arXiv subjects

Zhichao Chen

Publications and source records attributed to Zhichao Chen.

At least 37 records · Page 2Linked to original sources

arXiv2026

Fractal phenomenon in $c$- and $g$-vectors of the Markov quiver

We study the $C$- and $G$-patterns associated with rank $3$ skew-symmetrizable matrices of $B$-invariant type, including the Markov quiver. Motivated by the self-contained simple mutations in Markov-type cluster algebras, we prove that large classes of subpatterns of modified $c$- and $g$-vectors are linearly isomorphic, yielding a fractal structure of the corresponding $G$-fan. We further derive explicit recursive formulas for all modified $c$- and $g$-vectors in terms of integer pairs satisfying a recursion analogous to the Calkin-Wilf tree, which leads to a parameterization by coprime integers. As an application, we describe all connected components of the complement of the support of the $G$-fan, and show that they are generated recursively by three kinds of linear maps.

math.RT↗

arXiv2026

The Logarithmic Asymptotic Phenomenon for Generalized Markov-Hurwitz Equations

The purpose of this paper is twofold. First, we introduce a family of generalized Markov-Hurwitz equations, extending classical Markov-Hurwitz equations with additional degree n-1 interaction terms, Gyoda and Matsushita's generalized Markov equations from 3 variables to n variables. Second, we prove a logarithmic asymptotic phenomenon for the positive integer solutions of these equations.

math.NT↗

arXiv2026

PaCo-FR: Patch-Pixel Aligned End-to-End Codebook Learning for Facial Representation Pre-training

Facial representation pre-training is crucial for tasks like facial recognition, expression analysis, and virtual reality. However, existing methods face three key challenges: (1) failing to capture distinct facial features and fine-grained semantics, (2) ignoring the spatial structure inherent to facial anatomy, and (3) inefficiently utilizing limited labeled data. To overcome these, we introduce PaCo-FR, an unsupervised framework that combines masked image modeling with patch-pixel alignment. Our approach integrates three innovative components: (1) a structured masking strategy that preserves spatial coherence by aligning with semantically meaningful facial regions, (2) a novel patch-based codebook that enhances feature discrimination with multiple candidate tokens, and (3) spatial consistency constraints that preserve geometric relationships between facial components. PaCo-FR achieves state-of-the-art performance across several facial analysis tasks with just 2 million unlabeled images for pre-training. Our method demonstrates significant improvements, particularly in scenarios with varying poses, occlusions, and lighting conditions. We believe this work advances facial representation learning and offers a scalable, efficient solution that reduces reliance on expensive annotated datasets, driving more effective facial analysis systems.

cs.CV↗

arXiv2026

Towards Intrinsically Calibrated Uncertainty Quantification in Industrial Data-Driven Models via Diffusion Sampler

In modern process industries, data-driven models are important tools for real-time monitoring when key performance indicators are difficult to measure directly. While accurate predictions are essential, reliable uncertainty quantification (UQ) is equally critical for safety, reliability, and decision-making, but remains a major challenge in current data-driven approaches. In this work, we introduce a diffusion-based posterior sampling framework that inherently produces well-calibrated predictive uncertainty via faithful posterior sampling, eliminating the need for post-hoc calibration. In extensive evaluations on synthetic distributions, the Raman-based phenylacetic acid soft sensor benchmark, and a real ammonia synthesis case study, our method achieves practical improvements over existing UQ techniques in both uncertainty calibration and predictive accuracy. These results highlight diffusion samplers as a principled and scalable paradigm for advancing uncertainty-aware modeling in industrial applications.

