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Liang Chen

Publications and source records attributed to Liang Chen.

At least 289 records · Page 16Linked to original sources
arXiv2023

Stochastic Domain Decomposition Based on Variable-Separation Method

In this work, we propose a new stochastic domain decomposition method for solving steady-state partial differential equations (PDEs) with random inputs. Based on the efficiency of the Variable-separation (VS) method in simulating stochastic partial differential equations (SPDEs), we extend it to stochastic algebraic systems and apply it to stochastic domain decomposition. The resulting Stochastic Domain Decomposition based on the Variable-separation method (SDD-VS) effectively addresses the ``curse of dimensionality" by leveraging the explicit representation of stochastic functions derived from physical systems. The SDD-VS method aims to obtain a separated representation of the solution for the stochastic interface problem. To enhance efficiency, an offline-online computational decomposition is introduced. In the offline phase, the affine representation of stochastic algebraic systems is obtained through the successive application of the VS method. This serves as a crucial foundation for the SDD-VS method. In the online phase, the interface unknowns of SPDEs are estimated using a quasi-optimal separated representation, enabling the construction of efficient surrogate models for subproblems. The effectiveness of the proposed method is demonstrated via the numerical results of three concrete examples.

math.NA↗
arXiv2023

Synaptic delay induced macroscopic dynamics of the large-scale network of Izhikevich neurons

We consider a large network of Izhikevich neurons. Each neuron has a quadratic integrate-and-fire type model with a recovery variable modelling spike frequency adaptation (SFA). We introduce a biologically motivated synaptic current expression and a delay in the synaptic transmission. Following the Ott-Antonsen theory, we reduce the network model to a mean-field system of delayed differential equations. Numerical bifurcation analysis allows us to locate higher-codimension bifurcations and to identify the regions in the parameter space where the network exhibits changes in the macroscopic dynamics, including transitions between states where the individual neurons exhibit asynchronous tonic firing and different types of synchronous bursting. We investigate the impact of the heterogeneity of the quenched input current, the SFA mechanism and the synaptic delay on macroscopic dynamics. In the limit that the heterogeneity goes to zero, our perturbation and bifurcation analysis shows that the behaviour of the mean-field model remains consistent, although this limit breaks an assumption of the model reduction. For a single population of neurons with SFA, the synaptic delay has little effect on the generation of COs for weak coupling, but favours their emergence beyond that, and even induces new macroscopic dynamics. In particular, Torus bifurcations may occur, and these are a crucial mechanism for the emergence of population bursting with two nested frequencies. We discuss how these solutions may relate to cross-frequency coupling which is potentially relevant for understanding healthy and pathological brain functions.

q-bio.NC↗
arXiv2023

Matching Function Equilibria with Partial Assignment: Existence, Uniqueness and Estimation

We argue that models coming from a variety of fields, such as matching models and discrete choice models among others, share a common structure that we call matching function equilibria with partial assignment. This structure includes an aggregate matching function and a system of nonlinear equations. We provide a proof of existence and uniqueness of an equilibrium and propose an efficient algorithm to compute it. For a subclass of matching models, we also develop a new parameter-free approach for constructing the counterfactual matching equilibrium. It has the advantage of not requiring parametric estimation when computing counterfactuals. We use our procedure to analyze the impact of the elimination of the Social Security Student Benefit Program in 1982 on the marriage market in the United States. We estimate several candidate models from our general class of matching functions and select the best fitting model using information based criterion.

econ.GN↗
arXiv2023

Existence of a Competitive Equilibrium with Substitutes, with Applications to Matching and Discrete Choice Models

We propose new results for the existence and uniqueness of a general nonparametric and nonseparable competitive equilibrium with substitutes. These results ensure the invertibility of a general competitive system. The existing literature has focused on the uniqueness of a competitive equilibrium assuming that existence holds. We introduce three properties that our supply system must satisfy: weak substitutes, pivotal substitutes, and responsiveness. These properties are sufficient to ensure the existence of an equilibrium, thus providing the existence counterpart to Berry, Gandhi, and Haile (2013)'s uniqueness results. For two important classes of models, bipartite matching models with full assignment and discrete choice models, we show that both models can be reformulated as a competitive system such that our existence and uniqueness results can be readily applied. We also provide an algorithm to compute the unique competitive equilibrium. Furthermore, we argue that our results are particularly useful for studying imperfectly transferable utility matching models with full assignment and non-additive random utility models.

