arXiv subjects

Fan Chen

Publications and source records attributed to Fan Chen.

At least 109 records · Page 6Linked to original sources

arXiv2023

The $p$-Laplacian overdetermined problem on Riemannian manifolds

In this paper, we study the overdetermined problem for the $p$-Laplacian equation on complete noncompact Riemannian manifolds with nonnegative Ricci curvature. We prove that the regularity results of weak solutions of the $p$-Laplacian equation and obtain some integral identities. As their applications, we give the proof of the $p$-Laplacian overdetermined problem and obtain some well known results such as the Heintze-Karcher inequality and the Soap Bubble Theorem.

math.AP↗

arXiv2023

Programmable phase behavior in fluids with designable interactions

We introduce a method for solving the "inverse" phase equilibria problem: How should the interactions among a collection of molecular species be designed in order to achieve a target phase diagram? Using techniques from convex optimization theory, we show how to solve this problem for phase diagrams containing a large number of components and many coexisting phases with prescribed compositions. We apply our approach to commonly used mean-field models of multicomponent fluids and then use molecular simulations to verify that the designed interactions result in the target phase diagrams. Our approach enables the rational design of "programmable" fluids, such as biopolymer and colloidal mixtures, with complex phase behavior.

cond-mat.soft↗

arXiv2023

ENVIDR: Implicit Differentiable Renderer with Neural Environment Lighting

Recent advances in neural rendering have shown great potential for reconstructing scenes from multiview images. However, accurately representing objects with glossy surfaces remains a challenge for existing methods. In this work, we introduce ENVIDR, a rendering and modeling framework for high-quality rendering and reconstruction of surfaces with challenging specular reflections. To achieve this, we first propose a novel neural renderer with decomposed rendering components to learn the interaction between surface and environment lighting. This renderer is trained using existing physically based renderers and is decoupled from actual scene representations. We then propose an SDF-based neural surface model that leverages this learned neural renderer to represent general scenes. Our model additionally synthesizes indirect illuminations caused by inter-reflections from shiny surfaces by marching surface-reflected rays. We demonstrate that our method outperforms state-of-art methods on challenging shiny scenes, providing high-quality rendering of specular reflections while also enabling material editing and scene relighting.

cs.CV↗

arXiv2023

IQGAN: Robust Quantum Generative Adversarial Network for Image Synthesis On NISQ Devices

In this work, we propose IQGAN, a quantum Generative Adversarial Network (GAN) framework for multiqubit image synthesis that can be efficiently implemented on Noisy Intermediate Scale Quantum (NISQ) devices. We investigate the reasons for the inferior generative performance of current quantum GANs in our preliminary study and conclude that an adjustable input encoder is the key to ensuring high-quality data synthesis. We then propose the IQGAN architecture featuring a trainable multiqubit quantum encoder that effectively embeds classical data into quantum states. Furthermore, we propose a compact quantum generator that significantly reduces the design cost and circuit depth on NISQ devices. Experimental results on both IBM quantum processors and quantum simulators demonstrated that IQGAN outperforms state-of-the-art quantum GANs in qualitative and quantitative evaluation of the generated samples, model convergence, and quantum computing cost.

quant-ph↗

arXiv2023

Co-Driven Recognition of Semantic Consistency via the Fusion of Transformer and HowNet Sememes Knowledge

Semantic consistency recognition aims to detect and judge whether the semantics of two text sentences are consistent with each other. However, the existing methods usually encounter the challenges of synonyms, polysemy and difficulty to understand long text. To solve the above problems, this paper proposes a co-driven semantic consistency recognition method based on the fusion of Transformer and HowNet sememes knowledge. Multi-level encoding of internal sentence structures via data-driven is carried out firstly by Transformer, sememes knowledge base HowNet is introduced for knowledge-driven to model the semantic knowledge association among sentence pairs. Then, interactive attention calculation is carried out utilizing soft-attention and fusion the knowledge with sememes matrix. Finally, bidirectional long short-term memory network (BiLSTM) is exploited to encode the conceptual semantic information and infer the semantic consistency. Experiments are conducted on two financial text matching datasets (BQ, AFQMC) and a cross-lingual adversarial dataset (PAWSX) for paraphrase identification. Compared with lightweight models including DSSM, MwAN, DRCN, and pre-training models such as ERNIE etc., the proposed model can not only improve the accuracy of semantic consistency recognition effectively (by 2.19%, 5.57% and 6.51% compared with the DSSM, MWAN and DRCN models on the BQ dataset), but also reduce the number of model parameters (to about 16M). In addition, driven by the HowNet sememes knowledge, the proposed method is promising to adapt to scenarios with long text.

