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World models play a crucial role in decision-making within embodied environments, enabling cost-free explorations that would otherwise be expensive in the real world. To facilitate effective decision-making, world models must be equipped with strong generalizability to support faithful imagination in out-of-distribution (OOD) regions and provide reliable uncertainty estimation to assess the credibility of the simulated experiences, both of which present significant challenges for prior scalable approaches. This paper introduces WHALE, a framework for learning generalizable world models, consisting of two key techniques: behavior-conditioning and retracing-rollout. Behavior-conditioning addresses the policy distribution shift, one of the primary sources of the world model generalization error, while retracing-rollout enables efficient uncertainty estimation without the necessity of model ensembles. These techniques are universal and can be combined with any neural network architecture for world model learning. Incorporating these two techniques, we present Whale-ST, a scalable spatial-temporal transformer-based world model with enhanced generalizability. We demonstrate the superiority of Whale-ST in simulation tasks by evaluating both value estimation accuracy and video generation fidelity. Additionally, we examine the effectiveness of our uncertainty estimation technique, which enhances model-based policy optimization in fully offline scenarios. Furthermore, we propose Whale-X, a 414M parameter world model trained on 970K trajectories from Open X-Embodiment datasets. We show that Whale-X exhibits promising scalability and strong generalizability in real-world manipulation scenarios using minimal demonstrations.

Integrating textual data with imaging in liver tumor segmentation is essential for enhancing diagnostic accuracy. However, current multi-modal medical datasets offer only general text annotations, lacking lesion-specific details critical for extracting nuanced features, especially for fine-grained segmentation of tumor boundaries and small lesions. To address these limitations, we developed datasets with lesion-specific text annotations for liver tumors and introduced the TexLiverNet model. TexLiverNet employs an agent-based cross-attention module that integrates text features efficiently with visual features, significantly reducing computational costs. Additionally, enhanced spatial and adaptive frequency domain perception is proposed to precisely delineate lesion boundaries, reduce background interference, and recover fine details in small lesions. Comprehensive evaluations on public and private datasets demonstrate that TexLiverNet achieves superior performance compared to current state-of-the-art methods.

We study episodic linear mixture MDPs with the unknown transition and adversarial rewards under full-information feedback, employing dynamic regret as the performance measure. We start with in-depth analyses of the strengths and limitations of the two most popular methods: occupancy-measure-based and policy-based methods. We observe that while the occupancy-measure-based method is effective in addressing non-stationary environments, it encounters difficulties with the unknown transition. In contrast, the policy-based method can deal with the unknown transition effectively but faces challenges in handling non-stationary environments. Building on this, we propose a novel algorithm that combines the benefits of both methods. Specifically, it employs (i) an occupancy-measure-based global optimization with a two-layer structure to handle non-stationary environments; and (ii) a policy-based variance-aware value-targeted regression to tackle the unknown transition. We bridge these two parts by a novel conversion. Our algorithm enjoys an $\widetilde{\mathcal{O}}(d \sqrt{H^3 K} + \sqrt{HK(H + \bar{P}_K)})$ dynamic regret, where $d$ is the feature dimension, $H$ is the episode length, $K$ is the number of episodes, $\bar{P}_K$ is the non-stationarity measure. We show it is minimax optimal up to logarithmic factors by establishing a matching lower bound. To the best of our knowledge, this is the first work that achieves near-optimal dynamic regret for adversarial linear mixture MDPs with the unknown transition without prior knowledge of the non-stationarity measure., Comment: NeurIPS 2024

The dynamics of colloid-size particles trapped at a liquid interface is an extensively studied problem owing to its relevance to a wide range of engineering applications. Here we investigate the impact of interfacial deformations on the hydrodynamic force and torque exerted on a spherical particle with surface slip moving along a gas-liquid interface. Following a two-parameter asymptotic modeling approach, we perturb the interface from its planar state and apply the Lorentz reciprocal theorem to the zeroth and first-order approximations to analytically calculate the drag and torque on the particle. This allows us to explicitly account for the effect of physical parameters like the three-phase contact angle, the Bond number, and the slip coefficient on the particle motion. In addition, we study the interactions between two translating and rotating particles at a large separation. The interaction forces and torques exerted by the flow-induced deformations are calculated via the linear superposition approximation, where the interaction forces are identified as dipolar in terms of the azimuthal angle., Comment: 14 Figures

