arXiv subjects

Shengxin Zhu

Publications and source records attributed to Shengxin Zhu.

At least 19 recordsLinked to original sources

arXiv2026

Regularized Coupling Maps on Matrix Polytopes: From Assignment to Graph Matching and Optimal Transport

Three classical problems-linear assignment, graph matching, and optimal transport-share a common structure: they seek an optimal matrix-valued coupling on a matrix polytope. We study regularized coupling maps that encompass two families of regularization: entropy/KL regularization, which exponentiates the input score matrix and projects it onto the relevant matrix polytope via the KL-projection; and the Frobenius/Euclidean regularization, which performs the Euclidean projection of the scaled input matrix onto the same polytope. We trace how these two geometries yield complementary algorithmic tools for graph matching (CSGO, ASM, FRAM) and optimal transport (IP-EOT, PSN). The regularized coupling map serves as a direction generator in graph matching and as a solution representation in optimal transport, with the regularizer determining the geometry and the outer task determining the precision standard.

math.OC↗

arXiv2026

LoCA: Forward-Only LLM Tuning after One-Shot Calibration with Local Credit Assignment

Parameter-efficient post-training reduces the number of trainable parameters, but still requires repeated end-to-end backpropagation through the frozen backbone. Every adaptation step therefore needs backward-capable hardware and must store or recompute activations. We ask whether this repeated backward chain can be replaced by a one-time calibration. We introduce Local Credit Assignment (LoCA), a two-stage method for small-shift adaptation. One probe backward pass fits a low-rank map at each transformer block from the final prediction error to a local hidden-state correction. LoCA then reuses these maps to form blockwise regression targets from forward activations and fits low-rank adapters with closed-form ridge solves. No further backbone backward pass is required. We evaluate LoCA on five discriminative benchmarks with Qwen2.5 models from 0.5B to 14B. In 16 of 25 reported task--scale comparisons, LoCA yields lower evaluation cross-entropy than the corresponding LoRA run. Its measured full-run GPU peak, including calibration, is 26--29\% lower than LoRA's. After calibration, its CPU steady-state memory is 36--52\% lower and its per-pass time is 43--48\% lower. A shared scale-normalized candidate set is reused across all tested Qwen2.5 sizes and on SmolLM2-1.7B. LoCA thus amortizes global credit assignment into one calibration and enables later forward-only tuning when repeated backpropagation is impractical. The code associated with this paper is available \href{https://github.com/Xia12121/LoCA}{here}.

cs.AI↗

arXiv2026

Evolving in the Agent Jungle via History-Informed Opponent Awareness

Learning to adapt strategies through interaction is a key step toward more general and autonomous LLM agents. Existing approaches typically achieve behavioral adaptation by revising skill libraries. However, in multi-agent environments, opponents may simultaneously update their strategies, causing the environment itself to evolve continuously. Applying skill-revision methods designed for static environments in such settings therefore amounts to updating against an obsolete reference. To address this challenge, we introduce OASE (Opponent-Aware Selective Evolution), which identifies and adopts genuinely beneficial skill revisions in dynamic multi-agent environments. Specifically, OASE conducts paired comparisons between a candidate skill and the incumbent under identical conditions anchored by historical snapshots of opponent strategies, and adopts the candidate only when its estimated payoff gain exceeds an acceptance threshold. We evaluate OASE in two decision-making scenarios: first-price auctions and private-cost Cournot competition. Experimental results show that, compared with a Reflexion-style baseline, OASE achieves a lower final equilibrium distance in both environments while accepting substantially fewer skill revisions, thereby suppressing strategy changes that lack sufficient payoff support. OASE therefore replaces blind updating with evidence-anchored selection, allowing agents to adapt stably and efficiently even as opponents continuously evolve.

cs.AI↗

arXiv2026

GRAIN: Molecules Are Not the Right Granularity -- Active-Ingredient Modeling for Safe Medication Recommendation