cs.CL↗

arXiv2023

QTrojan: A Circuit Backdoor Against Quantum Neural Networks

We propose a circuit-level backdoor attack, \textit{QTrojan}, against Quantum Neural Networks (QNNs) in this paper. QTrojan is implemented by few quantum gates inserted into the variational quantum circuit of the victim QNN. QTrojan is much stealthier than a prior Data-Poisoning-based Backdoor Attack (DPBA), since it does not embed any trigger in the inputs of the victim QNN or require the access to original training datasets. Compared to a DPBA, QTrojan improves the clean data accuracy by 21\% and the attack success rate by 19.9\%.

quant-ph↗

arXiv2023

Lower Bounds for Learning in Revealing POMDPs

This paper studies the fundamental limits of reinforcement learning (RL) in the challenging \emph{partially observable} setting. While it is well-established that learning in Partially Observable Markov Decision Processes (POMDPs) requires exponentially many samples in the worst case, a surge of recent work shows that polynomial sample complexities are achievable under the \emph{revealing condition} -- A natural condition that requires the observables to reveal some information about the unobserved latent states. However, the fundamental limits for learning in revealing POMDPs are much less understood, with existing lower bounds being rather preliminary and having substantial gaps from the current best upper bounds. We establish strong PAC and regret lower bounds for learning in revealing POMDPs. Our lower bounds scale polynomially in all relevant problem parameters in a multiplicative fashion, and achieve significantly smaller gaps against the current best upper bounds, providing a solid starting point for future studies. In particular, for \emph{multi-step} revealing POMDPs, we show that (1) the latent state-space dependence is at least $Ω(S^{1.5})$ in the PAC sample complexity, which is notably harder than the $\widetildeΘ(S)$ scaling for fully-observable MDPs; (2) Any polynomial sublinear regret is at least $Ω(T^{2/3})$, suggesting its fundamental difference from the \emph{single-step} case where $\widetilde{O}(\sqrt{T})$ regret is achievable. Technically, our hard instance construction adapts techniques in \emph{distribution testing}, which is new to the RL literature and may be of independent interest.

cs.LG↗

arXiv2023

CryptoLight: An Electro-Optical Accelerator for Fully Homomorphic Encryption

Fully homomorphic encryption (FHE) protects data privacy in cloud computing by enabling computations to directly occur on ciphertexts. To improve the time-consuming FHE operations, we present an electro-optical (EO) FHE accelerator, CryptoLight. Compared to prior FHE accelerators, on average, CryptoLight reduces the latency of various FHE applications by >94.4% and the energy consumption by >95%

cs.CR↗

arXiv2022

Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning

This paper proposes Friedrichs learning as a novel deep learning methodology that can learn the weak solutions of PDEs via a minmax formulation, which transforms the PDE problem into a minimax optimization problem to identify weak solutions. The name "Friedrichs learning" is for highlighting the close relationship between our learning strategy and Friedrichs theory on symmetric systems of PDEs. The weak solution and the test function in the weak formulation are parameterized as deep neural networks in a mesh-free manner, which are alternately updated to approach the optimal solution networks approximating the weak solution and the optimal test function, respectively. Extensive numerical results indicate that our mesh-free method can provide reasonably good solutions to a wide range of PDEs defined on regular and irregular domains in various dimensions, where classical numerical methods such as finite difference methods and finite element methods may be tedious or difficult to be applied.

math.NA↗

arXiv2022

Partially Observable RL with B-Stability: Unified Structural Condition and Sharp Sample-Efficient Algorithms

Partial Observability -- where agents can only observe partial information about the true underlying state of the system -- is ubiquitous in real-world applications of Reinforcement Learning (RL). Theoretically, learning a near-optimal policy under partial observability is known to be hard in the worst case due to an exponential sample complexity lower bound. Recent work has identified several tractable subclasses that are learnable with polynomial samples, such as Partially Observable Markov Decision Processes (POMDPs) with certain revealing or decodability conditions. However, this line of research is still in its infancy, where (1) unified structural conditions enabling sample-efficient learning are lacking; (2) existing sample complexities for known tractable subclasses are far from sharp; and (3) fewer sample-efficient algorithms are available than in fully observable RL. This paper advances all three aspects above for Partially Observable RL in the general setting of Predictive State Representations (PSRs). First, we propose a natural and unified structural condition for PSRs called \emph{B-stability}. B-stable PSRs encompasses the vast majority of known tractable subclasses such as weakly revealing POMDPs, low-rank future-sufficient POMDPs, decodable POMDPs, and regular PSRs. Next, we show that any B-stable PSR can be learned with polynomial samples in relevant problem parameters. When instantiated in the aforementioned subclasses, our sample complexities improve substantially over the current best ones. Finally, our results are achieved by three algorithms simultaneously: Optimistic Maximum Likelihood Estimation, Estimation-to-Decisions, and Model-Based Optimistic Posterior Sampling. The latter two algorithms are new for sample-efficient learning of POMDPs/PSRs.