In this work, we investigate the generalized bathtub model, a nonlocal transport equation for describing network trip flows served by privately operated vehicles inside a road network. First, we establish the well-posedness of the mathematical model for both classical and weak solutions. Then we consider an inverse source problem of the model with model parameters embodying particular traffic situations. We establish a conditional Lipschitz stability of the inverse problem under suitable a priori regularity assumption on the problem data, using a Volterra integral formulation of the problem. Inspired by the analysis, we develop an easy-to-implement numerical method for reconstructing the flow rates, and provide the error analysis of the method. Further we present several numerical experiments to complement the theoretical analysis., Comment: 25 pages, 3 figures

Detecting mid-infrared (MIR) radiation has significant astronomical applications, although limited by unsatisfactory MIR detectors. Here we reported on the realization of a MIR up-conversion interferometer based on synthetic long base-line (SLBL) in the laboratory. The experimental system consisted of an interferometer and subsequent up-conversion detection part of mid-infrared signal, which streamlined the structure and enhanced the reliability of the system. By using a tungsten filament lamp as an imitated star, we not only achieved the single target angle resolution of 1.10 times 10^(-4) rad, but also obtained the field angle resolution of 3.0 times 10^(-4) rad of double star targets. The angular resolution is in inverse proportion to the length of baseline. The maximum length of simulated baseline in the laboratory is about 3cm. In a Keck Interferometer (KI) liked program, the base line can reach up to 85m leading to a corresponding angular resolution of 3.0 times 10^(-9) rad (about 1.8mas). The study will offer potential benefits in extending the usage of mid-infrared light in astronomical exploration., Comment: 11 pages, 4 figures. Accepted by Physics Review D

Vision-language models (VLMs) like CLIP have demonstrated impressive zero-shot ability in image classification tasks by aligning text and images but suffer inferior performance compared with task-specific expert models. On the contrary, expert models excel in their specialized domains but lack zero-shot ability for new tasks. How to obtain both the high performance of expert models and zero-shot ability is an important research direction. In this paper, we attempt to demonstrate that by constructing a model hub and aligning models with their functionalities using model labels, new tasks can be solved in a zero-shot manner by effectively selecting and reusing models in the hub. We introduce a novel paradigm, Model Label Learning (MLL), which bridges the gap between models and their functionalities through a Semantic Directed Acyclic Graph (SDAG) and leverages an algorithm, Classification Head Combination Optimization (CHCO), to select capable models for new tasks. Compared with the foundation model paradigm, it is less costly and more scalable, i.e., the zero-shot ability grows with the sizes of the model hub. Experiments on seven real-world datasets validate the effectiveness and efficiency of MLL, demonstrating that expert models can be effectively reused for zero-shot tasks. Our code will be released publicly.

The inverse problem of recovering point sources represents an important class of applied inverse problems. However, there is still a lack of neural network-based methods for point source identification, mainly due to the inherent solution singularity. In this work, we develop a novel algorithm to identify point sources, utilizing a neural network combined with a singularity enrichment technique. We employ the fundamental solution and neural networks to represent the singular and regular parts, respectively, and then minimize an empirical loss involving the intensities and locations of the unknown point sources, as well as the parameters of the neural network. Moreover, by combining the conditional stability argument of the inverse problem with the generalization error of the empirical loss, we conduct a rigorous error analysis of the algorithm. We demonstrate the effectiveness of the method with several challenging experiments., Comment: 22 pages

Gradient-variation online learning aims to achieve regret guarantees that scale with variations in the gradients of online functions, which has been shown to be crucial for attaining fast convergence in games and robustness in stochastic optimization, hence receiving increased attention. Existing results often require the smoothness condition by imposing a fixed bound on gradient Lipschitzness, which may be unrealistic in practice. Recent efforts in neural network optimization suggest a generalized smoothness condition, allowing smoothness to correlate with gradient norms. In this paper, we systematically study gradient-variation online learning under generalized smoothness. We extend the classic optimistic mirror descent algorithm to derive gradient-variation regret by analyzing stability over the optimization trajectory and exploiting smoothness locally. Then, we explore universal online learning, designing a single algorithm with the optimal gradient-variation regrets for convex and strongly convex functions simultaneously, without requiring prior knowledge of curvature. This algorithm adopts a two-layer structure with a meta-algorithm running over a group of base-learners. To ensure favorable guarantees, we design a new Lipschitz-adaptive meta-algorithm, capable of handling potentially unbounded gradients while ensuring a second-order bound to effectively ensemble the base-learners. Finally, we provide the applications for fast-rate convergence in games and stochastic extended adversarial optimization., Comment: NeurIPS 2024

