arXiv subjects

Yiyao Zhang

Publications and source records attributed to Yiyao Zhang.

14 recordsLinked to original sources

arXiv2026

Learning CNF Formulas from Uniform Random Solutions: Near-Tight Sample Complexity for Valiant's Algorithm

We revisit Valiant's algorithm (Commun. ACM'84) for learning $n$-variable CNF formulas with clause size $k$ and variable degree $d$ from i.i.d. uniform random solutions in the local lemma regime. For fixed $t\geq1$, under $k\gtrsim(1+1/t)\log d$, Valiant's algorithm achieves total variation error $\varepsilon$ with $\widetilde{O}(n^{\lceil t \rceil}/\varepsilon)$ sample complexity. For $t>1$, we prove a matching lower bound for Valiant's algorithm. At $t=1$ (covering $0<t<1$), we show Valiant's algorithm has optimal sample complexity up to logarithmic factors by an information-theoretic lower bound $\widetildeΩ(n/\varepsilon)$.

cs.LG↗

arXiv2026

A Counting Lovász Local Lemma

We establish a counting analogue of the Lovász Local Lemma: we give polynomial-time algorithms for approximately counting satisfying assignments of general constraint satisfaction problems (CSPs) in the local lemma regime $$ 4 \mathrm{e}\cdot p\cdot (D+1)^2\leq 1, $$ where $p$ is the maximum constraint violation probability and $D$ is the maximum dependency degree. This condition is tight up to constant factors, matching known lower bounds $pD^2\gtrsim 1$ for approximate counting in natural subclasses of CSPs. The core of our approach is a novel $2$-tree expansion for constraint marginal probabilities, which captures the decay of correlations in the local lemma regime.

cs.DS↗

arXiv2026

CausalNav: Reliability-Certified Causal World Models for Control under Physical-Parameter Shift

A world model is only useful for physical AI if it changes what the agent does, and only safe if it declines to do so when it is wrong. We study both halves of that requirement with CausalNav, a controller built around a signed, action-conditioned transition graph over identified state coordinates. At deployment CausalNav simulates a small library of intervention sequences, converts their objective error into policy-logit advice, and admits that advice only when a scale-free predictive-reliability certificate, a policy-margin gate, and an argmax-agreement gate all pass; otherwise it falls back exactly to its own model-based base controller. We evaluate against nine controlled baselines (transformer, recurrent, split-latent, graph, causal-induction, and three recent model-based reasoning modules) on CartPole-v1 and discretized Pendulum-v1 with physical-parameter shifts, under one shared PPO trainer, one interaction budget, and ten held-out seeds (200 runs). CausalNav attains the best average rank (1.25 of ten). The diagnostic result is more informative than the ranking: the learned graph recovers structure well above chance (CartPole F1 = 0.59 +/- 0.09), yet per-seed structural fidelity is uncorrelated with per-seed control benefit (r = -0.15, p = 0.67), and the certificate abstains on 10/10 Pendulum seeds, where forcing the planner on costs return. Model fidelity did not predict downstream control utility in our setting; certified abstention, not better prediction, is what made the world model safe to deploy.

cs.AI↗

arXiv2026

When the Judge Should Not Decide: Evidence-Locked, Non-Compensatory Selection Bounds LLM-Judge Failure in Reasoning Pipelines

An LLM judge deployed inside a reasoning pipeline does not merely measure quality, it decides which answer ships. We show that the cost of that decision depends less on judge accuracy than on the decision rule the judge is embedded in. On frozen candidate pools from four GRPO policies, an unconstrained scalar DeepSeek-R1-7B judge buys almost nothing over answer-level majority vote (+1.0 pp on 500 GSM8K questions, +0.34 EM on 300 HotpotQA questions), and on a frozen-rule 30-question confirmation split it is 10 points worse than majority, a judge that destroys accuracy while scoring candidates confidently. We then subordinate the same judge to Evidence-Locked Derive-Gate-Repair (EL-DGR), a task-adaptive non-compensatory rule under which a judge preference may override evidence-supported consensus only with an extractive evidence certificate, and a repair only when neither alternative is certified and the repair is. With no change to the judge, the candidates, or the budget, EL-DGR reaches 58.2% on GSM8K (vs. 56.8% judge, 55.8% majority, 55.4% first candidate) and 17.33 EM / 25.46 F1 on HotpotQA (vs. 15.67/23.49, 15.33/23.19, 15.33/22.97), improving on first-candidate GRPO by +2.8 pp (exact McNemar p=0.0026) and +2.00 EM (p=0.070, borderline). A decision audit shows why: EL-DGR overturns consensus on only 8 of 30 pilot questions and never converts a correct consensus into an incorrect answer. We also report what did not work: the same seven-channel decomposition used as a step-level gated training reward is null, and corrected channel-drop ablations show no channel is individually necessary (p=1.0 throughout). The practitioner-facing finding is negative about judges and positive about admissibility, bound the judge's blast radius rather than trying to make it accurate.