cs.LG↗

arXiv2026

Entire Space Counterfactual Learning for Reliable Content Recommendations

Post-click conversion rate (CVR) estimation is a fundamental task in developing effective recommender systems, yet it faces challenges from data sparsity and sample selection bias. To handle both challenges, the entire space multitask models are employed to decompose the user behavior track into a sequence of exposure $\rightarrow$ click $\rightarrow$ conversion, constructing surrogate learning tasks for CVR estimation. However, these methods suffer from two significant defects: (1) intrinsic estimation bias (IEB), where the CVR estimates are higher than the actual values; (2) false independence prior (FIP), where the causal relationship between clicks and subsequent conversions is potentially overlooked. To overcome these limitations, we develop a model-agnostic framework, namely Entire Space Counterfactual Multitask Model (ESCM$^2$), which incorporates a counterfactual risk minimizer within the ESMM framework to regularize CVR estimation. Experiments conducted on large-scale industrial recommendation datasets and an online industrial recommendation service demonstrate that ESCM$^2$ effectively mitigates IEB and FIP defects and substantially enhances recommendation performance.

cs.LG↗

arXiv2026

Proximity Matters: Local Proximity Enhanced Balancing for Treatment Effect Estimation

Heterogeneous treatment effect (HTE) estimation from observational data poses significant challenges due to treatment selection bias. Existing methods address this bias by minimizing distribution discrepancies between treatment groups in latent space, focusing on global alignment. However, the fruitful aspect of local proximity, where similar units exhibit similar outcomes, is often overlooked. In this study, we propose Proximity-enhanced CounterFactual Regression (CFR-Pro) to exploit proximity for enhancing representation balancing within the HTE estimation context. Specifically, we introduce a pair-wise proximity regularizer based on optimal transport to incorporate the local proximity in discrepancy calculation. However, the curse of dimensionality renders the proximity measure and discrepancy estimation ineffective -- exacerbated by limited data availability for HTE estimation. To handle this problem, we further develop an informative subspace projector, which trades off minimal distance precision for improved sample complexity. Extensive experiments demonstrate that CFR-Pro accurately matches units across different treatment groups, effectively mitigates treatment selection bias, and significantly outperforms competitors. Code is available at https://github.com/HowardZJU/CFR-Pro.

cs.LG↗

arXiv2026

From Text to Talk: Audio-Language Model Needs Non-Autoregressive Joint Training

Recent advances in large language models (LLMs) have attracted significant interest in extending their capabilities to multimodal scenarios, particularly for speech-to-speech conversational systems. However, existing multimodal models handling interleaved audio and text rely on autoregressive (AR) methods, overlooking that text depends on target-target relations whereas audio depends mainly on source-target relations. In this work, we propose Text-to-Talk (TtT), a unified audio-text framework that integrates AR text generation with non-autoregressive (NAR) audio diffusion in a single Transformer. By leveraging the any-order AR property of absorbing discrete diffusion, our approach provides a unified training objective for text and audio. To support this hybrid generation paradigm, we design a modality-aware attention mechanism that enforces causal decoding for text while allowing bidirectional modeling within audio spans, and further introduce three training strategies that reduce train-test discrepancies. During inference, TtT employs block-wise diffusion to synthesize audio in parallel while flexibly handling variable-length outputs. Comprehensive experiments on Audio-QA, ASR, AAC and speech-to-speech benchmarks show that TtT consistently surpasses strong AR and NAR baselines, with additional ablation and training-strategy analyses confirming the contribution of each component. We will open-source our models, data and code to facilitate future research in this direction.

cs.CL↗

arXiv2026

CausalRM: Causal-Theoretic Reward Modeling for RLHF from Observational User Feedbacks

