arXiv subjects

Lexing Ying

Publications and source records attributed to Lexing Ying.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Linear Combination of Hamiltonian Simulation for Dissipative Dynamics

Linear combination of Hamiltonian simulation (LCHS) is an efficient method for simulating dissipative dynamics on quantum computers. The choice of the LCHS kernel controls the cost of the algorithm. We prove that the kernel family proposed by Ni and Ying~\cite{NY26} minimizes the LCHS query cost in the minimax sense. For target accuracy $ε$, the minimum cost is asymptotically $\frac{2\mathrm{e}}π(\ln\frac1ε-\ln\ln\frac1ε+o(1))$, with optimal leading constant $\frac{2\mathrm{e}}π$. Our lower-bound proof combines weak duality with a realization lemma that approximates extremal dual functions by matrix elements of dissipative evolutions.

quant-ph↗

arXiv2026

Interacting Annealed Importance Sampling via Population-Based MCMC Kernels

Sampling from a multimodal distribution is a fundamental and challenging problem in computational science and statistics. Among various approaches proposed for this task, one popular method is Annealed Importance Sampling (AIS). In this paper, we propose an interaction-based version of AIS by combining it with population-based Monte Carlo methods to improve its efficiency. By keeping track of an ensemble instead of a single sampler along some continuation path between the starting distribution and the target distribution, we take advantage of the interaction within the ensemble to encourage the exploration of undiscovered modes. Specifically, our main idea is to utilize either the snooker algorithm or the genetic algorithm used in Evolutionary Monte Carlo. We discuss how the proposed algorithm can be implemented and derive a partial differential equation governing the evolution of the ensemble under the continuous time and mean-field limit. We also test the efficiency of the proposed algorithm on various continuous and discrete distributions.

stat.CO↗

arXiv2026

Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior sampling methods proposed for solving common BIPs rely on heuristic approximations to the generative process. To exploit the generative capability of DMs and avoid the usage of such approximations, we propose an ensemble-based algorithm that performs posterior sampling without the use of heuristic approximations. Our algorithm is motivated by existing work that combines DM-based methods with the sequential Monte Carlo (SMC) method. By examining how the prior evolves through the diffusion process encoded by the pre-trained score function, we derive a modified partial differential equation (PDE) governing the evolution of the corresponding posterior distribution. This PDE includes a modified diffusion term and a reweighting term, which can be simulated via stochastic weighted particle methods. Theoretically, we prove that the error between the true posterior and the empirical distribution of the generated samples can be bounded in terms of the training error of the pre-trained score function and the number of particles in the ensemble. Empirically, we validate our algorithm on several inverse problems in imaging to show that our method gives more accurate reconstructions compared to existing DM-based methods. Our code is available at the following Github repository~\url{https://github.com/HaoxuanSteveC00/AFDPS-TMLR}.

cs.LG↗

arXiv2026

FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models

Many inference-time tasks for pretrained discrete diffusion models and diffusion language models reduce to drawing samples from a tilted version of the pretrained distribution. Feynman-Kac sequential Monte Carlo (SMC) makes this correction exact in principle, but its prescribed weights routinely degenerate when the proposal dynamics are misaligned with the tilt, capping the practical gains from additional particles. We introduce FluxLite, a lightweight, training-free proposal-control framework for discrete diffusion. On the sparse directed graph of pretrained reverse rates, any sparse jump-rate perturbation can be exactly compensated by a $q_t$-weighted graph-divergence term in the Feynman-Kac potential; the target path is therefore preserved while the residual reweighting variance becomes a local convex objective. We instantiate this principle as two practical samplers: a one-hop local reallocation rule (HEU) and a small nonnegative quadratic program over pretrained-rate bases (D-VCG). We further prove population stability under the standard score-entropy training loss, identifying a tilted-path coverage factor that governs robustness to score error, together with finite-particle convergence for a fixed controlled Feynman-Kac recursion. Empirically, FluxLite improves over standard Feynman-Kac SMC baselines by up to two orders of magnitude in terminal KL on an analytically tractable finite-state CTMC benchmark, and reduces row-correlation MSE on 2D Ising sampling by 5-7x in geometric mean and up to 55x at peak.

