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Zhihui Zhu

Publications and source records attributed to Zhihui Zhu.

At least 19 recordsLinked to original sources
arXiv2026

QuantumMind: Constraint-Grounded Agentic Reasoning for Speedup Analysis in Quantum Computing

Identifying a meaningful quantum speedup requires more than matching a classical problem to a familiar quantum primitive: the claim must preserve the task, respect access and output models, expose required promises, and remain within a defensible complexity scope. We present QuantumMind, an auditable agentic workflow for generating and conservatively screening quantum-acceleration hypotheses. A fixed sequence of typed, role-specialized actions formalizes the public task, analyzes structure and classical bottlenecks, matches a source-linked registry of quantum primitives and barriers, and constructs a scoped candidate scheme. A deterministic ten-check validator assigns the authoritative verdict; completed states are compiled into a Quantum Acceleration Evidence Graph and passed through a downward-only research screen that cannot strengthen the decision. We evaluate QuantumMind against seven task-adapted prompting and agentic controls on 582 identical open-discovery tasks. Under the frozen Open-Discovery Score (ODS), QuantumMind obtains 53.1 mean ODS, exceeding the strongest baseline by 17.3 points (48.2% relative), and wins 355 of 582 paired tasks against that baseline. It passes the graph audit on 99.8% of tasks, compared with 43.6% for the strongest baseline, and ranks first in all seven task families. The results indicate that typed state transitions and deterministic evidence control contribute beyond fluent generation alone.

cs.AI↗
arXiv2026

Understanding Deep Representation Learning via Layerwise Feature Compression and Discrimination

Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this work, we attempt to unveil this mystery by investigating the structures of intermediate features. Motivated by our empirical findings that linear layers mimic the roles of deep layers in nonlinear networks for feature learning, we explore how deep linear networks transform input data into output by investigating the output (i.e., features) of each layer after training in the context of multi-class classification problems. Toward this goal, we first define metrics to measure within-class compression and between-class discrimination of intermediate features, respectively. Through theoretical analysis of these two metrics, we show that the evolution of features follows a simple and quantitative pattern from shallow to deep layers when the input data is nearly orthogonal and the network weights are minimum-norm, balanced, and approximate low-rank: Each layer of the linear network progressively compresses within-class features at a geometric rate and discriminates between-class features at a linear rate with respect to the number of layers that data have passed through. To the best of our knowledge, this is the first quantitative characterization of feature evolution in hierarchical representations of deep linear networks. Empirically, our extensive experiments not only validate our theoretical results numerically but also reveal a similar pattern in deep nonlinear networks which aligns well with recent empirical studies. Moreover, we demonstrate the practical implications of our results in transfer learning. Our code is available at https://github.com/Heimine/PNC_DLN.

cs.LG↗
arXiv2026

Structured Factorization Approaches for Quantum State Tomography

Since the complexity of quantum state tomography (QST) scales exponentially with system size, exploiting priors such as low-rankness, tensor-network structures, and neural-network representations is essential for scalable QST in terms of sample complexity and parameter complexity. In this paper, we introduce a unified framework, termed structured factorization, that builds on BurerMonteiro-type factorization by parametrizing the density matrix as $FF^\dagger$, where the factor $F$ is constrained to belong to a structured model class. This factorization guarantees physical validity by construction while allowing a broad range of structural priors to be incorporated directly through the choice of the factor space, ranging from the generic Cholesky decomposition to low-rank matrices, matrix product operators, and neural density operators based on multilayer perceptron and transformer architectures. Building on this structured factorization framework, we formulate QST as an optimization problem over the factor space from measurement data. We first develop a unified statistical analysis of the sample complexity of least-squares estimation for a broad class of structured quantum states. We then propose a projected gradient descent method that operates directly on the factor space and accommodates a wide range of structural parametrizations and reconstruction objectives. To further exploit the geometry of the maximum-likelihood estimation formulation and the constraints on the factors, we derive a power method that yields a step-size-free algorithm with fast convergence, recovering Covers method as a special case when the factor is unconstrained.