Due to the high noise caused by solar background radiation, the existing satellite-based free-space quantum key distribution (QKD) experiments are mainly carried out at night, hindering the establishment of a practical all-day real-time global-scale quantum network. Given that the 3-5 {\mu}m mid-infrared (MIR) band has extremely low solar background radiation and strong scattering resistance, it is one of the ideal bands for free-space quantum communication. Here, firstly, we report on the preparation of a high-quality MIR (3370 nm) and telecom band (1555 nm) two-color polarization-entangled photon source, then we use this source to realize a principle QKD based on free-space and fiber hybrid channels in a laboratory. The theoretical analysis clearly shows that a long-distance QKD over 500 km of free-space and 96 km of fiber hybrid channels can be reached simultaneously. This work represents a significant step toward developing all-day global-scale quantum communication networks., Comment: 24 pages, 9 figures

Polarimetric imaging, a technique that captures the invisible polarization-related properties of given materials, has broad applications from fundamental physics to advanced fields such as target recognition, stress detection, biomedical diagnosis and remote sensing. The introduction of quantum sources into classical imaging systems has demonstrated distinct advantages, yet few studies have explored their combination with polarimetric imaging. In this study, we present a quantum polarimetric imaging system that integrates polarization-entangled photon pairs into a polarizer-sample-compensator-analyzer (PSRA)-type polarimeter. Our system visualizes the birefringence properties of a periodical-distributed anisotropic material under decreasing illumination levels and diverse disturbing light sources. Compared to the classical system, the quantum approach reveals the superior sensitivity and robustness in low-light conditions, particularly useful in biomedical studies where the low illumination and non-destructive detection are urgently needed. The study also highlights the nonlocality of entangled photons in birefringence measurement, indicating the potential of quantum polarimetric system in the remote sensing domain.

In this work, we investigate a quasilinear subdiffusion model which involves a fractional derivative of order $\alpha \in (0,1)$ in time and a nonlinear diffusion coefficient. First, using smoothing properties of solution operators for linear subdiffusion and a perturbation argument, we prove several pointwise-in-time regularity estimates that are useful for numerical analysis. Then we develop a high-order time stepping scheme for solving quasilinear subdiffusion, based on convolution quadrature generated by second-order backward differentiation formula with correction at the first step. Further, we establish that the convergence order of the scheme is $O(\tau^{1+\alpha-\epsilon})$ without imposing any additional assumption on the regularity of the solution. The analysis relies on refined Sobolev regularity of the nonlinear perturbation remainder and smoothing properties of discrete solution operators. Several numerical experiments in two space dimensions show the sharpness of the error estimate., Comment: 21 pages, 1 figure

Identifying causal relations is crucial for a variety of downstream tasks. In additional to observational data, background knowledge (BK), which could be attained from human expertise or experiments, is usually introduced for uncovering causal relations. This raises an open problem that in the presence of latent variables, what causal relations are identifiable from observational data and BK. In this paper, we propose two novel rules for incorporating BK, which offer a new perspective to the open problem. In addition, we show that these rules are applicable in some typical causality tasks, such as determining the set of possible causal effects with observational data. Our rule-based approach enhances the state-of-the-art method by circumventing a process of enumerating block sets that would otherwise take exponential complexity.

We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem. Numerically, we develop an easily implementable iterative algorithm to recover the unknown coefficient, and also derive rigorous error bounds for the discrete reconstruction. These results are attained by using the (discrete) solution theory of direct problems, and applying error estimates that are optimal with respect to problem data regularity. Numerical simulations are provided to demonstrate the theoretical results., Comment: 25 pages