Medication recommendation from electronic health records must balance predictive accuracy against the risk of adverse drug-drug interactions (DDIs) under polypharmacy. Existing safety-aware recommenders operate at one of two granularities: the drug code, which treats each medication as an indivisible token, or the molecular substructure, which is finer than pharmacological interaction knowledge is actually organized. We argue that the active ingredient is the missing granularity, and introduce GRAIN, a medication recommendation framework built around it. GRAIN encodes longitudinal patient trajectories (diagnoses, procedures, past medications) with a selective state space backbone that handles long, irregular visit sequences in linear time. On top of it we introduce a joint objective unifying three knowledge sources aligned to a common medication vocabulary: a drug-level DDI graph, an ingredient-level DDI graph obtained by normalizing medication codes to active ingredients via RxNorm, and an EHR-derived co-prescription graph. A proportional controller adapts the accuracy-safety trade-off to the observed validation DDI rate rather than fixing it a priori. Under strictly matched settings -- identical preprocessing, cohort, vocabulary, split, and evaluation code -- GRAIN improves over a re-implemented MambaHealth baseline on MIMIC-IV across all standard multi-label metrics (Jaccard 0.4488 to 0.4983, PRAUC 0.6911 to 0.7485, F1 0.5989 to 0.6453) while reducing the drug-level DDI rate from 0.1875 to 0.0948. We further define an ingredient-level DDI rate, a safety measure invisible to drug-code-level evaluation. The results indicate that ingredient-level normalization recovers predictive signal erased by code-level aggregation, and that it is complementary to, rather than in competition with, accurate sequence modeling.

q-bio.QM↗

arXiv2026

An analysis on stochastic Lanczos quadrature with asymmetric quadrature nodes

This paper revisits the error analysis of the Stochastic Lanczos Quadrature (SLQ) method for approximating the trace of matrix functions, with a specific focus on asymmetric Lanczos quadrature rules. We reexplain an existing theoretical discrepancy regarding the necessity of a scaling factor when applying an affine transformation from the reference interval to the physical spectral interval. Furthermore, we introduce an optimized error reallocation technique for log-determinant estimation. Rather than evenly splitting the error tolerance between the Hutchinson trace estimator and the Lanczos quadrature, we formulate an optimization problem to strategically distribute the error budget. This approach minimizes the total number of matrix-vector multiplications (MVMs) required to reach a target accuracy for both Rademacher and Gaussian queries. Numerical experiments validate that this reallocation yields tighter theoretical bounds and provides a concrete rule-of-thumb for parameter configuration: to achieve a target accuracy efficiently, more computational resources should be allocated to the Lanczos process (larger m) rather than Monte Carlo sampling (smaller N).

math.NA↗

arXiv2026

AI Harness Engineering: A Runtime Substrate for Foundation-Model Software Agents

Foundation models have transformed automated code generation, yet autonomous software-engineering agents remain unreliable in realistic development settings. The dominant explanation locates this gap in model capability. We propose a different locus: software-engineering capability emerges from a model-harness-environment system, in which a runtime substrate -- the harness -- mediates how a foundation-model agent observes a project, acts on it, receives feedback, and establishes that a change is complete. We formalize this substrate as an AI Harness Engineering and identify eleven component responsibilities: task specification, context selection, tool access, project memory, task state, observability, failure attribution, verification, permissions, entropy auditing, and intervention recording. We operationalize the harness through a four-level ladder (H0-H3) that progressively exposes runtime support to the agent, and we propose a trace-based evaluation protocol that converts each agent run into an auditable episode package. Applied to a controlled validation task, the framework yields episode packages whose evidence structure varies systematically with harness level: lower levels produce only a final patch, higher levels produce reproduction logs, failure attributions, deterministic requirement checks, and structured verification reports. The framework reframes the central question of autonomous software engineering from whether a foundation model can produce a patch to whether the model-harness-environment system can produce a verifiably correct, attributed, and maintainable change. We outline a research program for the runtime systems that foundation-model software agents will require.

cs.SE↗

arXiv2026

On Symmetric Lanczos Quadrature for Stochastic Trace Estimation

A common approach to approximating quadratic forms of matrix functions is to use a quadrature rule derived from the Lanczos process, known as a Lanczos quadrature. Although symmetric quadrature rules are computationally favorable, it has remained unclear whether a symmetric Lanczos quadrature is practically feasible. In this work, we resolve this ambiguity by establishing necessary and sufficient conditions for the existence of symmetric Lanczos quadratures. We show that the sufficient condition can be met for a class of Jordan-Wielandt matrices by carefully constructing initial vectors with specific distributions for the Lanczos algorithm. Applying such a symmetric Lanczos quadrature to compute the Estrada index of bipartite or directed graphs ensures that the resulting stochastic trace estimators are unbiased. Furthermore, we observe that the variance of the quadratic form estimator based on the symmetric Lanczos quadrature is lower than that of the standard estimator.

