arXiv subjects

Kevin Li

Publications and source records attributed to Kevin Li.

At least 37 records · Page 2Linked to original sources

arXiv2025

Combination of open covers with $π_1$-constraints

Let~$G$ be a group and let~$\mathcal{F}$ be a family of subgroups of~$G$. The generalised Lusternik--Schnirelmann category~$\operatorname{cat}_\mathcal{F}(G)$ is the minimal cardinality of covers of~$BG$ by open subsets with fundamental group in~$\mathcal{F}$. We prove a combination theorem for~$\operatorname{cat}_\mathcal{F}(G)$ in terms of the stabilisers of contractible $G$-CW-complexes. As applications for the amenable category, we obtain vanishing results for the simplicial volume of gluings of manifolds (along not necessarily amenable boundaries) and of cyclic branched coverings. Moreover, we deduce an upper bound for Farber's topological complexity, generalising an estimate for amalgamated products of Dranishnikov--Sadykov.

math.AT↗

arXiv2025

The Serre spectral sequence in bounded cohomology

We construct the analogue of the Serre spectral sequence for the bounded cohomology of simplicial sets with seminormed local coefficients. As applications, we obtain a (non-isometric) generalization of Gromov's mapping theorem and some partial results on the simplicial volume of manifold bundles.

math.AT↗

arXiv2025

Exploiting Concavity Information in Gaussian Process Contextual Bandit Optimization

The contextual bandit framework is widely used to solve sequential optimization problems where the reward of each decision depends on auxiliary context variables. In settings such as medicine, business, and engineering, the decision maker often possesses additional structural information on the generative model that can potentially be used to improve the efficiency of bandit algorithms. We consider settings in which the mean reward is known to be a concave function of the action for each fixed context. Examples include patient-specific dose-response curves in medicine and expected profit in online advertising auctions. We propose a contextual bandit algorithm that accelerates optimization by conditioning the posterior of a Bayesian Gaussian Process model on this concavity information. We design a novel shape-constrained reward function estimator using a specially chosen regression spline basis and constrained Gaussian Process posterior. Using this model, we propose a UCB algorithm and derive corresponding regret bounds. We evaluate our algorithm on numerical examples and test functions used to study optimal dosing of Anti-Clotting medication.

stat.ML↗

arXiv2025

A note on finiteness properties of vertex stabilisers

We prove a criterion for the geometric and algebraic finiteness properties of vertex stabilisers of $G$-CW-complexes, given the finiteness properties of the group $G$ and of the stabilisers of positive dimensional cells. This generalises a result of Haglund--Wise for groups acting on trees to higher dimensions. As an application, for $n\ge 2$, we deduce the existence of uncountably many quasi-isometry classes of one-ended groups that are of type $\mathsf{FP}_n$ and not of type $\mathsf{FP}_{n+1}$.

math.GR↗

arXiv2025

How Far are App Secrets from Being Stolen? A Case Study on Android

Android apps can hold secret strings of themselves such as cloud service credentials or encryption keys. Leakage of such secret strings can induce unprecedented consequences like monetary losses or leakage of user private information. In practice, various security issues were reported because many apps failed to protect their secrets. However, little is known about the types, usages, exploitability, and consequences of app secret leakage issues. While a large body of literature has been devoted to studying user private information leakage, there is no systematic study characterizing app secret leakage issues. How far are Android app secrets from being stolen? To bridge this gap, we conducted the first systematic study to characterize app secret leakage issues in Android apps based on 575 potential app secrets sampled from 14,665 popular Android apps on Google Play. We summarized the common categories of leaked app secrets, assessed their security impacts and disclosed app bad practices in storing app secrets. We devised a text mining strategy using regular expressions and demonstrated that numerous app secrets can be easily stolen, even from the highly popular Android apps on Google. In a follow-up study, we harvested 3,711 distinct exploitable app secrets through automatic analysis. Our findings highlight the prevalence of this problem and call for greater attention to app secret protection.

cs.CR↗

arXiv2024

The Spectral Distribution of Random Graphs with Given Degree Sequences

In this article, we study random graphs with a given degree sequence $d_1, d_2, \cdots, d_n$ from the configuration model. We show that under mild assumptions of the degree sequence, the spectral distribution of the normalized Laplacian matrix of such random graph converges in distribution to the semicircle distribution as the number of vertices $n\rightarrow \infty$. This extends work by McKay (1981) and Tran, Vu and Wang (2013) which studied random regular graphs ($d_1=d_2=\cdots=d_n=d$). Furthermore, we extend the assumption to show that a slightly more general condition is equivalent to the weak convergence to semicircle distribution. The equivalence is also illustrated by numerical simulations.

