arXiv subjects

Yinan Li

Publications and source records attributed to Yinan Li.

At least 37 records · Page 2Linked to original sources

arXiv2025

Second-Order Bounds for [0,1]-Valued Regression via Betting Loss

We consider the $[0,1]$-valued regression problem in the i.i.d. setting. In a related problem called cost-sensitive classification, \citet{foster21efficient} have shown that the log loss minimizer achieves an improved generalization bound compared to that of the squared loss minimizer in the sense that the bound scales with the cost of the best classifier, which can be arbitrarily small depending on the problem at hand. Such a result is often called a first-order bound. For $[0,1]$-valued regression, we first show that the log loss minimizer leads to a similar first-order bound. We then ask if there exists a loss function that achieves a variance-dependent bound (also known as a second order bound), which is a strict improvement upon first-order bounds. We answer this question in the affirmative by proposing a novel loss function called the betting loss. Our result is ``variance-adaptive'' in the sense that the bound is attained \textit{without any knowledge about the variance}, which is in contrast to modeling label (or reward) variance or the label distribution itself explicitly as part of the function class such as distributional reinforcement learning.

cs.LG↗

arXiv2025

Online Quantum State Tomography via Stochastic Gradient Descent

We initiate the study of online quantum state tomography (QST), where the matrix representation of an unknown quantum state is reconstructed by sequentially performing a batch of measurements and updating the state estimate using only the measurement statistics from the current round. Motivated by recent advances in non-convex optimization algorithms for solving low-rank QST, we propose non-convex mini-batch stochastic gradient descent (SGD) algorithms to tackle online QST, which leverage the low-rank structure of the unknown quantum state and are well-suited for practical applications. Our main technical contribution is a rigorous convergence analysis of these algorithms. With proper initialization, we demonstrate that the SGD algorithms for online low-rank QST achieve linear convergence both in expectation and with high probability. Our algorithms achieve nearly optimal sample complexity while remaining highly memory-efficient. In particular, their time complexities are better than the state-of-the-art non-convex QST algorithms, in terms of the rank and the logarithm of the dimension of the unknown quantum state.

quant-ph↗

arXiv2025

Unleashing High-Quality Image Generation in Diffusion Sampling Using Second-Order Levenberg-Marquardt-Langevin

The diffusion models (DMs) have demonstrated the remarkable capability of generating images via learning the noised score function of data distribution. Current DM sampling techniques typically rely on first-order Langevin dynamics at each noise level, with efforts concentrated on refining inter-level denoising strategies. While leveraging additional second-order Hessian geometry to enhance the sampling quality of Langevin is a common practice in Markov chain Monte Carlo (MCMC), the naive attempts to utilize Hessian geometry in high-dimensional DMs lead to quadratic-complexity computational costs, rendering them non-scalable. In this work, we introduce a novel Levenberg-Marquardt-Langevin (LML) method that approximates the diffusion Hessian geometry in a training-free manner, drawing inspiration from the celebrated Levenberg-Marquardt optimization algorithm. Our approach introduces two key innovations: (1) A low-rank approximation of the diffusion Hessian, leveraging the DMs' inherent structure and circumventing explicit quadratic-complexity computations; (2) A damping mechanism to stabilize the approximated Hessian. This LML approximated Hessian geometry enables the diffusion sampling to execute more accurate steps and improve the image generation quality. We further conduct a theoretical analysis to substantiate the approximation error bound of low-rank approximation and the convergence property of the damping mechanism. Extensive experiments across multiple pretrained DMs validate that the LML method significantly improves image generation quality, with negligible computational overhead.

cs.CV↗

arXiv2025

Efficiently Access Diffusion Fisher: Within the Outer Product Span Space

Recent Diffusion models (DMs) advancements have explored incorporating the second-order diffusion Fisher information (DF), defined as the negative Hessian of log density, into various downstream tasks and theoretical analysis. However, current practices typically approximate the diffusion Fisher by applying auto-differentiation to the learned score network. This black-box method, though straightforward, lacks any accuracy guarantee and is time-consuming. In this paper, we show that the diffusion Fisher actually resides within a space spanned by the outer products of score and initial data. Based on the outer-product structure, we develop two efficient approximation algorithms to access the trace and matrix-vector multiplication of DF, respectively. These algorithms bypass the auto-differentiation operations with time-efficient vector-product calculations. Furthermore, we establish the approximation error bounds for the proposed algorithms. Experiments in likelihood evaluation and adjoint optimization demonstrate the superior accuracy and reduced computational cost of our proposed algorithms. Additionally, based on the novel outer-product formulation of DF, we design the first numerical verification experiment for the optimal transport property of the general PF-ODE deduced map.

