arXiv subjects

Zhen Qin

Publications and source records attributed to Zhen Qin.

At least 37 records · Page 2Linked to original sources

arXiv2026

Statistical and Algorithmic Foundations of Probing Quantum Systems with Compressive Measurements: A Review

Quantum state tomography (QST) is a fundamental task in quantum information science that aims to reconstruct unknown quantum states from measurement data. However, the exponential growth of Hilbert-space dimension with system size makes full tomography of general quantum states statistically and computationally prohibitive. This challenge has motivated extensive research on structured quantum state tomography, where prior structure, such as low-rankness, tensor-network representations, shallow quantum circuits, and neural quantum states, can substantially reduce the effective degrees of freedom and enable scalable recovery. In this review, we provide a unified perspective on QST for structured quantum states through three closely related themes: compact state representations, measurement design, and computational algorithms. After reviewing common models for structured quantum states, we survey existing work on geometric preservation properties of measurement frameworks, ranging from informationally complete POVMs to randomized measurements, and their implications for sample complexity. On the algorithmic side, we review optimization methods for reconstructing structured quantum states from empirical measurements. By connecting QST with broader principles from compressive sensing, matrix sensing, and structured inverse problems, this survey highlights common theoretical foundations underlying sample complexity, measurement efficiency, and scalable recovery.

quant-ph↗

arXiv2026

Higher-order Linear Attention

The quadratic cost of scaled dot-product attention is a central obstacle to scaling autoregressive language models to long contexts. Linear-time attention and State Space Models (SSMs) provide scalable alternatives but are typically restricted to first-order or kernel-based approximations, which can limit expressivity. We introduce Higher-order Linear Attention (HLA), a causal, streaming mechanism that realizes higher interactions via compact prefix sufficient statistics. In the second-order case, HLA maintains a constant-size state and computes per-token outputs in linear time without materializing any $n \times n$ matrices. We give closed-form streaming identities, a strictly causal masked variant using two additional summaries, and a chunk-parallel training scheme based on associative scans that reproduces the activations of a serial recurrence exactly. We further outline extensions to third and higher orders. Collectively, these results position HLA as a principled, scalable building block that combines attention-like, data-dependent mixing with the efficiency of modern recurrent architectures.

cs.LG↗

arXiv2026

A Tale of Two Problems: Multi-Task Bilevel Learning Meets Equality Constrained Multi-Objective Optimization

In recent years, bilevel optimization (BLO) has attracted significant attention for its broad applications in machine learning. However, most existing works on BLO remain confined to the single-task setting and rely on the lower-level strong convexity assumption, which significantly restricts their applicability to modern machine learning problems of growing complexity. In this paper, we make the first attempt to extend BLO to the multi-task setting under a relaxed lower-level general convexity (LLGC) assumption. To this end, we reformulate the multi-task bilevel learning (MTBL) problem with LLGC into an equality constrained multi-objective optimization (ECMO) problem. However, ECMO itself is a new problem that has not yet been studied in the literature. To address this gap, we first establish a new Karush-Kuhn-Tucker (KKT)-based Pareto stationarity as the convergence criterion for ECMO algorithm design. Based on this foundation, we propose a weighted Chebyshev (WC)-penalty algorithm that achieves a finite-time convergence rate of $O(ST^{-\frac{1}{2})$ to KKT-based Pareto stationarity in both deterministic and stochastic settings, where $S$ denotes the number of objectives, and $T$ is the total iterations. Moreover, by varying the preference vector over the $S$-dimensional simplex, our WC-penalty method systematically explores the Pareto front. Finally, solutions to the ECMO problem translate directly into solutions for the original MTBL problem, thereby closing the loop between these two foundational optimization frameworks.