cs.LG↗

arXiv2026

Periodic Weak Spots: Phase Sensitivity from Chunked KV-Cache Compression

Chunked KV-cache compression reduces the memory and attention costs of long-context inference by compressing windows of consecutive tokens into fewer cache entries at a fixed stride. Such compression also introduces a new positional coordinate: a token's phase, or its position relative to compression-window boundaries. We uncover a systematic asymmetry in models using such compression: the same information can be easy to retrieve at one phase and difficult at another. We call this periodic variation in retrieval performance phase sensitivity. In large open-weight models with such compression, long-context retrieval accuracy can differ by up to 40 percentage points across phases, revealing periodic weak spots that average benchmark scores can conceal. To investigate this behavior, we pretrain a family of transformers from scratch across multiple KV-compression designs, reproducing phase sensitivity across the variants. Mechanistic analysis using causal interventions in these models reveals phase specialization: different attention components contribute asymmetrically to retrieving information at different source phases. We further analyze idealized retrieval models, showing how gradient flow dynamics may favor sharp phase specialization. Evaluating models with chunked KV-cache compression thus requires measuring across compression phases: high average accuracy can coexist with systematic positional failures.

cs.LG↗

arXiv2026

Aligning One-Step Generative Models with Reward-Weighted Transport Distillation

One-step generators enable high-quality visual generation with a single network evaluation, but their post-training is difficult: general implicit generators provide neither tractable likelihoods nor denoising trajectories, and many rewards are non-differentiable. We introduce Reward-Weighted Transport Distillation (RWTD), a post-training method that requires only generated samples and scalar reward evaluations. Rather than aligning solely to the conventional reward-tilted reference distribution, RWTD constructs an adaptive target that mixes separately tilted current and reference distributions. The current component incorporates improvements discovered during training, while the reference component anchors the target to the pretrained generator. RWTD realizes this target through feature-space optimal transport and fixed-point regression. Theoretical analysis shows that the fixed-point distributions of RWTD interpolate between off-policy reward tilting of the reference and on-policy tilting of the current model, providing a principled approach to balancing reward adaptation with retention of prior knowledge. Empirically, RWTD substantially improves the GenEval score of the one-step SANA Sprint 1.6B backbone from 0.73 to 0.80, while separate preference alignment experiments demonstrate strong cross-reward generalization that yields balanced improvements and preservation of compositional capabilities.

cs.LG↗

arXiv2026

Convergence of the Cumulant Expansion and Polynomial-Time Algorithm for Weakly Interacting Fermions

We propose a randomized algorithm to compute the log-partition function of weakly interacting fermions with polynomial runtime in both the system size and precision. Although weakly interacting fermionic systems are considered tractable for many computational methods such as the diagrammatic quantum Monte Carlo, a mathematically rigorous proof of polynomial runtime has been lacking. In this work we first extend the proof techniques developed in previous works for proving the convergence of the cumulant expansion in periodic systems to the non-periodic case. A key equation used to analyze the sum of connected Feynman diagrams, which we call the tree-determinant expansion, reveals an underlying tree structure in the summation. This enables us to design a new randomized algorithm to compute the log-partition function through importance sampling augmented by belief propagation. This approach differs from the traditional method based on Markov chain Monte Carlo, whose efficiency is hard to guarantee, and enables us to obtain a algorithm with provable polynomial runtime.