cs.LG↗

arXiv2022

Robust Quantum Griffiths Singularity at above 1.5 Kelvin in Nitride Thin Films

Quantum Griffiths singularity (QGS), which is closely correlated with the quenched disorder, is characterized by the divergence of the dynamical critical exponent and the presence of activated scaling behavior. Typically such a quantum phenomenon is rather rare and only observed in extremely low temperatures. Here we report the experimental observation of a robust QGS in nitride thin films, NbN, which survives in a rather high temperature range. The electrical transport propertied were measured under the magnetic field up to 12 T. The field induced superconductor-metal transitions were observed with the continuously changed transition points with the decrease of temperature. The dynamical critical exponent based on the conventional power-law scaling reveals a divergent trend when approaching the the low temperature limit. Moreover, the temperature and field dependence of sheet resistance can be described by the activated scaling analysis in the temperature region up to 1.6 K $\leq T \leq$ 4.0 K. We argue that the robustness of QGS in the present system originates from the Pauli paramagnetic effect due to the strong coupling between the magnetic field and the spin degree of freedom.

cond-mat.supr-con↗

arXiv2022

A Unified Primal-Dual Algorithm Framework for Inequality Constrained Problems

In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers many existing algorithms such as PDHG, Chambolle-Pock (CP), GDA, OGDA and linearized ALM, but also guides us to design a new efficient algorithm called Simi-OGDA (SOGDA). Second, it enables us to study the role of the augmented penalty term in the convergence analysis. Interestingly, a properly selected penalty not only improves the numerical performance of the above methods, but also theoretically enables the convergence of algorithms like PDHG and SOGDA. Under properly designed step sizes and penalty term, our unified framework preserves the $\mathcal{O}(1/N)$ ergodic convergence while not requiring any prior knowledge about the magnitude of the optimal Lagrangian multiplier. Linear convergence rate for affine equality constrained problem is also obtained given appropriate conditions. Finally, numerical experiments on linear programming, $\ell_1$ minimization problem, and multi-block basis pursuit problem demonstrate the efficiency of our methods.

math.OC↗

arXiv2022

Independent Natural Policy Gradient Methods for Potential Games: Finite-time Global Convergence with Entropy Regularization

A major challenge in multi-agent systems is that the system complexity grows dramatically with the number of agents as well as the size of their action spaces, which is typical in real world scenarios such as autonomous vehicles, robotic teams, network routing, etc. It is hence in imminent need to design decentralized or independent algorithms where the update of each agent is only based on their local observations without the need of introducing complex communication/coordination mechanisms. In this work, we study the finite-time convergence of independent entropy-regularized natural policy gradient (NPG) methods for potential games, where the difference in an agent's utility function due to unilateral deviation matches exactly that of a common potential function. The proposed entropy-regularized NPG method enables each agent to deploy symmetric, decentralized, and multiplicative updates according to its own payoff. We show that the proposed method converges to the quantal response equilibrium (QRE) -- the equilibrium to the entropy-regularized game -- at a sublinear rate, which is independent of the size of the action space and grows at most sublinearly with the number of agents. Appealingly, the convergence rate further becomes independent with the number of agents for the important special case of identical-interest games, leading to the first method that converges at a dimension-free rate. Our approach can be used as a smoothing technique to find an approximate Nash equilibrium (NE) of the unregularized problem without assuming that stationary policies are isolated.

math.OC↗

arXiv2022

A Near-Optimal Primal-Dual Method for Off-Policy Learning in CMDP

As an important framework for safe Reinforcement Learning, the Constrained Markov Decision Process (CMDP) has been extensively studied in the recent literature. However, despite the rich results under various on-policy learning settings, there still lacks some essential understanding of the offline CMDP problems, in terms of both the algorithm design and the information theoretic sample complexity lower bound. In this paper, we focus on solving the CMDP problems where only offline data are available. By adopting the concept of the single-policy concentrability coefficient $C^*$, we establish an $Ω\left(\frac{\min\left\{|\mathcal{S}||\mathcal{A}|,|\mathcal{S}|+I\right\} C^*}{(1-γ)^3ε^2}\right)$ sample complexity lower bound for the offline CMDP problem, where $I$ stands for the number of constraints. By introducing a simple but novel deviation control mechanism, we propose a near-optimal primal-dual learning algorithm called DPDL. This algorithm provably guarantees zero constraint violation and its sample complexity matches the above lower bound except for an $\tilde{\mathcal{O}}((1-γ)^{-1})$ factor. Comprehensive discussion on how to deal with the unknown constant $C^*$ and the potential asynchronous structure on the offline dataset are also included.