quant-ph↗
arXiv2026

MolSafeEval: A Benchmark for Uncovering Safety Risks in AI-Generated Molecules

Current molecular generation benchmarks emphasize task complexity, molecule novelty, and property alignment; they largely overlook a critical concern: the potential safety risks of AI-generated molecules. In practice, many generative models may produce molecules with toxic, reactive, or otherwise hazardous characteristics - posing hidden dangers that remain insufficiently addressed. To address this gap, we introduce MolSafeEval, a benchmark dedicated to evaluating and analyzing the safety risks of molecular generation. Unlike prior approaches that rely on narrow toxicity predictors, MolSafeEval integrates heterogeneous safety knowledge - ranging from toxicological databases to hazard rules - into a structured molecular safety knowledge graph. This graph serves as a foundation for large language model-based reasoning, enabling systematic detection and explanation of unsafe features in generated compounds. We further categorize molecular generative models into four representative task types - unconditional generation, property optimization, target protein-based design, and text-based generation - and provide standardized datasets and safety evaluation protocols for each. By systematically revealing the safety vulnerabilities of current generative approaches, MolSafeEval offers a new lens for benchmarking molecular models and provides essential guidance toward safer, more trustworthy molecular design.

cs.LG↗
arXiv2026

Second-Order KKT Guarantees for Bregman ADMM in Nonconvex and Non-Lipschitz Optimization

We analyze Bregman ADMM for nonconvex linearly constrained problems under two-sided relative smoothness, a condition that replaces the standard Lipschitz gradient assumption with a Hessian comparison relative to a Bregman kernel. This setting covers polynomial objectives arising in matrix and tensor models for which a global Lipschitz-gradient constant need not exist. We show that on an invariant open state-space domain, one iteration of Bregman ADMM defines a smooth primal--dual fixed-point map whose strict-saddle KKT points are unstable fixed points; consequently, from random initialization the iterates converge to a strict saddle with probability zero. Combined with existing first-order convergence results, this yields almost-sure second-order stationarity of limiting KKT points. We extend the analysis to a multi-block star consensus formulation for distributed optimization. The technical novelty lies in a determinant reduction with a Bregman-specific symmetrization and scaling step in the two block spectral argument, together with a null space cancellation exploiting the star graph structure in the consensus case. Numerical experiments on distributed matrix factorization illustrate the theory, and a symmetric tensor factorization example demonstrates the broader Bregman proximal splitting idea beyond the separable consensus setting.

math.OC↗
arXiv2026

Evaluating the Representation Space of Diffusion Models via Self-Supervised Principles

Diffusion models have demonstrated remarkable generative capabilities and have also emerged as powerful self-supervised representation learners, yet the connection between these two abilities remains less explored. Drawing inspiration from self-supervised learning (SSL), we introduce a framework for jointly evaluating the representation and generation capabilities of diffusion models. Specifically, we decompose features into invariant and residual components and derive the Invariant Contamination Ratio (ICR), a Fisher-based metric that quantifies how residual variation contaminates invariant signal in feature space. We use this framework to analyze both discriminative and generative behavior of diffusion models. On the representation side, we find that invariance peaks at intermediate noise levels, which also yield the best downstream classification performance. On the generative side, we study how training transitions from genuine generalization to memorization in data-limited regimes, and show that ICR serves as a sensitive training-time indicator of early learning: increasing residual energy along Fisher directions marks the onset of memorization, detectable from training features alone without external evaluators or held-out test sets. Overall, our results show that diffusion models can be monitored from a self-supervised perspective through the geometry of their learned representations.

cs.LG↗
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

ChemVA: Advancing Large Language Models on Chemical Reaction Diagrams Understanding