math.NA↗

arXiv2025

Quantformer: from attention to profit with a quantitative transformer trading strategy

In traditional quantitative trading practice, navigating the complicated and dynamic financial market presents a persistent challenge. Fully capturing various market variables, including long-term information, as well as essential signals that may lead to profit remains a difficult task for learning algorithms. In order to tackle this challenge, this paper introduces quantformer, an enhanced neural network architecture based on transformer, to build investment factors. By transfer learning from sentiment analysis, quantformer not only exploits its original inherent advantages in capturing long-range dependencies and modeling complex data relationships, but is also able to solve tasks with numerical inputs and accurately forecast future returns over a given period. This work collects more than 5,000,000 rolling data of 4,601 stocks in the Chinese capital market from 2010 to 2023. The results of this study demonstrate the model's superior performance in predicting stock trends compared with other 100-factor-based quantitative strategies. Notably, the model's innovative use of transformer-like model to establish factors, in conjunction with market sentiment information, has been shown to enhance the accuracy of trading signals significantly, thereby offering promising implications for the future of quantitative trading strategies.

q-fin.MF↗

arXiv2025

FRAM: Frobenius-Regularized Assignment Matching with Mixed-Precision Computing

Graph matching, typically formulated as a Quadratic Assignment Problem (QAP), seeks to establish node correspondences between two graphs. To address the NP-hardness of QAP, some existing methods adopt projection-based relaxations that embed the problem into the convex hull of the discrete domain. However, these relaxations inevitably enlarge the feasible set, introducing two sources of error: numerical scale sensitivity and geometric misalignment between the relaxed and original domains. To alleviate these errors, we propose a novel relaxation framework by reformulating the projection step as a Frobenius-regularized Linear Assignment (FRA) problem, where a tunable regularization term mitigates feasible region inflation. This formulation enables normalization-based operations to preserve numerical scale invariance without compromising accuracy. To efficiently solve FRA, we propose the Scaling Doubly Stochastic Normalization (SDSN) algorithm. Building on its favorable computational properties, we develop a theoretically grounded mixed-precision architecture to achieve substantial acceleration. Comprehensive CPU-based benchmarks demonstrate that FRAM consistently outperforms all baseline methods under identical precision settings. When combined with a GPU-based mixed-precision architecture, FRAM achieves up to 370X speedup over its CPU-FP64 counterpart, with negligible loss in solution accuracy.

cs.LG↗

arXiv2025

GGBond: Growing Graph-Based AI-Agent Society for Socially-Aware Recommender Simulation

Current personalized recommender systems predominantly rely on static offline data for algorithm design and evaluation, significantly limiting their ability to capture long-term user preference evolution and social influence dynamics in real-world scenarios. To address this fundamental challenge, we propose a high-fidelity social simulation platform integrating human-like cognitive agents and dynamic social interactions to realistically simulate user behavior evolution under recommendation interventions. Specifically, the system comprises a population of Sim-User Agents, each equipped with a five-layer cognitive architecture that encapsulates key psychological mechanisms, including episodic memory, affective state transitions, adaptive preference learning, and dynamic trust-risk assessments. In particular, we innovatively introduce the Intimacy--Curiosity--Reciprocity--Risk (ICR2) motivational engine grounded in psychological and sociological theories, enabling more realistic user decision-making processes. Furthermore, we construct a multilayer heterogeneous social graph (GGBond Graph) supporting dynamic relational evolution, effectively modeling users' evolving social ties and trust dynamics based on interest similarity, personality alignment, and structural homophily. During system operation, agents autonomously respond to recommendations generated by typical recommender algorithms (e.g., Matrix Factorization, MultVAE, LightGCN), deciding whether to consume, rate, and share content while dynamically updating their internal states and social connections, thereby forming a stable, multi-round feedback loop. This innovative design transcends the limitations of traditional static datasets, providing a controlled, observable environment for evaluating long-term recommender effects.