cs.LG↗

arXiv2022

QMLP: An Error-Tolerant Nonlinear Quantum MLP Architecture using Parameterized Two-Qubit Gates

Despite potential quantum supremacy, state-of-the-art quantum neural networks (QNNs) suffer from low inference accuracy. First, the current Noisy Intermediate-Scale Quantum (NISQ) devices with high error rates of 0.001 to 0.01 significantly degrade the accuracy of a QNN. Second, although recently proposed Re-Uploading Units (RUUs) introduce some non-linearity into the QNN circuits, the theory behind it is not fully understood. Furthermore, previous RUUs that repeatedly upload original data can only provide marginal accuracy improvements. Third, current QNN circuit ansatz uses fixed two-qubit gates to enforce maximum entanglement capability, making task-specific entanglement tuning impossible, resulting in poor overall performance. In this paper, we propose a Quantum Multilayer Perceptron (QMLP) architecture featured by error-tolerant input embedding, rich nonlinearity, and enhanced variational circuit ansatz with parameterized two-qubit entangling gates. Compared to prior arts, QMLP increases the inference accuracy on the 10-class MNIST dataset by 10% with 2 times fewer quantum gates and 3 times reduced parameters. Our source code is available and can be found in [1]

cs.ET↗

arXiv2022

Instant Response Few-shot Object Detection with Meta Strategy and Explicit Localization Inference

Aiming at recognizing and localizing the object of novel categories by a few reference samples, few-shot object detection (FSOD) is a quite challenging task. Previous works often depend on the fine-tuning process to transfer their model to the novel category and rarely consider the defect of fine-tuning, resulting in many application drawbacks. For example, these methods are far from satisfying in the episode-changeable scenarios due to excessive fine-tuning times, and their performance on low-quality (e.g., low-shot and class-incomplete) support sets degrades severely. To this end, this paper proposes an instant response few-shot object detector (IR-FSOD) that can accurately and directly detect the objects of novel categories without the fine-tuning process. To accomplish the objective, we carefully analyze the defects of individual modules in the Faster R-CNN framework under the FSOD setting and then extend it to IR-FSOD by improving these defects. Specifically, we first propose two simple but effective meta-strategies for the box classifier and RPN module to enable the object detection of novel categories with instant response. Then, we introduce two explicit inferences into the localization module to alleviate its over-fitting to the base categories, including explicit localization score and semi-explicit box regression. Extensive experiments show that the IR-FSOD framework not only achieves few-shot object detection with the instant response but also reaches state-of-the-art performance in precision and recall under various FSOD settings.

cs.CV↗

arXiv2022

A local pointwise inequality for a biharmonic equation with negative exponents

In this paper, we are inspired by Ngô, Nguyen and Phan's [15] study of the pointwise inequality for positive $C^{4}$-solutions of biharmonic equations with negative exponent by using the growth condition of solutions. They propose an open question of whether the growth condition is necessary to obtain the pointwise inequality. We give a positive answer to this open question. We establish the following local pointwise inequality $$-\frac{Δu}{u}+α\frac{|\nabla u|^{2}}{u^{2}}+βu^{-\frac{q+1}{2}}\leq\frac{C}{R^{2}}$$ for positive $C^{4}$-solutions of the biharmonic equations with negative exponent $$-Δ^{2}u=u^{-q} \ in \ B_{R}$$ where $B_{R}$ denotes the ball centered at $x_{0}$ with radius $R$, $n\geq3$, $q>1$, and some constants $α\geq0$, $β>0$, $C>0$.

math.AP↗

arXiv2021

Enhancing Prototypical Few-Shot Learning by Leveraging the Local-Level Strategy

Aiming at recognizing the samples from novel categories with few reference samples, few-shot learning (FSL) is a challenging problem. We found that the existing works often build their few-shot model based on the image-level feature by mixing all local-level features, which leads to the discriminative location bias and information loss in local details. To tackle the problem, this paper returns the perspective to the local-level feature and proposes a series of local-level strategies. Specifically, we present (a) a local-agnostic training strategy to avoid the discriminative location bias between the base and novel categories, (b) a novel local-level similarity measure to capture the accurate comparison between local-level features, and (c) a local-level knowledge transfer that can synthesize different knowledge transfers from the base category according to different location features. Extensive experiments justify that our proposed local-level strategies can significantly boost the performance and achieve 2.8%-7.2% improvements over the baseline across different benchmark datasets, which also achieves state-of-the-art accuracy.

cs.CV↗