arXiv subjects

Huy Nguyen

Publications and source records attributed to Huy Nguyen.

At least 19 recordsLinked to original sources

arXiv2026

Fractional colorings of $K_r$-free graphs with local demands

We study fractional coloring with local demands, a framework introduced by Kelly and Postle in which one seeks a probability distribution on the independent sets of a graph such that each vertex $v$ is included with probability at least a prescribed target $ϕ(v)$. For $K_r$-free graphs, Kelly and Postle conjectured that such a distribution exists provided $ϕ(v)\le c_r\frac{\log d(v)}{d(v)}$ for a fixed $c_r>0$, where $d(v)$ is the degree of $v$, and they established this up to a factor of $(\log\log d(v))^2$. In this paper, we prove their conjecture, showing that \[ ϕ(v)\le\frac{c}{r}\frac{\log(d(v)+2)}{d(v)+1} \] suffices for an absolute constant $c>0$. As a corollary, we obtain a lower bound on the independence number of $K_r$-free graphs in terms of their degree sequence. This strengthens the bound that OpenAI proved in resolving the Ajtai-Erdős-Komlós-Szemerédi conjecture. Moreover, our argument yields a deterministic algorithm that produces the desired probability distribution in time $2^{O(r^2)}n^{O(1)}$, where $n$ is the number of vertices and the implied constants are absolute.

math.CO↗

arXiv2026

When Does Sparse Routing Help? The Geometry of Expert Separation in Mixture of Experts

Sparse mixtures of experts combine multiple prediction models while evaluating only a small subset for each input. Although this architecture reduces computation, how expert separation and routing sparsity jointly govern expert recovery remains an open problem. In this paper, we address this question for location Gaussian mixtures of experts with a fixed number of experts by establishing how expert separation and spatial arrangement determine recovery rates. For dense models, our results reveal that when experts form well-separated clusters, the separation geometry is governed by the size of the largest cluster; without a prescribed cluster structure, this geometry is instead driven by the total number of experts. For sparse models, the separation geometry on retained routing regions is determined by the number of active experts, while the contribution of omitted regions is controlled by their total probability. Consequently, activating fewer experts reduces the separation complexity in these bounds. Furthermore, Top-1 routing yields a particularly striking result: experts can be recovered at a rate independent of the separation quantity. Our technical approach combines polynomial interpolation and Gaussian reproducing-kernel Hilbert space (RKHS) test functions with quantitative restriction inequalities that extend pointwise comparisons to expert functions.

stat.ML↗

arXiv2026

Anchored Exploration in Product Evolution: A Phylogenetic Network Framework for Semiconductor Designs

We develop a product phylogenetic network framework for examining anchored exploration. Using 102,465 semiconductor products grouped into 45,996 design families, we distinguish accumulated design continuity (Anchor) from externally precedented feature additions (horizontal transfer, HT). Fitted regressions yield non-monotonic relationships for HT occurrence and descendant carriage, alongside increasing within-family carriage over observed support. These patterns connect technological trajectories and recombination by distinguishing the continuity associated with incorporating external features from that associated with reproducing them in subsequent products.

physics.soc-ph↗

arXiv2026

Joint Estimation and Feature Selection in Overspecified Finite Mixture of Regressions

We investigate joint estimation and feature selection in sparse finite mixtures of regressions with an overspecified number of mixture components or mixture order. More specifically, given a conservative fixed upper bound on the unknown mixture order, we deliberately overspecify the order and propose a double-penalized likelihood approach for simultaneous parameter estimation and feature selection. We establish consistent recovery of the sparsity structure of the underlying mixing measure in terms of its regression coefficients, showing that the true sparsity of the mixture regression can be consistently identified even under order over-specification. The proposed methodology incorporates two complementary penalties: the first penalizes small (near-zero) mixing proportions, inducing an asymptotic Voronoi-type partition of the estimated regression vectors into clusters associated with the true sparse regression vectors; the second penalizes regression coefficients, resulting in sparsity through the selection of relevant features. Although the sparsity penalty is applied to individual regression coefficients, the combined effect of the two penalties yields an asymptotic group feature selection property where the same features tend to be selected or not selected within each Voronoi cluster. We develop a modified EM algorithm combined with proximal gradient for numerical implementations. Extensive simulations and a real data application demonstrate the effectiveness of the proposed approach.