Collaborative Edge Computing (CEC) is an emerging paradigm that collaborates heterogeneous edge devices as a resource pool to compute DNN inference tasks in proximity such as edge video analytics. Nevertheless, as the key knob to improve network utility in CEC, existing works mainly focus on the workload routing strategies among edge devices with the aim of minimizing the routing cost, remaining an open question for joint workload allocation and routing optimization problem from a system perspective. To this end, this paper presents a holistic, learned optimization for CEC towards maximizing the total network utility in an online manner, even though the utility functions of task input rates are unknown a priori. In particular, we characterize the CEC system in a flow model and formulate an online learning problem in a form of cross-layer optimization. We propose a nested-loop algorithm to solve workload allocation and distributed routing iteratively, using the tools of gradient sampling and online mirror descent. To improve the convergence rate over the nested-loop version, we further devise a single-loop algorithm. Rigorous analysis is provided to show its inherent convexity, efficient convergence, as well as algorithmic optimality. Finally, extensive numerical simulations demonstrate the superior performance of our solutions., Comment: Accepted by IEEE/ACM TRANSACTIONS ON NETWORKING (ToN)

Metamorphic testing has become one mainstream technique to address the notorious oracle problem in software testing, thanks to its great successes in revealing real-life bugs in a wide variety of software systems. Metamorphic relations, the core component of metamorphic testing, have continuously attracted research interests from both academia and industry. In the last decade, a rapidly increasing number of studies have been conducted to systematically generate metamorphic relations from various sources and for different application domains. In this article, based on the systematic review on the state of the art for metamorphic relations' generation, we summarize and highlight visions for further advancing the theory and techniques for identifying and constructing metamorphic relations, and discuss potential research trends in related areas., Comment: Accepted by International Workshop on Software Engineering in 2030

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, which can be further improved through few-shot prompting techniques. However, the current evaluation primarily focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing and contradictory conditions, known as ill-defined problems. Our observations suggest that existing few-shot prompting techniques are ineffective in such scenarios, often providing overconfident answers or hallucination. To further study this problem, we develop a benchmark called Problems with Missing and Contradictory conditions (PMC) and introduce two novel metrics to evaluate the performance of few-shot prompting methods in these scenarios. Our analysis using the PMC benchmark reveals a trade-off dilemma between the performance of mathematical reasoning for well-defined problems and the ability to recognize ill-defined problems. To address the challenges posed by PMC, we propose a novel few-shot prompting method called SMT-LIB Prompting (SLP), which utilizes the SMT-LIB language to model the problems instead of solving them directly. Subsequently, a double-check solving strategy checks the satisfiability and uniqueness of the solution and provides final feedback. Extensive experiments demonstrate the superiority of our SLP approach compared to existing few-shot prompting methods when dealing with problems with missing and contradictory conditions. We will open-source our benchmark and code to facilitate future research., Comment: Preprint. arXiv admin note: text overlap with arXiv:2304.09797

Large language models (LLMs), including both proprietary and open-source models, have showcased remarkable capabilities in addressing a wide range of downstream tasks. Nonetheless, when it comes to practical Chinese legal tasks, these models fail to meet the actual requirements. Proprietary models do not ensure data privacy for sensitive legal cases, while open-source models demonstrate unsatisfactory performance due to their lack of legal knowledge. To address this problem, we introduce LawGPT, the first open-source model specifically designed for Chinese legal applications. LawGPT comprises two key components: legal-oriented pre-training and legal supervised fine-tuning. Specifically, we employ large-scale Chinese legal documents for legal-oriented pre-training to incorporate legal domain knowledge. To further improve the model's performance on downstream legal tasks, we create a knowledge-driven instruction dataset for legal supervised fine-tuning. Our experimental results demonstrate that LawGPT outperforms the open-source LLaMA 7B model. Our code and resources are publicly available at https://github.com/pengxiao-song/LaWGPT and have received 5.7K stars on GitHub., Comment: Technical Report

Vision-language models (VLMs), such as CLIP, have demonstrated impressive zero-shot capabilities for various downstream tasks. Their performance can be further enhanced through few-shot prompt tuning methods. However, current studies evaluate the performance of learned prompts separately on base and new classes. This evaluation lacks practicality for real-world applications since downstream tasks cannot determine whether the data belongs to base or new classes in advance. In this paper, we explore a problem setting called Open-world Prompt Tuning (OPT), which involves tuning prompts on base classes and evaluating on a combination of base and new classes. By introducing Decomposed Prompt Tuning framework (DePT), we theoretically demonstrate that OPT can be solved by incorporating out-of-distribution detection into prompt tuning, thereby enhancing the base-to-new discriminability. Based on DePT, we present a novel prompt tuning approach, namely, Decomposed Context Optimization (DeCoOp), which introduces new-class detectors and sub-classifiers to further enhance the base-class and new-class discriminability. Experimental results on 11 benchmark datasets validate the effectiveness of DePT and demonstrate that DeCoOp outperforms current state-of-the-art methods, providing a significant 2% average accuracy improvement., Comment: Accepted by ICML 2024. Code is available at: https://wnjxyk.github.io/DeCoOp