quant-ph↗

arXiv2026

Multi-Mask Diffusion Language Models for Few-Step Generation

Masked diffusion models (MDMs) are a promising family of language generators, but achieving high-quality few-step generation remains challenging. In MDMs, all forward trajectories collapse to a single fully masked state, leaving no terminal entropy for consistency-style few-step generation. While recent few-step alternatives based on uniform-state diffusion avoid this degeneracy, it becomes harder to distinguish clean tokens from noise than MDMs, which usually harms modeling quality and training efficiency. In this work, we propose a multi-mask diffusion model (MultiMDM) that preserves the masking structure towards few-step generation. In the forward process, each clean token is first pushed towards a designated mask and then gradually mixes over the mask set. As a result, the backward process has a drafting capability by predicting a designated mask before refining to a clean token. We derive a closed-form ELBO training objective for MultiMDM that supports continual training from pretrained MDMs. In addition, we formulate a purely discrete-state consistency distillation scheme, with a shared-Gumbel coupling to reduce pathwise entropy. Experiments on pretraining and distillation show that MultiMDM provides an effective foundation for principled few-step generation.

cs.CL↗

arXiv2026

Quantum Eigenvalue Transformation via Linear Combination of Hamiltonian Simulation: A Weyl Calculus Approach

Linear combination of Hamiltonian simulation (LCHS) provides an efficient method for implementing matrix exponentials $e^{-tA}$ on quantum computers. In this paper, we develop LCHS formulas for computing general matrix functions $f(A)$ when $f$ is analytic on the numerical range of $A$, with $A$ possibly non-normal. The essential technical tool is Weyl calculus, which reduces the construction of LCHS formulas for noncommuting operators to scalar Fourier approximation problems. Our construction yields a quantum eigenvalue transformation algorithm with optimal $\mathcal{O}(\log\frac{1}ε)$ query complexity scaling. Furthermore, our Weyl-calculus-based theory gives rise to an ansatz-free convex optimization framework that directly produces discrete LCHS formulas. This circumvents the inefficiencies of traditional quadrature rules and yields formulas highly optimized for coherent implementation on quantum computers. In addition, both our theory and optimization framework apply to the simulation of time-dependent dissipative ODE $\frac{\mathrm{d}}{\mathrm{d} t} ψ(t) = -A(t)ψ(t)$, for which we achieve a $2.1\times$ cost reduction over prior art.

quant-ph↗

arXiv2026

Variational inference and density estimation with non-negative tensor of hierarchical tucker format

In this work, we present an efficient method to compress a high-dimensional discrete probability function, i.e., a probability tensor, into a non-negative hierarchical Tucker format. The methodology is a two-stage procedure. In the first stage, we take an existing interpolation method to compress the target tensor into a hierarchical Tucker (HT) in a manner similar to the CUR decomposition for low-rank matrix reconstruction. In the second stage, we fit the first-stage output against a non-negative hierarchical Tucker ansatz using a second-order method tailored specifically for this setting. When the tensor is of order $d$, both stages admit an $\mathcal{O}(d)$ computational complexity, and therefore the proposed methodology readily extends into high-dimensional settings. Numerical experiments show success in compressing various high-dimensional probability tensors.

math.NA↗

arXiv2026

Thermal expectation estimation via single-trajectory Gibbs sampling with non-destructive measurements

Estimating thermal expectation values of quantum many-body systems is a central challenge in physics, chemistry, and materials science. Standard quantum Gibbs sampling protocols address this task by preparing the Gibbs state from scratch after every measurement, incurring a full mixing time cost at each step. Recent advances in single-trajectory Gibbs sampling [Jiang et al. 2026] substantially reduce this overhead: once stationarity is reached, measurements can be collected along a single trajectory without re-thermalizing, provided the measurement channel preserves the Gibbs ensemble. However, explicit constructions of such non-destructive measurements have been limited primarily to observables that commute with the Hamiltonian. In this work, we fundamentally extend the single-trajectory framework to arbitrary, non-commuting observables. We provide two measurement constructions that extract measurement information without fully destroying the Gibbs state, thereby eliminating the need for full re-mixing between samples. First, we construct a measurement that satisfies exact detailed balance. This ensures the system remains in equilibrium throughout the trajectory, allowing measurement outcomes to decorrelate in an autocorrelation time that could be significantly shorter than the global mixing time. Second, assuming the underlying quantum Gibbs sampler has a positive spectral gap, we design a simplified measurement scheme that ensures the post-selected state serves as a warm start for rapid re-mixing. This approach successfully decouples the resampling cost from the global mixing time. Both measurement schemes admit efficient quantum circuit implementations, requiring only polylogarithmic Hamiltonian simulation time.