math.PR↗

arXiv2024

Faster randomized partial trace estimation

We develop randomized matrix-free algorithms for estimating partial traces, a generalization of the trace arising in quantum physics and chemistry. Our algorithm improves on the typicality-based approach used in [T. Chen and Y-C. Cheng, \emph{Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems}, J. Chem. Phys. 157, 064106 (2022)] by deflating important subspaces (e.g. corresponding to the low-energy eigenstates) explicitly. This results in a significant variance reduction, leading to several order-of-magnitude speedups over the previous state of the art. We then apply our algorithm to study the thermodynamics of several Heisenberg spin systems, particularly the entanglement spectrum and ergotropy.

math.NA↗

arXiv2024

TalkMosaic: Interactive PhotoMosaic with Multi-modal LLM Q&A Interactions

We use images of cars of a wide range of varieties to compose an image of an animal such as a bird or a lion for the theme of environmental protection to maximize the information about cars in a single composed image and to raise the awareness about environmental challenges. We present a novel way of image interaction with an artistically-composed photomosaic image, in which a simple operation of "click and display" is used to demonstrate the interactive switch between a tile image in a photomosaic image and the corresponding original car image, which will be automatically saved on the Desktop. We build a multimodal custom GPT named TalkMosaic by incorporating car images information and the related knowledge to ChatGPT. By uploading the original car image to TalkMosaic, we can ask questions about the given car image and get the corresponding answers efficiently and effectively such as where to buy the tire in the car image that satisfies high environmental standards. We give an in-depth analysis on how to speed up the inference of multimodal LLM using sparse attention and quantization techniques with presented probabilistic FlashAttention (PrFlashAttention) and Staircase Adaptive Quantization (SAQ) methods. The implemented prototype demonstrates the feasibility and effectiveness of the presented approach.

cs.CV↗

arXiv2024

Analysis on Riemann Hypothesis with Cross Entropy Optimization and Reasoning

In this paper, we present a novel framework for the analysis of Riemann Hypothesis [27], which is composed of three key components: a) probabilistic modeling with cross entropy optimization and reasoning; b) the application of the law of large numbers; c) the application of mathematical inductions. The analysis is mainly conducted by virtue of probabilistic modeling of cross entropy optimization and reasoning with rare event simulation techniques. The application of the law of large numbers [2, 3, 6] and the application of mathematical inductions make the analysis of Riemann Hypothesis self-contained and complete to make sure that the whole complex plane is covered as conjectured in Riemann Hypothesis. We also discuss the method of enhanced top-p sampling with large language models (LLMs) for reasoning, where next token prediction is not just based on the estimated probabilities of each possible token in the current round but also based on accumulated path probabilities among multiple top-k chain of thoughts (CoTs) paths. The probabilistic modeling of cross entropy optimization and reasoning may suit well with the analysis of Riemann Hypothesis as Riemann Zeta functions are inherently dealing with the sums of infinite components of a complex number series. We hope that our analysis in this paper could shed some light on some of the insights of Riemann Hypothesis. The framework and techniques presented in this paper, coupled with recent developments with chain of thought (CoT) or diagram of thought (DoT) reasoning in large language models (LLMs) with reinforcement learning (RL) [1, 7, 18, 21, 24, 34, 39-41], could pave the way for eventual proof of Riemann Hypothesis [27].

cs.AI↗

arXiv2024

Cross-Entropy Optimization for Hyperparameter Optimization in Stochastic Gradient-based Approaches to Train Deep Neural Networks

In this paper, we present a cross-entropy optimization method for hyperparameter optimization in stochastic gradient-based approaches to train deep neural networks. The value of a hyperparameter of a learning algorithm often has great impact on the performance of a model such as the convergence speed, the generalization performance metrics, etc. While in some cases the hyperparameters of a learning algorithm can be part of learning parameters, in other scenarios the hyperparameters of a stochastic optimization algorithm such as Adam [5] and its variants are either fixed as a constant or are kept changing in a monotonic way over time. We give an in-depth analysis of the presented method in the framework of expectation maximization (EM). The presented algorithm of cross-entropy optimization for hyperparameter optimization of a learning algorithm (CEHPO) can be equally applicable to other areas of optimization problems in deep learning. We hope that the presented methods can provide different perspectives and offer some insights for optimization problems in different areas of machine learning and beyond.

