arXiv subjects

Yinan Li

Publications and source records attributed to Yinan Li.

At least 19 recordsLinked to original sources

arXiv2026

Virtual quantum neural networks

Quantum neural networks are a prominent model of quantum machine learning. Their training consists in the minimization of a given loss function over a parametrized family of quantum circuits, mathematically described by unitary operators, or, more generally, completely positive linear maps. In this work, we extend the notion of quantum neural network, using random sampling and classical data processing to enlarge the optimization space in a way that includes linear combinations of completely positive maps. Our extended model, called virtual quantum neural networks, leverages its enlarged optimization space to achieve increased expressivity and improved noise robustness. These benefits are illustrated in three representative tasks: quantum error mitigation, binary classification, and estimation of ground-state energies. Overall, virtual quantum neural networks offer a flexible learning paradigm that expands the space of achievable computations and strengthens the applications of near-term quantum hardware.

quant-ph↗

arXiv2026

One Is Not Enough: The Untold Story of Multiple Security Patches for One Vulnerability

Security patches (SPs) are the main mechanism for fixing software vulnerabilities, yet a single vulnerability is not always resolved by a single patch: fixes may be completed incrementally, propagated across maintained branches, or replicated across related repositories. When patch records are incomplete, downstream users may observe only part of the required fix set and therefore apply only partial patching. However, comprehensive patch discovery remains difficult because the prevalence and causes of the multi-SP phenomenon are still poorly understood. In this paper, we present the first large-scale empirical study of multi-SP vulnerabilities. By merging four major vulnerability databases, we construct a dataset of 6,053 multi-SP CVEs with 16,260 SPs, showing that 20.6% of CVEs with patches involve multiple SPs and that merging databases increases recognized multi-SP CVE counts by 36-55% over any single source. We further analyze why a vulnerability is associated with multiple SPs and derive a two-level taxonomy with 6 categories and 16 sub-categories. Based on these findings, we develop SPectre, a taxonomy-driven prototype for comprehensive patch discovery. On 300 multi-SP CVEs, after manually verifying ground-truth SPs, SPectre improves multi-SP patch coverage over representative patch localization baselines, achieving 0.927 recall on same-repository cases and 0.873 recall on cross-repository cases after manual ground truth verification. On 100 recent CVEs recorded as single-patch by all public databases, SPectre further discovers 28 previously unreported SPs across 20 CVEs. Our results show that multi-SP vulnerabilities are both prevalent and systematically underreported, motivating stronger patch-completeness awareness, improved vulnerability database curation, and relation-aware security tooling.

cs.SE↗

arXiv2026

A quantum-assisted framework for PDE-based Bayesian inverse problems

Quantum computing offers potential advantages for solving partial differential equations (PDEs). However, most existing quantum PDE solvers primarily focus on preparing quantum states for solutions, while the efficient recovery of classical information from these states remains less explored. Motivated by the readout limitation, we propose a quantum-classical hybrid framework for Bayesian PDE inversion problems: The quantum processor evolves the PDE and evaluate the loss function with sampling noises, while the classical computer tunes the hyper-parameters in the Gaussian Process Regression to explore the next trial candidate. To match the quantum solvers for linear and semi-linear autonomous evolution PDEs, we suggest to use a normalized quantum-state loss as the data-misfit function and evaluate the new misfit by combining quantum PDE solvers with the Hadamard test, thereby allowing us to extract useful classical information using only a limited number of quantum state copies without reconstructing the full solution vector. The analysis of error propagation and overall complexity of loss evaluation under a prescribed accuracy shows that the new data-misfit function outperforms the conventional L2-loss under quantum measurements. Quantum circuit simulations of 1D and 2D linear convection diffusion equations under approximate and finite sampling loss evaluations, together with classical numerical experiments on a nonlinear forced viscous Burgers equation, demonstrate the feasibility of the proposed approach for parameter inversion even when the loss evaluations are affected by sampling noise. This framework may provide a viable quantum-assisted scheme for PDE-based inverse problems and elucidate the potential of quantum PDE algorithms in addressing a complete quantum-to-end optimization stack.

