, our SAE-based prediction model can perfectly predict the Electoral College election results in all 44 states where polling data were available. In addition to such desirable prediction accuracy, we introduce the probability of incorrect prediction (PoIP) to rigorously analyze prediction uncertainty. Since the standard bootstrap method appears inadequate for estimating PoIP, we propose a conformal inference method that yields reliable uncertainty quantification. We further investigate potential pollster biases by the means of sensitivity analyses and conclude that swing states are particularly vulnerable to polling bias in the prediction of the 2024 USPE.
Cross-view object geo-localization enables high-precision object localization through cross-view matching, with critical applications in autonomous driving, urban management, and disaster response. However, existing methods rely on keypoint-based positional encoding, which captures only 2D coordinates while neglecting object shape information, resulting in sensitivity to annotation shifts and limited cross-view matching capability. To address these limitations, we propose a mask-based positional encoding scheme that leverages segmentation masks to capture both spatial coordinates and object silhouettes, thereby upgrading the model from "location-aware" to "object-aware." Furthermore, to tackle the challenge of large-span objects (e.g., elongated buildings) in satellite imagery, we design a context enhancement module. This module employs horizontal and vertical strip convolutional kernels to extract long-range contextual features, enhancing feature discrimination among strip-like objects. Integrating MPE and CEM, we present EDGeo, an end-to-end framework for robust cross-view object geo-localization. Extensive experiments on two public datasets (CVOGL and VIGOR-Building) demonstrate that our method achieves state-of-the-art performance, with a 3.39% improvement in localization accuracy under challenging ground-to-satellite scenarios. This work provides a robust positional encoding paradigm and a contextual modeling framework for advancing cross-view geo-localization research.
The $L_p$ chord Minkowski problem was recently introduced by Lutwak, Xi, Yang and Zhang, which seeks to determine the necessary and sufficient conditions for a given finite Borel measure such that it is the $L_p$ chord measure of a convex body. In this paper, we solve the $L_p$ chord Minkowski problem for the super-critical exponents by combining a nonlocal Gauss curvature flow introduced in \cite{HHLW exi} and a topological argument developed in \cite{GLW2022}. Notably, we provide a simplified argument for the topological part.
Quantum repeaters incorporating quantum memory play a pivotal role in mitigating loss in transmitted quantum information (photons) due to link attenuation over a long-distance quantum communication network. However, limited availability of available storage in such quantum repeaters and the impact on the time spent within the memory unit presents a trade-off between quantum information fidelity (a metric that quantifies the degree of similarity between a pair of quantum states) and qubit transmission rate. Thus, effective management of storage time for qubits becomes a key consideration in multi-hop quantum networks. To address these challenges, we propose Q-REACH, which leverages queuing theory in caching networks to tune qubit transmission rate while considering fidelity as the cost metric. Our contributions in this work include (i) utilizing a method of repetition that encodes and broadcasts multiple qubits through different quantum paths, (ii) analytically estimating the time spent by these emitted qubits as a function of the number of paths and repeaters, as well as memory units within a repeater, and (iii) formulating optimization problem that leverages this analysis to correct the transmitted logic qubit and select the optimum repetition rate at the transmitter.
Non-classical light sources emitting bundles of N-photons with strong correlation represent versatile resources of interdisciplinary importance with applications ranging from fundamental tests of quantum mechanics to quantum information processing. Yet, high-order correlations, gN(0),quantifying photon correlation, are still limited to hundreds. Here, we report the generation of a super-bunching light source in photonic crystal fiber with g2(0) reaching 5.86*104 and g5(0) up to 2.72*108, through measuring its photon number probability distributions. under giant g2(0) values, the super-bunching light source presents upturned-tail photon distributions and ubiquitous extreme multi-photon events, where 31 photons from a single light pulse at a mean of 1.99*10-4 photons per pulse have been determined. The probability of this extreme event has been enhanced by 10139 folds compared to a coherent laser with Poissonian distribution. By varying the power of the pumping laser, both photon number distributions and corresponding high-order correlations of this light source can be substantially tailored from Poissonian to super-bunching distributions. These phenomena are attributed to the synchronized nonlinear interactions in photonic crystal fibers pumping by bright squeezed light, and the theoretical simulations agree well with the experimental results. Our research showcases the ability to achieve non-classical light sources with giant high-order correlations and extreme multi-photon events, paving the way for high-order correlation imaging, extreme nonlinear optical effects, quantum information processing, and exploring light-matter interactions with multi-photon physics.