cs.AI↗

arXiv2026

Near-Optimal Parallel Approximate Counting via Sampling

The computational equivalence between approximate counting and sampling is well established for polynomial-time algorithms. The most efficient general reduction from counting to sampling is achieved via simulated annealing, where the counting problem is formulated in terms of estimating the ratio $Q={Z(β_{\max})}/{Z(β_{\min})}$ between partition functions $Z(β)=\sum_{x\in Ω} \exp(βH(x))$ of Gibbs distributions $μ_β$ over $Ω$ with Hamiltonian $H$, given access to a sampling oracle that produces samples from $μ_β$ for $β\in [β_{\min}, β_{\max}]$. The best bound achieved by known annealing algorithms with relative error $\varepsilon$ is $O(q \log h / \varepsilon^2)$, where $q, h$ are parameters which respectively bound $\ln Q$ and $H$. However, all known algorithms attaining this near-optimal complexity are inherently sequential, or *adaptive*: the queried parameters $β$ depend on previous samples. We develop a simple non-adaptive algorithm for approximate counting using $O(q \log^2 h / \varepsilon^2)$ samples, as well as an algorithm that achieves $O(q \log h / \varepsilon^2)$ samples with just two rounds of adaptivity, matching the best sample complexity of sequential algorithms. These algorithms naturally give rise to work-efficient parallel (RNC) counting algorithms. We discuss applications to RNC counting algorithms for several classic models, including the anti-ferromagnetic 2-spin, monomer-dimer and ferromagnetic Ising models.

cs.DS↗

arXiv2026

Learning $\mathsf{AC}^0$ under Locally Sampleable Graphical Models

The problem of learning constant-depth circuits holds profound implications for computational learning theory. In a seminal result, by introducing the low-degree algorithm, Linial, Mansour, and Nisan (J. ACM 1993) presented a quasipolynomial-time learner for $\mathsf{AC}^0$ under the uniform distribution. However, obtaining comparable learning guarantees for broader classes of correlated distributions has remained a longstanding challenge. Recently, Chandrasekaran, Gaitonde, Moitra, and Vasilyan (arXiv 2026) extended these guarantees to Gibbs distributions on bounded-degree graphical models with both strong spatial mixing and polynomial growth. In this paper, we give a quasipolynomial-time learner for $\mathsf{AC}^0$ under graphical models that admit efficient local samplers, circumventing the polynomial-growth requirement in prior work. The key ingredient is a new low-degree approximation for Gibbs distributions, established by simulating and suitably truncating the classical Glauber dynamics. As applications, this framework yields learners for two-spin systems, including the hard-core model and Ising model, on arbitrary bounded-degree graphs, in regimes approaching their respective sampling thresholds.

cs.LG↗

arXiv2026

AgenticVM: Agentic AI for Adaptive Software Vulnerability Management

As software systems grow in scale and complexity, vulnerability management is increasingly strained by high alert volumes, fragmented toolchains, and manual triage processes. We introduce AgenticVM, a multi-agent framework that integrates large language models with security tools to automate vulnerability detection, assessment, prioritization, and reporting. AgenticVM combines rule-based processing, a BERT-based CVSS prediction module, and specialised LLM-driven agents, leveraging data from sources such as the National Vulnerability Database and the European Union Vulnerability Database. Across multiple evaluation scenarios, AgenticVM reduces raw scanner outputs into compact, actionable queues, achieving up to 98% alert reduction (e.g., from 3,983 findings to 82 high-priority items), while predicting missing CVSS attributes with 89.3% accuracy. These results demonstrate improved prioritisation efficiency and reduced analyst workload without compromising risk visibility. Beyond performance, the framework provides practical design insights into agent decomposition, tool-LLM integration, and human-in-the-loop governance for real-world deployment.