econ.GN↗
arXiv2023

Incorporating Surprisingly Popular Algorithm and Euclidean Distance-based Adaptive Topology into PSO

While many Particle Swarm Optimization (PSO) algorithms only use fitness to assess the performance of particles, in this work, we adopt Surprisingly Popular Algorithm (SPA) as a complementary metric in addition to fitness. Consequently, particles that are not widely known also have the opportunity to be selected as the learning exemplars. In addition, we propose a Euclidean distance-based adaptive topology to cooperate with SPA, where each particle only connects to k number of particles with the shortest Euclidean distance during each iteration. We also introduce the adaptive topology into heterogeneous populations to better solve large-scale problems. Specifically, the exploration sub-population better preserves the diversity of the population while the exploitation sub-population achieves fast convergence. Therefore, large-scale problems can be solved in a collaborative manner to elevate the overall performance. To evaluate the performance of our method, we conduct extensive experiments on various optimization problems, including three benchmark suites and two real-world optimization problems. The results demonstrate that our Euclidean distance-based adaptive topology outperforms the other widely adopted topologies and further suggest that our method performs significantly better than state-of-the-art PSO variants on small, medium, and large-scale problems.

cs.NE↗
arXiv2023

Making Large Language Models Better Reasoners with Alignment

Reasoning is a cognitive process of using evidence to reach a sound conclusion. The reasoning capability is essential for large language models (LLMs) to serve as the brain of the artificial general intelligence agent. Recent studies reveal that fine-tuning LLMs on data with the chain of thought (COT) reasoning process can significantly enhance their reasoning capabilities. However, we find that the fine-tuned LLMs suffer from an \textit{Assessment Misalignment} problem, i.e., they frequently assign higher scores to subpar COTs, leading to potential limitations in their reasoning abilities. To address this problem, we introduce an \textit{Alignment Fine-Tuning (AFT)} paradigm, which involves three steps: 1) fine-tuning LLMs with COT training data; 2) generating multiple COT responses for each question, and categorizing them into positive and negative ones based on whether they achieve the correct answer; 3) calibrating the scores of positive and negative responses given by LLMs with a novel constraint alignment loss. Specifically, the constraint alignment loss has two objectives: a) Alignment, which guarantees that positive scores surpass negative scores to encourage answers with high-quality COTs; b) Constraint, which keeps the negative scores confined to a reasonable range to prevent the model degradation. Beyond just the binary positive and negative feedback, the constraint alignment loss can be seamlessly adapted to the ranking situations when ranking feedback is accessible. Furthermore, we also delve deeply into recent ranking-based alignment methods, such as DPO, RRHF, and PRO, and discover that the constraint, which has been overlooked by these approaches, is also crucial for their performance. Extensive experiments on four reasoning benchmarks with both binary and ranking feedback demonstrate the effectiveness of AFT.

cs.CL↗
arXiv2023

Astrophysically sourced quantum coherent photonic signals

Stimulated emission is shown to be robust in stars. Through Bose enhancement this produces quantum states of aligned, monochromatic photons similar to a laser. The probability of creating such states is computed. We show that from the solar corona such quantum states would propagate outside of the solar region and through the Solar System without decoherence. For a $1 {\rm m}^2$ detector at the distance of the Earth from the Sun we estimate rates of such quantum states in the few per second thus potentially detectable. The same process should lead to such quantum states also arriving from stars at interstellar distances.