cs.LG↗

arXiv2025

On average orders of automorphism groups of bilinear maps over finite fields

Let $φ:V\times V\to W$ be a bilinear map of finite vector spaces $V$ and $W$ over a finite field $\mathbb{F}_q$. We present asymptotic bounds on the number of isomorphism classes of bilinear maps under the natural action of $\mathrm{GL}(V)$ and $\mathrm{GL}(W)$, when $\dim(V)$ and $\dim(W)$ are linearly related. As motivations and applications of the results, we present almost tight upper bounds on the number of $p$-groups of Frattini class $2$ as first studied by Higman (Proc. Lond. Math. Soc., 1960). Such bounds lead to answers for some open questions by Blackburn, Neumann, and Venkataraman (Cambridge Tracts in Mathematics, 2007). Further applications include sampling matrix spaces with the trivial automorphism group, and asymptotic bounds on the number of isomorphism classes of finite cube-zero commutative algebras.

math.CO↗

arXiv2024

Noise-Augmented $\ell_0$ Regularization of Tensor Regression with Tucker Decomposition

Tensor data are multi-dimension arrays. Low-rank decomposition-based regression methods with tensor predictors exploit the structural information in tensor predictors while significantly reducing the number of parameters in tensor regression. We propose a method named NA$_0$CT$^2$ (Noise Augmentation for $\ell_0$ regularization on Core Tensor in Tucker decomposition) to regularize the parameters in tensor regression (TR), coupled with Tucker decomposition. We establish theoretically that NA$_0$CT$^2$ achieves exact $\ell_0$ regularization on the core tensor from the Tucker decomposition in linear TR and generalized linear TR. To our knowledge, NA$_0$CT$^2$ is the first Tucker decomposition-based regularization method in TR to achieve $\ell_0$ in core tensors. NA$_0$CT$^2$ is implemented through an iterative procedure and involves two straightforward steps in each iteration -- generating noisy data based on the core tensor from the Tucker decomposition of the updated parameter estimate and running a regular GLM on noise-augmented data on vectorized predictors. We demonstrate the implementation of NA$_0$CT$^2$ and its $\ell_0$ regularization effect in both simulation studies and real data applications. The results suggest that NA$_0$CT$^2$ can improve predictions compared to other decomposition-based TR approaches, with or without regularization and it identifies important predictors though not designed for that purpose.

stat.ML↗

arXiv2024

Non-asymptotic Approximation Error Bounds of Parameterized Quantum Circuits

Parameterized quantum circuits (PQCs) have emerged as a promising approach for quantum neural networks. However, understanding their expressive power in accomplishing machine learning tasks remains a crucial question. This paper investigates the expressivity of PQCs for approximating general multivariate function classes. Unlike previous Universal Approximation Theorems for PQCs, which are either nonconstructive or rely on parameterized classical data processing, we explicitly construct data re-uploading PQCs for approximating multivariate polynomials and smooth functions. We establish the first non-asymptotic approximation error bounds for these functions in terms of the number of qubits, quantum circuit depth, and number of trainable parameters. Notably, we demonstrate that for approximating functions that satisfy specific smoothness criteria, the quantum circuit size and number of trainable parameters of our proposed PQCs can be smaller than those of deep ReLU neural networks. We further validate the approximation capability of PQCs through numerical experiments. Our results provide a theoretical foundation for designing practical PQCs and quantum neural networks for machine learning tasks that can be implemented on near-term quantum devices, paving the way for the advancement of quantum machine learning.

quant-ph↗

arXiv2024

Efficient Active Learning Halfspaces with Tsybakov Noise: A Non-convex Optimization Approach