cs.MA↗

arXiv2025

Unleashing the potential of prompt engineering for large language models

This comprehensive review delves into the pivotal role of prompt engineering in unleashing the capabilities of Large Language Models (LLMs). The development of Artificial Intelligence (AI), from its inception in the 1950s to the emergence of advanced neural networks and deep learning architectures, has made a breakthrough in LLMs, with models such as GPT-4o and Claude-3, and in Vision-Language Models (VLMs), with models such as CLIP and ALIGN. Prompt engineering is the process of structuring inputs, which has emerged as a crucial technique to maximize the utility and accuracy of these models. This paper explores both foundational and advanced methodologies of prompt engineering, including techniques such as self-consistency, chain-of-thought, and generated knowledge, which significantly enhance model performance. Additionally, it examines the prompt method of VLMs through innovative approaches such as Context Optimization (CoOp), Conditional Context Optimization (CoCoOp), and Multimodal Prompt Learning (MaPLe). Critical to this discussion is the aspect of AI security, particularly adversarial attacks that exploit vulnerabilities in prompt engineering. Strategies to mitigate these risks and enhance model robustness are thoroughly reviewed. The evaluation of prompt methods is also addressed through both subjective and objective metrics, ensuring a robust analysis of their efficacy. This review also reflects the essential role of prompt engineering in advancing AI capabilities, providing a structured framework for future research and application.

cs.CL↗

arXiv2025

Adaptive Softassign via Hadamard-Equipped Sinkhorn

Softassign is a pivotal method in graph matching and other learning tasks. Many softassign-based algorithms exhibit performance sensitivity to a parameter in the softassign. However, tuning the parameter is challenging and almost done empirically. This paper proposes an adaptive softassign method for graph matching by analyzing the relationship between the objective score and the parameter. This method can automatically tune the parameter based on a given error bound to guarantee accuracy. The Hadamard-Equipped Sinkhorn formulas introduced in this study significantly enhance the efficiency and stability of the adaptive softassign. Moreover, these formulas can also be used in optimal transport problems. The resulting adaptive softassign graph matching algorithm enjoys significantly higher accuracy than previous state-of-the-art large graph matching algorithms while maintaining comparable efficiency.

math.OC↗

arXiv2025

When Lanczos Iterations Generate Symmetric Quadrature Nodes?

The Golub-Welsch algorithm [ Math. Comp., 23: 221-230 (1969)] has long been assumed symmetric for estimating quadratic forms. Recent research indicates that asymmetric quadrature nodes may be more often and the existence of a practical symmetric quadrature for estimating matrix quadratic form is even doubtful.This paper derives a sufficient condition for symmetric quadrature nodes for estimating quadratic forms involving the Jordan-Wielandt matrices which frequently arise from many applications. The condition is closely related to how to construct an initial vector for the underlying Lanczos process. Applications of such constructive results are demonstrated by estimating the Estrada index in complex network analysis.

math.NA↗

arXiv2024

CSGO: Constrained-Softassign Gradient Optimization For Large Graph Matching

Graph matching aims to find correspondences between two graphs. This paper integrates several well-known graph matching algorithms into a framework: the constrained gradient method. The primary difference among these algorithms lies in tuning a step size parameter and constraining operators. By leveraging these insights, we propose an adaptive step size parameter to guarantee the underlying algorithms' convergence, simultaneously enhancing their efficiency and robustness. For the constraining operator, we introduce a scalable softassign for large graph matching problems. Compared to the original softassign, our approach offers increased speed, improved robustness, and reduced risk of overflow. The advanced constraining operator enables a CSGO for large graph matching, which outperforms state-of-the-art methods in experiments. Notably, in attributed graph matching tasks, CSGO achieves an over 10X increase in speed compared to current constrained gradient algorithms.

math.CO↗

arXiv2024

Can bidirectional encoder become the ultimate winner for downstream applications of foundation models?