cs.CR↗

arXiv2026

Work-Efficient Parallel Counting via Sampling

A canonical approach to approximating the partition function of a Gibbs distribution via sampling is simulated annealing. This method has led to efficient reductions from counting to sampling, including: $\bullet$ classic non-adaptive (parallel) algorithms with sub-optimal cost (Dyer-Frieze-Kannan '89; Bezáková-Štefankovič-Vazirani-Vigoda '08); $\bullet$ adaptive (sequential) algorithms with near-optimal cost (Štefankovič-Vempala-Vigoda '09; Huber '15; Kolmogorov '18; Harris-Kolmogorov '24). We present an algorithm that achieves both near-optimal total work and efficient parallelism, providing a reduction from counting to sampling with logarithmic depth and near-optimal work. As consequences, we obtain work-efficient parallel counting algorithms for several important models, including the hardcore and Ising models within the uniqueness regime.

cs.DS↗

arXiv2026

Explainable Autonomous Cyber Defense using Adversarial Multi-Agent Reinforcement Learning

Autonomous agents are increasingly deployed in both offensive and defensive cyber operations, creating high-speed, closed-loop interactions in critical infrastructure environments. Advanced Persistent Threat (APT) actors exploit "Living off the Land" techniques and targeted telemetry perturbations to induce ambiguity in monitoring systems, causing automated defenses to overreact or misclassify benign behavior as malicious activity. Existing monolithic and multi-agent defense pipelines largely operate on correlation-based signals, lack structural constraints on response actions, and are vulnerable to reasoning drift under ambiguous or adversarial inputs. We present the Causal Multi-Agent Decision Framework (C-MADF), a structurally constrained architecture for autonomous cyber defense that integrates causal modeling with adversarial dual-policy control. C-MADF first learns a Structural Causal Model (SCM) from historical telemetry and compiles it into an investigation-level Directed Acyclic Graph (DAG) that defines admissible response transitions. This roadmap is formalized as a Markov Decision Process (MDP) whose action space is explicitly restricted to causally consistent transitions. Decision-making within this constrained space is performed by a dual-agent reinforcement learning system in which a threat-optimizing Blue-Team policy is counterbalanced by a conservatively shaped Red-Team policy. Inter-policy disagreement is quantified through a Policy Divergence Score and exposed via a human-in-the-loop interface equipped with an Explainability-Transparency Score that serves as an escalation signal under uncertainty. On the real-world CICIoT2023 dataset, C-MADF reduces the false-positive rate from 11.2%, 9.7%, and 8.4% in three cutting-edge literature baselines to 1.8%, while achieving 0.997 precision, 0.961 recall, and 0.979 F1-score.

cs.CR↗

arXiv2025

Learning CNF formulas from uniform random solutions in the local lemma regime

We study the problem of learning a $n$-variables $k$-CNF formula $Φ$ from its i.i.d. uniform random solutions, which is equivalent to learning a Boolean Markov random field (MRF) with $k$-wise hard constraints. Revisiting Valiant's algorithm (Commun. ACM'84), we show that it can exactly learn (1) $k$-CNFs with bounded clause intersection size under Lovász local lemma type conditions, from $O(\log n)$ samples; and (2) random $k$-CNFs near the satisfiability threshold, from $\widetilde{O}(n^{\exp(-\sqrt{k})})$ samples. These results significantly improve the previous $O(n^k)$ sample complexity. We further establish new information-theoretic lower bounds on sample complexity for both exact and approximate learning from i.i.d. uniform random solutions.

cs.DS↗

arXiv2025

RegimeFolio: A Regime Aware ML System for Sectoral Portfolio Optimization in Dynamic Markets

