arXiv subjects

Hui Jiang

Publications and source records attributed to Hui Jiang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Phase-space Generalized Brillouin Zone for spatially inhomogeneous non-Hermitian systems

The generalized Brillouin zone (GBZ) has been highly successful in characterizing the topology and band structure of non-Hermitian systems. However, its applicability has been challenged in spatially inhomogeneous settings, where the non-locality of non-Hermitian pumping competes with Wannier-Stark localization and quantum interference, potentially leading to highly non-exponential state accumulation. To transcend this major conceptual bottleneck, we develop a general phase-space GBZ formalism that encodes non-Bloch deformations in both position and momentum space, such as to accurately represent spatially inhomogeneous non-Hermitian pumping. A key new phenomenon is the bifurcation of the phase-space GBZ branches, which allows certain eigenstates to jump abruptly between different GBZ solutions at various points in real space. The freedom in the locations of such jumps opens up an emergent degree of freedom that protects the stability of real spectra and, more impressively, the robustness of a new class of topological zero modes unique to GBZ bifurcation.The response from these novel spectral and GBZ singularities can be readily demonstrated in mature metamaterial platforms such as photonic crystals or circuit arrays, where effective real-space hoppings can be engineered in a versatile manner.Our framework directly generalizes to more complicated unit cells and further hoppings, opening up a vast new arena for exploring unconventional spectral and topological transitions as well as GBZ fragmentation in spatially inhomogeneous non-Hermitian settings.

cond-mat.mes-hall↗

arXiv2024

Segmented Private Data Aggregation in the Multi-message Shuffle Model

The shuffle model of differential privacy (DP) offers compelling privacy-utility trade-offs in decentralized settings (e.g., internet of things, mobile edge networks). Particularly, the multi-message shuffle model, where each user may contribute multiple messages, has shown that accuracy can approach that of the central model of DP. However, existing studies typically assume a uniform privacy protection level for all users, which may deter conservative users from participating and prevent liberal users from contributing more information, thereby reducing the overall data utility, such as the accuracy of aggregated statistics. In this work, we pioneer the study of segmented private data aggregation within the multi-message shuffle model of DP, introducing flexible privacy protection for users and enhanced utility for the aggregation server. Our framework not only protects users' data but also anonymizes their privacy level choices to prevent potential data leakage from these choices. To optimize the privacy-utility-communication trade-offs, we explore approximately optimal configurations for the number of blanket messages and conduct almost tight privacy amplification analyses within the shuffle model. Through extensive experiments, we demonstrate that our segmented multi-message shuffle framework achieves a reduction of about 50\% in estimation error compared to existing approaches, significantly enhancing both privacy and utility.

cs.CR↗

arXiv2024

From Pixels to Gigapixels: Bridging Local Inductive Bias and Long-Range Dependencies with Pixel-Mamba

Histopathology plays a critical role in medical diagnostics, with whole slide images (WSIs) offering valuable insights that directly influence clinical decision-making. However, the large size and complexity of WSIs may pose significant challenges for deep learning models, in both computational efficiency and effective representation learning. In this work, we introduce Pixel-Mamba, a novel deep learning architecture designed to efficiently handle gigapixel WSIs. Pixel-Mamba leverages the Mamba module, a state-space model (SSM) with linear memory complexity, and incorporates local inductive biases through progressively expanding tokens, akin to convolutional neural networks. This enables Pixel-Mamba to hierarchically combine both local and global information while efficiently addressing computational challenges. Remarkably, Pixel-Mamba achieves or even surpasses the quantitative performance of state-of-the-art (SOTA) foundation models that were pretrained on millions of WSIs or WSI-text pairs, in a range of tumor staging and survival analysis tasks, {\bf even without requiring any pathology-specific pretraining}. Extensive experiments demonstrate the efficacy of Pixel-Mamba as a powerful and efficient framework for end-to-end WSI analysis.

cs.CV↗

arXiv2024

From Histopathology Images to Cell Clouds: Learning Slide Representations with Hierarchical Cell Transformer