While Large Language Models (LLMs) have revolutionized scientific text processing, they exhibit a significant capability gap when interpreting chemical reaction diagrams. We identify two fundamental bottlenecks restricting current systems: a Visual Deficit, where generic vision encoders struggle to resolve the strict topological connectivity of dense molecular graphs, and a Semantic Disconnect, where standard linear strings, such as SMILES, fail to effectively activate the model's latent chemical reasoning. To bridge these gaps, we propose the Chemical Visual Activation (ChemVA) framework, which employs a Visual Anchor mechanism to ground functional groups via hybrid-granularity detection, followed by a semantic alignment approach that translates visual features into entity names to maximize knowledge activation in LLMs. We evaluate our approach on OCRD-Bench, a newly constructed dataset featuring dense visual-semantic contexts and comprehensive reaction coverage to evaluate the full spectrum from recognition to reasoning. Extensive experiments on OCRD-Bench demonstrate that ChemVA achieves 92.0% structural recognition accuracy. By bridging visual and semantic bottlenecks, our framework delivers a consistent performance gain of approximately 20 percentage points across 9 diverse LLMs, enabling open-weight models to rival proprietary SOTA systems in complex chemical reasoning tasks.

cs.AI↗
arXiv2026

SMCEvolve: Principled Scientific Discovery via Sequential Monte Carlo Evolution

LLM-driven program evolution has emerged as a powerful tool for automated scientific discovery, yet existing frameworks offer no principled guide for designing their individual components and provide no guarantee that the search converges. We introduce SMCEvolve, which recasts program search as sampling from a reward-tilted target distribution and approximates it with a Sequential Monte Carlo (SMC) sampler. From this view, three core mechanisms emerge as principled components: adaptive parent resampling, mixture of mutation with acceptance, and automatic convergence control. We further provide a finite-sample complexity analysis that bounds the LLM-call budget required to reach a target approximation error. Across math, algorithm efficiency, symbolic regression, and end-to-end ML research benchmarks, SMCEvolve surpasses state-of-the-art evolving systems while using fewer LLM calls under self-determined termination. The code is available at https://github.com/kongwanbianjinyu/SMCEvolve.

cs.AI↗
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

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

An Illusion of Unlearning? Assessing Machine Unlearning Through Internal Representations

While numerous machine unlearning (MU) methods have recently been developed with promising results in erasing the influence of forgotten data, classes, or concepts, they are also highly vulnerable-for example, simple fine-tuning can inadvertently reintroduce erased concepts. In this paper, we address this contradiction by examining the internal representations of unlearned models, in contrast to prior work that focuses primarily on output-level behavior. Our analysis shows that many state-of-the-art MU methods appear successful mainly due to a misalignment between last-layer features and the classifier, a phenomenon we call feature-classifier misalignment. In fact, hidden features remain highly discriminative, and simple linear probing can recover near-original accuracy. Assuming neural collapse in the original model, we further demonstrate that adjusting only the classifier can achieve negligible forget accuracy while preserving retain accuracy, and we corroborate this with experiments using classifier-only fine-tuning. Motivated by these findings, we propose MU methods based on a class-mean features (CMF) classifier, which explicitly enforces alignment between features and classifiers. Experiments on standard benchmarks show that CMF-based unlearning reduces forgotten information in representations while maintaining high retain accuracy, highlighting the need for faithful representation-level evaluation of MU.

cs.LG↗
arXiv2026

Embodied Science: Closing the Discovery Loop with Agentic Embodied AI

Artificial intelligence has demonstrated remarkable capability in predicting scientific properties, yet scientific discovery remains an inherently physical, long-horizon pursuit governed by experimental cycles. Most current computational approaches are misaligned with this reality, framing discovery as isolated, task-specific predictions rather than continuous interaction with the physical world. Here, we argue for embodied science, a paradigm that reframes scientific discovery as a closed loop tightly coupling agentic reasoning with physical execution. We propose a unified Perception-Language-Action-Discovery (PLAD) framework, wherein embodied agents perceive experimental environments, reason over scientific knowledge, execute physical interventions, and internalize outcomes to drive subsequent exploration. By grounding computational reasoning in robust physical feedback, this approach bridges the gap between digital prediction and empirical validation, offering a roadmap for autonomous discovery systems in the life and chemical sciences.

cs.AI↗
arXiv2026

Understanding Representation Dynamics of Diffusion Models via Low-Dimensional Modeling