cs.LG↗

arXiv2026

Group Representational Position Encoding

We present GRAPE (Group Representational Position Encoding), a unified framework for positional encoding based on group actions. GRAPE unifies two families of mechanisms: (i) multiplicative rotations (Multiplicative GRAPE) in $\operatorname{SO}(d)$ and (ii) additive logit biases (Additive GRAPE) arising from unipotent actions in the general linear group $\mathrm{GL}$. In Multiplicative GRAPE, a position $n \in \mathbb{Z}$ (or $t \in \mathbb{R}$) acts as $\mathbf{G}(n) = \exp(n \, ω\, \mathbf{L})$ with a rank-2 skew-symmetric generator $\mathbf{L} \in \mathbb{R}^{d \times d}$, yielding a relative, compositional, norm-preserving map with a closed-form matrix exponential. RoPE is recovered exactly when the $d/2$ planes correspond to canonical coordinate pairs with a log-uniform spectrum. Learned commuting subspaces and compact non-commuting mixtures strictly extend this geometry to capture cross-subspace feature coupling at $O(d)$ and $O(r d)$ cost per head, respectively. In Additive GRAPE, additive logits arise from rank-1 (or low-rank) unipotent actions, recovering ALiBi and the Forgetting Transformer (FoX) as exact special cases while preserving an exact relative law and streaming cacheability. Overall, GRAPE provides a principled design space for positional geometry in long-context models, subsuming RoPE and ALiBi as special cases. Project page: https://github.com/model-architectures/GRAPE.

cs.LG↗

arXiv2026

An Exponential Advantage for Adaptive Tomography of Structured States under Pauli Basis Measurements

Broad claims about whether adaptivity helps in quantum state tomography can be misleading unless the state family, measurement architecture, and error metric are specified carefully. We study a restricted but physically important regime: single-copy quantum state tomography under local Pauli basis measurements, where the allowed measurement settings are tensor-product measurement operators built from local single-qubit Pauli operators, and performance is measured in trace distance with high probability in a minimax sense over a known structured family. We construct an explicit discrete prefix/tree family of states for which adaptive measurement selection achieves polynomial copy complexity, while every non-adaptive design requires exponentially many copies in the worst case. The adaptive upper bound comes from stagewise prefix recovery using hierarchical breadcrumb information revealed by partial prefix matches. The non-adaptive lower bound is based on a rare-prefix mechanism: every fixed design under-samples some deep prefix subset, and outside that subset the competing hypotheses induce identical one-shot laws, so only an exponentially small fraction of the measurement budget contributes to the KL divergence between the full data distributions. The result isolates a concrete regime in which adaptivity provably changes the sample-complexity scaling under the experimentally common local Pauli measurement architecture.

quant-ph↗

arXiv2026

On the Convergence of Gradient Descent on Learning Transformers with Residual Connections

Transformer models have emerged as fundamental tools across various scientific and engineering disciplines, owing to their outstanding performance in diverse applications. Despite this empirical success, the theoretical foundations of Transformers remain relatively underdeveloped, particularly in understanding their training dynamics. Existing research predominantly examines isolated components--such as self-attention mechanisms and feedforward networks--without thoroughly investigating the interdependencies between these components, especially when residual connections are present. In this paper, we aim to bridge this gap by analyzing the convergence behavior of a structurally complete yet single-layer Transformer, comprising self-attention, a feedforward network, and residual connections. We demonstrate that, under appropriate initialization, gradient descent exhibits a linear convergence rate, where the convergence speed is determined by the minimum and maximum singular values of the output matrix from the attention layer. Moreover, our analysis reveals that residual connections serve to ameliorate the ill-conditioning of this output matrix, an issue stemming from the low-rank structure imposed by the softmax operation, thereby promoting enhanced optimization stability. We also extend our theoretical findings to a multi-layer Transformer architecture, confirming the linear convergence rate of gradient descent under suitable initialization. Empirical results corroborate our theoretical insights, illustrating the beneficial role of residual connections in promoting convergence stability.