It is clinically crucial and potentially very beneficial to be able to analyze and model directly the spatial distributions of cells in histopathology whole slide images (WSI). However, most existing WSI datasets lack cell-level annotations, owing to the extremely high cost over giga-pixel images. Thus, it remains an open question whether deep learning models can directly and effectively analyze WSIs from the semantic aspect of cell distributions. In this work, we construct a large-scale WSI dataset with more than 5 billion cell-level annotations, termed WSI-Cell5B, and a novel hierarchical Cell Cloud Transformer (CCFormer) to tackle these challenges. WSI-Cell5B is based on 6,998 WSIs of 11 cancers from The Cancer Genome Atlas Program, and all WSIs are annotated per cell by coordinates and types. To the best of our knowledge, WSI-Cell5B is the first WSI-level large-scale dataset integrating cell-level annotations. On the other hand, CCFormer formulates the collection of cells in each WSI as a cell cloud and models cell spatial distribution. Specifically, Neighboring Information Embedding (NIE) is proposed to characterize the distribution of cells within the neighborhood of each cell, and a novel Hierarchical Spatial Perception (HSP) module is proposed to learn the spatial relationship among cells in a bottom-up manner. The clinical analysis indicates that WSI-Cell5B can be used to design clinical evaluation metrics based on counting cells that effectively assess the survival risk of patients. Extensive experiments on survival prediction and cancer staging show that learning from cell spatial distribution alone can already achieve state-of-the-art (SOTA) performance, i.e., CCFormer strongly outperforms other competing methods.

cs.CV↗

arXiv2024

End-to-end Multi-source Visual Prompt Tuning for Survival Analysis in Whole Slide Images

Survival analysis using pathology images poses a considerable challenge, as it requires the localization of relevant information from the multitude of tiles within whole slide images (WSIs). Current methods typically resort to a two-stage approach, where a pre-trained network extracts features from tiles, which are then used by survival models. This process, however, does not optimize the survival models in an end-to-end manner, and the pre-extracted features may not be ideally suited for survival prediction. To address this limitation, we present a novel end-to-end Visual Prompt Tuning framework for survival analysis, named VPTSurv. VPTSurv refines feature embeddings through an efficient encoder-decoder framework. The encoder remains fixed while the framework introduces tunable visual prompts and adaptors, thus permitting end-to-end training specifically for survival prediction by optimizing only the lightweight adaptors and the decoder. Moreover, the versatile VPTSurv framework accommodates multi-source information as prompts, thereby enriching the survival model. VPTSurv achieves substantial increases of 8.7% and 12.5% in the C-index on two immunohistochemical pathology image datasets. These significant improvements highlight the transformative potential of the end-to-end VPT framework over traditional two-stage methods.

eess.IV↗

arXiv2024

Determining the Number of Common Functional Factors with Twice Cross-Validation

The semiparametric factor model serves as a vital tool to describe the dependence patterns in the data. It recognizes that the common features observed in the data are actually explained by functions of specific exogenous variables.Unlike traditional factor models, where the focus is on selecting the number of factors, our objective here is to identify the appropriate number of common functions, a crucial parameter in this model. In this paper, we develop a novel data-driven method to determine the number of functional factors using cross validation (CV). Our proposed method employs a two-step CV process that ensures the orthogonality of functional factors, which we refer to as Functional Twice Cross-Validation (FTCV). Extensive simulations demonstrate that FTCV accurately selects the number of common functions and outperforms existing methods in most cases.Furthermore, by specifying market volatility as the exogenous force, we provide real data examples that illustrate the interpretability of selected common functions in characterizing the influence on U.S. Treasury Yields and the cross correlations between Dow30 returns.

stat.ME↗

arXiv2024

Algorithmic Analysis of Termination Problems for Nondeterministic Quantum Programs