stat.ME↗

arXiv2026

Sparsity Saves Compute, Not Samples: Oracle Inequalities for Dense and Sparse Mixture of Experts

Mixture-of-Experts (MoE) models combine specialized experts through an input-dependent routing mechanism, and their sparse variants underpin many modern large-scale systems. Yet the statistical cost of adaptive routing remains only partially understood. We study the estimation error of least-squares MoE estimators when both the experts and the gating network are Lipschitz in their parameters. We represent each MoE as a gate--expert pair in a Gated Hilbert Space, whose norm $\|\cdot\|_Δ$ separates the contributions of routing and expert discrepancies. Using its empirical representation, we derive an oracle inequality with a fast rate of order $\tilde{\mathcal O}\big((Kd_{\mathrm{pr},e}+d_{\mathrm{pr},g})/n\big)$ for dense MoEs with $K$ experts. For sparse Top-$k$ and Top-$p$ routing, the selection map is discontinuous in the gating parameters. We handle this by partitioning the gating class according to the selection patterns it induces on the sample. The resulting bounds match the dense rate up to an additive routing cost governed by the Natarajan dimension of the selector. We show that such a routing-complexity condition cannot be dropped: Lipschitz continuity in the parameters alone does not suffice. For linear softmax gating, the routing cost is of the same order as the gating term. Finally, for linear experts, we establish a matching minimax lower bound of order $Kd_{\mathrm{pr},e}/n$, showing that the rates are optimal up to logarithmic factors.

cs.LG↗

arXiv2026

Meme Template Identification in the Wild: Comparing Methods for Semi-Open-Set Recognition

Image-with-text memes are a dominant form of online communication, and much of their spread happens through meme templates which are recurring visual formats that users adapt with new text or imagery. Most prior work scores memes individually for engagement or harmful content, an approach that is structurally blind to templates. Templates might amplify these patterns and enable coordinated harassment, which becomes visible only when memes are grouped by shared template. We formalize meme template identification as a semi-open-set recognition problem, requiring methods to both classify known templates and reject template-free memes and non-meme content. We introduce an evaluation framework spanning a controlled setting (1,704 ImgFlip templates) and a heterogeneous real-world social media sample, comparing supervised CNN- and distance-based methods, unsupervised density-based clustering, a novel fused SigLIP2+DINOv2 representation, and a retrieval-augmented LLM pipeline. In real-world social media sources dedicated to meme sharing, we find that only 21% of images use a known template, while 58% are template-free and 21% are not memes at all; identification performance also drops sharply from the controlled setting (best MCC 0.974 to 0.684). The loss comes mainly from deciding whether an image is a template-based meme at all, rather than identifying the template. Our dataset of 1.1M soft-labeled social media images, together with code for reproducibility, is available upon request.

cs.CY↗

arXiv2026

Characterizing Heterogeneous Rates in Finite Mixture Estimation via Partial Optimal Transport

