arXiv subjects

Youjia Wang

Publications and source records attributed to Youjia Wang.

16 recordsLinked to original sources

arXiv2026

Bregman projections and partition design for accelerating finite Markov chains

We study Gibbs averaging of finite Markov chains with a prescribed stationary distribution $π$. Given a transition matrix $P$ and the Gibbs kernel $G$ induced by a state-space partition, we prove that $GPG$ is an information projection for every admissible Bregman generator $ϕ$, with divergences defined using transition probabilities relative to $π$. A Pythagorean identity characterizes this projection and recovers the relative entropy and weighted Frobenius cases. A dual characterization identifies $GPG$ as a kernel closest to stationarity among those with the same projection chain as $P$; for relative entropy, it maximizes the entropy rate. The identities also give monotonicity under partition coarsening. For every reversible ergodic baseline $P$, Gibbs averaging cannot increase the squared weighted Frobenius distance to stationarity at any positive integer time, and the inequality is strict unless $P=GPG$. The corresponding mixing time therefore cannot increase. To choose the partition, we identify the divergence of $G$ from stationarity as the exact worst-case divergence of $GPG$ over all $π$-stationary baselines $P$. This objective depends only on the block masses. We give an exact algorithm for concave block costs, including those arising from relative entropy and power generators $ϕ(u)=u^p$ with $1 2$. For power generators $ϕ(u)=u^p$ with $p>1$, the objective is proportional to Tsallis entropy of order $2-p$: its minimization favors imbalanced block masses when $1 2$, while all $k$-block partitions have the same objective value when $p=2$. A numerical experiment compares the resulting projected chains with a local Metropolis sampler on a multi-modal $π$.

math.PR↗

arXiv2026

MouseGPT: A Large-scale Vision-Language Model for Mouse Behavior Analysis

Analyzing animal behavior is crucial in neuroscience, yet deciphering its intricate dynamics remains challenging. Traditional machine vision approaches detect spontaneous behaviors but are constrained by limited interpretability and reliance on manual labeling, restricting exploration of the full behavioral spectrum. Here, we introduce MouseGPT, an integrated vision-language model and analytical framework that translates raw video of animal activity into natural language to automate open-vocabulary behavior analysis. Built upon a comprehensive dataset of over 42 million frames spanning diverse psychiatric conditions, MouseGPT maps multi-view or single-camera recordings directly into computable semantic representations. An agentic framework leverages these representations for detailed behavior profiling, cross-view stable clustering, and zero-shot novel behavior discovery without requiring labor-intensive annotation. Surpassing conventional kinematics-based pipelines and generalist vision-language models in behavioral precision and adaptability, MouseGPT establishes continuous semantic representations as a powerful tool for deciphering complex ethological dynamics in animal models.

cs.CV↗

arXiv2026

Printing the Underdetermined: Materializing Multi-solutionness in Figurative Paintings

Figurative paintings are often approached as if they depict a single recoverable 3D scene: viewers infer depth and occlusion, and reconstruction pipelines attempt to converge to one stable model. We instead foreground multi-solutionness, the non-uniqueness of 3D configurations compatible with a single painted image, and propose a workflow that keeps this non-uniqueness visible and material. Multi-solutionness arises from two sources: unobserved content, where backsides and occluded volumes admit multiple plausible completions, and observed cues, where perspective, shading, and occlusion still underconstrain geometry. When additional views are synthesized by a video generative model without explicit 3D constraints, small frame-level drifts become inevitable rather than exceptional. Our pipeline samples multiple camera-orbit multi-view video sequences from one painting, reconstructs each sequence with 3D Gaussian Splatting into a point-based Gaussian scene representation where density halos and ghosting expose unresolved degrees of freedom, and fabricates these representations as physical artifacts using DreamPrinting. By treating multiple compatible interpretations as explicit outputs rather than residual error, we provide a computational framework for spatial readings of figurative painting that can be inspected, compared, and discussed in both digital and physical form.

cs.GR↗

arXiv2026

Beyond Routine Compliance: Cunning Data Cultivates Safety Vigilance in Large Language Models

