arXiv subjects

Yancheng Yuan

Publications and source records attributed to Yancheng Yuan.

At least 19 recordsLinked to original sources

arXiv2026

A New Perspective on Clustering: A Mixed-norm Model and its Solution by Progressive Integer Programming

Extending the classical $K$-means and $K$-medians models, this paper introduces an $\ell_{p,q}$ mixed-norm clustering model where the centroid updates and cluster assignments are under the $\ell_p$ and $\ell_q$ norms, respectively. The model is formulated as a mixed-integer program (MIP) with Heaviside composite constraints that describe the nearest-center assignments. The framework recovers $K$-means and $K$-medians when $p=q=2$ and $p=q=1$, respectively, and yields new models when $p\ne q$. To address the computational challenges, we develop a progressive integer programming (PIP) method that adaptively fixes confident assignments and solves restricted mixed-integer subproblems. For $q=1$, we develop a convex inner approximation of the difference-of-convex constraints in the restricted subproblems, for which a global solution can be computed. Importantly, we establish the connection between the local minimizer and the strong center-local minimizer of the mixed-norm clustering problem and the global optimal solution of the restricted subproblems under certain assumptions. This connection provides a practical certificate of a local minimizer of the nonconvex mixed-norm clustering model. We further develop techniques for constructing adaptive fixing sets and working sets for $q=1$. Extensive numerical experiments demonstrate the superior performance of the mixed-norm clustering model and the efficiency of PIP for solving the MIP model, which may be intractable otherwise. In particular, the $\ell_{2,1}$ mixed-norm clustering model is effective under coordinate-sparse, mean-balanced contamination, whereas the $\ell_{1,2}$ model is preferred under dense coordinatewise Cauchy contamination. The numerical results also show that PIP can escape poor alternating solutions and obtain substantially better feasible clustering, while preserving strong warm starts when no improvement is found.

math.OC↗

arXiv2026

ADMM Fails to Achieve an $O(K^{-1})$ Ergodic KKT Residual Bound

The Karush--Kuhn--Tucker (KKT) residual is a fundamental measure of first-order optimality and, under an error bound condition, is comparable to the distance to the KKT solution set up to constant factors. Despite the $O(K^{-1})$ ergodic rates known for objective error and feasibility violations, we show that the KKT residual of classical ADMM cannot, in general, satisfy a uniform $O(K^{-1})$ bound. Specifically, we construct a fixed-dimensional, horizon-dependent family of two-block convex optimization problems for which the KKT residual is $\Omega(K^{-1/2})$ at both the last iterate and the equal-weight ergodic average at the prescribed horizon $K$. Consequently, a uniform $O(K^{-1})$ KKT residual bound is impossible for either output.

math.OC↗

arXiv2026

ASAP: Reimagining the Data Lifecycle using Application Semantic-Aware Processing

Across many domains (e.g., observability, networking, security), data processing pipelines face what we refer to as the CSP problem: achieving low Cost at large Scale, while maintaining high Performance. In response, we see several efforts to tackle CSP in various stages of the Collect-Transmit-Store-Analyze data lifecycle; such as approximate query processing in databases or sketches in network routers. Our work is driven by the simple insight: "seeing the forest for the trees". These proposed solutions (e.g., AQP, sketching, compression, rollups) addressing CSP share a common property - they exploit semantic-preserving opportunities to support application needs. In this paper, we make a case for ASAP, a paradigm that makes Application Semantic-Aware Processing (ASAP) a first-class design principle in data processing pipelines. We argue that by taking a unified view across ASAP primitives developed in different domains, across the entire data lifecycle, we can unlock new opportunities to tackle the CSP problem. In particular, we can: (i) enable novel cross-lifecycle optimizations such as analytics run directly on sketches computed at the source; (ii) leverage primitives developed in other application domains; and (iii) enable widespread adoption of these powerful techniques. We discuss research challenges in socializing the benefits of the ASAP paradigm, and show preliminary evidence that adopting ASAP can yield up to 3 orders of magnitude improvements in the CSP tradeoff for many application domains.