Parameter estimation in finite mixture models can exhibit highly heterogeneous convergence behavior: locally isolated components may be estimated substantially faster than groups of competing components. Existing analyses based on Wasserstein distances typically characterize only the worst-case rate and therefore do not fully capture this local heterogeneity. In this paper, we introduce a Voronoi-based partial optimal transport (VPOT) framework for obtaining refined local and global convergence guarantees for the maximum likelihood estimator of the mixing measure. The key geometric idea is to localize the comparison of two mixing measures to extended Voronoi neighborhoods and use partial optimal transport to accommodate the unequal masses of their local restrictions. Within each neighborhood, the first-order POT discrepancy is raised to a power determined by the number of locally competing atoms, allowing the resulting loss to adapt to the local degree of singularity. Under suitable regularity and strong identifiability conditions, we establish uniform local and global upper bounds for a maximum likelihood estimator under the VPOT loss. These bounds reveal a configuration-dependent form of parameter estimation: less singular local configurations admit faster convergence, whereas the most singular configuration recovers the classical worst-case behavior characterized by Wasserstein-based analyses. We further establish a minimax lower bound showing that the convergence rate for estimating the mixing measure under the VPOT loss is optimal. Our results hold in arbitrary fixed dimension without requiring mixing proportions to be uniformly bounded away from zero or prior knowledge of the true number of mixture components. Overall, VPOT provides a configuration-adaptive framework for capturing heterogeneous parameter-estimation behavior in finite mixture models.

math.ST↗

arXiv2026

Fractional DP-colorings of $d$-degenerate locally sparse graphs

Bernshteyn, Kostochka, and Zhu (2020) introduced the notion of fractional DP-coloring, which generalizes both fractional coloring and fractional list coloring. Among several foundational results, they proved that every $d$-degenerate bipartite graph $G$ satisfies $χ_f^{\mathrm{DP}} \le (1 + o(1))\frac{d}{\log d}$, and that this bound is optimal---a stark contrast to ordinary fractional coloring. In this paper, we extend this upper bound to all $d$-degenerate triangle-free graphs, proving that $χ_f^{\mathrm{DP}} \le (4 + o(1))\frac{d}{\log d}$. This generalizes a recent result of Martinsson and Steiner (2025) for ordinary fractional coloring. We derive this result as a corollary of a more general upper bound concerning locally sparse graph orderings. Specifically, a $d$-degenerate graph $G$ is left $k$-locally-sparse if it admits a degeneracy ordering in which, for every vertex $v$, the subgraph induced by its back-neighbors contains at most $k$ edges. We show that if a $d$-degenerate graph $G$ is left $\frac{d^2}{f}$-locally-sparse, then \[ χ_f^{\mathrm{DP}}(G) \le (8 + o(1))\frac{d}{\log f}. \] This immediately yields an identical upper bound on the ordinary fractional chromatic number $χ_f(G)$, improving upon the leading constants of previously known bounds. Additionally, we establish the asymptotic sharpness of this result up to the leading constant. For any $1 \ll f \le d^2$, we construct $d$-degenerate graphs that are left $\frac{d^2}{f}$-locally-sparse and satisfy $χ_f(G) \ge (1 - o(1))\frac{d}{\log f}$. Finally, as applications of our main theorem, we obtain improved upper bounds on the fractional DP-chromatic number of $d$-degenerate $K_{1,t,t}$-free graphs, as well as $K_{t,t,t}$-free graphs with maximum degree $Δ$. Notably, these bounds improve upon existing results even in the setting of ordinary fractional coloring.

math.CO↗

arXiv2026

Is Your Neighborhood Safe? Place-based Stigma in Large Language Models' Urban Safety Judgments

Large language models are increasingly used to inform safety decisions in cities, such as where it is safe to walk, rent, or travel. We ask whether such judgments track measured risk or the patterns attached to an urban neighborhood's name. We probe seven instruct-tuned models under three conditions that dissociate name from geography: coordinates-only, name-only, and name+coordinates, across 186 neighborhoods in Los Angeles and Chicago, joined to violent crime and American Community Survey data. First, ratings are nearly flat under coordinates for six of seven models, while names carry most between neighborhood variation and are moderately calibrated to violent crime; only at frontier scale does the coordinate channel show appreciable variation. Second, names lower safety ratings more for neighborhoods with higher shares of the locally dominant marginalized group (percent Black in Chicago, percent Hispanic in Los Angeles), and this name effect tracks demographic share in all seven models and both cities. In Los Angeles, where demographic share and crime are more separable, the effect survives controls for crime and income and is confirmed by crime-matched pairs. An enforcement-elasticity analysis further shows that over-caution tracks near-fully-reported homicide rather than discretionary, deployment-driven offenses. Third, the effect scales with geographic knowledge: models that better distinguish real neighborhoods apply more demographic stereotype to them. Because neighborhood names carry both genuine crime signal and demographic stereotype, removing names reduces both bias and accuracy. We discuss implications for deploying LLMs in advice and decision-support settings.