hep-ph↗
arXiv2023

Complex quantum momentum due to correlation

Real numbers provide a sufficient description of classical physics and all measurable phenomena; however, complex numbers are occasionally utilized as a convenient mathematical tool to aid our calculations. On the other hand, the formalism of quantum mechanics integrates complex numbers within its fundamental principles, and whether this arises out of necessity or not is an important question that many have attempted to answer. Here, we will consider two electrons in a one-dimensional quantum well where the interaction potential between the two electrons is attractive as opposed to the usual repulsive coulomb potential. Pairs of electrons exhibiting such effective attraction towards each other occur in other settings, namely within superconductivity. We will demonstrate that this attractive interaction leads to the necessity of complex momentum solutions, which further emphasizes the significance of complex numbers in quantum theory. The complex momentum solutions are solved using a perturbative analysis approach in tandem with Newton's method. The probability densities arising from these complex momentum solutions allow for a comparison with the probability densities of the typical real momentum solutions occurring from the standard repulsive interaction potential.

quant-ph↗
arXiv2023

Large Language Models are not Fair Evaluators

In this paper, we uncover a systematic bias in the evaluation paradigm of adopting large language models~(LLMs), e.g., GPT-4, as a referee to score and compare the quality of responses generated by candidate models. We find that the quality ranking of candidate responses can be easily hacked by simply altering their order of appearance in the context. This manipulation allows us to skew the evaluation result, making one model appear considerably superior to the other, e.g., Vicuna-13B could beat ChatGPT on 66 over 80 tested queries with ChatGPT as an evaluator. To address this issue, we propose a calibration framework with three simple yet effective strategies: 1) Multiple Evidence Calibration, which requires the evaluator model to generate multiple evaluation evidence before assigning ratings; 2) Balanced Position Calibration, which aggregates results across various orders to determine the final score; 3) Human-in-the-Loop Calibration, which introduces a balanced position diversity entropy to measure the difficulty of each example and seeks human assistance when needed. We also manually annotate the "win/tie/lose" outcomes of responses from ChatGPT and Vicuna-13B in the Vicuna Benchmark's question prompt, and extensive experiments demonstrate that our approach successfully mitigates evaluation bias, resulting in closer alignment with human judgments. We release our code and human annotation at \url{https://github.com/i-Eval/FairEval} to facilitate future research.

cs.CL↗
arXiv2023

2D Single Crystal of High-Temperature Phase Cuprous Iodide under Ambient Conditions

Two-dimensional (2D) materials, with their structural uniqueness, exceptional properties, and wide-ranging applications, show unprecedented prospects in fundamental physics research and industrial applications. 2D \b{eta}-phase cuprous iodide (\b{eta}-CuI) is a promising candidate for overcoming the challenges of insufficient P-type transparent conductive materials, with multiple predicted unique properties. Previous experimental results show that \b{eta}-CuI only occurs at elevated temperatures between 645 and 675 K. Many efforts are made to stabilize \b{eta}-CuI at room temperature through surface/interface engineering. However, the resulting composites limit the performance and application of pure 2D \b{eta}-CuI. Here, we demonstrate experimentally that isolated 2D \b{eta}-CuI single crystals can exist stably under ambient conditions, a high-temperature phase CuI found at room temperature. We validate the simultaneous existence of γ-CuI and \b{eta}-CuI in the synthesized CuI. The previous neglect of \b{eta}-CuI crystals can be ascribed to factors including their low content, small dimensions, and lack of ingenious experimental characterization. Moreover, the theoretical calculation further confirms dynamically and thermally stable of the monolayer \b{eta}-CuI, which has an ultra-wide direct band-gap (3.66 eV). Our findings challenge the traditional understanding of \b{eta}-CuI as a high-temperature phase of CuI, instead providing a new definition that 2D \b{eta}-CuI exhibits remarkable stability under ambient conditions.

cond-mat.mtrl-sci↗
arXiv2023

Domain Generalization via Rationale Invariance

This paper offers a new perspective to ease the challenge of domain generalization, which involves maintaining robust results even in unseen environments. Our design focuses on the decision-making process in the final classifier layer. Specifically, we propose treating the element-wise contributions to the final results as the rationale for making a decision and representing the rationale for each sample as a matrix. For a well-generalized model, we suggest the rationale matrices for samples belonging to the same category should be similar, indicating the model relies on domain-invariant clues to make decisions, thereby ensuring robust results. To implement this idea, we introduce a rationale invariance loss as a simple regularization technique, requiring only a few lines of code. Our experiments demonstrate that the proposed approach achieves competitive results across various datasets, despite its simplicity. Code is available at \url{https://github.com/liangchen527/RIDG}.