cs.DB↗

arXiv2026

Diagnosing and Mitigating Thinking Collapse in On-Policy Self-Distillation

On-Policy Self-Distillation (OPSD) has emerged as a crucial paradigm for enhancing and aligning Large Language Models (LLMs). However, in complex reasoning tasks, OPSD paradoxically degrades downstream performance. In this paper, we systematically investigate this pathology and identify a severe optimization trap we define as \textbf{Thinking Collapse} -- a sharp decline in the model's native intermediate reasoning behavior, measured by epistemic-token density (ET per 1k). Through entropy-based gradient masking and token-level target analysis, we show that this collapse is triggered by aggressive teacher gradients at high-student-entropy decision forks, where student epistemic tokens are frequently suppressed into teacher non-epistemic targets and are highly concentrated in high pointwise student-teacher divergence regions. To resolve this optimization pathology, we propose \textbf{Adaptive Dual-Perspective OPSD (AD-OPSD)}, a robust control framework that dynamically moderates the self-distillation objective. AD-OPSD selectively anchors high-suppression-risk sandboxed tokens to a reference prior derived from the frozen base model via an asymmetrical pointwise divergence gate, preserving native thinking capacity while retaining OPSD's error-correcting power. Extensive experiments across competitive mathematical benchmarks show that AD-OPSD improves over standard OPSD by up to \textbf{+4.1\%} absolute average accuracy across diverse model scales and datasets. Further analysis demonstrates that AD-OPSD mitigates thinking collapse and generalizes robustly to different post-training paradigms.

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arXiv2026

PrunePath: Towards Highly Structured Sparse Language Models

Feed-forward networks (FFNs) dominate the parameter count and computation of modern language models, yet existing pruning methods often struggle to convert sparsity into hardware-friendly inference efficiency gains. We introduce \textbf{PrunePath}, a budget-adaptive structured sparsification framework for FFN layers. Built on MoEfication, PrunePath replaces independent expert-wise thresholding with a softmax-normalized routing distribution and activates important experts under a cumulative-mass threshold. This formulation imposes a token-level probability budget, enabling adaptive expert counts and a direct inference-time sparsity knob from a single checkpoint. Across NLU, NLG, and instruction-tuning evaluations, PrunePath achieves a favorable sparsity--performance trade-off compared with existing static pruning and MoEfication-based methods. We further implement Triton kernels for KV-cache decoding to translate the resulting structured sparsity into practical memory savings and measurable decoding-speed improvements. These results demonstrate the superior performance of PrunePath for building highly sparse, deployment-friendly large language models.

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arXiv2026

Teaching Large Language Models When Not to Know: Learning Temporal Critique for Ex-Ante Reasoning

Large language models (LLMs) often fail to reason under temporal cutoffs: when prompted to answer from the standpoint of an earlier time, they exploit knowledge that became available only later. We study this failure through the lens of ex-ante reasoning, where a model must rely exclusively on information knowable before a cutoff. Through a systematic analysis of prompt-level interventions, we find that temporal leakage is highly sensitive to cutoff formulation and instruction placement: explicit cutoff statements outperform implicit historical framings, and prefix constraints reduce leakage more effectively than suffix constraints. These findings indicate that prompting can steer models into a temporal frame, but does not endow them with the ability to verify whether a response is temporally admissible. We further argue that supervised fine-tuning is insufficient, since ex-ante correctness is not an intrinsic property of an answer, but a relation between the answer and the cutoff. To address this gap, we propose TCFT, a Temporal Critique Fine-Tuning framework that trains models to acquire cutoff-aware temporal verification. Given a query, a cutoff, and a candidate response, TCFT teaches the model to identify post-cutoff leakage, explain temporal boundary violations, and judge temporal admissibility. Experiments with Qwen2.5-7B-Instruct and Qwen2.5-14B-Instruct show that TCFT consistently outperforms prompting and SFT baselines, reducing average leakage by 41.89 and 37.79 percentage points, respectively.

cs.AI↗

arXiv2026

Efficient and provably convergent end-to-end training of deep neural networks with linear constraints

Training a deep neural network with the outputs of selected layers satisfying linear constraints is required in many contemporary data-driven applications. While this can be achieved by incorporating projection layers into the neural network, its end-to-end training remains challenging due to the lack of rigorous theory and efficient algorithms for backpropagation. A key difficulty in developing the theory and efficient algorithms for backpropagation arose from the nonsmoothness of the solution mapping of the projection layer. To address this bottleneck, we introduce an efficiently computable HS-Jacobian to the projection layer. Importantly, we prove that the HS-Jacobian is a conservative mapping for the projection operator onto the polyhedral set, enabling its seamless integration into the nonsmooth automatic differentiation framework for backpropagation. Therefore, many efficient algorithms, such as Adam, can be applied for end-to-end training of deep neural networks with linear constraints. Particularly, we establish convergence guarantees of the HS-Jacobian based Adam algorithm for training linearly constrained deep neural networks. Extensive experiment results on several important applications, including finance, computer vision, and network architecture design, demonstrate the superior performance of our method compared to other existing popular methods.