cs.LG↗

arXiv2026

Retrieval Augmented Conversational Recommendation with Reinforcement Learning

Large language models (LLMs) exhibit enhanced capabilities in language understanding and generation. By utilizing their embedded knowledge, LLMs are increasingly used as conversational recommender systems (CRS), achieving improved performance across diverse scenarios. However, existing LLM-based methods rely on pretrained knowledge without external retrieval mechanisms for novel items. Additionally, the lack of a unified corpus poses challenges for integrating retrieval augmentation into CRS. Motivated by these challenges, we present RAR, a novel two-stage retrieval augmented conversational recommendation framework that aligns retrieval and generation to enhance both performance and factuality. To support this framework and provide a unified corpus, we construct a large-scale movie corpus, comprising over 300k movies with rich metadata, such as titles, casts and plot summaries. Leveraging this data, our primary contribution is RAR, the first framework to departs from standard two-stage CRS by dynamically bridging retrieval and generation. First, a retriever model generates candidate items based on user history; in the subsequent stage, an LLM refines the recommendations by incorporating conversational context with retrieved results. In addition, we introduce a novel reinforcement learning (RL) method that leverages LLM feedback to iteratively update the retriever. By creating a collaborative feedback loop that reinforces sampled candidate sets with higher ranking metrics, RAR effectively mitigates the misalignment between the retrieval and generation stages. Furthermore, grounding the LLM in factual metadata allows our RL-driven approach to capture subtle user intentions and generate context-aware recommendations with reduced hallucinations. We validate our approach through extensive experiments on multiple benchmarks, where RAR consistently outperforms state-of-the-art baseline methods.

cs.IR↗

arXiv2026

Learning to Adapt: In-Context Learning Beyond Stationarity

Transformer models have become foundational across a wide range of scientific and engineering domains due to their strong empirical performance. A key capability underlying their success is in-context learning (ICL): when presented with a short prompt from an unseen task, transformers can perform per-token and next-token predictions without any parameter updates. Recent theoretical efforts have begun to uncover the mechanisms behind this phenomenon, particularly in supervised regression settings. However, these analyses predominantly assume stationary task distributions, which overlook a broad class of real-world scenarios where the target function varies over time. In this work, we bridge this gap by providing a theoretical analysis of ICL under non-stationary regression problems. We study how the gated linear attention (GLA) mechanism adapts to evolving input-output relationships and rigorously characterize its advantages over standard linear attention in this dynamic setting. To model non-stationarity, we adopt a first-order autoregressive process and show that GLA achieves lower training and testing errors by adaptively modulating the influence of past inputs -- effectively implementing a learnable recency bias. Our theoretical findings are further supported by empirical results, which validate the benefits of gating mechanisms in non-stationary ICL tasks.

cs.LG↗

arXiv2026

A Heavy-Load-Enhanced and Changeable-Periodicity-Perceived Workload Prediction Network

Cloud providers can greatly benefit from accurate workload prediction. However, the workload of cloud servers is highly variable, with occasional workload bursts, which makes workload prediction challenging. The time series forecasting methods relying on periodicity information, often assume fixed and known periodicity length, which does not align with the periodicity-changeable nature of cloud service workloads. Although many state-of-the-art time-series forecasting methods do not rely on periodicity information and achieve high overall accuracy, they are vulnerable to data imbalance between heavy workloads and regular workloads. As a result, their prediction accuracy on rare heavy workloads is limited. Unfortunately, heavyload-prediction accuracy is more important than overall one, as errors in heavyload prediction are more likely to cause Service Level Agreement violations than errors in normal-load prediction. Thus, we propose a changeable-periodicity-perceived workload prediction network (PePNet) to fuse periodic information adaptively for periodicity-changeable time series and improve rare heavy workload prediction accuracy. It has two distinctive characteristics: (i) A Periodicity-Perceived Mechanism to detect the periodicity length automatically and fuses periodic information adaptively, which is suitable for periodicity-changeable time series, and (ii) An Achilles' Heel Loss Function that is used to iteratively optimize the most under-fitting part in predicting sequence for each step, thus evidently improving the prediction accuracy of heavy load. Extensive experiments conducted on real-world datasets demonstrate that PePNet improves accuracy for overall workload by 11.8% averagely, compared with state-of-the-art methods. Especially, PePNet improves accuracy for heavy workload by 21.0% averagely.