math.NA↗

arXiv2026

Quantum simulation of slow analytic time-dependent Hamiltonians

We develop a quantum algorithm for slow analytic Hamiltonians $\widetilde H(t)=H(t/T)$ with $\|H(s)\|\leq\alpha$ that achieves nearly additive query complexity and low gate overhead. Our main technical contribution is a periodic Gevrey extension of $H(s)$, together with Fourier component decay and truncation bounds that enable an efficient finite-dimensional simulation. Combined with Floquet embedding and optimal time-independent Hamiltonian simulation technique, this gives query complexity $\widetilde{\mathcal O}\!\left(\alpha T+\log(1/\varepsilon)\right)$ and additional gate complexity $\widetilde{\mathcal O}\!\left((\alpha T+\log(1/\varepsilon))^2\log(1/\varepsilon)\right)$, assuming coherent access to $H'(s)$ and endpoint derivatives. For slow analytic control Hamiltonians, only block encodings of the time-independent control operators are required, with the same query complexity and lower gate overhead. Our method also extends to Gevrey Hamiltonians and improves the precision dependence for simulating slow analytic semi-dissipative linear differential equations.

quant-ph↗

arXiv2026

PortraitGen: Exemplar-Driven GRPO with Dual-Reward Guidance for Photorealistic Portrait Generation

Reinforcement Learning like Group Relative Policy Optimization (GRPO) has significantly advanced text-to-image post-training. However, current methods often favor superficial aesthetics, such as over-saturated colors, leaving critical flaws like AI artifacts and biological implausibilities unresolved. We attribute these limitations to two primary factors: (1) The absence of real images during post-training confines GRPO sampling to the original distribution, failing to break inherent generative boundaries; (2) the optimization process lacks specific rewards targeting fine-grained artifacts like overly oily skin and other AI artifacts. To address this, we propose PortraitGen, a novel framework tailored for photorealistic portrait generation. First, we break inherent generative boundaries by directly introducing real images into the GRPO sampling groups, where image inversion is employed to obtain their transition probabilities and latents. Second, to explicitly steer the model toward photorealism, we introduce a complementary dual-reward mechanism: OmniReward for general quality and AI-Portrait for human-centric fidelity. Furthermore, we curate PortraitBench, a comprehensive portrait-centric benchmark. Extensive experiments demonstrate that PortraitGen significantly outperforms existing baselines, effectively suppressing AI artifacts and achieving unprecedented photorealism.

cs.CV↗

arXiv2026

Patching Control Lyapunov Barrier Functions for Temporal Logic Specifications with Bounded Controls

We propose an abstraction-free framework for controller synthesis for continuous-time dynamical systems subject to Linear Temporal Logic (LTL) specifications and bounded control inputs. The proposed method combines the sequential decomposition of LTL tasks with the use of formally certified Control Lyapunov-Barrier Functions (CLBFs). By formulating local specifications as a sequence of safe-stabilization problems, we systematically approximate and patch the winning sets of the decomposed subtasks. The satisfaction of these local constraints is guaranteed by the offline-computed level sets of the CLBFs. As a result, our framework yields formally verified switching feedback controllers that enable efficient online planning and dynamic re-planning. This ensures robust continuous specification satisfaction in the presence of state perturbations, avoiding the explicit state-space abstractions commonly required in the literature. The approach is validated through numerical simulations and a hardware demonstration on a Crazyflie quadrotor.