quant-ph↗

arXiv2026

Sketch Tomography: Hybridizing Classical Shadow and Matrix Product State

We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a matrix product state (MPS). The density matrix of the ground truth state admits a tensor train ansatz as a result of the MPS assumption, and we estimate the tensor components of the ansatz through a series of observable estimations, thus outputting an approximation of the density matrix. The procedure is provably convergent with a sample complexity that scales quadratically in the system size. We conduct extensive numerical experiments to show that the procedure outputs an accurate approximation to the quantum state. For observable estimation tasks involving moderately large subsystems, we show that our procedure gives rise to a more accurate estimation than the classical shadow protocol. We also show that sketch tomography is more accurate in observable estimation than quantum states trained from the maximum likelihood estimation formulation.

quant-ph↗

arXiv2026

GiVA: Gradient-Informed Bases for Vector-Based Adaptation

As model sizes continue to grow, parameter-efficient fine-tuning has emerged as a powerful alternative to full fine-tuning. While LoRA is widely adopted among these methods, recent research has explored vector-based adaptation methods due to their extreme parameter efficiency. However, these methods typically require substantially higher ranks than LoRA to match its performance, leading to increased training costs. This work introduces GiVA, a gradient-based initialization strategy for vector-based adaptation. It achieves training times comparable to LoRA and maintains the extreme parameter efficiency of vector-based adaptation. We evaluate GiVA across diverse benchmarks, including natural language understanding, natural language generation, and image classification. Experiments show that our approach consistently outperforms or achieves performance competitive with existing vector-based adaptation methods and LoRA while reducing rank requirements by a factor of eight ($8\times$).

cs.CL↗

arXiv2026

A Unified Approach to Analysis and Design of Denoising Markov Models

Probabilistic generative models based on measure transport, such as diffusion and flow-based models, are often formulated in the language of Markovian stochastic dynamics, where the choice of the underlying process impacts both algorithmic design choices and theoretical analysis. In this paper, we aim to establish a rigorous mathematical foundation for denoising Markov models, a broad class of generative models that postulate a forward process transitioning from the target distribution to a simple, easy-to-sample distribution, alongside a backward process particularly constructed to enable efficient sampling in the reverse direction. Leveraging deep connections with nonequilibrium statistical mechanics and generalized Doob's $h$-transform, we propose a minimal set of assumptions that ensure: (1) explicit construction of the backward generator, (2) a unified variational objective directly minimizing the measure transport discrepancy, and (3) adaptations of the classical score-matching approach across diverse dynamics. Our framework unifies existing formulations of continuous and discrete diffusion models, identifies the most general form of denoising Markov models under certain regularity assumptions on forward generators, and provides a systematic recipe for designing denoising Markov models driven by arbitrary Lévy-type processes. We illustrate the versatility and practical effectiveness of our approach through novel denoising Markov models employing geometric Brownian motion and jump processes as forward dynamics, highlighting the framework's potential flexibility and capability in modeling complex distributions.

cs.LG↗

arXiv2026

DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models

We study inference-time scaling for diffusion models, where the goal is to adapt a pre-trained model to new target distributions without retraining. Existing guidance-based methods are simple but introduce bias, while particle-based corrections suffer from weight degeneracy and high computational cost. We introduce DriftLite, a lightweight, training-free particle-based approach that steers the inference dynamics on the fly with provably optimal stability control. DriftLite exploits a previously unexplored degree of freedom in the Fokker-Planck equation between the drift and particle potential, and yields two practical instantiations: Variance- and Energy-Controlling Guidance (VCG/ECG) for approximating the optimal drift with minimal overhead. Across Gaussian mixture models, particle systems, and large-scale protein-ligand co-folding problems, DriftLite consistently reduces variance and improves sample quality over pure guidance and sequential Monte Carlo baselines. These results highlight a principled, efficient route toward scalable inference-time adaptation of diffusion models. Our source code is publicly available at https://github.com/yinuoren/DriftLite.