We consider the two categories of termination problems of quantum programs with nondeterminism: 1) Is an input of a program terminating with probability one under all schedulers? If not, how can a scheduler be synthesized to evidence the nontermination? 2) Are all inputs terminating with probability one under their respective schedulers? If yes, a further question asks whether there is a scheduler that forces all inputs to be terminating with probability one together with how to synthesize it; otherwise, how can an input be provided to refute the universal termination? For the effective verification of the first category, we over-approximate the reachable set of quantum program states by the reachable subspace, whose algebraic structure is a linear space. On the other hand, we study the set of divergent states from which the program terminates with probability zero under some scheduler. The divergent set has an explicit algebraic structure. Exploiting them, we address the decision problem by a necessary and sufficient condition, i.e. the disjointness of the reachable subspace and the divergent set. Furthermore, the scheduler synthesis is completed in exponential time. For the second category, we reduce the decision problem to the existence of invariant subspace, from which the program terminates with probability zero under all schedulers. The invariant subspace is characterized by linear equations. The states on that invariant subspace are evidence of the nontermination. Furthermore, the scheduler synthesis is completed by seeking a pattern of finite schedulers that forces all inputs to be terminating with positive probability. The repetition of that pattern yields the desired universal scheduler that forces all inputs to be terminating with probability one. All the problems in the second category are shown to be solved in polynomial time.

quant-ph↗

arXiv2023

Moderate deviations for the mildly stationary autoregressive models with dependent errors

In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive (AR(1)) model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale methods, we establish the moderate deviations for the least squares estimators of the regressor and error, which can be applied to understand the near-integrated second order autoregressive processes. As an application, we also obtain the moderate deviations for the Durbin-Watson statistic.

math.PR↗

arXiv2023

A Sample-Driven Solving Procedure for the Repeated Reachability of Quantum CTMCs

Reachability analysis plays a central role in system design and verification. The reachability problem, denoted $\Diamond^J\,Φ$, asks whether the system will meet the property $Φ$ after some time in a given time interval $J$. Recently, it has been considered on a novel kind of real-time systems -- quantum continuous-time Markov chains (QCTMCs), and embedded into the model-checking algorithm. In this paper, we further study the repeated reachability problem in QCTMCs, denoted $\Box^I\,\Diamond^J\,Φ$, which concerns whether the system starting from each \emph{absolute} time in $I$ will meet the property $Φ$ after some coming \emph{relative} time in $J$. First of all, we reduce it to the real root isolation of a class of real-valued functions (exponential polynomials), whose solvability is conditional to Schanuel's conjecture being true. To speed up the procedure, we employ the strategy of sampling. The original problem is shown to be equivalent to the existence of a finite collection of satisfying samples. We then present a sample-driven procedure, which can effectively refine the sample space after each time of sampling, no matter whether the sample itself is successful or conflicting. The improvement on efficiency is validated by randomly generated instances. Hence the proposed method would be promising to attack the repeated reachability problems together with checking other $ω$-regular properties in a wide scope of real-time systems.

cs.LO↗

arXiv2023

Nonlinear perturbation of a high-order exceptional point: skin discrete breathers and the hierarchical power-law scaling

We study the nonlinear perturbation of a high-order exceptional point (EP) of the order equal to the system site number $L$ in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity. Notably, We find a class of discrete breathers that aggregate to one boundary, here named as skin discrete breathers (SDBs). The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP. Specifically, the response of nonlinear energy to the perturbation is given by $E_m\propto \varGamma^{α_{m}}$, where $α_m=3^{m-1}$ is the power with $m=1,\cdots,L$ labeling the nonlinear energy bands. This is in sharp contrast to the $L$-th root of a linear perturbation in general. These SDBs decay in a double-exponential manner, unlike the edge states or skin modes in linear systems, which decay exponentially. Furthermore, these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity. They are also stable, as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis. As nonreciprocal nonlinear models may be experimentally realized in various platforms, such as the classical platform of optical waveguides, where Kerr nonlinearity is naturally present, and the quantum platform of optical lattices with Bose-Einstein condensates, our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity, particularly on high-order EPs, and benchmark the relevant simulations.