Full waveform inversion (FWI) is an advanced seismic inversion technique for quantitatively estimating subsurface properties. However, with FWI, it is hard to converge to a geologically-realistic subsurface model. Thus, we propose a DiffusionInv approach by integrating a pretrained diffusion model representation of the velocity into FWI within a Bayesian framework. We first train the diffusion model on realistic and expected velocity model samples, preferably prepared based on our geological knowledge of the subsurface, to learn their prior distribution. Once this pretraining is complete, we fine-tune the neural network parameters of the diffusion model by using an L2 norm of data misfit between simulated and observed seismic data as a loss function. This process enables the model to elegantly learn the posterior distribution of velocity models given seismic observations starting from the previously learned prior distribution. The approximate representation of the posterior probability distribution provides valuable insights into the inversion uncertainty for physics-constrained FWI given the seismic data and prior model information. Compared to regularized FWI methods, the diffusion model under a probabilistic framework allows for a more adaptable integration of prior information into FWI, thus mitigating the multi-solution issue and enhancing the reliability of the inversion result. Compared to data-driven FWI methods, the integration of physical constraints in DiffusionInv enhances its ability to generalize across diverse seismic scenarios. The test results in the Hess and Otway examples demonstrate that the DiffusionInv method is capable of recovering the velocity model with high resolution by incorporating the prior model information. The estimated posterior probability distribution helps us understand the inversion uncertainty.
Superbunching effect with second-order correlations larger than 2, $g^{(2)}(0)>2$, indicating the N-photon bundles emission and strong correlation among photons, has a broad range of fascinating applications in quantum illumination, communication, and computation. However, the on-demand manipulation of the superbunching effect in colloidal quantum dots (QDs) under pulsed excitation, which is beneficial to integrated photonics and lab-on-a-chip quantum devices, is still challenging. Here, we disclosed the evolution of $g^{(2)}(0)$ with the parameters of colloidal QDs by Mento Carlo simulations and performed second-order correlation measurements on CdSe/ZnS core/shell QDs under both continuous wave (CW) and pulsed lasers. The photon statistics of a single colloidal QD have been substantially tailored from sub-Poissonian distribution $g^{(2)}(0) <1$) to superbunching emission, with the maximum $g^{(2)}(0)$ reaching 69 and 20 under CW and pulsed excitation, respectively. We have achieved correlated biphoton imaging (CPI), employing the coincidence of the biexciton and bright exciton in one laser pulse, with the stray light and background noise up to 53 times stronger than PL emission of single colloidal QDs. By modulating the PL intensity, the Fourier-domain CPI with reasonably good contrast has been determined, with the stray light noise up to 107 times stronger than PL emission and 75600 times stronger than the counts of biphotons. Our noise-resistance CPI may enable laboratory-based quantum imaging to be applied to real-world applications with the highly desired suppression of strong background noise and stray light.
Machine Learning models are being extensively used in safety critical applications where errors from these models could cause harm to the user. Such risks are amplified when multiple machine learning models, which are deployed concurrently, interact and make errors simultaneously. This paper explores three scenarios where error correlations between multiple models arise, resulting in such aggregated risks. Using real-world data, we simulate these scenarios and quantify the correlations in errors of different models. Our findings indicate that aggregated risks are substantial, particularly when models share similar algorithms, training datasets, or foundational models. Overall, we observe that correlations across models are pervasive and likely to intensify with increased reliance on foundational models and widely used public datasets, highlighting the need for effective mitigation strategies to address these challenges.
We investigate a Tikhonov regularization scheme specifically tailored for shallow neural networks within the context of solving a classic inverse problem: approximating an unknown function and its derivatives within a unit cubic domain based on noisy measurements. The proposed Tikhonov regularization scheme incorporates a penalty term that takes three distinct yet intricately related network (semi)norms: the extended Barron norm, the variation norm, and the Radon-BV seminorm. These choices of the penalty term are contingent upon the specific architecture of the neural network being utilized. We establish the connection between various network norms and particularly trace the dependence of the dimensionality index, aiming to deepen our understanding of how these norms interplay with each other. We revisit the universality of function approximation through various norms, establish rigorous error-bound analysis for the Tikhonov regularization scheme, and explicitly elucidate the dependency of the dimensionality index, providing a clearer understanding of how the dimensionality affects the approximation performance and how one designs a neural network with diverse approximating tasks.
Advanced classification algorithms are being increasingly used in safety-critical applications like health-care, engineering, etc. In such applications, miss-classifications made by ML algorithms can result in substantial financial or health-related losses. To better anticipate and prepare for such losses, the algorithm user seeks an estimate for the probability that the algorithm miss-classifies a sample. We refer to this task as the risk-assessment. For a variety of models and datasets, we numerically analyze the performance of different methods in solving the risk-assessment problem. We consider two solution strategies: a) calibration techniques that calibrate the output probabilities of classification models to provide accurate probability outputs; and b) a novel approach based upon the prediction interval generation technique of conformal prediction. Our conformal prediction based approach is model and data-distribution agnostic, simple to implement, and provides reasonable results for a variety of use-cases. We compare the different methods on a broad variety of models and datasets.