eess.SY↗

arXiv2026

$\varepsilon$-Good Action Identification in Fixed-Budget Monte Carlo Tree Search

We study the fixed-budget max-min action identification problem in depth-2 max-min trees, an important special case of Monte Carlo Tree Search. A learner sequentially allocates $T$ samples to leaves and then recommends a subtree whose minimum leaf value is largest. Motivated by approximate planning, we focus on $\varepsilon$-good subtree identification, where any subtree whose min value is within $\varepsilon$ of the optimal maximin value is acceptable. Our main contribution is an $\varepsilon$-agnostic algorithm: it does not require $\varepsilon$ as input, but achieves instance-dependent error bounds for every meaningful $\varepsilon$. We show that the misidentification probability decays as $\exp(-\widetilde{\Theta}(T/H_2(\varepsilon)))$, where $H_2(\varepsilon)$ captures both cross-subtree and within-subtree gaps. When each subtree has a single leaf, the problem reduces to standard fixed-budget best-arm identification, and our analysis recovers, up to accelerating factors, known $\varepsilon$-good guarantees for halving-style methods while giving a new $\varepsilon$-good guarantee for Successive Rejects. On the lower-bound side, we provide complementary positive and negative results showing that max-min identification has a different hardness structure from standard $K$-armed bandits. To our knowledge, this is the first provable fixed-budget algorithmic guarantee for max-min action identification.

cs.LG↗

arXiv2026

On the average-case complexity landscape for Tensor-Isomorphism-complete problems over finite fields

In Grochow and Qiao (SIAM J. Comput., 2021), the complexity class Tensor Isomorphism (TI) was introduced and isomorphism problems for groups, algebras, and polynomials were shown to be TI-complete. In this paper, we study average-case algorithms for several TI-complete problems over finite fields, including algebra isomorphism, matrix code conjugacy, and $4$-tensor isomorphism. Our main results are as follows. Over the finite field of order $q$, we devise (1) average-case polynomial-time algorithms for algebra isomorphism and matrix code conjugacy that succeed in a $1/\Theta(q)$ fraction of inputs and (2) an average-case polynomial-time algorithm for the $4$-tensor isomorphism that succeeds in a $1/q^{\Theta(1)}$ fraction of inputs. Prior to our work, algorithms for algebra isomorphism with rigorous average-case analyses ran in exponential time, albeit succeeding on a larger fraction of inputs (Li--Qiao, FOCS'17; Brooksbank--Li--Qiao--Wilson, ESA'20; Grochow--Qiao--Tang, STACS'21). These results reveal a finer landscape of the average-case complexities of TI-complete problems, providing guidance for cryptographic systems based on isomorphism problems. Our main technical contribution is to introduce the spectral properties of random matrices into algorithms for TI-complete problems. This leads to not only new algorithms but also new questions in random matrix theory over finite fields. To settle these questions, we need to extend both the generating function approach as in Neumann and Praeger (J. London Math. Soc., 1998) and the characteristic sum method of Gorodetsky and Rodgers (Trans. Amer. Math. Soc., 2021).

cs.CC↗

arXiv2026

Simulation of Adjoints and Petz Recovery Maps for Unknown Quantum Channels

Transformations of quantum channels, such as the transpose, complex conjugate, and adjoint, are fundamental to quantum information theory. Given access to an unknown channel, a central problem is whether these transformations can be implemented physically with quantum supermaps. While such supermaps are known for unitary operations, the situation for general quantum channels is fundamentally different. In this work, we establish a strict hierarchy of physical realizability for the transposition, complex conjugation, and adjoint transformation of an unknown quantum channel. We present a probabilistic protocol that exactly implements the transpose with a single query. In contrast, we prove no-go theorems showing that neither the complex conjugate nor the adjoint can be implemented by any completely positive supermap, even probabilistically. We then overcome this impossibility by designing a virtual protocol for the complex conjugate based on quasi-probability decomposition, and show its optimality in terms of the diamond norm. As a key application, we propose a protocol to estimate the expectation values resulting from the Petz recovery map of an unknown channel, achieving an improved query complexity compared to existing methods.

quant-ph↗

arXiv2026

Fixed Budget is No Harder Than Fixed Confidence in Best-Arm Identification up to Logarithmic Factors