We study a new class of MDPs that employs multinomial logit (MNL) function approximation to ensure valid probability distributions over the state space. Despite its benefits, introducing the non-linear function raises significant challenges in both computational and statistical efficiency. The best-known result of Hwang and Oh [2023] has achieved an $\widetilde{\mathcal{O}}(\kappa^{-1}dH^2\sqrt{K})$ regret, where $\kappa$ is a problem-dependent quantity, $d$ is the feature dimension, $H$ is the episode length, and $K$ is the number of episodes. While this result attains the same rate in $K$ as linear cases, the method requires storing all historical data and suffers from an $\mathcal{O}(K)$ computation cost per episode. Moreover, the quantity $\kappa$ can be exponentially small in the worst case, leading to a significant gap for the regret compared to linear function approximation. In this work, we first address the computational and storage issue by proposing an algorithm that achieves the same regret with only $\mathcal{O}(1)$ cost. Then, we design an enhanced algorithm that leverages local information to enhance statistical efficiency. It not only maintains an $\mathcal{O}(1)$ computation and storage cost per episode but also achieves an improved regret of $\widetilde{O}(dH^2\sqrt{K} + d^2H^2\kappa^{-1})$, nearly closing the gap with linear function approximation. Finally, we establish the first lower bound for MNL function approximation, justifying the optimality of our results in $d$ and $K$., Comment: NeurIPS 2024

With edge intelligence, AI models are increasingly pushed to the edge to serve ubiquitous users. However, due to the drift of model, data, and task, AI model deployed at the edge suffers from degraded accuracy in the inference serving phase. Model retraining handles such drifts by periodically retraining the model with newly arrived data. When colocating model retraining and model inference serving for the same model on resource-limited edge servers, a fundamental challenge arises in balancing the resource allocation for model retraining and inference, aiming to maximize long-term inference accuracy. This problem is particularly difficult due to the underlying mathematical formulation being time-coupled, non-convex, and NP-hard. To address these challenges, we introduce a lightweight and explainable online approximation algorithm, named ORRIC, designed to optimize resource allocation for adaptively balancing the accuracy of model training and inference. The competitive ratio of ORRIC outperforms that of the traditional Inference-Only paradigm, especially when data drift persists for a sufficiently lengthy time. This highlights the advantages and applicable scenarios of colocating model retraining and inference. Notably, ORRIC can be translated into several heuristic algorithms for different resource environments. Experiments conducted in real scenarios validate the effectiveness of ORRIC., Comment: This paper has been accepted by the IEEE INFOCOM 2024 Main Conference

In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting decay behavior of the observation in time, we establish a novel H{\"o}lder type stability estimate for a large terminal time $T$. This is achieved by novel decay estimates of the (fractional) time derivative of the solution. To numerically recover the diffusion coefficient, we employ the standard output least-squares formulation with an $H^1(\Omega)$-seminorm penalty, and discretize the regularized problem by the Galerkin finite element method with continuous piecewise linear finite elements in space and backward Euler convolution quadrature in time. Further, we provide an error analysis of discrete approximations, and prove a convergence rate that matches the stability estimate. The derived $L^2(\Omega)$ error bound depends explicitly on the noise level, regularization parameter and discretization parameter(s), which gives a useful guideline of the \textsl{a priori} choice of discretization parameters with respect to the noise level in practical implementation. The error analysis is achieved using the conditional stability argument and discrete maximum-norm resolvent estimates. Several numerical experiments are also given to illustrate and complement the theoretical analysis., Comment: 22 pages, 2 figures