Safety alignment teaches large language models (LLMs) to recognize harmful requests and reject risky instructions. Yet aligned models can fail when harmful intent is concealed within seemingly benign contexts. Robust safety therefore requires both knowledge of safety boundaries and \textbf{vigilance}: the ability to detect unusual premises, misleading reasoning, and latent risks beneath surface-level semantics. Vigilance requires models to scrutinize a request's underlying intent and assumptions before acting. To cultivate this capability, we introduce \textbf{cunning questions}, which are not necessarily safety-related but contain misleading premises, atypical reasoning, or subtle inconsistencies. We hypothesize that learning to look beyond such reasoning traps can transfer to safety-critical scenarios. Experiments show that Cunning training improves robustness to out-of-distribution jailbreak attacks and strengthens subsequent safety fine-tuning. Furthermore, augmenting an existing state-of-the-art safety alignment pipeline with Cunning establishes a new state of the art across our evaluated settings, reducing mean ASR across nine backbone--benchmark combinations from 17.40\% to 15.05\%. Trace analysis after matched safety fine-tuning suggests that safety judgments are more likely to govern responses before harmful planning begins. A conditional theoretical analysis further characterizes when invariance learned from cunning data can transfer to safety-related inputs. These findings suggest that cunning data can strengthen model vigilance and complement conventional safety alignment.

cs.AI↗

arXiv2026

Group-averaged Markov chains II: tuning of group action in finite state space

We study group-averaged Markov chains obtained by augmenting a $π$-stationary kernel $P$ with orbit kernels induced by a group action. We analyse the Gibbs ($G$), Metropolis--Hastings ($M$), and Barker ($B$) kernels, their sandwiches $QPQ$, and mixtures $\tfrac{1}{2}(P+Q)$, where $Q\in\{G,M,B\}$. Under suitable conditions, $M^t$ and $B^t$ converge blockwise to $G$. The projection chains of $GPG$ and $P$ coincide, while every sandwich $QPQ$ has absolute spectral gap no smaller than that of reversible $P$. For $GPG$, we derive an additive asymptotic-variance bound, prove monotonicity for $G$-invariant observables, and identify it as the Kullback--Leibler (KL) information projection of $P$ onto the $G$-invariant kernels. For a fixed orbit partition, the spectral and KL properties of $GPG$ reduce to those of a lower-dimensional orbit-space chain. Among Gibbs projections with a prescribed number of orbits, we identify the partition minimizing KL divergence to stationarity and characterize exact stationarity. Finally, alternating group projections converge at a rate determined by singular values of an overlap matrix and, in structured cases, can yield exact sampling with logarithmically many group actions. These results motivate tuning heuristics and yield polynomial mixing for a Curie--Weiss example in a regime where Glauber dynamics is exponentially slow.

math.PR↗

arXiv2026

Spectral partitioning for $k$-block averaging kernels of finite Markov chains

We develop spectral algorithms for selecting state-space partitions that define averaging kernels for finite, ergodic and reversible Markov chains. For a partition $\mathcal O$, the Gibbs kernel $G_{\mathcal O}$ resamples within the current block from the stationary conditional distribution; when this update is tractable, composing or mixing it with a baseline kernel $P$ can accelerate convergence. We select $\mathcal O$ by rounding the bottom nonconstant eigenfunctions of $P^2$, or the algebraically smallest eigenfunctions of $P$ for additive mixtures, using weighted $k$-means. For $F(\mathcal O)=\|G_{\mathcal O}P-Π\|_{F,π}^2$, we derive exact trace and normalized-cut representations and show that $F$ equals the Pearson $χ^2$-mutual information between the initial block label and the state after one transition, giving this matrix objective a natural probabilistic interpretation. In the two-block case, a threshold sweep exactly solves the associated one-dimensional weighted two-means rounding problem. For general $k \geq 2$, weighted $k$-means rounds the bottom $(k-1)$-dimensional embedding, after which candidates are rescored by $F$; the rounding distortion is a distance between subspaces that yields spectral approximation bounds. We extend the framework to additive mixtures, finite-horizon objectives, and discounted infinite-horizon objectives. In contrast to classical normalized spectral clustering, which uses top nonconstant modes to find low-flow persistent clusters, our method uses bottom modes to favor large normalized cross-block flow and rapid loss of block-label information. Experiments on a controlled-spectrum graph, a mean-field Ising model, and Bayesian variable selection show notable per-iteration improvements in convergence and statistical estimation.

