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Chao Gao

Publications and source records attributed to Chao Gao.

At least 91 records · Page 5Linked to original sources

Minimax Signal Detection in Sparse Additive Models

Sparse additive models are an attractive choice in circumstances calling for modelling flexibility in the face of high dimensionality. We study the signal detection problem and establish the minimax separation rate for the detection of a sparse additive signal. Our result is nonasymptotic and applicable to the general case where the univariate component functions belong to a generic reproducing kernel Hilbert space. Unlike the estimation theory, the minimax separation rate reveals a nontrivial interaction between sparsity and the choice of function space. We also investigate adaptation to sparsity and establish an adaptive testing rate for a generic function space; adaptation is possible in some spaces while others impose an unavoidable cost. Finally, adaptation to both sparsity and smoothness is studied in the setting of Sobolev space, and we correct some existing claims in the literature.

math.ST↗

Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey

Large models represent a groundbreaking advancement in multiple application fields, enabling remarkable achievements across various tasks. However, their unprecedented scale comes with significant computational costs. These models, often consisting of billions of parameters, require vast amounts of computational resources for execution. Especially, the expansive scale and computational demands pose considerable challenges when customizing them for particular downstream tasks, particularly over the hardware platforms constrained by computational capabilities. Parameter Efficient Fine-Tuning (PEFT) provides a practical solution by efficiently adjusting the large models over the various downstream tasks. In particular, PEFT refers to the process of adjusting the parameters of a pre-trained large model to adapt it to a specific task or domain while minimizing the number of additional parameters introduced or computational resources required. This approach is particularly important when dealing with large-scale language models with high parameter counts, as fine-tuning these models from scratch can be computationally expensive and resource-intensive, posing considerable challenges in the supporting system platform design. In this survey, we present comprehensive studies of various PEFT algorithms, examining their performance and computational overhead. Moreover, we provide an overview of applications developed using different PEFT algorithms and discuss common techniques employed to mitigate computation costs for PEFT. In addition to providing an extensive survey from an algorithmic standpoint, we also examine various real-world system designs to investigate the implementation costs associated with different PEFT approaches. This survey serves as a valuable resource for researchers aiming to understand both the PEFT algorithm and its system implementation, offering detailed ......

cs.LG↗

Locally sharp goodness-of-fit testing in sup norm for high-dimensional counts

We consider testing the goodness-of-fit of a distribution against alternatives separated in sup norm. We study the twin settings of Poisson-generated count data with a large number of categories and high-dimensional multinomials. In previous studies of different separation metrics, it has been found that the local minimax separation rate exhibits substantial heterogeneity and is a complicated function of the null distribution; the rate-optimal test requires careful tailoring to the null. In the setting of sup norm, this remains the case and we establish that the local minimax separation rate is determined by the finer decay behavior of the category rates. The upper bound is obtained by a test involving the sample maximum, and the lower bound argument involves reducing the original heteroskedastic null to an auxiliary homoskedastic null determined by the decay of the rates. Further, in a particular asymptotic setup, the sharp constants are identified.

math.ST↗

State estimation of timed automata under partial observation [Draft version]

In this paper, we consider partially observable timed automata endowed with a single clock. A time interval is associated with each transition specifying at which clock values it may occur. In addition, a resetting condition associated to a transition specifies how the clock value is updated upon its occurrence. This work deals with the estimation of the current state given a timed observation, i.e., a succession of pairs of an observable event and the time instant at which the event has occurred. The problem of state reachability in the timed automaton is reduced to the reachability analysis of the associated zone automaton, which provides a purely discrete event description of the behaviour of the timed automaton. An algorithm is formulated to provide an offline approach for state estimation of a timed automaton based on the assumption that the clock is reset upon the occurrence of each observable transition.

cs.FL↗

Computational Lower Bounds for Graphon Estimation via Low-degree Polynomials

Graphon estimation has been one of the most fundamental problems in network analysis and has received considerable attention in the past decade. From the statistical perspective, the minimax error rate of graphon estimation has been established by Gao et al (2015) for both stochastic block model and nonparametric graphon estimation. The statistical optimal estimators are based on constrained least squares and have computational complexity exponential in the dimension. From the computational perspective, the best-known polynomial-time estimator is based universal singular value thresholding, but it can only achieve a much slower estimation error rate than the minimax one. The computational optimality of the USVT or the existence of a computational barrier in graphon estimation has been a long-standing open problem. In this work, we provide rigorous evidence for the computational barrier in graphon estimation via low-degree polynomials. Specifically, in SBM graphon estimation, we show that for low-degree polynomial estimators, their estimation error rates cannot be significantly better than that of the USVT under a wide range of parameter regimes and in nonparametric graphon estimation, we show low-degree polynomial estimators achieve estimation error rates strictly slower than the minimax rate. Our results are proved based on the recent development of low-degree polynomials by Schramm and Wein (2022), while we overcome a few key challenges in applying it to the general graphon estimation problem. By leveraging our main results, we also provide a computational lower bound on the clustering error for community detection in SBM with a growing number of communities and this yields a new piece of evidence for the conjectured Kesten-Stigum threshold for efficient community recovery. Finally, we extend our computational lower bounds to sparse graphon estimation and biclustering.