cs.LG↗

arXiv2026

Solving the Fokker-Planck equation of discretized Dean-Kawasaki models with functional hierarchical tensor

We introduce a novel numerical scheme for solving the Fokker-Planck equation of discretized Dean-Kawasaki models with a functional tensor network ansatz. The Dean-Kawasaki model describes density fluctuations of interacting particle systems, and it is a highly singular stochastic partial differential equation. By performing a finite-volume discretization of the Dean-Kawasaki model, we derive a stochastic differential equation (SDE). To fully characterize the discretized Dean-Kawasaki model, we solve the associated Fokker-Planck equation of the SDE dynamics. In particular, we use a particle-based approach whereby the solution to the Fokker-Planck equation is obtained by performing a series of density estimation tasks from the simulated trajectories, and we use a functional hierarchical tensor model to represent the density. To address the challenge that the sample trajectories are supported on a simplex, we apply a coordinate transformation from the simplex to a Euclidean space by logarithmic parameterization, after which we apply a sketching-based density estimation procedure on the transformed variables. Our approach is general and can be applied to general density estimation tasks over a simplex. We apply the proposed method successfully to the 1D and 2D Dean-Kawasaki models. Moreover, we show that the proposed approach is highly accurate in the presence of external potential and particle interaction.

math.NA↗

arXiv2025

Sampling on Metric Graphs

Metric graphs are structures obtained by associating edges in a standard graph with segments of the real line and gluing these segments at the vertices of the graph. The resulting structure has a natural metric that allows for the study of differential operators and stochastic processes on the graph. Brownian motions in these domains have been extensively studied theoretically using their generators. However, less work has been done on practical algorithms for simulating these processes. We introduce the first algorithm for simulating Brownian motions on metric graphs through a timestep splitting Euler-Maruyama-based discretization of their corresponding stochastic differential equation. By applying this scheme to Langevin diffusions on metric graphs, we also obtain the first algorithm for sampling on metric graphs. We provide theoretical guarantees on the number of timestep splittings required for the algorithm to converge to the underlying stochastic process. We also show that the exit probabilities of the simulated particle converge to the vertex-edge jump probabilities of the underlying stochastic differential equation as the timestep goes to zero. Finally, since this method is highly parallelizable, we provide fast, memory-aware implementations of our algorithm in the form of custom CUDA kernels that are up to ~8000x faster than a GPU implementation using PyTorch on simple star metric graphs. Beyond simple star graphs, we benchmark our algorithm on a real cortical vascular network extracted from a DuMuX tissue-perfusion model for tracer transport. Our algorithm is able to run stable simulations with timesteps significantly larger than the stable limit of the finite volume method used in DuMuX while also achieving speedups of up to ~1500x.

math.NA↗

arXiv2025

Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity

Diffusion models have become a leading method for generative modeling of both image and scientific data. As these models are costly to train and \emph{evaluate}, reducing the inference cost for diffusion models remains a major goal. Inspired by the recent empirical success in accelerating diffusion models via the parallel sampling technique~\cite{shih2024parallel}, we propose to divide the sampling process into $\mathcal{O}(1)$ blocks with parallelizable Picard iterations within each block. Rigorous theoretical analysis reveals that our algorithm achieves $\widetilde{\mathcal{O}}(\mathrm{poly} \log d)$ overall time complexity, marking \emph{the first implementation with provable sub-linear complexity w.r.t. the data dimension $d$}. Our analysis is based on a generalized version of Girsanov's theorem and is compatible with both the SDE and probability flow ODE implementations. Our results shed light on the potential of fast and efficient sampling of high-dimensional data on fast-evolving modern large-memory GPU clusters.

cs.LG↗