stat.ML↗

arXiv2026

Geometry and factorization of multivariate Markov chains with applications to MCMC acceleration and approximate inference

This paper analyzes the factorizability and geometry of transition matrices of multivariate Markov chains. Specifically, we demonstrate that the induced chains on factors of a product space can be regarded as information projections with respect to the Kullback-Leibler divergence. This perspective yields Han-Shearer type inequalities and submodularity of the entropy rate of Markov chains, as well as applications in the context of large deviations and mixing time comparison. As concrete algorithmic applications in Markov chain Monte Carlo (MCMC) and approximate inference, we provide three illustrations based on lifted MCMC, swapping algorithm and factored filtering to demonstrate projection samplers improve mixing over the original samplers. The projection sampler based on the swapping algorithm resamples the highest-temperature coordinate at stationarity at each step, and we prove that such practice accelerates the mixing time by multiplicative factors related to the number of temperatures and the dimension of the underlying state space when compared with the original swapping algorithm. Through simple numerical experiments on a bimodal target distribution, we show that the projection samplers mix effectively, in contrast to lifted MCMC and the swapping algorithm, which mix less well. In filtering, our proposed factored filtering scheme is able to scale to high dimensions with linear-in-dimension computational cost per step at the price of an approximation error that can be tracked using the distance to independence, compared with the exponential-in-dimension cost per step of the exact filter.

math.PR↗

arXiv2025

Group-averaged Markov chains: mixing improvement

For Markov kernels $P$ on a general state space $\mathcal{X}$, we introduce a new class of averaged Markov kernels $P_{da}(G,ν)$ of $P$ induced by a group $G$ that acts on $\mathcal{X}$ and a probability measure $ν$ on $G \times G$. Notable special cases are the group-orbit average $\overline{P}$, left-average $P_{la}$, right-average $P_{ra}$ and the independent-double-average $(P_{la})_{ra}$. For $π$-stationary $P$ in which $π$ is invariant with respect to $G$, we show that in general $P_{da}$ enjoys favorable convergence properties than $P$ based on metrics such as spectral gap or asymptotic variance, and within the family of $P_{da}$ the most preferable kernel is in general $(P_{la})_{ra}$. We demonstrate that $P_{la}, P_{ra}, (P_{la})_{ra}$ are comparable in terms of mixing times, which supports the use of $P_{la}, P_{ra}$ in practice as computationally cheaper alternatives over $(P_{la})_{ra}$. These averaged kernels also admit natural geometric interpretations: they emerge as unique projections of $P$ onto specific $G$-invariant structures under the Kullback-Leibler divergence or the Hilbert-Schmidt norm and satisfy Pythagorean identities. On the other hand, in the general case if $π$ is not invariant with respect to $G$, we propose and study a technique that we call state-dependent averaging of Markov kernels which generalizes the earlier results to this setting. As examples and applications, this averaging perspective not only allows us to recast state-of-the-art Markov chain samplers such as Hamiltonian Monte Carlo or piecewise-deterministic Markov processes as specific cases of $P_{da}$, but also enables improvements to existing samplers such as Metropolis-Hastings, achieving rapid mixing in some toy models or when $π$ is the discrete uniform distribution.

math.PR↗

arXiv2025

Improving the convergence of Markov chains via permutations and projections

This paper aims at improving the convergence to equilibrium of finite ergodic Markov chains via permutations and projections. First, we prove that a specific mixture of permuted Markov chains arises naturally as a projection under the KL divergence or the squared-Frobenius norm. We then compare various mixing properties of the mixture with other competing Markov chain samplers and demonstrate that it enjoys improved convergence. This geometric perspective motivates us to propose samplers based on alternating projections to combine different permutations and to analyze their rate of convergence. We give necessary, and under some additional assumptions also sufficient, conditions for the projection to achieve stationarity in the limit in terms of the trace of the transition matrix. We proceed to discuss tuning strategies of the projection samplers when these permutations are viewed as parameters. Along the way, we reveal connections between the mixture and a Markov chain Sylvester's equation as well as assignment problems, and highlight how these can be used to understand and improve Markov chain mixing. We provide two examples as illustrations. In the first example, the projection sampler (with a suitable choice of the permutation) improves upon Metropolis-Hastings in a discrete bimodal distribution with a reduced relaxation time from exponential to polynomial in the system size, while in the second example, the mixture of permuted Markov chain yields a mixing time that is logarithmic in system size (with high probability under random permutation), compared to a linear mixing time in the Diaconis-Holmes-Neal sampler. Finally, we provide numerical experiments on simple statistical physics models to illustrate the improved mixing performance of the proposed projection samplers over standard Metropolis-Hastings.