Diffusion models, though originally designed for generative tasks, have demonstrated impressive self-supervised representation learning capabilities. A particularly intriguing phenomenon in these models is the emergence of unimodal representation dynamics, where the quality of learned features peaks at an intermediate noise level. In this work, we conduct a comprehensive theoretical and empirical investigation of this phenomenon. Leveraging the inherent low-dimensionality structure of image data, we theoretically demonstrate that the unimodal dynamic emerges when the diffusion model successfully captures the underlying data distribution. The unimodality arises from an interplay between denoising strength and class confidence across noise scales. Empirically, we further show that, in classification tasks, the presence of unimodal dynamics reliably reflects the generalization of the diffusion model: it emerges when the model generates novel images and gradually transitions to a monotonically decreasing curve as the model begins to memorize the training data.

cs.LG↗
arXiv2026

DeltaEvolve: Accelerating Scientific Discovery through Momentum-Driven Evolution

LLM-driven evolutionary systems have shown promise for automated science discovery, yet existing approaches such as AlphaEvolve rely on full-code histories that are context-inefficient and potentially provide weak evolutionary guidance. In this work, we first formalize the evolutionary agents as a general Expectation-Maximization framework, where the language model samples candidate programs (E-step) and the system updates the control context based on evaluation feedback (M-step). Under this view, constructing context via full-code snapshots constitutes a suboptimal M-step, as redundant implement details dilutes core algorithmic ideas, making it difficult to provide clear inspirations for evolution. To address this, we propose DeltaEvolve, a momentum-driven evolutionary framework that replaces full-code history with structured semantic delta capturing how and why modifications between successive nodes affect performance. As programs are often decomposable, semantic delta usually contains many effective components which are transferable and more informative to drive improvement. By organizing semantic delta through multi-level database and progressive disclosure mechanism, input tokens are further reduced. Empirical evaluations on tasks across diverse scientific domains show that our framework can discover better solution with less token consumption over full-code-based evolutionary agents.

cs.AI↗
arXiv2026

Evaluating Reward Model Generalization via Pairwise Maximum Discrepancy Competitions

Reward models (RMs) are central to aligning large language models, yet their practical effectiveness hinges on generalization to unseen prompts and shifting distributions. Most existing RM evaluations rely on static, pre-annotated preference datasets, which provide limited coverage and often fail to faithfully assess generalization in open-world settings. We introduce Pairwise Maximum Discrepancy Competition (PMDC), a dynamic and annotation-efficient framework for evaluating RM generalization using a large, unlabeled, open-domain prompt pool. PMDC actively selects prompt--response pairs that maximize disagreement between two RMs, yielding a compact set of highly contentious test cases. These cases are adjudicated by an oracle, and the resulting outcomes are aggregated via a Bradley--Terry model to produce a global ranking and pairwise win-rate landscape of RMs. We apply PMDC to re-evaluate 10 representative RMs and observe substantial rank reshuffling compared with conventional benchmarks. Qualitative analyses further uncover systematic generalization failures, providing valuable insights for improving reward modeling.

cs.CL↗
arXiv2025

ClinDEF: A Dynamic Evaluation Framework for Large Language Models in Clinical Reasoning

Clinical diagnosis begins with doctor-patient interaction, during which physicians iteratively gather information, determine examination and refine differential diagnosis through patients' response. This dynamic clinical-reasoning process is poorly represented by existing LLM benchmarks that focus on static question-answering. To mitigate these gaps, recent methods explore dynamic medical frameworks involving interactive clinical dialogues. Although effective, they often rely on limited, contamination-prone datasets and lack granular, multi-level evaluation. In this work, we propose ClinDEF, a dynamic framework for assessing clinical reasoning in LLMs through simulated diagnostic dialogues. Grounded in a disease knowledge graph, our method dynamically generates patient cases and facilitates multi-turn interactions between an LLM-based doctor and an automated patient agent. Our evaluation protocol goes beyond diagnostic accuracy by incorporating fine-grained efficiency analysis and rubric-based assessment of diagnostic quality. Experiments show that ClinDEF effectively exposes critical clinical reasoning gaps in state-of-the-art LLMs, offering a more nuanced and clinically meaningful evaluation paradigm.

cs.CL↗