quant-ph↗

arXiv2023

A Latent Space Theory for Emergent Abilities in Large Language Models

Languages are not created randomly but rather to communicate information. There is a strong association between languages and their underlying meanings, resulting in a sparse joint distribution that is heavily peaked according to their correlations. Moreover, these peak values happen to match with the marginal distribution of languages due to the sparsity. With the advent of LLMs trained on big data and large models, we can now precisely assess the marginal distribution of languages, providing a convenient means of exploring the sparse structures in the joint distribution for effective inferences. In this paper, we categorize languages as either unambiguous or ε-ambiguous and present quantitative results to demonstrate that the emergent abilities of LLMs, such as language understanding, in-context learning, chain-of-thought prompting, and effective instruction fine-tuning, can all be attributed to Bayesian inference on the sparse joint distribution of languages.

cs.CL↗

arXiv2023

Accurate and Efficient Estimation of Small P-values with the Cross-Entropy Method: Applications in Genomic Data Analysis

$\textbf{Motivation:}$ Small $p$-values are often required to be accurately estimated in large-scale genomic studies for the adjustment of multiple hypothesis tests and the ranking of genomic features based on their statistical significance. For those complicated test statistics whose cumulative distribution functions are analytically intractable, existing methods usually do not work well with small $p$-values due to lack of accuracy or computational restrictions. We propose a general approach for accurately and efficiently estimating small $p$-values for a broad range of complicated test statistics based on the principle of the cross-entropy method and Markov chain Monte Carlo sampling techniques. $\textbf{Results:}$ We evaluate the performance of the proposed algorithm through simulations and demonstrate its application to three real-world examples in genomic studies. The results show that our approach can accurately evaluate small to extremely small $p$-values (e.g. $10^{-6}$ to $10^{-100}$). The proposed algorithm is helpful for the improvement of some existing test procedures and the development of new test procedures in genomic studies.

stat.AP↗

arXiv2023

Efficiently estimating small p-values in permutation tests using importance sampling and cross-entropy method

Permutation tests are widely used for statistical hypothesis testing when the sampling distribution of the test statistic under the null hypothesis is analytically intractable or unreliable due to finite sample sizes. One critical challenge in the application of permutation tests in genomic studies is that an enormous number of permutations are often needed to obtain reliable estimates of very small $p$-values, leading to intensive computational effort. To address this issue, we develop algorithms for the accurate and efficient estimation of small $p$-values in permutation tests for paired and independent two-group genomic data, and our approaches leverage a novel framework for parameterizing the permutation sample spaces of those two types of data respectively using the Bernoulli and conditional Bernoulli distributions, combined with the cross-entropy method. The performance of our proposed algorithms is demonstrated through the application to two simulated datasets and two real-world gene expression datasets generated by microarray and RNA-Seq technologies and comparisons to existing methods such as crude permutations and SAMC, and the results show that our approaches can achieve orders of magnitude of computational efficiency gains in estimating small $p$-values. Our approaches offer promising solutions for the improvement of computational efficiencies of existing permutation test procedures and the development of new testing methods using permutations in genomic data analysis.

stat.CO↗

arXiv2023

Dimensional transmutation from non-Hermiticity

Dimensionality plays a fundamental role in the classification of novel phases and their responses. In generic lattices of 2D and beyond, however, we found that non-Hermitian couplings do not merely distort the Brillouin zone (BZ), but can in fact alter its effective dimensionality. This is due to the fundamental non-commutativity of multi-dimensional non-Hermitian pumping, which obstructs the usual formation of a generalized complex BZ. As such, basis states are forced to assume "entangled" profiles that are orthogonal in a lower dimensional effective BZ, completely divorced from any vestige of lattice Bloch states unlike conventional skin states. Characterizing this reduced dimensionality is an emergent winding number intimately related to the homotopy of non-contractible spectral paths. We illustrate this dimensional transmutation through a 2D model whose topological zero modes are protected by a 1D, not 2D, topological invariant. Our findings can be readily demonstrated via the bulk properties of non-reciprocally coupled platforms such as circuit arrays, and provokes us to rethink about the fundamental role of geometric obstruction in the dimensional classification of topological states.

cond-mat.mes-hall↗

arXiv2023

FedBIAD: Communication-Efficient and Accuracy-Guaranteed Federated Learning with Bayesian Inference-Based Adaptive Dropout