math.PR↗

arXiv2025

DreamPrinting: Volumetric Printing Primitives for High-Fidelity 3D Printing

Translating the rich visual fidelity of volumetric rendering techniques into physically realizable 3D prints remains an open challenge. We introduce DreamPrinting, a novel pipeline that transforms radiance-based volumetric representations into explicit, material-centric Volumetric Printing Primitives (VPPs). While volumetric rendering primitives (e.g., NeRF) excel at capturing intricate geometry and appearance, they lack the physical constraints necessary for real-world fabrication, such as pigment compatibility and material density. DreamPrinting addresses these challenges by integrating the Kubelka-Munk model with a spectrophotometric calibration process to characterize and mix pigments for accurate reproduction of color and translucency. The result is a continuous-to-discrete mapping that determines optimal pigment concentrations for each voxel, ensuring fidelity to both geometry and optical properties. A 3D stochastic halftoning procedure then converts these concentrations into printable labels, enabling fine-grained control over opacity, texture, and color gradients. Our evaluations show that DreamPrinting achieves exceptional detail in reproducing semi-transparent structures-such as fur, leaves, and clouds-while outperforming traditional surface-based methods in managing translucency and internal consistency. Furthermore, by seamlessly integrating VPPs with cutting-edge 3D generation techniques, DreamPrinting expands the potential for complex, high-quality volumetric prints, providing a robust framework for printing objects that closely mirror their digital origins.

cs.GR↗

arXiv2025

Information-theoretic classification of the cutoff phenomenon in Markov processes

We investigate the cutoff phenomenon for Markov processes under information divergences such as $f$-divergences and Rényi divergences. We classify most common divergences into four types, namely $L^2$-type, $\mathrm{TV}$-type, separation-type and $\mathrm{KL}$ divergence, in which we prove that the cutoff phenomenon are equivalent and relate the cutoff time and window among members within each type. To justify that this classification is natural, we provide examples in which the family of Markov processes exhibit cutoff in one type but not in another. We also establish new product conditions in these settings for the processes to exhibit cutoff, along with new results in non-reversible or non-normal situations. The proofs rely on a functional analytic approach towards cutoff.

math.PR↗

arXiv2024

Capturing the Unseen: Vision-Free Facial Motion Capture Using Inertial Measurement Units

We present Capturing the Unseen (CAPUS), a novel facial motion capture (MoCap) technique that operates without visual signals. CAPUS leverages miniaturized Inertial Measurement Units (IMUs) as a new sensing modality for facial motion capture. While IMUs have become essential in full-body MoCap for their portability and independence from environmental conditions, their application in facial MoCap remains underexplored. We address this by customizing micro-IMUs, small enough to be placed on the face, and strategically positioning them in alignment with key facial muscles to capture expression dynamics. CAPUS introduces the first facial IMU dataset, encompassing both IMU and visual signals from participants engaged in diverse activities such as multilingual speech, facial expressions, and emotionally intoned auditions. We train a Transformer Diffusion-based neural network to infer Blendshape parameters directly from IMU data. Our experimental results demonstrate that CAPUS reliably captures facial motion in conditions where visual-based methods struggle, including facial occlusions, rapid movements, and low-light environments. Additionally, by eliminating the need for visual inputs, CAPUS offers enhanced privacy protection, making it a robust solution for vision-free facial MoCap.

cs.CV↗

arXiv2023

Information divergences of Markov chains and their applications

In this paper, we first introduce and define several new information divergences in the space of transition matrices of finite Markov chains which measure the discrepancy between two Markov chains. These divergences offer natural generalizations of classical information-theoretic divergences, such as the $f$-divergences and the Rényi divergence between probability measures, to the context of finite Markov chains. We begin by detailing and deriving fundamental properties of these divergences and notably gives a Markov chain version of the Pinsker's inequality and Chernoff information. We then utilize these notions in a few applications. First, we investigate the binary hypothesis testing problem of Markov chains, where the newly defined Rényi divergence between Markov chains and its geometric interpretation play an important role in the analysis. Second, we propose and analyze information-theoretic (Cesàro) mixing times and ergodicity coefficients, along with spectral bounds of these notions in the reversible setting. Examples of the random walk on the hypercube, as well as the connections between the critical height of the low-temperature Metropolis-Hastings chain and these proposed ergodicity coefficients, are highlighted.