In recent work it has been shown that determining a feedforward ReLU neural network to within high uniform accuracy from point samples suffers from the curse of dimensionality in terms of the number of samples needed. As a consequence, feedforward ReLU neural networks are of limited use for applications where guaranteed high uniform accuracy is required. We consider the question of whether the sampling complexity can be improved by restricting the specific neural network architecture. To this end, we investigate invertible residual neural networks which are foundational architectures in deep learning and are widely employed in models that power modern generative methods. Our main result shows that the residual neural network architecture and invertibility do not help overcome the complexity barriers encountered with simpler feedforward architectures. Specifically, we demonstrate that the computational complexity of approximating invertible residual neural networks from point samples in the uniform norm suffers from the curse of dimensionality. Similar results are established for invertible convolutional Residual neural networks.
Full waveform inversion (FWI) is capable of reconstructing subsurface properties with high resolution from seismic data. However, conventional FWI faces challenges such as cycle-skipping and high computational costs. Recently, deep learning method has emerged as a promising solution for efficient velocity estimation. We develop DiffusionVel, a data-driven technique based on the state-of-the-art generative diffusion models (GDMs) with integration of multiple information including seismic data, background velocity, geological knowledge, and well logs. We use two separate conditional GDMs, namely the seismic-data GDM and the well-log GDM, and an unconditional GDM, i.e., the geology-oriented GDM, to adapt the generated velocity model to the constraints of seismic data, well logs, and prior geological knowledge, respectively. Besides, the background velocity can be incorporated into the generated velocity model with a low-pass filter. The generation of these GDM are then combined together with a weighted summation in the sampling process. We can flexibly control the constraints from each information by adjusting the weighting factors. We make a comprehensive comparison between the proposed DiffusionVel and three previously-developed methods including conventional FWI, InversionNet, and VelocityGAN by using the OpenFWI datasets and the Hess VTI model example. The test results demonstrate that the proposed DiffusionVel method predicts the velocity model reasonably by integrating multiple information effectively.
Same-day deliveries (SDD) have become a new standard to satisfy the "instant gratification" of online customers. Despite the existing powerful technologies deployed in last-mile delivery, SDD services face new decision-making challenges related to the trade-off between delivery cost and time. In addition, new challenges related to environmental issues, customer satisfaction, or fairness arise. Researchers have explored various approaches to face these challenges in the context of SDD, where stochastic and dynamic data uncertainty plays a fundamental role. In this paper, we carefully review the emerging routing problems and solutions proposed in the existing literature for SDD services. We survey papers related to how to deal with dynamic arrival times of orders, how to allocate time slots to deliveries, how to select the right delivery options, how to design pickup and delivery routes, or how to partition the delivery areas and decide the composition of the fleet. We also formulate and compare models for representative problems elaborating on the pros and cons that might guide practitioners in choosing the most appropriate objectives and constraints. Finally, we sketch challenges and identify future research directions.
In this paper, we study a sequential decision-making problem faced by e-commerce carriers related to when to send out a vehicle from the central depot to serve customer requests, and in which order to provide the service, under the assumption that the time at which parcels arrive at the depot is stochastic and dynamic. The objective is to maximize the expected number of parcels that can be delivered during service hours. We propose two reinforcement learning (RL) approaches for solving this problem. These approaches rely on a look-ahead strategy in which future release dates are sampled in a Monte-Carlo fashion and a batch approach is used to approximate future routes. Both RL approaches are based on value function approximation - one combines it with a consensus function (VFA-CF) and the other one with a two-stage stochastic integer linear programming model (VFA-2S). VFA-CF and VFA-2S do not need extensive training as they are based on very few hyper-parameters and make good use of integer linear programming (ILP) and branch-and-cut-based exact methods to improve the quality of decisions. We also establish sufficient conditions for partial characterization of optimal policy and integrate them into VFA-CF/VFA-2S. In an empirical study, we conduct a competitive analysis using upper bounds with perfect information. We also show that VFA-CF and VFA-2S greatly outperform alternative approaches that: 1) do not rely on future information, or 2) are based on point estimation of future information, or 3) employ heuristics rather than exact methods, or 4) use exact evaluations of future rewards.
Inferring networks from observed time series data presents a clear glimpse into the interconnections among nodes. Network inference models, when dealing with real-world open cases, especially in the presence of observational noise, experience a sharp decline in performance, significantly undermining their practical applicability. We find that in real-world scenarios, noisy samples cause parameter updates in network inference models to deviate from the correct direction, leading to a degradation in performance. Here, we present an elegant and efficient model-agnostic framework tailored to amplify the capabilities of model-based and model-free network inference models for real-world cases. Extensive experiments across nonlinear dynamics, evolutionary games, and epidemic spreading, showcases substantial performance augmentation under varied noise types, particularly thriving in scenarios enriched with clean samples.