cs.AI↗

arXiv2026

REST API Testing with Verified LLM-Inferred Dependencies and Response-Driven Refinement

Testing RESTful APIs requires generating sequences of API calls that satisfy dependencies among operations, parameters, and runtime-created resources. Recent LLM-based approaches infer such dependencies and generate test sequences from OpenAPI specifications, but they often treat LLM-inferred relationships as correct without execution-based validation. This can introduce spurious dependencies, miss feasible operation chains, and produce infeasible tests. In this paper, we propose APIPilot}, an execution-validated framework for REST API testing. APIPilot first derives candidate producer-consumer dependencies from OpenAPI specifications using structural heuristics and LLM-based semantic reasoning. It then treats these dependencies as hypotheses and validates them through concrete API executions before using them for test generation. The validated dependencies are organized into a dependency graph from which APIPilot constructs coverage-aware workflows via bounded top-k graph traversal, separating semantic dependency inference from sequence construction. To improve subsequent tests, APIPilot further performs response-driven refinement: runtime responses are analyzed to update resource pools, adjust input-generation constraints, and prune or revise invalid dependency mappings. Empirical evaluation on 16 real-world REST API services shows that APIPilot achieves 92.3% operation coverage, up to 58.6% code coverage, and an 88.1% workflow execution success rate, outperforming both LLM-based and traditional REST API testing baselines. APIPilot also detects 197 unique 5xx failures and specification-execution mismatches, demonstrating the benefit of grounding dependency inference in execution feedback.

cs.SE↗

arXiv2026

DualMine: Static-Dynamic REST API Constraint Discovery with Dual Validation

REST API constraints capture semantic properties of API responses and are essential for automated test oracle generation, but they are difficult to discover reliably. Static approaches infer constraints from API specifications and documentation, but their results may be affected by incomplete, ambiguous, or outdated specifications. Dynamic approaches mine invariants from execution traces, but their results depend on execution coverage and may include coincidental properties that hold only for the observed executions. This paper presents DualMine, a hybrid framework for REST API constraint discovery that integrates specification-based constraint mining with runtime invariant mining. It first extracts candidate constraints from OpenAPI specifications using an LLM-based static miner and from request-response traces using dynamic invariant mining. It then performs asymmetric dual validation: runtime evidence is used to validate or refute specification-derived constraints, while specification-aware LLM reasoning is used to filter implausible log-derived invariants~without discarding plausible undocumented behaviors. Finally, it applies counterexample-guided refinement by performing targeted API executions to resolve uncertain, overlapping, or conflicting constraints. We evaluate DualMine on 39 real-world REST APIs and compare it against state-of-the-art static-only, dynamic-only, and constraint discovery approaches. The results show that it improves the quality of discovered constraints by reducing unsupported constraints, retaining complementary constraints missed by individual approaches, which helps detect 48 real REST API faults.

cs.SE↗

arXiv2026

Adaptive Stopping for Multi-Turn LLM Reasoning

Large Language Models (LLMs) increasingly rely on multi-turn reasoning and interaction, such as adaptive retrieval-augmented generation (RAG) and ReAct-style agents, to answer difficult questions. These methods improve accuracy by iteratively retrieving information, reasoning, or acting, but introduce a key challenge: \textbf{When should the model stop?} Existing approaches rely on heuristic stopping rules or fixed turn budgets and provide no formal guarantees that the final prediction still contains the correct answer. This limitation is particularly problematic in high-stakes domains such as finance and healthcare, where unnecessary turns increase cost and latency, while stopping too early risks incorrect decisions. Conformal prediction (CP) provides formal coverage guarantees, but existing LLM-CP methods only apply to a single model output and cannot handle multi-turn pipelines with adaptive stopping. To address this gap, we propose Multi-Turn Language Models with Conformal Prediction (MiCP), the first CP framework for multi-turn reasoning. MiCP allocates different error budgets across turns, enabling the model to stop early while maintaining an overall coverage guarantee. We demonstrate MiCP on adaptive RAG and ReAct, where it achieves the target coverage on both single-hop and multi-hop question answering benchmarks while reducing the number of turns, inference cost, and prediction set size. We further introduce a new metric that jointly evaluates coverage validity and answering efficiency.