cs.LG↗

arXiv2024

Diffusion Explainer: Visual Explanation for Text-to-image Stable Diffusion

Diffusion-based generative models' impressive ability to create convincing images has garnered global attention. However, their complex structures and operations often pose challenges for non-experts to grasp. We present Diffusion Explainer, the first interactive visualization tool that explains how Stable Diffusion transforms text prompts into images. Diffusion Explainer tightly integrates a visual overview of Stable Diffusion's complex structure with explanations of the underlying operations. By comparing image generation of prompt variants, users can discover the impact of keyword changes on image generation. A 56-participant user study demonstrates that Diffusion Explainer offers substantial learning benefits to non-experts. Our tool has been used by over 10,300 users from 124 countries at https://poloclub.github.io/diffusion-explainer/.

cs.CL↗

arXiv2024

Demystifying Device-specific Compatibility Issues in Android Apps

The Android ecosystem is profoundly fragmented due to the frequent updates of the Android system and the prevalent customizations by mobile device manufacturers. Previous research primarily focused on identifying and repairing evolution-induced API compatibility issues, with limited consideration of devices-specific compatibility issues (DSC issues). To fill this gap, we conduct an empirical study of 197 DSC issues collected from 94 open-source repositories on GitHub. We introduce a new perspective for comprehending these issues by categorizing them into two principal groups, Functionality Breaks, and OEM Features, based on their manifestations and root causes. The functionality break issues disrupt standard Android system behaviors, lead to crashes or unexpected behaviors on specific devices, and require developers to implement workarounds to preserve the original functionality. The OEM feature issues involve the introduction of device-specific functionalities or features beyond the basic Android system. The different nature of functionality break issues and OEM feature issues lead to unique challenges in addressing them. Common solutions for functionality break issues involve calling additional APIs, substituting problematic ones, or using specific parameters, while resolving OEM feature issues often relies on Android inter-component communication methods and reflection, with additional unconventional strategies. Such observations highlight the distinctive challenges in addressing DSC issues in Android apps and will facilitate the future development of testing and analysis tools targeting these issues. Our study demonstrates that Functionality break and OEM feature issues have different characteristics, and future research may need to investigate them separately.

cs.SE↗

arXiv2024

Multivariate Bayesian dynamic modeling for causal prediction

Bayesian forecasting is developed in multivariate time series analysis for causal inference. Causal evaluation of sequentially observed time series data from control and treated units focuses on the impacts of interventions using contemporaneous outcomes in control units. Methodological developments here concern multivariate dynamic models for time-varying effects across multiple treated units with explicit foci on sequential learning and aggregation of intervention effects. Analysis explores dimension reduction across multiple synthetic counterfactual predictors. Computational advances leverage fully conjugate models for efficient sequential learning and inference, including cross-unit correlations and their time variation. This allows full uncertainty quantification on model hyper-parameters via Bayesian model averaging. A detailed case study evaluates interventions in a supermarket promotions experiment, with coupled predictive analyses in selected regions of a large-scale commercial system. Comparisons with existing methods highlight the issues of appropriate uncertainty quantification in casual inference in aggregation across treated units, among other practical concerns.

stat.ME↗

arXiv2024

Compositional dynamic modelling for causal prediction in multivariate time series

Theoretical developments in sequential Bayesian analysis of multivariate dynamic models underlie new methodology for causal prediction. This extends the utility of existing models with computationally efficient methodology, enabling routine exploration of Bayesian counterfactual analyses with multiple selected time series as synthetic controls. Methodological contributions also define the concept of outcome adaptive modelling to monitor and inferentially respond to changes in experimental time series following interventions designed to explore causal effects. The benefits of sequential analyses with time-varying parameter models for causal investigations are inherited in this broader setting. A case study in commercial causal analysis-- involving retail revenue outcomes related to marketing interventions-- highlights the methodological advances.

stat.ME↗

arXiv2024

Interactive Visual Learning for Stable Diffusion

Diffusion-based generative models' impressive ability to create convincing images has garnered global attention. However, their complex internal structures and operations often pose challenges for non-experts to grasp. We introduce Diffusion Explainer, the first interactive visualization tool designed to elucidate how Stable Diffusion transforms text prompts into images. It tightly integrates a visual overview of Stable Diffusion's complex components with detailed explanations of their underlying operations. This integration enables users to fluidly transition between multiple levels of abstraction through animations and interactive elements. Offering real-time hands-on experience, Diffusion Explainer allows users to adjust Stable Diffusion's hyperparameters and prompts without the need for installation or specialized hardware. Accessible via users' web browsers, Diffusion Explainer is making significant strides in democratizing AI education, fostering broader public access. More than 7,200 users spanning 113 countries have used our open-sourced tool at https://poloclub.github.io/diffusion-explainer/. A video demo is available at https://youtu.be/MbkIADZjPnA.