cs.CV↗
arXiv2023

Measurement of ultra-high-energy diffuse gamma-ray emission of the Galactic plane from 10 TeV to 1 PeV with LHAASO-KM2A

The diffuse Galactic $γ$-ray emission, mainly produced via interactions between cosmic rays and the interstellar medium and/or radiation field, is a very important probe of the distribution, propagation, and interaction of cosmic rays in the Milky Way. In this work we report the measurements of diffuse $γ$-rays from the Galactic plane between 10 TeV and 1 PeV energies, with the square kilometer array of the Large High Altitude Air Shower Observatory (LHAASO). Diffuse emissions from the inner ($15^{\circ} 10$~TeV). The energy spectrum in the inner Galaxy regions can be described by a power-law function with an index of $-2.99\pm0.04$, which is different from the curved spectrum as expected from hadronic interactions between locally measured cosmic rays and the line-of-sight integrated gas content. Furthermore, the measured flux is higher by a factor of $\sim3$ than the prediction. A similar spectrum with an index of $-2.99\pm0.07$ is found in the outer Galaxy region, and the absolute flux for $10\lesssim E\lesssim60$ TeV is again higher than the prediction for hadronic cosmic ray interactions. The latitude distributions of the diffuse emission are consistent with the gas distribution, while the longitude distributions show clear deviation from the gas distribution. The LHAASO measurements imply that either additional emission sources exist or cosmic ray intensities have spatial variations.

astro-ph.HE↗
arXiv2023

SAILOR: Structural Augmentation Based Tail Node Representation Learning

Graph Neural Networks (GNNs) have achieved state-of-the-art performance in representation learning for graphs recently. However, the effectiveness of GNNs, which capitalize on the key operation of message propagation, highly depends on the quality of the topology structure. Most of the graphs in real-world scenarios follow a long-tailed distribution on their node degrees, that is, a vast majority of the nodes in the graph are tail nodes with only a few connected edges. GNNs produce inferior node representations for tail nodes since they lack structural information. In the pursuit of promoting the expressiveness of GNNs for tail nodes, we explore how the deficiency of structural information deteriorates the performance of tail nodes and propose a general Structural Augmentation based taIL nOde Representation learning framework, dubbed as SAILOR, which can jointly learn to augment the graph structure and extract more informative representations for tail nodes. Extensive experiments on public benchmark datasets demonstrate that SAILOR can significantly improve the tail node representations and outperform the state-of-the-art baselines.

cs.LG↗
arXiv2023

GUARD: Graph Universal Adversarial Defense

Graph convolutional networks (GCNs) have been shown to be vulnerable to small adversarial perturbations, which becomes a severe threat and largely limits their applications in security-critical scenarios. To mitigate such a threat, considerable research efforts have been devoted to increasing the robustness of GCNs against adversarial attacks. However, current defense approaches are typically designed to prevent GCNs from untargeted adversarial attacks and focus on overall performance, making it challenging to protect important local nodes from more powerful targeted adversarial attacks. Additionally, a trade-off between robustness and performance is often made in existing research. Such limitations highlight the need for developing an effective and efficient approach that can defend local nodes against targeted attacks, without compromising the overall performance of GCNs. In this work, we present a simple yet effective method, named Graph Universal Adversarial Defense (GUARD). Unlike previous works, GUARD protects each individual node from attacks with a universal defensive patch, which is generated once and can be applied to any node (node-agnostic) in a graph. GUARD is fast, straightforward to implement without any change to network architecture nor any additional parameters, and is broadly applicable to any GCNs. Extensive experiments on four benchmark datasets demonstrate that GUARD significantly improves robustness for several established GCNs against multiple adversarial attacks and outperforms state-of-the-art defense methods by large margins.