Despite the success of reinforcement learning from human feedback (RLHF) in aligning language models, current reward modeling heavily relies on experimental feedback data collected from human annotators under controlled and costly conditions. In this work, we introduce observational reward modeling -- learning reward models with observational user feedback (e.g., clicks, copies, and upvotes) -- as a scalable and cost-effective alternative. We identify two fundamental challenges in this setting: (1) observational feedback is noisy due to annotation errors, which deviates it from true user preference; (2) observational feedback is biased by user preference, where users preferentially provide feedback on responses they feel strongly about, which creats a distribution shift between training and inference data. To address these challenges, we propose CausalRM, a causal-theoretic reward modeling framework that aims to learn unbiased reward models from observational feedback. To tackle challenge (1), CausalRM introduces a noise-aware surrogate loss term that is provably equivalent to the primal loss under noise-free conditions by explicitly modeling the annotation error generation process. To tackle challenge (2), CausalRM uses propensity scores -- the probability of a user providing feedback for a given response -- to reweight training samples, yielding a loss function that eliminates user preference bias. Extensive experiments across diverse LLM backbones and benchmark datasets validate that CausalRM effectively learns accurate reward signals from noisy and biased observational feedback and delivers substantial performance improvements on downstream RLHF tasks -- including a 49.2% gain on WildGuardMix and a 32.7% improvement on HarmBench. Code is available on our project website.

cs.LG↗

arXiv2026

InterveneBench: Benchmarking LLMs for Intervention Reasoning and Causal Study Design in Real Social Systems

Causal inference in social science relies on end-to-end, intervention-centered research-design reasoning grounded in real-world policy interventions, but current benchmarks fail to evaluate this capability of large language models (LLMs). We present InterveneBench, a benchmark designed to assess such reasoning in realistic social settings. Each instance in InterveneBench is derived from an empirical social science study and requires models to reason about policy interventions and identification assumptions without access to predefined causal graphs or structural equations. InterveneBench comprises 744 peer-reviewed studies across diverse policy domains. Experimental results show that state-of-the-art LLMs struggle under this setting. To address this limitation, we further propose a multi-agent framework, STRIDES. It achieves significant performance improvements over state-of-the-art reasoning models. Our code and data are available at https://github.com/Sii-yuning/STRIDES.

cs.CY↗

arXiv2026

Slack More, Predict Better: Proximal Relaxation for Probabilistic Latent Variable Model-based Soft Sensors

Nonlinear Probabilistic Latent Variable Models (NPLVMs) are a cornerstone of soft sensor modeling due to their capacity for uncertainty delineation. However, conventional NPLVMs are trained using amortized variational inference, where neural networks parameterize the variational posterior. While facilitating model implementation, this parameterization converts the distributional optimization problem within an infinite-dimensional function space to parameter optimization within a finite-dimensional parameter space, which introduces an approximation error gap, thereby degrading soft sensor modeling accuracy. To alleviate this issue, we introduce KProxNPLVM, a novel NPLVM that pivots to relaxing the objective itself and improving the NPLVM's performance. Specifically, we first prove the approximation error induced by the conventional approach. Based on this, we design the Wasserstein distance as the proximal operator to relax the learning objective, yielding a new variational inference strategy derived from solving this relaxed optimization problem. Based on this foundation, we provide a rigorous derivation of KProxNPLVM's optimization implementation, prove the convergence of our algorithm can finally sidestep the approximation error, and propose the KProxNPLVM by summarizing the abovementioned content. Finally, extensive experiments on synthetic and real-world industrial datasets are conducted to demonstrate the efficacy of the proposed KProxNPLVM.

cs.LG↗

arXiv2026

Analyzing and Improving Diffusion Models for Time-Series Data Imputation: A Proximal Recursion Perspective

Diffusion models (DMs) have shown promise for Time-Series Data Imputation (TSDI); however, their performance remains inconsistent in complex scenarios. We attribute this to two primary obstacles: (1) non-stationary temporal dynamics, which can bias the inference trajectory and lead to outlier-sensitive imputations; and (2) objective inconsistency, since imputation favors accurate pointwise recovery whereas DMs are inherently trained to generate diverse samples. To better understand these issues, we analyze DM-based TSDI process through a proximal-operator perspective and uncover that an implicit Wasserstein distance regularization inherent in the process hinders the model's ability to counteract non-stationarity and dissipative regularizer, thereby amplifying diversity at the expense of fidelity. Building on this insight, we propose a novel framework called SPIRIT (Semi-Proximal Transport Regularized time-series Imputation). Specifically, we introduce entropy-induced Bregman divergence to relax the mass preserving constraint in the Wasserstein distance, formulate the semi-proximal transport (SPT) discrepancy, and theoretically prove the robustness of SPT against non-stationarity. Subsequently, we remove the dissipative structure and derive the complete SPIRIT workflow, with SPT serving as the proximal operator. Extensive experiments demonstrate the effectiveness of the proposed SPIRIT approach.