We study the problem of computationally and label efficient PAC active learning $d$-dimensional halfspaces with Tsybakov Noise~\citep{tsybakov2004optimal} under structured unlabeled data distributions. Inspired by~\cite{diakonikolas2020learning}, we prove that any approximate first-order stationary point of a smooth nonconvex loss function yields a halfspace with a low excess error guarantee. In light of the above structural result, we design a nonconvex optimization-based algorithm with a label complexity of $\tilde{O}(d (\frac{1}ε)^{\frac{8-6α}{3α-1}})$, under the assumption that the Tsybakov noise parameter $α\in (\frac13, 1]$, which narrows down the gap between the label complexities of the previously known efficient passive or active algorithms~\citep{diakonikolas2020polynomial,zhang2021improved} and the information-theoretic lower bound in this setting.

cs.LG↗

arXiv2024

Quantum Compiling with Reinforcement Learning on a Superconducting Processor

To effectively implement quantum algorithms on noisy intermediate-scale quantum (NISQ) processors is a central task in modern quantum technology. NISQ processors feature tens to a few hundreds of noisy qubits with limited coherence times and gate operations with errors, so NISQ algorithms naturally require employing circuits of short lengths via quantum compilation. Here, we develop a reinforcement learning (RL)-based quantum compiler for a superconducting processor and demonstrate its capability of discovering novel and hardware-amenable circuits with short lengths. We show that for the three-qubit quantum Fourier transformation, a compiled circuit using only seven CZ gates with unity circuit fidelity can be achieved. The compiler is also able to find optimal circuits under device topological constraints, with lengths considerably shorter than those by the conventional method. Our study exemplifies the codesign of the software with hardware for efficient quantum compilation, offering valuable insights for the advancement of RL-based compilers.

quant-ph↗

arXiv2024

AdapTics: A Toolkit for Creative Design and Integration of Real-Time Adaptive Mid-Air Ultrasound Tactons

Mid-air ultrasound haptic technology can enhance user interaction and immersion in extended reality (XR) applications through contactless touch feedback. Yet, existing design tools for mid-air haptics primarily support creating tactile sensations (i.e., tactons) which cannot change at runtime. These tactons lack expressiveness in interactive scenarios where a continuous closed-loop response to user movement or environmental states is desirable. This paper introduces AdapTics, a toolkit featuring a graphical interface for rapid prototyping of adaptive tactons-dynamic sensations that can adjust at runtime based on user interactions, environmental changes, or other inputs. A software library and a Unity package accompany the graphical interface to enable integration of adaptive tactons in existing applications. We present the design space offered by AdapTics for creating adaptive mid-air ultrasound tactons and show the design tool can improve Creativity Support Index ratings for Exploration and Expressiveness in a user study with 12 XR and haptic designers.

cs.HC↗

arXiv2023

HGE: Embedding Temporal Knowledge Graphs in a Product Space of Heterogeneous Geometric Subspaces

Temporal knowledge graphs represent temporal facts $(s,p,o,τ)$ relating a subject $s$ and an object $o$ via a relation label $p$ at time $τ$, where $τ$ could be a time point or time interval. Temporal knowledge graphs may exhibit static temporal patterns at distinct points in time and dynamic temporal patterns between different timestamps. In order to learn a rich set of static and dynamic temporal patterns and apply them for inference, several embedding approaches have been suggested in the literature. However, as most of them resort to single underlying embedding spaces, their capability to model all kinds of temporal patterns was severely limited by having to adhere to the geometric property of their one embedding space. We lift this limitation by an embedding approach that maps temporal facts into a product space of several heterogeneous geometric subspaces with distinct geometric properties, i.e.\ Complex, Dual, and Split-complex spaces. In addition, we propose a temporal-geometric attention mechanism to integrate information from different geometric subspaces conveniently according to the captured relational and temporal information. Experimental results on standard temporal benchmark datasets favorably evaluate our approach against state-of-the-art models.

cs.AI↗

arXiv2023

Dynamic quantum circuit compilation

Quantum computing has shown tremendous promise in addressing complex computational problems, yet its practical realization is hindered by the limited availability of qubits for computation. Recent advancements in quantum hardware have introduced mid-circuit measurements and resets, enabling the reuse of measured qubits and significantly reducing the qubit requirements for executing quantum algorithms. In this work, we present a systematic study of dynamic quantum circuit compilation, a process that transforms static quantum circuits into their dynamic equivalents with a reduced qubit count through qubit-reuse. We establish the first general framework for optimizing the dynamic circuit compilation via graph manipulation. In particular, we completely characterize the optimal quantum circuit compilation using binary integer programming, provide efficient algorithms for determining whether a given quantum circuit can be reduced to a smaller circuit and present heuristic algorithms for devising dynamic compilation schemes in general. Furthermore, we conduct a thorough analysis of quantum circuits with practical relevance, offering optimal compilations for well-known quantum algorithms in quantum computation, ansatz circuits utilized in quantum machine learning, and measurement-based quantum computation crucial for quantum networking. We also perform a comparative analysis against state-of-the-art approaches, demonstrating the superior performance of our methods in both structured and random quantum circuits. Our framework lays a rigorous foundation for comprehending dynamic quantum circuit compilation via qubit-reuse, bridging the gap between theoretical quantum algorithms and their physical implementation on quantum computers with limited resources.