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arXiv2026

VAE-Inf: A statistically interpretable generative paradigm for imbalanced classification

Imbalanced classification remains a pervasive challenge in machine learning, particularly when minority samples are too scarce to provide a robust discriminative boundary. In such extreme scenarios, conventional models often suffer from unstable decision boundaries and a lack of reliable error control. To bridge the gap between generative modeling and discriminative classification, we propose a two-stage framework \textbf{VAE-Inf} that integrates deep representation learning with statistically interpretable hypothesis testing. In the first stage, we adopt a one-class modeling perspective by training a variational autoencoder (VAE) exclusively on majority-class data to capture the underlying reference distribution. The resulting latent posteriors are aggregated via a Wasserstein barycenter to construct a global Gaussian reference model, providing a geometrically principled baseline for the majority class. In the second stage, we transform this generative foundation into a discriminative classifier by fine-tuning the encoder with limited minority samples. This is achieved through a novel distribution-aware loss that enforces probabilistic separation between classes based on variance-normalized projection statistics. For inference, we introduce a projection-based score that admits a natural hypothesis testing interpretation, allowing for a distribution-free calibration procedure. This approach yields exact finite-sample control of the Type-I error (false positive rate) without relying on restrictive parametric assumptions. Extensive experiments on diverse real-world benchmarks demonstrate that our framework achieves competitive performance against other approaches. The codes are available upon request.

cs.LG↗

arXiv2026

DARE: Aligning LLM Agents with the R Statistical Ecosystem via Distribution-Aware Retrieval

Large Language Model (LLM) agents can automate data-science workflows, but many rigorous statistical methods implemented in R remain underused because LLMs struggle with statistical knowledge and tool retrieval. Existing retrieval-augmented approaches focus on function-level semantics and ignore data distribution, producing suboptimal matches. We propose DARE (Distribution-Aware Retrieval Embedding), a lightweight, plug-and-play retrieval model that incorporates data distribution information into function representations for R package retrieval. Our main contributions are: (i) RPKB, a curated R Package Knowledge Base derived from 8,191 high-quality CRAN packages; (ii) DARE, an embedding model that fuses distributional features with function metadata to improve retrieval relevance; and (iii) RCodingAgent, an R-oriented LLM agent for reliable R code generation and a suite of statistical analysis tasks for systematically evaluating LLM agents in realistic analytical scenarios. Empirically, DARE achieves an NDCG at 10 of 93.47%, outperforming state-of-the-art open-source embedding models by up to 17% on package retrieval while using substantially fewer parameters. Integrating DARE into RCodingAgent yields significant gains on downstream analysis tasks. This work helps narrow the gap between LLM automation and the mature R statistical ecosystem.

cs.IR↗

arXiv2026

Max-Min Bilinear Completely Positive Programs: A Semidefinite Relaxation with Tightness Guarantees

Max-min bilinear optimization models, where one agent maximizes and an adversary minimizes a common bilinear objective, serve as canonical saddle-point formulations in optimization theory. They capture, among others, two-player zero-sum games, robust and distributionally robust optimization, and adversarial machine learning. This study focuses on the subclass whose variables lie in the completely positive (CP) cone, capturing a broad family of mixed-binary quadratic max-min problems through the modelling power of completely positive programming. We show that such problems admit an equivalent single-stage linear reformulation over the COP-CP cone, defined as the Cartesian product of the copositive (COP) and CP cones. Because testing membership in COP cones is co-NP-complete, the resulting COP-CP program inherits NP-hardness. To address this challenge, we develop a hierarchy of semidefinite relaxations based on moment and sum-of-squares representations of the COP and CP cones, and flat truncation conditions are applied to certify the tightness. We show that the tightness of the hierarchy is guaranteed under mild conditions. The framework extends existing CP/COP approaches for distributionally robust optimization and polynomial games. We apply the framework to the cyclic Colonel Blotto game, an extension of Borel's classic allocation contest. Across multiple instances, the semidefinite relaxation meets the flat-truncation conditions and solves the exact mixed-strategy equilibrium.

math.OC↗

arXiv2026

Efficient Equivariant High-Order Crystal Tensor Prediction via Cartesian Local-Environment Many-Body Coupling