cs.LG↗

arXiv2026

DeepFilter: A Transformer-style Framework for Accurate and Efficient Process Monitoring

The process monitoring task is characterized by stringent demands for accuracy and efficiency. Current transformer-based methods, characterized by self-attention for temporal fusion, exhibit limitations in accurately understanding the semantic context and efficiently processing monitoring logs, rendering them inadequate for process monitoring. To address these limitations, we introduce DeepFilter, which revises the self-attention mechanism to improve both accuracy and efficiency. As a straightforward yet versatile approach, DeepFilter provides an instrumental baseline for practitioners in process monitoring, whether initiating new projects or enhancing existing capabilities.

cs.AI↗

arXiv2025

Sign-coherence and tropical sign pattern for rank $3$ real cluster-cyclic exchange matrices

The sign-coherence about $c$-vectors was conjectured by Fomin-Zelevinsky and solved completely by Gross-Hacking-Keel-Kontsevich for integer skew-symmetrizable case. We prove this conjecture associated with $c$-vectors for rank 3 real cluster-cyclic skew-symmetrizable case. Simultaneously, we establish their self-contained recursion and monotonicity. Then, these $c$-vectors are proved to be roots of certain quadratic equations. Based on these results, we prove that the corresponding exchange graphs of $C$-pattern and $G$-pattern are $3$-regular trees. We also study the structure of tropical signs and equip the dihedral group $\mathrm{D}_6$ with a cluster realization via certain mutations.

math.CO↗

arXiv2025

Degradation-Aware Model Predictive Control for Battery Swapping Stations under Energy Arbitrage

Battery swapping stations (BSS) offer a fast and scalable alternative to conventional electric vehicle (EV) charging, gaining growing policy support worldwide. However, existing BSS control strategies typically rely on heuristics or low-fidelity degradation models, limiting profitability and service level. This paper proposes BSS-MPC: a real-time, degradation-aware Model Predictive Control (MPC) framework for BSS operations to trade off economic incentives from energy market arbitrage and long-term battery degradation effects. BSS-MPC integrates a high-fidelity, physics informed battery aging model that accurately predicts the degradation level and the remaining capacity of battery packs. The resulting multiscale optimization-jointly considering energy arbitrage, swapping logistics, and battery health-is formulated as a mixed-integer optimal control problem and solved with tailored algorithms. Simulation results show that BSS-MPC outperforms rule-based and low-fidelity baselines, achieving lower energy cost, reduced capacity fade, and strict satisfaction of EV swapping demands.

math.OC↗

arXiv2025

Tropicalization and cluster asymptotic phenomenon of generalized Markov equations

The generalized Markov equations are deeply connected with the generalized cluster algebras of Markov type. We construct a deformed Fock-Goncharov tropicalization for the generalized Markov equations and prove that their tropicalized tree structure is essentially the same as that of the classical Euclid tree. We then define the generalized Euclid tree and prove that it converges to the classical Euclid tree up to a scalar multiple. Moreover, by means of cluster mutations, we exhibit an asymptotic phenomenon, up to some limit q, between the logarithmic generalized Markov tree and the classical Euclid tree. A rationality conjecture of q is then put forward. We also propose a generalized Markov uniqueness conjecture for the generalized Markov equations, which illustrates an application of the asymptotic phenomenon.

math.NT↗

arXiv2025

Exploiting Electrolyzer Flexibility via Multiscale Model Predictive Control Cross Heterogeneous Energy Markets