Deep Neural Network (DNN) inference on serverless functions is gaining prominence due to its potential for substantial budget savings. Existing works on serverless DNN inference solely optimize batching requests from one application with a single Service Level Objective (SLO) on CPU functions. However, production serverless DNN inference traces indicate that the request arrival rate of applications is surprisingly low, which inevitably causes a long batching time and SLO violations. Hence, there is an urgent need for batching multiple DNN inference requests with diverse SLOs (i.e., multi-SLO DNN inference) in serverless platforms. Moreover, the potential performance and cost benefits of deploying heterogeneous (i.e., CPU and GPU) functions for DNN inference have received scant attention. In this paper, we present HarmonyBatch, a cost-efficient resource provisioning framework designed to achieve predictable performance for multi-SLO DNN inference with heterogeneous serverless functions. Specifically, we construct an analytical performance and cost model of DNN inference on both CPU and GPU functions, by explicitly considering the GPU time-slicing scheduling mechanism and request arrival rate distribution. Based on such a model, we devise a two-stage merging strategy in HarmonyBatch to judiciously batch the multi-SLO DNN inference requests into application groups. It aims to minimize the budget of function provisioning for each application group while guaranteeing diverse performance SLOs of inference applications. We have implemented a prototype of HarmonyBatch on Alibaba Cloud Function Compute. Extensive prototype experiments with representative DNN inference workloads demonstrate that HarmonyBatch can provide predictable performance to serverless DNN inference workloads while reducing the monetary cost by up to 82.9% compared to the state-of-the-art methods., Comment: 10 pages, 14 figures, accepted by IWQOS24

Based on the integral field unit (IFU) data from Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, we develop a new method to select galaxies with biconical ionized structures, building a sample of 142 edge-on biconical ionized galaxies. We classify these 142 galaxies into 81 star-forming galaxies, 31 composite galaxies, and 30 AGNs (consisting of 23 Seyferts and 7 LI(N)ERs) according to the {\nii}-BPT diagram. The star-forming bicones have bar-like structures while AGN bicones display hourglass structures, and composite bicones exhibit transitional morphologies between them due to both black hole and star-formation activities. Star-forming bicones have intense star-formation activities in their central regions, and the primary driver of biconical structures is the central star formation rate surface density. The lack of difference in the strength of central black hole activities (traced by dust attenuation corrected {\oiii}$\lambda$5007 luminosity and Eddington ratio) between Seyfert bicones and their control samples can be naturally explained as that the accretion disk and the galactic disk are not necessarily coplanar. Additionally, the biconical galaxies with central LI(N)ER-like line ratios are edge-on disk galaxies that show strong central dust attenuation. The radial gradients of {\ha} surface brightness follow the $r^{-2.35}$ relation, roughly consistent with $r^{-2}$ profile, which is expected in the case of photoionization by a central point-like source. These observations indicate obscured AGNs or AGN echoes as the primary drivers of biconical structures in LI(N)ERs., Comment: 12 pages, 9 figures, 1 table, Accepted for publication in MNRAS

The energy dissipation law and the maximum bound principle are two critical physical properties of the Allen--Cahn equations. While many existing time-stepping methods are known to preserve the energy dissipation law, most apply to a modified form of energy. In this work, we demonstrate that, when the nonlinear term of the Allen--Cahn equation is Lipschitz continuous, a class of arbitrarily high-order exponential time differencing Runge--Kutta (ETDRK) schemes preserve the original energy dissipation property, under a mild step-size constraint. Additionally, we guarantee the Lipschitz condition on the nonlinear term by applying a rescaling post-processing technique, which ensures that the numerical solution unconditionally satisfies the maximum bound principle. Consequently, our proposed schemes maintain both the original energy dissipation law and the maximum bound principle and can achieve arbitrarily high-order accuracy. We also establish an optimal error estimate for the proposed schemes. Some numerical experiments are carried out to verify our theoretical results.

In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the order, and length of the interval) from one pair of lateral Cauchy data. The lateral Cauchy data are given on disjoint sets in time with a single excitation and the measurement is made on a time sequence located outside the support of the excitation. We prove two uniqueness results for different lateral Cauchy data. The analysis is based on the solution representation, analyticity of the observation and a refined version of inverse Sturm-Liouville theory due to Sini [35]. Our results heavily exploit the memory effect of fractional diffusion for the unique recovery of the coefficients in the model. Several numerical experiments are also presented to complement the analysis., Comment: 17 pages, 7 figures