cs.DC↗

arXiv2026

SeDa: A Unified System for Dataset Discovery and Multi-Entity Augmented Semantic Exploration

The continuous expansion of open data platforms and research repositories has led to a fragmented dataset ecosystem, posing significant challenges for cross-source data discovery and interpretation. To address these challenges, we introduce SeDa--a unified framework for dataset discovery, semantic annotation, and multi-entity augmented navigation. SeDa integrates more than 7.6 million datasets from over 200 platforms, spanning governmental, academic, and industrial domains. The framework first performs semantic extraction and standardization to harmonize heterogeneous metadata representations. On this basis, a topic-tagging mechanism constructs an extensible tag graph that supports thematic retrieval and cross-domain association, while a provenance assurance module embedded within the annotation process continuously validates dataset sources and monitors link availability to ensure reliability and traceability. Furthermore, SeDa employs a multi-entity augmented navigation strategy that organizes datasets within a knowledge space of sites, institutions, and enterprises, enabling contextual and provenance-aware exploration beyond traditional search paradigms. Comparative experiments with popular dataset search platforms, such as ChatPD and Google Dataset Search, demonstrate that SeDa achieves superior coverage, timeliness, and traceability. Taken together, SeDa establishes a foundation for trustworthy, semantically enriched, and globally scalable dataset exploration.

cs.IR↗

arXiv2026

RuCL: Stratified Rubric-Based Curriculum Learning for Multimodal Large Language Model Reasoning

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a prevailing paradigm for enhancing reasoning in Multimodal Large Language Models (MLLMs). However, relying solely on outcome supervision risks reward hacking, where models learn spurious reasoning patterns to satisfy final answer checks. While recent rubric-based approaches offer fine-grained supervision signals, they suffer from high computational costs of instance-level generation and inefficient training dynamics caused by treating all rubrics as equally learnable. In this paper, we propose Stratified Rubric-based Curriculum Learning (RuCL), a novel framework that reformulates curriculum learning by shifting the focus from data selection to reward design. RuCL generates generalized rubrics for broad applicability and stratifies them based on the model's competence. By dynamically adjusting rubric weights during training, RuCL guides the model from mastering foundational perception to tackling advanced logical reasoning. Extensive experiments on various visual reasoning benchmarks show that RuCL yields a remarkable +7.83% average improvement over the Qwen2.5-VL-7B model, achieving a state-of-the-art accuracy of 60.06%.

cs.CL↗

arXiv2026

Reinforcement Fine-Tuning for History-Aware Dense Retriever in RAG

Retrieval-augmented generation (RAG) enables large language models (LLMs) to produce evidence-based responses, and its performance hinges on the matching between the retriever and LLMs. Retriever optimization has emerged as an efficient alternative to fine-tuning LLMs. However, existing solutions suffer from objective mismatch between retriever optimization and the goal of RAG pipeline. Reinforcement learning (RL) provides a promising solution to address this limitation, yet applying RL to retriever optimization introduces two fundamental challenges: 1) the deterministic retrieval is incompatible with RL formulations, and 2) state aliasing arises from query-only retrieval in multi-hop reasoning. To address these challenges, we replace deterministic retrieval with stochastic sampling and formulate RAG as a Markov decision process, making retriever optimizable by RL. Further, we incorporate retrieval history into the state at each retrieval step to mitigate state aliasing. Extensive experiments across diverse RAG pipelines, datasets, and retriever scales demonstrate consistent improvements of our approach in RAG performance.

cs.LG↗

arXiv2026

Adaptive Dual-Weighting Framework for Federated Learning via Out-of-Distribution Detection