Green hydrogen production via electrolysis is crucial for decarbonization but faces significant economic hurdles primarily due to the high cost of the electricity. However, current electrolyzer-based hydrogen production processes predominantly rely on the single-scale Day-Ahead Market (DAM) for electricity procurement, failing to fully exploit the economic benefits offered by multi-scale electricity market that integrates both the DAM and the Real-Time Market (RTM), thereby eliminating the opportunity to reduce the overall cost. To mitigate this technical gap, this research investigates a dynamic operational strategy enabling electrolyzers to strategically navigate between the DAM and RTM to minimize net operation costs. Using a rolling horizon optimization framework to coordinate bidding and operation, we demonstrate a strategy where electrolyzers secure primary energy via exclusive DAM purchases, then actively engage the RTM to buy supplemental energy cheaply or, critically, sell procured DAM energy back at a profit during high RTM price periods. Our analysis reveals that this coordinated multi-scale electricity market participation strategy can dramatically reduce net electricity expenditures, achieving near-zero or even negative effective electricity costs for green hydrogen production under realistic market scenarios, effectively meaning the operation can profit from its electricity market interactions. By transforming electrolyzers from simple price-takers into active participants capable of arbitrage between market timescales, this approach unlocks a financially compelling pathway for green hydrogen, accelerating its deployment while simultaneously enhancing power grid flexibility.

math.OC↗

arXiv2025

YAP+: Pad-Layout-Aware Yield Modeling and Simulation for Hybrid Bonding

Three-dimensional (3D) integration continues to advance Moore's Law by facilitating dense interconnects and enabling multi-tier system architectures. Among the various integration approaches, Cu-Cu hybrid bonding has emerged as a leading solution for achieving high interconnect density in chiplet integration. In this work, we present YAP+, a yield modeling framework specifically tailored for wafer-to-wafer (W2W) and die-to-wafer (D2W) hybrid bonding processes. YAP+ incorporates a comprehensive set of yield-impacting failure mechanisms, including overlay misalignment, particle defects, Cu recess variations, surface roughness, and Cu pad density. Furthermore, YAP+ supports pad layout-aware yield analysis, considering critical, redundant, and dummy pads across arbitrary 2D physical layout patterns. To support practical evaluation, we developed an open-source yield simulator, demonstrating that our near-analytical model matches simulation accuracy while achieving over 1,000x speedup in runtime. This performance makes YAP+ a valuable tool for co-optimizing packaging technologies, assembly design rules, and system-level design strategies. Beyond W2W-D2W comparisons, we leverage YAP+ to investigate the impact of pad layout patterns, bonding pitch, and pad ratios across different pad types, and explore the benefits of strategically placing redundant pad replicas.

cs.AR↗

arXiv2025

Relaxing Probabilistic Latent Variable Models' Specification via Infinite-Horizon Optimal Control

In this paper, we address the issue of model specification in probabilistic latent variable models (PLVMs) using an infinite-horizon optimal control approach. Traditional PLVMs rely on joint distributions to model complex data, but introducing latent variables results in an ill-posed parameter learning problem. To address this issue, regularization terms are typically introduced, leading to the development of the expectation-maximization (EM) algorithm, where the latent variable distribution is restricted to a predefined normalized distribution family to facilitate the expectation step. To overcome this limitation, we propose representing the latent variable distribution as a finite set of instances perturbed via an ordinary differential equation with a control policy. This approach ensures that the instances asymptotically converge to the true latent variable distribution as time approaches infinity. By doing so, we reformulate the distribution inference problem as an optimal control policy determination problem, relaxing the model specification to an infinite-horizon path space. Building on this formulation, we derive the corresponding optimal control policy using the Pontryagin's maximum principle and provide a closed-form expression for its implementation using the reproducing kernel Hilbert space. After that, we develop a novel, convergence-guaranteed EM algorithm for PLVMs based on this infinite-horizon-optimal-control-based inference strategy. Finally, extensive experiments are conducted to validate the effectiveness and superiority of the proposed approach.

eess.SY↗