cs.HC↗

arXiv2024

Dynamic control of 2D non-Hermitian photonic corner states in synthetic dimensions

Non-Hermitian models describe the physics of ubiquitous open systems with gain and loss. One intriguing aspect of non-Hermitian models is their inherent topology that can produce intriguing boundary phenomena like resilient higher-order topological insulators (HOTIs) and non-Hermitian skin effects (NHSE). Recently, time-multiplexed lattices in synthetic dimensions have emerged as a versatile platform for the investigation of these effects free of geometric restrictions. Despite holding broad applications, studies of these effects have been limited to static cases so far, and full dynamical control over the non-Hermitian effects has remained elusive. Here, we demonstrate the emergence of topological non-Hermitian corner states with remarkable temporal controllability and robustness in a two-dimensional photonic synthetic time lattice. Specifically, we showcase various dynamic control mechanisms for light confinement and flow, including spatial mode tapering, sequential non-Hermiticity on-off switching, dynamical corner state relocation, and light steering. Moreover, we establish the corner state's robustness in the presence of intensity modulation randomness and quantitatively determine its breakdown regime. Our findings extend non-Hermitian and topological photonic effects into higher synthetic dimensions, offering remarkable flexibility and real-time control possibilities. This opens avenues for topological classification, quantum walk simulations of many-body dynamics, and robust Floquet engineering, free from the limitations of physical geometries.

physics.optics↗

arXiv2023

Using Guided Transfer Learning to Predispose AI Agent to Learn Efficiently from Small RNA-sequencing Datasets

Given the increasing availability of RNA-seq data and its complex and heterogeneous nature, there has been growing interest in applying AI/machine learning methodologies to work with such data modalities. However, because omics data is characterized by high dimensionality and low sample size (HDLSS), current attempts at integrating AI in this domain require significant human guidance and expertise to mitigate overfitting. In this work we look at how transfer learning can be improved to learn from small RNA-seq sample sizes without significant human interference. The strategy is to gain general prior knowledge about a particular domain of data (e.g. RNA-seq data) by pre-training on a general task with a large aggregate of data, then fine-tuning to various specific, downstream target tasks in the same domain. Because previous attempts have shown traditional transfer learning failing on HLDSS, we propose to improve performance by using Guided Transfer Learning (GTL). Collaborating with Robots Go Mental, the AI we deploy here not only learns good initial parameters during pre-training, but also learns inductive biases that affect how the AI learns downstream tasks. In this approach, we first pre-trained on recount3 data, a collection of over 400,000 mouse RNA-seq samples sourced from thousands of individual studies. With such a large collection, patterns of expression between the ~30,000 genes in mammalian systems were pre-determined. Such patterns were sufficient for the pre-trained AI agent to efficiently learn new downstream tasks involving RNA-seq datasets with very low sample sizes and performed notably better on few-shot learning tasks compared to the same model without pre-training.

q-bio.GN↗

arXiv2023

ProSpar-GP: scalable Gaussian process modeling with massive non-stationary datasets

Gaussian processes (GPs) are a popular class of Bayesian nonparametric models, but its training can be computationally burdensome for massive training datasets. While there has been notable work on scaling up these models for big data, existing methods typically rely on a stationary GP assumption for approximation, and can thus perform poorly when the underlying response surface is non-stationary, i.e., it has some regions of rapid change and other regions with little change. Such non-stationarity is, however, ubiquitous in real-world problems, including our motivating application for surrogate modeling of computer experiments. We thus propose a new Product of Sparse GP (ProSpar-GP) method for scalable GP modeling with massive non-stationary data. The ProSpar-GP makes use of a carefully-constructed product-of-experts formulation of sparse GP experts, where different experts are placed within local regions of non-stationarity. These GP experts are fit via a novel variational inference approach, which capitalizes on mini-batching and GPU acceleration for efficient optimization of inducing points and length-scale parameters for each expert. We further show that the ProSpar-GP is Kolmogorov-consistent, in that its generative distribution defines a valid stochastic process over the prediction space; such a property provides essential stability for variational inference, particularly in the presence of non-stationarity. We then demonstrate the improved performance of the ProSpar-GP over the state-of-the-art, in a suite of numerical experiments and an application for surrogate modeling of a satellite drag simulator.

stat.ME↗