The best-arm identification (BAI) problem is one of the most fundamental problems in interactive machine learning, which has two flavors: the fixed-budget setting (FB) and the fixed-confidence setting (FC). For $K$-armed bandits with a unique best arm, the optimal sample complexities for both settings have been settled down, and they match up to logarithmic factors. This prompts an interesting research question about the generic, potentially structured BAI problems: is FB harder than FC or the other way around? In this paper, we show that FB is no harder than FC up to logarithmic factors. We do this constructively: we propose a novel algorithm called FC2FB (fixed confidence to fixed budget), which is a meta algorithm that takes in an FC algorithm $\mathcal{A}$ and turn it into an FB algorithm. We prove that FC2FB enjoys a sample complexity that matches, up to logarithmic factors, that of the sample complexity of $\mathcal{A}$. This means that the optimal FC sample complexity is an upper bound of the optimal FB sample complexity up to logarithmic factors. Our result not only reveals a fundamental relationship between FB and FC, but also has a significant implication: FC2FB combined with existing state-of-the-art FC algorithms leads to improved sample complexity for a number of FB problems.

stat.ML↗

arXiv2026

Sound2Hap: Learning Audio-to-Vibrotactile Haptic Generation from Human Ratings

Environmental sounds like footsteps, keyboard typing, or dog barking carry rich information and emotional context, making them valuable for designing haptics in user applications. Existing audio-to-vibration methods, however, rely on signal-processing rules tuned for music or games and often fail to generalize across diverse sounds. To address this, we first investigated user perception of four existing audio-to-haptic algorithms, then created a data-driven model for environmental sounds. In Study 1, 34 participants rated vibrations generated by the four algorithms for 1,000 sounds, revealing no consistent algorithm preferences. Using this dataset, we trained Sound2Hap, a CNN-based autoencoder, to generate perceptually meaningful vibrations from diverse sounds with low latency. In Study 2, 15 participants rated its output higher than signal-processing baselines on both audio-vibration match and Haptic Experience Index (HXI), finding it more harmonious with diverse sounds. This work demonstrates a perceptually validated approach to audio-haptic translation, broadening the reach of sound-driven haptics.

cs.HC↗

arXiv2025

Near-optimal Prediction Error Estimation for Quantum Machine Learning Models

Understanding the theoretical capabilities and limitations of quantum machine learning (QML) models to solve machine learning tasks is crucial to advancing both quantum software and hardware developments. Similarly to the classical setting, the performance of QML models can be significantly affected by the limited access to the underlying data set. Previous studies have focused on proving generalization error bounds for any QML models trained on a limited finite training set. We focus on the optimal QML models obtained by training them on a finite training set and establish a tight prediction error bound in terms of the number of trainable gates and the size of training sets. To achieve this, we derive covering number upper bounds and packing number lower bounds for the data re-uploading QML models and linear QML models, respectively, which may be of independent interest. We support our theoretical findings by numerically simulating the QML strategies for function approximation and quantum phase recognition.

quant-ph↗

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

No-Go Theorems for Universal Quantum State Purification via Classically Simulable Operations

Quantum state purification, a process that aims to recover a state closer to a system's principal eigenstate from multiple copies of an unknown noisy quantum state, is crucial for restoring noisy states to a more useful form in quantum information processing. Fault-tolerant quantum computation relies on stabilizer operations, which are classically simulable protocols critical for error correction but inherently limited in computational power. In this work, we investigate the limitations of classically simulable operations for quantum state purification. We demonstrate that while certain classically simulable operations can enhance fidelity for specific noisy state ensembles, they cannot achieve universal purification. We prove that neither deterministic nor probabilistic protocols using only classically simulable operations can achieve universal purification of two-copy noisy states for qubit systems and all odd dimensions. We further extend this no-go result of state purification using three and four copies via numerical solutions of semidefinite programs. Our findings highlight the indispensable role of non-stabilizer resources and the inherent limitations of classically simulable operations in quantum state purification, emphasizing the necessity of harnessing the full power of quantum operations for more robust quantum information processing.

quant-ph↗

arXiv2025

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

Let $\varphi:V\times V\to W$ 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↗