math.ST↗

The third virial coefficient of a two-component unitary Fermi gas across an Efimov-effect threshold

We consider a mixture of two single-spin-state fermions with an interaction of negligible range and infinite $s$-wave scattering length. By varying the mass ratio $α$ across $α_c\simeq 13.6069$ one can switch on-and-off the Efimov effect. We determine analytically the third cluster coefficient of the gas. We show that it is a smooth function of $α$ across $α_c$ since, unexpectedly, the three-body parameter characterizing the interaction is relevant even on the non-Efimovian side $α<α_c$.

cond-mat.quant-gas↗

Three-dimensional Moiré Crystal

The work intends to extend the moiré physics to three dimensions. Three-dimensional moiré patterns can be realized in ultracold atomic gases by coupling two spin states in spin-dependent optical lattices with a relative twist, a structure currently unachievable in solid-state materials. We give the commensurate conditions under which the three-dimensional moiré pattern features a periodic structure, termed a three-dimensional moiré crystal. We emphasize a key distinction of three-dimensional moiré physics: in three dimensions, the twist operation generically does not commute with the rotational symmetry of the original lattice, unlike in two dimensions, where these two always commute. Consequently, the moiré crystal can exhibit a crystalline structure that differs from the original underlying lattice. We demonstrate that twisting a simple cubic lattice can generate various crystal structures. This capability of altering crystal structures by twisting offers a broad range of tunability for three-dimensional band structures.

cond-mat.quant-gas↗

Fractal spectrum in twisted bilayer optical lattice

The translation symmetry of a lattice is greatly modified when subjected to a perpendicular magnetic field [Zak, Phys. Rev. \textbf{134}, A1602 (1964)]. This change in symmetry can lead to magnetic unit cells that are substantially larger than the original ones. Similarly, the translation properties of a double-layered lattice alters drastically while two monolayers are relatively twisted by a small angle, resulting in large-scale moiré unit cells. Intrigued by the resemblance, we calculate the complete band structures of a twisted bilayer optical lattice and show that the geometric moiré effect can induce fractal band structures. The fractals are controlled by the twist angle between two monolayers and are closely connected to the celebrated butterfly spectrum of two-dimensional Bloch electrons in a magnetic field [Hofstadter, Phys. Rev. B \textbf{14}, 2239 (1976)]. We demonstrate this by proving that the twisted bilayer optical lattice can be mapped to a generalized Hofstadter's model with long-range hopping. Furthermore, we provide numerical evidence on the infinite recursive structures of the spectrum and give an algorithm for computing these structures.

cond-mat.mes-hall↗

DLoRA: Distributed Parameter-Efficient Fine-Tuning Solution for Large Language Model

To enhance the performance of large language models (LLM) on downstream tasks, one solution is to fine-tune certain LLM parameters and make it better align with the characteristics of the training dataset. This process is commonly known as parameter-efficient fine-tuning (PEFT). Due to the scale of LLM, PEFT operations are usually executed in the public environment (e.g., cloud server). This necessitates the sharing of sensitive user data across public environments, thereby raising potential privacy concerns. To tackle these challenges, we propose a distributed PEFT framework called DLoRA. DLoRA enables scalable PEFT operations to be performed collaboratively between the cloud and user devices. Coupled with the proposed Kill and Revive algorithm, the evaluation results demonstrate that DLoRA can significantly reduce the computation and communication workload over the user devices while achieving superior accuracy and privacy protection.