Federated Learning (FL) enables collaborative model training across large-scale distributed service nodes while preserving data privacy, making it a cornerstone of intelligent service systems in edge-cloud environments. However, in real-world service-oriented deployments, data generated by heterogeneous users, devices, and application scenarios are inherently non-IID. This severe data heterogeneity critically undermines the convergence stability, generalization ability, and ultimately the quality of service delivered by the global model. To address this challenge, we propose FLood, a novel FL framework inspired by out-of-distribution (OOD) detection. FLood dynamically counteracts the adverse effects of heterogeneity through a dual-weighting mechanism that jointly governs local training and global aggregation. At the client level, it adaptively reweights the supervised loss by upweighting pseudo-OOD samples, thereby encouraging more robust learning from distributionally misaligned or challenging data. At the server level, it refines model aggregation by weighting client contributions according to their OOD confidence scores, prioritizing updates from clients with higher in-distribution consistency and enhancing the global model's robustness and convergence stability. Extensive experiments across multiple benchmarks under diverse non-IID settings demonstrate that FLood consistently outperforms state-of-the-art FL methods in both accuracy and generalization. Furthermore, FLood functions as an orthogonal plug-in module: it seamlessly integrates with existing FL algorithms to boost their performance under heterogeneity without modifying their core optimization logic. These properties make FLood a practical and scalable solution for deploying reliable intelligent services in real-world federated environments.

cs.LG↗

arXiv2026

Can Vision-Language Models Handle Long-Context Code? An Empirical Study on Visual Compression

Large Language Models (LLMs) struggle with long-context code due to window limitations. Existing textual code compression methods mitigate this via selective filtering but often disrupt dependency closure, causing semantic fragmentation. To address this, we introduce LongCodeOCR, a visual compression framework that renders code into compressed two-dimensional image sequences for Vision-Language Models (VLMs). By preserving a global view, this approach avoids the dependency breakage inherent in filtering. We systematically evaluate LongCodeOCR against the state-of-the-art LongCodeZip across four benchmarks spanning code summarization, code question answering, and code completion. Our results demonstrate that visual code compression serves as a viable alternative for tasks requiring global understanding. At comparable compression ratios ($\sim$1.7$\times$), LongCodeOCR improves CompScore on Long Module Summarization by 36.85 points over LongCodeZip. At a 1M-token context length with Glyph (a specialized 9B VLM), LongCodeOCR maintains higher accuracy than LongCodeZip while operating at about 4$\times$ higher compression. Moreover, compared with LongCodeZip, LongCodeOCR drastically reduces compression-stage overhead (reducing latency from $\sim$4.3 hours to $\sim$1 minute at 1M tokens). Finally, our results characterize a fundamental coverage--fidelity trade-off: visual code compression retains broader context coverage to support global dependencies, yet faces fidelity bottlenecks on exactness-critical tasks; by contrast, textual code compression preserves symbol-level precision while sacrificing structural coverage.

cs.SE↗

arXiv2026

Structuring Reasoning for Complex Rules Beyond Flat Representations

Large language models (LLMs) face significant challenges when processing complex rule systems, as they typically treat interdependent rules as unstructured textual data rather than as logically organized frameworks. This limitation results in reasoning divergence, where models often overlook critical rule dependencies essential for accurate interpretation. Although existing approaches such as Chain-of-Thought (CoT) reasoning have shown promise, they lack systematic methodologies for structured rule processing and are particularly susceptible to error propagation through sequential reasoning chains. To address these limitations, we propose the Dynamic Adjudication Template (DAT), a novel framework inspired by expert human reasoning processes. DAT structures the inference mechanism into three methodical stages: qualitative analysis, evidence gathering, and adjudication. During the qualitative analysis phase, the model comprehensively evaluates the contextual landscape. The subsequent evidence gathering phase involves the targeted extraction of pertinent information based on predefined template elements ([placeholder]), followed by systematic verification against applicable rules. Finally, in the adjudication phase, the model synthesizes these validated components to formulate a comprehensive judgment. Empirical results demonstrate that DAT consistently outperforms conventional CoT approaches in complex rule-based tasks. Notably, DAT enables smaller language models to match, and in some cases exceed, the performance of significantly larger LLMs, highlighting its efficiency and effectiveness in managing intricate rule systems.