quant-ph↗

arXiv2023

Semi-Supervised Panoptic Narrative Grounding

Despite considerable progress, the advancement of Panoptic Narrative Grounding (PNG) remains hindered by costly annotations. In this paper, we introduce a novel Semi-Supervised Panoptic Narrative Grounding (SS-PNG) learning scheme, capitalizing on a smaller set of labeled image-text pairs and a larger set of unlabeled pairs to achieve competitive performance. Unlike visual segmentation tasks, PNG involves one pixel belonging to multiple open-ended nouns. As a result, existing multi-class based semi-supervised segmentation frameworks cannot be directly applied to this task. To address this challenge, we first develop a novel SS-PNG Network (SS-PNG-NW) tailored to the SS-PNG setting. We thoroughly investigate strategies such as Burn-In and data augmentation to determine the optimal generic configuration for the SS-PNG-NW. Additionally, to tackle the issue of imbalanced pseudo-label quality, we propose a Quality-Based Loss Adjustment (QLA) approach to adjust the semi-supervised objective, resulting in an enhanced SS-PNG-NW+. Employing our proposed QLA, we improve BCE Loss and Dice loss at pixel and mask levels, respectively. We conduct extensive experiments on PNG datasets, with our SS-PNG-NW+ demonstrating promising results comparable to fully-supervised models across all data ratios. Remarkably, our SS-PNG-NW+ outperforms fully-supervised models with only 30% and 50% supervision data, exceeding their performance by 0.8% and 1.1% respectively. This highlights the effectiveness of our proposed SS-PNG-NW+ in overcoming the challenges posed by limited annotations and enhancing the applicability of PNG tasks. The source code is available at https://github.com/nini0919/SSPNG.

cs.CV↗

arXiv2023

On linear-algebraic notions of expansion

A fundamental fact about bounded-degree graph expanders is that three notions of expansion -- vertex expansion, edge expansion, and spectral expansion -- are all equivalent. In this paper, we study to what extent such a statement is true for linear-algebraic notions of expansion. There are two well-studied notions of linear-algebraic expansion, namely dimension expansion (defined in analogy to graph vertex expansion) and quantum expansion (defined in analogy to graph spectral expansion). Lubotzky and Zelmanov proved that the latter implies the former. We prove that the converse is false: there are dimension expanders which are not quantum expanders. Moreover, this asymmetry is explained by the fact that there are two distinct linear-algebraic analogues of graph edge expansion. The first of these is quantum edge expansion, which was introduced by Hastings, and which he proved to be equivalent to quantum expansion. We introduce a new notion, termed dimension edge expansion, which we prove is equivalent to dimension expansion and which is implied by quantum edge expansion. Thus, the separation above is implied by a finer one: dimension edge expansion is strictly weaker than quantum edge expansion. This new notion also leads to a new, more modular proof of the Lubotzky--Zelmanov result that quantum expanders are dimension expanders.

math.CO↗

arXiv2022

Clover: Towards A Unified Video-Language Alignment and Fusion Model

Building a universal Video-Language model for solving various video understanding tasks (\emph{e.g.}, text-video retrieval, video question answering) is an open challenge to the machine learning field. Towards this goal, most recent works build the model by stacking uni-modal and cross-modal feature encoders and train it with pair-wise contrastive pre-text tasks. Though offering attractive generality, the resulted models have to compromise between efficiency and performance. They mostly adopt different architectures to deal with different downstream tasks. We find this is because the pair-wise training cannot well \emph{align} and \emph{fuse} features from different modalities. We then introduce \textbf{Clover}\textemdash a Correlated Video-Language pre-training method\textemdash towards a universal Video-Language model for solving multiple video understanding tasks with neither performance nor efficiency compromise. It improves cross-modal feature alignment and fusion via a novel tri-modal alignment pre-training task. Additionally, we propose to enhance the tri-modal alignment via incorporating learning from semantic masked samples and a new pair-wise ranking loss. Clover establishes new state-of-the-arts on multiple downstream tasks, including three retrieval tasks for both zero-shot and fine-tuning settings, and eight video question answering tasks. Codes and pre-trained models will be released at \url{https://github.com/LeeYN-43/Clover}.