Over the past few decades, Artificial Intelligence(AI) has progressed from the initial machine learning stage to the deep learning stage, and now to the stage of foundational models. Foundational models have the characteristics of pre-training, transfer learning, and self-supervised learning, and pre-trained models can be fine-tuned and applied to various downstream tasks. Under the framework of foundational models, models such as Bidirectional Encoder Representations from Transformers(BERT) and Generative Pre-trained Transformer(GPT) have greatly advanced the development of natural language processing(NLP), especially the emergence of many models based on BERT. BERT broke through the limitation of only using one-way methods for language modeling in pre-training by using a masked language model. It can capture bidirectional context information to predict the masked words in the sequence, this can improve the feature extraction ability of the model. This makes the model very useful for downstream tasks, especially for specialized applications. The model using the bidirectional encoder can better understand the domain knowledge and be better applied to these downstream tasks. So we hope to help understand how this technology has evolved and improved model performance in various natural language processing tasks under the background of foundational models and reveal its importance in capturing context information and improving the model's performance on downstream tasks. This article analyzes one-way and bidirectional models based on GPT and BERT and compares their differences based on the purpose of the model. It also briefly analyzes BERT and the improvements of some models based on BERT. The model's performance on the Stanford Question Answering Dataset(SQuAD) and General Language Understanding Evaluation(GLUE) was compared.

cs.CL↗

arXiv2024

Stochastic diagonal estimation with adaptive parameter selection

In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter selection. We explore the influence of different eigenvalue distributions on diagonal estimation and analyze the necessity of introducing the projection method and adaptive parameter optimization into the stochastic diagonal estimator. Based on this analysis, we derive a lower bound on the number of random query vectors needed to satisfy a given probabilistic error bound, which forms the foundation of our adaptive stochastic diagonal estimation algorithm. Finally, numerical experiments demonstrate the effectiveness of the proposed estimator for various matrix types, showcasing its efficiency and stability compared to other existing stochastic diagonal estimation methods.

stat.ML↗

arXiv2024

Movie Recommendation with Poster Attention via Multi-modal Transformer Feature Fusion

Pre-trained models learn general representations from large datsets which can be fine-turned for specific tasks to significantly reduce training time. Pre-trained models like generative pretrained transformers (GPT), bidirectional encoder representations from transformers (BERT), vision transfomers (ViT) have become a cornerstone of current research in machine learning. This study proposes a multi-modal movie recommendation system by extract features of the well designed posters for each movie and the narrative text description of the movie. This system uses the BERT model to extract the information of text modality, the ViT model applied to extract the information of poster/image modality, and the Transformer architecture for feature fusion of all modalities to predict users' preference. The integration of pre-trained foundational models with some smaller data sets in downstream applications capture multi-modal content features in a more comprehensive manner, thereby providing more accurate recommendations. The efficiency of the proof-of-concept model is verified by the standard benchmark problem the MovieLens 100K and 1M datasets. The prediction accuracy of user ratings is enhanced in comparison to the baseline algorithm, thereby demonstrating the potential of this cross-modal algorithm to be applied for movie or video recommendation.

cs.IR↗

arXiv2024

EchoMamba4Rec: Harmonizing Bidirectional State Space Models with Spectral Filtering for Advanced Sequential Recommendation

Predicting user preferences and sequential dependencies based on historical behavior is the core goal of sequential recommendation. Although attention-based models have shown effectiveness in this field, they often struggle with inference inefficiency due to the quadratic computational complexity inherent in attention mechanisms, especially with long-range behavior sequences. Drawing inspiration from the recent advancements of state space models (SSMs) in control theory, which provide a robust framework for modeling and controlling dynamic systems, we introduce EchoMamba4Rec. Control theory emphasizes the use of SSMs for managing long-range dependencies and maintaining inferential efficiency through structured state matrices. EchoMamba4Rec leverages these control relationships in sequential recommendation and integrates bi-directional processing with frequency-domain filtering to capture complex patterns and dependencies in user interaction data more effectively. Our model benefits from the ability of state space models (SSMs) to learn and perform parallel computations, significantly enhancing computational efficiency and scalability. It features a bi-directional Mamba module that incorporates both forward and reverse Mamba components, leveraging information from both past and future interactions. Additionally, a filter layer operates in the frequency domain using learnable Fast Fourier Transform (FFT) and learnable filters, followed by an inverse FFT to refine item embeddings and reduce noise. We also integrate Gate Linear Units (GLU) to dynamically control information flow, enhancing the model's expressiveness and training stability. Experimental results demonstrate that EchoMamba significantly outperforms existing models, providing more accurate and personalized recommendations.

cs.LG↗