cs.CL↗

arXiv2026

On the Geometry of Separation in Finite Gaussian Mixtures

We study an open problem of understanding the effects of the minimum component separation on the convergence rates of parameter estimation in finite Gaussian mixtures. We address this by developing a unified geometric framework based on novel Hellinger lower bounds that directly relate discrepancies between mixture densities directly to Wasserstein distances between their underlying mixing measures, with explicit dependence on both the minimum separation and the minimum weight. Our approach combines carefully designed interpolation polynomials with confluent divided difference techniques to construct specialized moment-extraction test functions. When the number of components is known, these bounds uncover a localization phenomenon: the separation complexity is driven strictly by the spatial configuration of mixture components, namely, whether they are concentrated in a single cluster, partitioned into multiple clusters separated by a macroscopic gap, or arranged without any structural constraints. On the other hand, when the number of components becomes unknown and is over-specified, the separation complexity is slightly reduced, while the minimum mixture weight disappears entirely from the convergence rates due to a transition from first-order to second-order Wasserstein geometry. As a consequence, we obtain separation-dependent convergence rates that continuously interpolate between point-wise and uniform estimation regimes, thereby settling the fundamental limits of parameter recovery in finite Gaussian mixtures.

math.ST↗

arXiv2026

FIBER: A Differentially Private Optimizer with Filter-Aware Innovation Bias Correction

Differentially private (DP) training protects individual examples by adding noise to gradients, but the injected noise interacts nontrivially with adaptive optimizers. Recent DP methods temporally filter privatized gradients to reduce variance; however, filtering also changes the DP noise statistics seen by AdamW's second-moment accumulator. As a result, bias corrections derived for unfiltered DP noise, such as subtracting sigma_w squared, can become miscalibrated when filtering is present. We propose FiBeR, a DP optimizer designed for temporally filtered privatized gradients. FiBeR (i) performs denoising in innovation space by filtering the residual stream and integrating it to form the filtered gradient estimate, (ii) decouples the two-point observation geometry from the innovation gain to enable independent tuning, and (iii) introduces a filter-aware second-moment calibration that subtracts the attenuated DP noise contribution A(omega) sigma_w squared, where A(omega) is derived in closed form for the innovation filter and can be computed for general stable linear filters. Across vision and language benchmarks, FiBeR consistently demonstrates substantial improvements in the performance of DP optimizers, surpassing state-of-the-art results under equivalent privacy constraints on multiple tasks.

cs.LG↗

arXiv2026

On Bayesian Softmax-Gated Mixture-of-Experts Models

Mixture-of-experts models provide a flexible framework for learning complex probabilistic input-output relationships by combining multiple expert models through an input-dependent gating mechanism. These models have become increasingly prominent in modern machine learning, yet their theoretical properties in the Bayesian framework remain largely unexplored. In this paper, we study Bayesian mixture-of-experts models, focusing on the ubiquitous softmax-based gating mechanism. Specifically, we investigate the asymptotic behavior of the posterior distribution for three fundamental statistical tasks: density estimation, parameter estimation, and model selection. First, we establish posterior contraction rates for density estimation, both in the regimes with a fixed, known number of experts and with a random learnable number of experts. We then analyze parameter estimation and derive convergence guarantees based on tailored Voronoi-type losses, which account for the complex identifiability structure of mixture-of-experts models. Finally, we propose and analyze two complementary strategies for selecting the number of experts. Taken together, these results provide one of the first systematic theoretical analyses of Bayesian mixture-of-experts models with softmax gating, and yield several theory-grounded insights for practical model design.