cs.CV↗

arXiv2022

Connections between graphs and matrix spaces

Given a bipartite graph $G$, the graphical matrix space $\mathcal{S}_G$ consists of matrices whose non-zero entries can only be at those positions corresponding to edges in $G$. Tutte (J. London Math. Soc., 1947), Edmonds (J. Res. Nat. Bur. Standards Sect. B, 1967) and Lovász (FCT, 1979) observed connections between perfect matchings in $G$ and full-rank matrices in $\mathcal{S}_G$. Dieudonné ({Arch. Math., 1948) proved a tight upper bound on the dimensions of those matrix spaces containing only singular matrices. The starting point of this paper is a simultaneous generalization of these two classical results: we show that the largest dimension over subspaces of $\mathcal{S}_G$ containing only singular matrices is equal to the maximum size over subgraphs of $G$ without perfect matchings, based on Meshulam's proof of Dieudonné's result (Quart. J. Math., 1985). Starting from this result, we go on to establish more connections between properties of graphs and matrix spaces. For example, we establish connections between acyclicity and nilpotency, between strong connectivity and irreducibility, and between isomorphism and conjugacy/congruence. For each connection, we study three types of correspondences, namely the basic correspondence, the inherited correspondence (for subgraphs and subspaces), and the induced correspondence (for induced subgraphs and restrictions). Some correspondences lead to intriguing generalizations of classical results, such as for Dieudonné's result mentioned above, and for a celebrated theorem of Gerstenhaber regarding the largest dimension of nil matrix spaces (Amer. J. Math., 1958). Finally, we show some implications of our results to quantum information and present open problems in computational complexity motivated by these results.

math.CO↗

arXiv2022

On a tracial version of Haemers bound

We extend upper bounds on the quantum independence number and the quantum Shannon capacity of graphs to their counterparts in the commuting operator model. We introduce a von Neumann algebraic generalization of the fractional Haemers bound (over $\mathbb{C}$) and prove that the generalization upper bounds the commuting quantum independence number. We call our bound the tracial Haemers bound, and we prove that it is multiplicative with respect to the strong product. In particular, this makes it an upper bound on the Shannon capacity. The tracial Haemers bound is incomparable with the Lovász theta function, another well-known upper bound on the Shannon capacity. We show that separating the tracial and fractional Haemers bounds would refute Connes' embedding conjecture. Along the way, we prove that the tracial rank and tracial Haemers bound are elements of the (commuting quantum) asymptotic spectrum of graphs (Zuiddam, Combinatorica, 2019). We also show that the inertia bound (an upper bound on the quantum independence number) upper bounds the commuting quantum independence number.

quant-ph↗

arXiv2022

Adaptive Noisy Data Augmentation for Regularized Estimation and Inference in Generalized Linear Models

We propose the AdaPtive Noise Augmentation (PANDA) procedure to regularize the estimation and inference of generalized linear models (GLMs). PANDA iteratively optimizes the objective function given noise augmented data until convergence to obtain the regularized model estimates. The augmented noises are designed to achieve various regularization effects, including $l_0$, bridge (lasso and ridge included), elastic net, adaptive lasso, and SCAD, as well as group lasso and fused ridge. We examine the tail bound of the noise-augmented loss function and establish the almost sure convergence of the noise-augmented loss function and its minimizer to the expected penalized loss function and its minimizer, respectively. We derive the asymptotic distributions for the regularized parameters, based on which, inferences can be obtained simultaneously with variable selection. PANDA exhibits ensemble learning behaviors that help further decrease the generalization error. Computationally, PANDA is easy to code, leveraging existing software for implementing GLMs, without resorting to complicated optimization techniques. We demonstrate the superior or similar performance of PANDA against the existing approaches of the same type of regularizers in simulated and real-life data. We show that the inferences through PANDA achieve nominal or near-nominal coverage and are far more efficient compared to a popular existing post-selection procedure.

stat.ML↗