cs.LG↗
arXiv2023

Deep Richardson-Lucy Deconvolution for Low-Light Image Deblurring

Images taken under the low-light condition often contain blur and saturated pixels at the same time. Deblurring images with saturated pixels is quite challenging. Because of the limited dynamic range, the saturated pixels are usually clipped in the imaging process and thus cannot be modeled by the linear blur model. Previous methods use manually designed smooth functions to approximate the clipping procedure. Their deblurring processes often require empirically defined parameters, which may not be the optimal choices for different images. In this paper, we develop a data-driven approach to model the saturated pixels by a learned latent map. Based on the new model, the non-blind deblurring task can be formulated into a maximum a posterior (MAP) problem, which can be effectively solved by iteratively computing the latent map and the latent image. Specifically, the latent map is computed by learning from a map estimation network (MEN), and the latent image estimation process is implemented by a Richardson-Lucy (RL)-based updating scheme. To estimate high-quality deblurred images without amplified artifacts, we develop a prior estimation network (PEN) to obtain prior information, which is further integrated into the RL scheme. Experimental results demonstrate that the proposed method performs favorably against state-of-the-art algorithms both quantitatively and qualitatively on synthetic and real-world images.

cs.CV↗
arXiv2023

Ensemble Knowledge Distillation for CTR Prediction

Recently, deep learning-based models have been widely studied for click-through rate (CTR) prediction and lead to improved prediction accuracy in many industrial applications. However, current research focuses primarily on building complex network architectures to better capture sophisticated feature interactions and dynamic user behaviors. The increased model complexity may slow down online inference and hinder its adoption in real-time applications. Instead, our work targets at a new model training strategy based on knowledge distillation (KD). KD is a teacher-student learning framework to transfer knowledge learned from a teacher model to a student model. The KD strategy not only allows us to simplify the student model as a vanilla DNN model but also achieves significant accuracy improvements over the state-of-the-art teacher models. The benefits thus motivate us to further explore the use of a powerful ensemble of teachers for more accurate student model training. We also propose some novel techniques to facilitate ensembled CTR prediction, including teacher gating and early stopping by distillation loss. We conduct comprehensive experiments against 12 existing models and across three industrial datasets. Both offline and online A/B testing results show the effectiveness of our KD-based training strategy.

cs.LG↗
arXiv2023

GUT origins of general electroweak multiplets and their oblique parameters

We survey the scalar electroweak multiplets that can originate from a grand unified theory (GUT) like $SU(5)$, $SO(10)$ or $E_6$. We compute the oblique parameters $S$, $T$ and $U$ for a general scalar electroweak multiplet and then apply the results to the leptoquark, as well as the color sextet and octet cases, allowed by the GUT survey. Constraints from precision measurement data of the Standard Model $W$ boson mass and $ρ$ parameter to the mass splittings within each of these multiplets are presented. Extension to general vector electroweak multiplets is briefly discussed.

hep-ph↗
arXiv2023

A Coupled Hybridizable Discontinuous Galerkin and Boundary Integral Method for Analyzing Electromagnetic Scattering

A coupled hybridizable discontinuous Galerkin (HDG) and boundary integral (BI) method is proposed to efficiently analyze electromagnetic scattering from inhomogeneous/composite objects. The coupling between the HDG and the BI equations is realized using the numerical flux operating on the equivalent current and the global unknown of the HDG. This approach yields sparse coupling matrices upon discretization. Inclusion of the BI equation ensures that the only error in enforcing the radiation conditions is the discretization. However, the discretization of this equation yields a dense matrix, which prohibits the use of a direct matrix solver on the overall coupled system as often done with traditional HDG schemes. To overcome this bottleneck, a "hybrid" method is developed. This method uses an iterative scheme to solve the overall coupled system but within the matrix-vector multiplication subroutine of the iterations, the inverse of the HDG matrix is efficiently accounted for using a sparse direct matrix solver. The same subroutine also uses the multilevel fast multipole algorithm to accelerate the multiplication of the guess vector with the dense BI matrix. The numerical results demonstrate the accuracy, the efficiency, and the applicability of the proposed HDG-BI solver.

cs.CE↗