Financial markets are inherently non-stationary, with shifting volatility regimes that alter asset co-movements and return distributions. Standard portfolio optimization methods, typically built on stationarity or regime-agnostic assumptions, struggle to adapt to such changes. To address these challenges, we propose RegimeFolio, a novel regime-aware and sector-specialized framework that, unlike existing regime-agnostic models such as DeepVol and DRL optimizers, integrates explicit volatility regime segmentation with sector-specific ensemble forecasting and adaptive mean-variance allocation. This modular architecture ensures forecasts and portfolio decisions remain aligned with current market conditions, enhancing robustness and interpretability in dynamic markets. RegimeFolio combines three components: (i) an interpretable VIX-based classifier for market regime detection; (ii) regime and sector-specific ensemble learners (Random Forest, Gradient Boosting) to capture conditional return structures; and (iii) a dynamic mean-variance optimizer with shrinkage-regularized covariance estimates for regime-aware allocation. We evaluate RegimeFolio on 34 large cap U.S. equities from 2020 to 2024. The framework achieves a cumulative return of 137 percent, a Sharpe ratio of 1.17, a 12 percent lower maximum drawdown, and a 15 to 20 percent improvement in forecast accuracy compared to conventional and advanced machine learning benchmarks. These results show that explicitly modeling volatility regimes in predictive learning and portfolio allocation enhances robustness and leads to more dependable decision-making in real markets.

q-fin.PM↗

arXiv2024

Breaking the Limitations with Sparse Inputs by Variational Frameworks (BLIss) in Terahertz Super-Resolution 3D Reconstruction

Data acquisition, image processing, and image quality are the long-lasting issues for terahertz (THz) 3D reconstructed imaging. Existing methods are primarily designed for 2D scenarios, given the challenges associated with obtaining super-resolution (SR) data and the absence of an efficient SR 3D reconstruction framework in conventional computed tomography (CT). Here, we demonstrate BLIss, a new approach for THz SR 3D reconstruction with sparse 2D data input. BLIss seamlessly integrates conventional CT techniques and variational framework with the core of the adapted Euler-Elastica-based model. The quantitative 3D image evaluation metrics, including the standard deviation of Gaussian, mean curvatures, and the multi-scale structural similarity index measure (MS-SSIM), validate the superior smoothness and fidelity achieved with our variational framework approach compared with conventional THz CT modal. Beyond its contributions to advancing THz SR 3D reconstruction, BLIss demonstrates potential applicability in other imaging modalities, such as X-ray and MRI. This suggests extensive impacts on the broader field of imaging applications.

physics.optics↗

arXiv2024

DaISy: Diffuser-aided Sub-THz Imaging System

Sub-terahertz (Sub-THz) waves possess exceptional attributes, capable of penetrating non-metallic and non-polarized materials while ensuring bio-safety. However, their practicality in imaging is marred by the emergence of troublesome speckle artifacts, primarily due to diffraction effects caused by wavelengths comparable to object dimensions. In addressing this limitation, we present the Diffuser-aided sub-THz Imaging System (DaISy), which utilizes a diffuser and a focusing lens to convert coherent waves into incoherent counterparts. The cornerstone of our progress lies in a coherence theory-based theoretical framework, pivotal for designing and validating the THz diffuser, and systematically evaluating speckle phenomena. Our experimental results utilizing DaISy reveal substantial improvements in imaging quality and nearly diffraction-limited spatial resolution. Moreover, we demonstrate a tangible application of DaISy in the scenario of security scanning, highlighting the versatile potential of sub-THz waves in miscellaneous fields.

physics.optics↗

arXiv2023

Super-Resolution Surface Reconstruction from Few Low-Resolution Slices

In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing the resolution of such surfaces becomes crucial. This paper proposes a new variational model for solving this problem, based on an Euler-Elastica-based regulariser. Further, we propose and implement two numerical algorithms for solving the model, a projected gradient descent method and the alternating direction method of multipliers. Numerical experiments using real-life examples (including two from outputs of another variational model) have been illustrated for effectiveness. The advantages of the new model are shown through quantitative comparisons by the standard deviation of Gaussian curvatures and mean curvatures from the viewpoint of discrete geometry.

math.AP↗