Four wave mixing (FWM) is an important way to generate supercontinuum and frequency combs in the mid-infrared band. Here, we obtain simultaneous synthetic FWM in the visible and mid-infrared bands by cascading quadratic nonlinear processes in a periodically poled lithium niobate crystal (PPLN), which has a 110dB(at 3000nm) higher conversion efficiency than the FWM directly generated by third-order susceptibilities in bulk PPLN crystals. A general model of this process is developed that is in full agreement with the experimental verifications. The frequency difference between the new frequency components can be freely tuned by changing the frequency difference of the dual pump lasers. Furthermore, by increasing the conversion bandwidth and efficiency of the cascaded processes, it is feasible to generate frequency combs in three bands the visible, near-infrared and mid-infrared bands simultaneously through high-order cascaded processes. This work opens up a new avenue toward free-tuning multiband frequency comb generation with multi-octaves frequency spanning, which will have significant applications in fields such as mid-infrared gas sensing, lidar and precision spectroscopy.

We study reinforcement learning with linear function approximation, unknown transition, and adversarial losses in the bandit feedback setting. Specifically, we focus on linear mixture MDPs whose transition kernel is a linear mixture model. We propose a new algorithm that attains an $\widetilde{O}(d\sqrt{HS^3K} + \sqrt{HSAK})$ regret with high probability, where $d$ is the dimension of feature mappings, $S$ is the size of state space, $A$ is the size of action space, $H$ is the episode length and $K$ is the number of episodes. Our result strictly improves the previous best-known $\widetilde{O}(dS^2 \sqrt{K} + \sqrt{HSAK})$ result in Zhao et al. (2023a) since $H \leq S$ holds by the layered MDP structure. Our advancements are primarily attributed to (i) a new least square estimator for the transition parameter that leverages the visit information of all states, as opposed to only one state in prior work, and (ii) a new self-normalized concentration tailored specifically to handle non-independent noises, originally proposed in the dynamic assortment area and firstly applied in reinforcement learning to handle correlations between different states., Comment: AISTATS 2024

Entanglement enables many promising applications in quantum technology. Devising new generation methods and harnessing entanglement are prerequisites for practical applications. Here we realize a distinct polarization-entangled source by simultaneously achieving type-0 and type-I backward quasi-phase matching (BQPM) through spontaneous parametric down-conversion in a single bulk crystal, which is different from all previous entangled-source configurations. Pumping the crystal with a single polarized beam generates a non-maximally polarization-entangled state, which can be further projected to a maximal Bell state with a pair of Brewster windows. Hong-Ou-Mandel interference experiments are done on polarization-degenerate photon pairs for both type-0 and type-I BQPM processes for the first time. The emitted photons in both processes have a bandwidth as narrow as 15.7 GHz. The high quality of this source is characterized by various methods. The rather simple configuration, narrow bandwidth, and high entanglement quality make the source very promising for many quantum information tasks.

A high-quality narrowband polarization-entangled source in the telecom band is preferred to avoid frequency dispersion for long-distance transmission in optical fibers and to efficiently couple with telecom band quantum memories. Here, we report narrowband, telecom-band, polarization-entangled photon pair generation based on the superposition of single-longitudinal-mode photon pairs from two monolithic nonlinear crystal cavities in a passively stable interferometer based on beam displacers. The photon pairs generated from the cavities exhibit a high coincidence to accidental coincidence ratio of 20000 and a bandwidth below 500 MHz. Two-photon polarization interference, Bell-inequality, and quantum state tomography are performed to indicate the high quality of the entangled source. The current configuration demonstrates greater stability than traditional free space cavity-enhanced polarization-entangled state generation, which is promising for quantum communication applications.

An ellipsometer is a vital precision tool used for measuring optical parameters with wide applications in many fields, including accurate measurements in film thickness, optical constants, structural profiles, etc. However, the precise measurement of photosensitive materials meets huge obstacles because of the excessive input photons, therefore the requirement of enhancing detection accuracy under low incident light intensity is an essential topic in the precision measurement. In this work, by combining a polarization-entangled photon source with a classical transmission-type ellipsometer, the quantum ellipsometer with the PSA (Polarizer-Sample-Analyzer) and the Senarmount method is constructed firstly to measure the phase retardation of the birefringent materials. The experimental results show that the accuracy can reach to nanometer scale at extremely low input intensity, and the stability are within 1% for all specimens tested with a compensator involved. Our work paves the way for precision measurement at low incident light intensity, with potential applications in measuring photosensitive materials, active-biological samples and other remote monitoring scenarios., Comment: 13 pages, 5 figures. This work has been submitted for possible publication