stat.ML↗

arXiv2026

From Attribution to Abstention: Training-Free Attention-Based Auditing for Clinical Summarization

Deploying multimodal large language models (MLLMs) for clinical summarization demands not only fluent generation but also transparency about where each statement originates-and a mechanism to flag when statements lack evidential support. We present ClinTrace, a training-free framework that extracts two clinically useful signals from the decoder attention weights that every transformer-based MLLM already produces during generation: (i) fine-grained source attributions linking each output sentence to supporting text spans or images, and (ii) per-sentence groundedness scores that identify poorly supported claims as candidate hallucinations. Both signals are derived from the same attention tensors in a single pass, requiring no retraining, no auxiliary models, and no additional inference cost. We evaluate on two clinical summarization tasks: doctor-patient dialogue summarization (CliConSummation) and radiology report summarization (MIMIC-CXR) using a general-purpose MLLM (Qwen3-8B) and a medical-finetuned model (HuatuoGPT-Vision-7B). For source attribution, ClinTrace achieves over 92% text F1 on radiology and 88% on dialogue summarization, substantially outperforming embedding-based and self-attribution baselines. For hallucination detection, groundedness scores achieve 0.77 AUROC with the medical-finetuned model: competitive with embedding-based confidence at zero additional cost, and enable an abstention mechanism that improves faithfulness from 61.7% to 72.6% by withholding the least: grounded 20% of output for clinician review. Notably, medical finetuning substantially improves the reliability of attention-based hallucination detection, suggesting that domain adaptation produces more semantically structured attention patterns amenable to self-auditing.

cs.CL↗

arXiv2026

Lizard: An Efficient Linearization Framework for Large Language Models

We propose Lizard, a linearization framework that transforms pretrained Transformer-based Large Language Models (LLMs) into subquadratic architectures. Transformers faces severe computational and memory bottlenecks with long sequences due to the quadratic complexity of softmax attention and the growing Key-Value (KV) cache that makes inference memory-bound by context length. Lizard addresses these limitations by introducing a subquadratic attention mechanism that closely approximates softmax attention while preserving model quality. Unlike prior linearization methods constrained by fixed, non-adaptive structures, Lizard augments the architecture with compact, learnable modules that enable adaptive memory control and robust length generalization. Moreover, we introduce a hardwareaware algorithm that solves numerical instability in gated attention to accelerate training. Extensive experiments show that Lizard achieves near-lossless recovery of its teacher model's performance, significantly outperforming previous methods by up to 9.4 - 24.5 points on the 5-shot MMLU benchmark and demonstrating superior associative recall.

cs.CL↗

arXiv2026

An Approach to Probing Particles and Quasi-particles in the Condensed Bose-Hubbard Model

Measurement plays a crucial role in a quantum system beyond just learning about the system state: it changes the post-measurement state and hence influences the subsequent time evolution; further, measurement can even create entanglement in the post-measurement conditional state. In this work, we study how careful choice of parameters for a typical measurement process on cold atoms systems -- phase contrast imaging -- has a strong impact on both what the experimentalist observes but also on the backaction the measurement has on the system, including the creation and diffusion of quasiparticles emerging from the quantum many-body dynamics. We focus on the case of a Bose-Einstein-condensate array, in the low-temperature and low-momentum limit. Our theoretical investigation reveals regimes where the imaging light probes either the bare particle or quasiparticle dynamics. Moreover, we find a path to selectively measuring quasiparticle modes directly, as well as controlling over the measurement-induced creation and diffusion of quasiparticles into different momentum states. This lays a foundation for understanding the effects of both experimental approaches for probing many-body systems, but also more speculative directions such as observable consequences of `spontaneous collapse' predictions from novel models of quantum gravity on aspects of the Standard Model.

cond-mat.quant-gas↗