Federated Learning (FL) emerges as a distributed machine learning paradigm without end-user data transmission, effectively avoiding privacy leakage. Participating devices in FL are usually bandwidth-constrained, and the uplink is much slower than the downlink in wireless networks, which causes a severe uplink communication bottleneck. A prominent direction to alleviate this problem is federated dropout, which drops fractional weights of local models. However, existing federated dropout studies focus on random or ordered dropout and lack theoretical support, resulting in unguaranteed performance. In this paper, we propose Federated learning with Bayesian Inference-based Adaptive Dropout (FedBIAD), which regards weight rows of local models as probability distributions and adaptively drops partial weight rows based on importance indicators correlated with the trend of local training loss. By applying FedBIAD, each client adaptively selects a high-quality dropping pattern with accurate approximations and only transmits parameters of non-dropped weight rows to mitigate uplink costs while improving accuracy. Theoretical analysis demonstrates that the convergence rate of the average generalization error of FedBIAD is minimax optimal up to a squared logarithmic factor. Extensive experiments on image classification and next-word prediction show that compared with status quo approaches, FedBIAD provides 2x uplink reduction with an accuracy increase of up to 2.41% even on non-Independent and Identically Distributed (non-IID) data, which brings up to 72% decrease in training time.

cs.DC↗

arXiv2023

Why Learning of Large-Scale Neural Networks Behaves Like Convex Optimization

In this paper, we present some theoretical work to explain why simple gradient descent methods are so successful in solving non-convex optimization problems in learning large-scale neural networks (NN). After introducing a mathematical tool called canonical space, we have proved that the objective functions in learning NNs are convex in the canonical model space. We further elucidate that the gradients between the original NN model space and the canonical space are related by a pointwise linear transformation, which is represented by the so-called disparity matrix. Furthermore, we have proved that gradient descent methods surely converge to a global minimum of zero loss provided that the disparity matrices maintain full rank. If this full-rank condition holds, the learning of NNs behaves in the same way as normal convex optimization. At last, we have shown that the chance to have singular disparity matrices is extremely slim in large NNs. In particular, when over-parameterized NNs are randomly initialized, the gradient decent algorithms converge to a global minimum of zero loss in probability.

cs.LG↗

arXiv2023

FedTrip: A Resource-Efficient Federated Learning Method with Triplet Regularization

In the federated learning scenario, geographically distributed clients collaboratively train a global model. Data heterogeneity among clients significantly results in inconsistent model updates, which evidently slow down model convergence. To alleviate this issue, many methods employ regularization terms to narrow the discrepancy between client-side local models and the server-side global model. However, these methods impose limitations on the ability to explore superior local models and ignore the valuable information in historical models. Besides, although the up-to-date representation method simultaneously concerns the global and historical local models, it suffers from unbearable computation cost. To accelerate convergence with low resource consumption, we innovatively propose a model regularization method named FedTrip, which is designed to restrict global-local divergence and decrease current-historical correlation for alleviating the negative effects derived from data heterogeneity. FedTrip helps the current local model to be close to the global model while keeping away from historical local models, which contributes to guaranteeing the consistency of local updates among clients and efficiently exploring superior local models with negligible additional computation cost on attaching operations. Empirically, we demonstrate the superiority of FedTrip via extensive evaluations. To achieve the target accuracy, FedTrip outperforms the state-of-the-art baselines in terms of significantly reducing the total overhead of client-server communication and local computation.

cs.DC↗

arXiv2023

Stochastic volatility modeling of high-frequency CSI 300 index and dynamic jump prediction driven by machine learning

This paper models stochastic process of price time series of CSI 300 index in Chinese financial market, analyzes volatility characteristics of intraday high-frequency price data. In the new generalized Barndorff-Nielsen and Shephard model, the lag caused by asynchrony of market information is considered, and the problem of lack of long-term dependence is solved. To speed up the valuation process, several machine learning and deep learning algorithms are used to estimate parameter and evaluate forecast results. Tracking historical jumps of different magnitudes offers promising avenues for simulating dynamic price processes and predicting future jumps. Numerical results show that the deterministic component of stochastic volatility processes would always be captured over short and longer-term windows. Research finding could be suitable for influence investors and regulators interested in predicting market dynamics based on realized volatility.

q-fin.ST↗