cs.IT↗

arXiv2023

Improved Langevin Monte Carlo for stochastic optimization via landscape modification

Given a target function $H$ to minimize or a target Gibbs distribution $π_β^0 \propto e^{-βH}$ to sample from in the low temperature, in this paper we propose and analyze Langevin Monte Carlo (LMC) algorithms that run on an alternative landscape as specified by $H^f_{β,c,1}$ and target a modified Gibbs distribution $π^f_{β,c,1} \propto e^{-βH^f_{β,c,1}}$, where the landscape of $H^f_{β,c,1}$ is a transformed version of that of $H$ which depends on the parameters $f,β$ and $c$. While the original Log-Sobolev constant affiliated with $π^0_β$ exhibits exponential dependence on both $β$ and the energy barrier $M$ in the low temperature regime, with appropriate tuning of these parameters and subject to assumptions on $H$, we prove that the energy barrier of the transformed landscape is reduced which consequently leads to polynomial dependence on both $β$ and $M$ in the modified Log-Sobolev constant associated with $π^f_{β,c,1}$. This yield improved total variation mixing time bounds and improved convergence toward a global minimum of $H$. We stress that the technique developed in this paper is not only limited to LMC and is broadly applicable to other gradient-based optimization or sampling algorithms.

math.PR↗

arXiv2022

NARRATE: A Normal Assisted Free-View Portrait Stylizer

In this work, we propose NARRATE, a novel pipeline that enables simultaneously editing portrait lighting and perspective in a photorealistic manner. As a hybrid neural-physical face model, NARRATE leverages complementary benefits of geometry-aware generative approaches and normal-assisted physical face models. In a nutshell, NARRATE first inverts the input portrait to a coarse geometry and employs neural rendering to generate images resembling the input, as well as producing convincing pose changes. However, inversion step introduces mismatch, bringing low-quality images with less facial details. As such, we further estimate portrait normal to enhance the coarse geometry, creating a high-fidelity physical face model. In particular, we fuse the neural and physical renderings to compensate for the imperfect inversion, resulting in both realistic and view-consistent novel perspective images. In relighting stage, previous works focus on single view portrait relighting but ignoring consistency between different perspectives as well, leading unstable and inconsistent lighting effects for view changes. We extend Total Relighting to fix this problem by unifying its multi-view input normal maps with the physical face model. NARRATE conducts relighting with consistent normal maps, imposing cross-view constraints and exhibiting stable and coherent illumination effects. We experimentally demonstrate that NARRATE achieves more photorealistic, reliable results over prior works. We further bridge NARRATE with animation and style transfer tools, supporting pose change, light change, facial animation, and style transfer, either separately or in combination, all at a photographic quality. We showcase vivid free-view facial animations as well as 3D-aware relightable stylization, which help facilitate various AR/VR applications like virtual cinematography, 3D video conferencing, and post-production.

cs.CV↗

arXiv2021

Neural Relighting and Expression Transfer On Video Portraits

Photo-realistic video portrait reenactment benefits virtual production and numerous VR/AR experiences. The task remains challenging as the reenacted expression should match the source while the lighting should be adjustable to new environments. We present a neural relighting and expression transfer technique to transfer the facial expressions from a source performer to a portrait video of a target performer while enabling dynamic relighting. Our approach employs 4D reflectance field learning, model-based facial performance capture and target-aware neural rendering. Specifically, given a short sequence of the target performer's OLAT, we apply a rendering-to-video translation network to first synthesize the OLAT result of new sequences with unseen expressions. We then design a semantic-aware facial normalization scheme along with a multi-frame multi-task learning strategy to encode the content, segmentation, and motion flows for reliably inferring the reflectance field. This allows us to simultaneously control facial expression and apply virtual relighting. Extensive experiments demonstrate that our technique can robustly handle challenging expressions and lighting environments and produce results at a cinematographic quality.

cs.CV↗