End-to-end prediction of high-order crystal tensor properties from atomic structures remains challenging: while spherical-harmonic equivariant models are expressive, their Clebsch-Gordan tensor products incur substantial compute and memory costs for higher-order targets. We propose the Cartesian Environment Interaction Tensor Network (CEITNet), an approach that constructs a multi-channel Cartesian local environment tensor for each atom and performs flexible many-body mixing via a learnable channel-space interaction. By performing learning in channel space and using Cartesian tensor bases to assemble equivariant outputs, CEITNet enables efficient construction of high-order tensor. Across benchmark datasets for order-2 dielectric, order-3 piezoelectric, and order-4 elastic tensor prediction, CEITNet surpasses prior high-order prediction methods on key accuracy criteria while offering high computational efficiency.

cs.LG↗

arXiv2026

Think Dense, Not Long: Dynamic Decoupled Conditional Advantage for Efficient Reasoning

Reinforcement Learning with Verifiable Rewards (RLVR) can elicit strong multi-step reasoning, yet it often encourages overly verbose traces. Moreover, naive length penalties in group-relative optimization can severely hurt accuracy. We attribute this failure to two structural issues: (i) Dilution of Length Baseline, where incorrect responses (with zero length reward) depress the group baseline and over-penalize correct solutions; and (ii) Difficulty-Penalty Mismatch, where a static penalty cannot adapt to problem difficulty, suppressing necessary reasoning on hard instances while leaving redundancy on easy ones. We propose Dynamic Decoupled Conditional Advantage (DDCA) to decouple efficiency optimization from correctness. DDCA computes length advantages conditionally within the correct-response cluster to eliminate baseline dilution, and dynamically scales the penalty strength using the group pass rate as a proxy for difficulty. Experiments on GSM8K, MATH500, AMC23, and AIME25 show that DDCA consistently improves the efficiency--accuracy trade-off relative to adaptive baselines, reducing generated tokens by approximately 60% on simpler tasks (e.g., GSM8K) versus over 20% on harder benchmarks (e.g., AIME25), thereby maintaining or improving accuracy. Code is available at https://github.com/alphadl/DDCA.

cs.CL↗

arXiv2026

DSAEval: Evaluating Data Science Agents on a Wide Range of Real-World Data Science Problems

Recent LLM-based data agents aim to automate data science tasks ranging from data analysis to deep learning. However, the open-ended nature of real-world data science problems, which often span multiple taxonomies and lack standard answers, poses a significant challenge for evaluation. To address this, we introduce DSAEval, a benchmark comprising 641 real-world data science problems grounded in 285 diverse datasets, covering both structured and unstructured data (e.g., image and text). DSAEval incorporates three distinctive features: (1) Multimodal Environment Perception, which enables agents to interpret observations from multiple modalities, including text and vision; (2) Multi-Query Interactions, which mirror the iterative and cumulative nature of real-world data science projects; and (3) Multi-Dimensional Evaluation, which provides a holistic assessment across reasoning, code, and results. We systematically evaluate 13 recent advanced agentic LLMs using DSAEval. Our results show that Claude-Sonnet-4.5 achieves the strongest overall performance, MiMo-V2-Pro and GPT-5.2 lead in duration and step efficiency, respectively, and MiMo-V2-Flash is the most cost-effective. We further demonstrate that multimodal perception consistently improves performance on vision-related tasks, with gains ranging from 2.04% to 11.30%. Overall, while current data science agents perform well on structured data and routine data analysis workflows, substantial challenges remain in unstructured domains. Finally, we offer critical insights and outline future research directions.

cs.AI↗

arXiv2026

A Perturbed DCA for Computing d-Stationary Points of Nonsmooth DC Programs

This paper introduces an efficient perturbed difference-of-convex algorithm (perturbed DCA) for computing d-stationary points of an important class of structured nonsmooth difference-of-convex problems. Compared to the principal algorithms introduced in [J.-S. Pang, M. Razaviyayn, and A. Alvarado, Math. Oper. Res. 42(1):95--118 (2017)], which may require solving several subproblems for a one-step update, perturbed DCA only requires solving a single subproblem. Therefore, the per-iteration computational cost of perturbed DCA is comparable to the widely used difference-of-convex algorithm (DCA) introduced in [D. T. Pham and H. A. Le Thi, Acta Math. Vietnam. 22(1):289--355 (1997)] for computing a critical point. We establish the subsequential and almost sure convergence of the perturbed DCA to d-stationary points under certain conditions. To decouple the perturbation radii from the local convergence rate of the iterates, we further propose a hybrid variant of the perturbed DCA that independently samples the perturbation radius and direction with a safeguard using a proximal DCA step. Importantly, under more relaxed and practical assumptions, we prove that every accumulation point of the sequence generated by the hybrid perturbed DCA is a d-stationary point almost surely. Numerical results on several important examples demonstrate the efficiency of the proposed methods for computing d-stationary points.