cs.LG↗

Topological phases and edge modes of an uneven ladder

We investigate the topological properties of a two-chain quantum ladder with uneven legs, i.e. the two chains differ in their periods by a factor of two. Such an uneven ladder presents rich band structures classified by the closure of either direct or indirect bandgaps. It also provides opportunities to explore fundamental concepts concerning band topology and edge modes, including the difference of intracellular and intercellular Zak phases, and the role of the inversion symmetry (IS). We calculate the Zak phases of the two kinds and find excellent agreement with the dipole moment and extra charge accumulation, respectively. We also find that configurations with IS feature a pair of degenerate two-side edge modes emerging as the closure of the direct bandgap, while configurations without IS feature one-side edge modes emerging as not only the closure of both direct and indirect bandgap but also within the band continuum. Furthermore, by projecting to the two sublattices, we find that the effective Bloch Hamiltonian corresponds to that of a generalized Su-Schrieffer-Heeger model or Rice-Mele model whose hopping amplitudes depend on the quasimomentum. In this way, the topological phases can be efficiently extracted through winding numbers. We propose that uneven ladders can be realized by spin-dependent optical lattices and their rich topological characteristics can be examined by near future experiments.

cond-mat.mes-hall↗

GIN-SD: Source Detection in Graphs with Incomplete Nodes via Positional Encoding and Attentive Fusion

Source detection in graphs has demonstrated robust efficacy in the domain of rumor source identification. Although recent solutions have enhanced performance by leveraging deep neural networks, they often require complete user data. In this paper, we address a more challenging task, rumor source detection with incomplete user data, and propose a novel framework, i.e., Source Detection in Graphs with Incomplete Nodes via Positional Encoding and Attentive Fusion (GIN-SD), to tackle this challenge. Specifically, our approach utilizes a positional embedding module to distinguish nodes that are incomplete and employs a self-attention mechanism to focus on nodes with greater information transmission capacity. To mitigate the prediction bias caused by the significant disparity between the numbers of source and non-source nodes, we also introduce a class-balancing mechanism. Extensive experiments validate the effectiveness of GIN-SD and its superiority to state-of-the-art methods.

cs.SI↗

Propagation Dynamics of Rumor vs. Non-rumor across Multiple Social Media Platforms Driven by User Characteristics

Studying information propagation dynamics in social media can elucidate user behaviors and patterns. However, previous research often focuses on single platforms and fails to differentiate between the nuanced roles of source users and other participants in cascades. To address these limitations, we analyze propagation cascades on Twitter and Weibo combined with a crawled dataset of nearly one million users with authentic attributes. Our preliminary findings from multiple platforms robustly indicate that rumors tend to spread more deeply, while non-rumors distribute more broadly. Interestingly, we discover that the spread of rumors is slower, persists longer, and, in most cases, involves fewer participants than that of non-rumors. And an undiscovered highlight is that reputable active users, termed `onlookers', inadvertently or unwittingly spread rumors due to their extensive online interactions and the allure of sensational fake news. Conversely, celebrities exhibit caution, mindful of releasing unverified information. Additionally, we identify cascade features aligning with exponential patterns, highlight the Credibility Erosion Effect (CEE) phenomenon in the propagation process, and discover the different contents and policies between the two platforms. Our findings enhance current understanding and provide a valuable statistical analysis for future research.

cs.SI↗

Dynamical nonlinear excitations induced by interaction quench in a two-dimensional box-trapped Bose-Einstein condensate

Manipulating nonlinear excitations, including solitons and vortices, is an essential topic in quantum many-body physics. A recent progress in this direction is a new protocol proposed in [Phys. Rev. Res. 2, 043256 (2020)] to produce dark solitons in a one-dimensional atomic Bose-Einstein condensate (BEC) by quenching inter-atomic interaction. Motivated by this work, we generalize the protocol to a two-dimensional BEC and investigate the general scenario of its post-quench dynamics. For an isotropic disk trap with a hard-wall boundary, we find that successive inward-moving ring dark solitons (RDSs) can be induced from the edge, and the number of RDSs can be controlled by tuning the ratio of the after- and before-quench interaction strength across different critical values. The role the quench played on the profiles of the density, phase, and sound velocity is also investigated. Due to the snake instability, the RDSs then become vortex-antivortex pairs with peculiar dynamics managed by the initial density and the after-quench interaction. By tuning the geometry of the box traps, demonstrated as polygonal ones, more subtle dynamics of solitons and vortices are enabled. Our proposed protocol and the discovered rich dynamical effects on nonlinear excitations can be realized in future cold-atom experiments.

cond-mat.quant-gas↗

Monte Carlo Tree Search in the Presence of Transition Uncertainty

Monte Carlo Tree Search (MCTS) is an immensely popular search-based framework used for decision making. It is traditionally applied to domains where a perfect simulation model of the environment is available. We study and improve MCTS in the context where the environment model is given but imperfect. We show that the discrepancy between the model and the actual environment can lead to significant performance degradation with standard MCTS. We therefore develop Uncertainty Adapted MCTS (UA-MCTS), a more robust algorithm within the MCTS framework. We estimate the transition uncertainty in the given model, and direct the search towards more certain transitions in the state space. We modify all four MCTS phases to improve the search behavior by considering these estimates. We prove, in the corrupted bandit case, that adding uncertainty information to adapt UCB leads to tighter regret bound than standard UCB. Empirically, we evaluate UA-MCTS and its individual components on the deterministic domains from the MinAtar test suite. Our results demonstrate that UA-MCTS strongly improves MCTS in the presence of model transition errors.