The learnware paradigm proposed by Zhou [2016] aims to enable users to reuse numerous existing well-trained models instead of building machine learning models from scratch, with the hope of solving new user tasks even beyond models' original purposes. In this paradigm, developers worldwide can submit their high-performing models spontaneously to the learnware dock system (formerly known as learnware market) without revealing their training data. Once the dock system accepts the model, it assigns a specification and accommodates the model. This specification allows the model to be adequately identified and assembled to reuse according to future users' needs, even if they have no prior knowledge of the model. This paradigm greatly differs from the current big model direction and it is expected that a learnware dock system housing millions or more high-performing models could offer excellent capabilities for both planned tasks where big models are applicable; and unplanned, specialized, data-sensitive scenarios where big models are not present or applicable. This paper describes Beimingwu, the first open-source learnware dock system providing foundational support for future research of learnware paradigm.The system significantly streamlines the model development for new user tasks, thanks to its integrated architecture and engine design, extensive engineering implementations and optimizations, and the integration of various algorithms for learnware identification and reuse. Notably, this is possible even for users with limited data and minimal expertise in machine learning, without compromising the raw data's security. Beimingwu supports the entire process of learnware paradigm. The system lays the foundation for future research in learnware-related algorithms and systems, and prepares the ground for hosting a vast array of learnwares and establishing a learnware ecosystem.

The numerical analysis of stochastic time fractional evolution equations presents considerable challenges due to the limited regularity of the model caused by the nonlocal operator and the presence of noise. The existing time-stepping methods exhibit a significantly low order convergence rate. In this work, we introduce a smoothing technique and develop the novel high-order schemes for solving the linear stochastic fractional evolution equations driven by integrated additive noise. Our approach involves regularizing the additive noise through an $m$-fold integral-differential calculus, and discretizing the equation using the $k$-step BDF convolution quadrature. This novel method, which we refer to as the ID$m$-BDF$k$ method, is able to achieve higher-order convergence in solving the stochastic models. Our theoretical analysis reveals that the convergence rate of the ID$2$-BDF2 method is $O(\tau^{\alpha + \gamma -1/2})$ for $1< \alpha + \gamma \leq 5/2$, and $O(\tau^{2})$ for $5/2< \alpha + \gamma <3$, where $\alpha \in (1, 2)$ and $\gamma \in (0, 1)$ denote the time fractional order and the order of the integrated noise, respectively. Furthermore, this convergence rate could be improved to $O(\tau^{\alpha + \gamma -1/2})$ for any $\alpha \in (1, 2)$ and $\gamma \in (0, 1)$, if we employ the ID$3$-BDF3 method. The argument could be easily extended to the subdiffusion model with $\alpha \in (0, 1)$. Numerical examples are provided to support and complement the theoretical findings., Comment: 22pages

GPUs have become the \emph{defacto} hardware devices for accelerating Deep Neural Network (DNN) inference workloads. However, the conventional \emph{sequential execution mode of DNN operators} in mainstream deep learning frameworks cannot fully utilize GPU resources, even with the operator fusion enabled, due to the increasing complexity of model structures and a greater diversity of operators. Moreover, the \emph{inadequate operator launch order} in parallelized execution scenarios can lead to GPU resource wastage and unexpected performance interference among operators. In this paper, we propose \emph{Opara}, a resource- and interference-aware DNN \underline{Op}erator \underline{para}llel scheduling framework to accelerate DNN inference on GPUs. Specifically, \emph{Opara} first employs \texttt{CUDA Streams} and \texttt{CUDA Graph} to \emph{parallelize} the execution of multiple operators automatically. To further expedite DNN inference, \emph{Opara} leverages the resource demands of operators to judiciously adjust the operator launch order on GPUs, overlapping the execution of compute-intensive and memory-intensive operators. We implement and open source a prototype of \emph{Opara} based on PyTorch in a \emph{non-intrusive} manner. Extensive prototype experiments with representative DNN and Transformer-based models demonstrate that \emph{Opara} outperforms the default sequential \texttt{CUDA Graph} in PyTorch and the state-of-the-art operator parallelism systems by up to $1.68\times$ and $1.29\times$, respectively, yet with acceptable runtime overhead., Comment: 9 pages,10 figures