math.OC↗

arXiv2025

On the Convergence Analysis of an Inexact Preconditioned Stochastic Model-Based Algorithm

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the fixed-metric stochastic model-based algorithm to its preconditioned and inexact variants. Convergence guarantees are established under mild assumptions for both weakly convex and convex settings, without requiring smoothness or global Lipschitz continuity of the objective function. By assuming a local Lipschitz condition, we derive nonasymptotic and asymptotic convergence rates measured by the gradient of the Moreau envelope. Furthermore, convergence rates in terms of the distance to the optimal solution set are obtained under an additional quadratic growth condition on the objective function. Numerical experiment results demonstrate the theoretical findings for the proposed algorithm.

math.OC↗

arXiv2025

dHPR: A Distributed Halpern Peaceman--Rachford Method for Non-smooth Distributed Optimization Problems

This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$ iteration complexity regarding Karush--Kuhn--Tucker residual. By leveraging the symmetric Gauss--Seidel decomposition, the dHPR effectively decouples the linear operators in the objective functions and consensus constraints while maintaining parallelizability and avoiding additional large proximal terms, leading to a decentralized implementation with provably fast convergence. The superior performance of dHPR is demonstrated through comprehensive numerical experiments on distributed LASSO, group LASSO, and $L_1$-regularized logistic regression problems.

math.OC↗

arXiv2025

Magnitude-Modulated Equivariant Adapter for Parameter-Efficient Fine-Tuning of Equivariant Graph Neural Networks

Pretrained equivariant graph neural networks based on spherical harmonics offer efficient and accurate alternatives to computationally expensive ab-initio methods, yet adapting them to new tasks and chemical environments still requires fine-tuning. Conventional parameter-efficient fine-tuning (PEFT) techniques, such as Adapters and LoRA, typically break symmetry, making them incompatible with those equivariant architectures. ELoRA, recently proposed, is the first equivariant PEFT method. It achieves improved parameter efficiency and performance on many benchmarks. However, the relatively high degrees of freedom it retains within each tensor order can still perturb pretrained feature distributions and ultimately degrade performance. To address this, we present Magnitude-Modulated Equivariant Adapter (MMEA), a novel equivariant fine-tuning method which employs lightweight scalar gating to modulate feature magnitudes on a per-order and per-multiplicity basis. We demonstrate that MMEA preserves strict equivariance and, across multiple benchmarks, consistently improves energy and force predictions to state-of-the-art levels while training fewer parameters than competing approaches. These results suggest that, in many practical scenarios, modulating channel magnitudes is sufficient to adapt equivariant models to new chemical environments without breaking symmetry, pointing toward a new paradigm for equivariant PEFT design.

cs.LG↗

arXiv2025

MLLMEraser: Achieving Test-Time Unlearning in Multimodal Large Language Models through Activation Steering

Multimodal large language models (MLLMs) have demonstrated remarkable capabilities across vision-language tasks, yet their large-scale deployment raises pressing concerns about memorized private data, outdated knowledge, and harmful content. Existing unlearning approaches for MLLMs typically adapt training-based strategies such as gradient ascent or preference optimization, but these methods are computationally expensive, irreversible, and often distort retained knowledge. In this work, we propose MLLMEraser, an input-aware, training-free framework for test-time unlearning. Our approach leverages activation steering to enable dynamic knowledge erasure without parameter updates. Specifically, we construct a multimodal erasure direction by contrasting adversarially perturbed, knowledge-recall image-text pairs with knowledge-erasure counterparts, capturing both textual and visual discrepancies. To prevent unnecessary interference, we further design an input-aware steering mechanism that adaptively determines when and how the erasure direction should be applied, preserving utility on retained knowledge while enforcing forgetting on designated content. Experiments on LLaVA-1.5 and Qwen-2.5-VL demonstrate that MLLMEraser consistently outperforms state-of-the-art MLLM unlearning baselines, achieving stronger forgetting performance with lower computational cost and minimal utility degradation.

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