cs.AI↗

GAMC: An Unsupervised Method for Fake News Detection using Graph Autoencoder with Masking

With the rise of social media, the spread of fake news has become a significant concern, potentially misleading public perceptions and impacting social stability. Although deep learning methods like CNNs, RNNs, and Transformer-based models like BERT have enhanced fake news detection, they primarily focus on content, overlooking social context during news propagation. Graph-based techniques have incorporated this social context but are limited by the need for large labeled datasets. Addressing these challenges, this paper introduces GAMC, an unsupervised fake news detection technique using the Graph Autoencoder with Masking and Contrastive learning. By leveraging both the context and content of news propagation as self-supervised signals, our method negates the requirement for labeled datasets. We augment the original news propagation graph, encode these with a graph encoder, and employ a graph decoder for reconstruction. A unique composite loss function, including reconstruction error and contrast loss, is designed. The method's contributions are: introducing self-supervised learning to fake news detection, proposing a graph autoencoder integrating two distinct losses, and validating our approach's efficacy through real-world dataset experiments.

cs.SI↗

Adaptive Multi-band Modulation for Robust and Low-complexity Faster-than-Nyquist Non-Orthogonal FDM IM-DD System

Faster-than-Nyquist non-orthogonal frequency-division multiplexing (FTN-NOFDM) is robust against the steep frequency roll-off by saving signal bandwidth. Among the FTN-NOFDM techniques, the non-orthogonal matrix precoding (NOM-p) based FTN has high compatibility with the conventional orthogonal frequency division multiplexing (OFDM), in terms of the advanced digital signal processing already used in OFDM. In this work, by dividing the single band into multiple sub-bands in the NOM-p-based FTN-NOFDM system, we propose a novel FTN-NOFDM scheme with adaptive multi-band modulation. The proposed scheme assigns different quadrature amplitude modulation (QAM) levels to different sub-bands, effectively utilizing the low-pass-like channel and reducing the complexity. The impacts of sub-band number and bandwidth compression factor on the bit-error-rate (BER) performance and implementation complexity are experimentally analyzed with a 32.23-Gb/s and 20-km intensity modulation-direct detection (IM-DD) optical transmission system. Results show that the proposed scheme with proper sub-band numbers can lower BER and greatly reduce the complexity compared to the conventional single-band way.

eess.SP↗

Graph Analytics on Evolving Data (Abstract)

We consider the problem of graph analytics on evolving graphs. In this scenario, a query typically needs to be applied to different snapshots of the graph over an extended time window. We propose CommonGraph, an approach for efficient processing of queries on evolving graphs. We first observe that edge deletions are significantly more expensive than addition operations. CommonGraph converts all deletions to additions by finding a common graph that exists across all snapshots. After computing the query on this graph, to reach any snapshot, we simply need to add the missing edges and incrementally update the query results. CommonGraph also allows sharing of common additions among snapshots that require them, and breaks the sequential dependency inherent in the traditional streaming approach where snapshots are processed in sequence, enabling additional opportunities for parallelism. We incorporate the CommonGraph approach by extending the KickStarter streaming framework. CommonGraph achieves 1.38x-8.17x improvement in performance over Kickstarter across multiple benchmarks.

cs.DB↗

Sequential Attention Source Identification Based on Feature Representation

Snapshot observation based source localization has been widely studied due to its accessibility and low cost. However, the interaction of users in existing methods does not be addressed in time-varying infection scenarios. So these methods have a decreased accuracy in heterogeneous interaction scenarios. To solve this critical issue, this paper proposes a sequence-to-sequence based localization framework called Temporal-sequence based Graph Attention Source Identification (TGASI) based on an inductive learning idea. More specifically, the encoder focuses on generating multiple features by estimating the influence probability between two users, and the decoder distinguishes the importance of prediction sources in different timestamps by a designed temporal attention mechanism. It's worth mentioning that the inductive learning idea ensures that TGASI can detect the sources in new scenarios without knowing other prior knowledge, which proves the scalability of TGASI. Comprehensive experiments with the SOTA methods demonstrate the higher detection performance and scalability in different scenarios of TGASI.

cs.SI↗