cs.AI↗

arXiv2026

Tensor Product Attention Is All You Need

Scaling language models to handle longer input sequences typically necessitates large key-value (KV) caches, resulting in substantial memory overhead during inference. In this paper, we propose Tensor Product Attention (TPA), a novel attention mechanism that uses tensor decompositions to represent queries, keys, and values compactly, substantially shrinking the KV cache size at inference time. By factorizing these representations into contextual low-rank components and seamlessly integrating with Rotary Position Embedding (RoPE), TPA achieves improved model quality alongside memory efficiency. Based on TPA, we introduce the Tensor ProducT ATTenTion Transformer (T6), a new model architecture for sequence modeling. Through extensive empirical evaluation on language modeling tasks, we demonstrate that T6 surpasses or matches the performance of standard Transformer baselines including Multi-Head Attention (MHA), Multi-Query Attention (MQA), Grouped-Query Attention (GQA), and Multi-Head Latent Attention (MLA) across various metrics, including perplexity and a range of established evaluation benchmarks. Notably, TPA's memory efficiency and computational efficiency at decoding stage enables processing longer sequences under fixed resource constraints, addressing a critical scalability challenge in modern language models. Project Page: https://github.com/tensorgi/TPA.

cs.CL↗

arXiv2025

Learning Spatial Decay for Vision Transformers

Vision Transformers (ViTs) have revolutionized computer vision, yet their self-attention mechanism lacks explicit spatial inductive biases, leading to suboptimal performance on spatially-structured tasks. Existing approaches introduce data-independent spatial decay based on fixed distance metrics, applying uniform attention weighting regardless of image content and limiting adaptability to diverse visual scenarios. Inspired by recent advances in large language models where content-aware gating mechanisms (e.g., GLA, HGRN2, FOX) significantly outperform static alternatives, we present the first successful adaptation of data-dependent spatial decay to 2D vision transformers. We introduce \textbf{Spatial Decay Transformer (SDT)}, featuring a novel Context-Aware Gating (CAG) mechanism that generates dynamic, data-dependent decay for patch interactions. Our approach learns to modulate spatial attention based on both content relevance and spatial proximity. We address the fundamental challenge of 1D-to-2D adaptation through a unified spatial-content fusion framework that integrates manhattan distance-based spatial priors with learned content representations. Extensive experiments on ImageNet-1K classification and generation tasks demonstrate consistent improvements over strong baselines. Our work establishes data-dependent spatial decay as a new paradigm for enhancing spatial attention in vision transformers.

cs.CV↗

arXiv2025

Optimal Error Analysis of Channel Estimation for IRS-assisted MIMO Systems

As intelligent reflecting surface (IRS) has emerged as a new and promising technology capable of configuring the wireless environment favorably, channel estimation for IRS-assisted multiple-input multiple-output (MIMO) systems has garnered extensive attention in recent years. Despite the development of numerous algorithms to address this challenge, a comprehensive theoretical characterization of the optimal recovery error is still lacking. This paper aims to address this gap by providing theoretical guarantees in terms of stable recovery of channel matrices for noisy measurements. We begin by establishing the equivalence between IRS-assisted MIMO systems in the uplink scenario and a compact tensor train (TT)-based tensor-on-tensor (ToT) regression. Building on this equivalence, we then investigate the restricted isometry property (RIP) for complex-valued subgaussian measurements. Our analysis reveals that successful recovery hinges on the relationship between the number of user terminals and the number of time slots during which channel matrices remain invariant. Utilizing the RIP condition, we establish a theoretical upper bound on the recovery error for solutions to the constrained least-squares optimization problem, as well as a minimax lower bound for the considered model. Our analysis demonstrates that the recovery error decreases inversely with the number of time slots, and increases proportionally with the total number of unknown entries in the channel matrices, thereby quantifying the fundamental trade-offs in channel estimation accuracy. In addition, we explore a multi-hop IRS scheme and analyze the corresponding recovery errors. Finally, we have performed numerical experiments to support our theoretical findings.

cs.IT↗