arXiv subjects

Son Nguyen

Publications and source records attributed to Son Nguyen.

At least 19 recordsLinked to original sources

arXiv2026

Skew Hives, Skew Skeps, Skew Schur Log-Concavity

Knutson and Tao's hives is a combinatorial model to compute Littlewood--Richardson coefficients. Similar to hives, Speyer introduced skeps and used them to prove a Schur log-concavity conjecture by Lam--Postnikov--Pylyavskyy. We first introduce skew hive and skew skep models, which specialize to both hives and skeps, and use this to prove a skew Schur log-concavity result generalizing Lam--Postnikov--Pylyavskyy conjecture. As a consequence, we obtain some log-concavity results concerning Newell--Littlewood numbers and shadow skew Schur functions. Finally, we explain bijections between (skew) hives, (skew) skeps, and peelable tableaux by Nguyen--Nguyen--Woodruff, answering Speyer's question.

math.CO↗

arXiv2026

High Precision Fundamental Physics Experiments at JLab with Spin-transparent Storage Rings of Low-energy Polarized Electron Beams

A breakthrough in fundamental physics experiments measuring particle spin precession may happen if spin-transparent storage rings become adopted tools for such experiments. We present a new design of highly specialized table-sized storage rings, which use low-energy polarized electron beams and Mott polarimetry. Based on the spin transparency ansatz, the spin precession stemming from the magnetic dipole moment is canceled at any beam energy after an electron's turn along the periodic orbit in the ring. Meanwhile, a spin precession induced by the fundamental physics of interest, e.g., the electron's permanent electric dipole moment (EDM) and/or ultralight-dark-matter-mediated forces such as axions, will accumulate. However, capitalizing on such types of rings is not only desirable for measurements of EDMs and axion searches relevant to $CP$ violation and matter-antimatter asymmetry in the Universe, but may also find very promising applications in quantum computing.

nucl-ex↗

arXiv2026

Noise-Aware Framework for Correcting Corrupted Labels

High-quality labeled data is essential for training reliable ML/DL models. However, real-world datasets often contain a considerable proportion of corrupted labels, which can severely degrade model performance. To address this problem, we propose CANOLA, a novel framework for correcting corrupted labels through noise-aware learning and iterative label refinement. CANOLA explicitly estimates the underlying noise distribution of the dataset and incorporates this information into the training of a noise-aware Deep Neural Network. By incorporating noise characteristics during learning, CANOLA enables the model to down-weight unreliable supervision signals and focus on trustworthy patterns, thereby improving robustness and generalization. Label correction is performed via cautious, iterative soft label refinement, in which model predictions are blended with observed labels to prevent premature or erroneous updates. This progressive refinement allows the dataset to be repaired in a stable and controlled manner. We evaluate CANOLA on six widely used datasets under realistic noisy labeling scenarios. Experimental results show that CANOLA consistently outperforms SOTA label correction methods, achieving relative improvements ranging from 19% to 52% in error reduction. Moreover, models trained on datasets corrected by CANOLA obtain substantial downstream performance gains. Even simple classifiers trained on CANOLA's corrected data can outperform complex model-centric approaches by margins of up to 67%.

cs.LG↗

arXiv2026

A Data-Centric Framework for Detecting and Correcting Corrupted Labels

The performance of machine learning and deep learning models largely depends on the quality of the training data. However, the quality of the real-world datasets is often compromised by noisy labels, which can substantially degrade model accuracy and reliability. To address this challenge, we propose Relabeler, an end-to-end data-centric framework for detecting and correcting corrupted labels. For corrupted label detection, Relabeler jointly leverages both local and global relationships among data instances to identify potentially noisy samples. After detecting suspicious instances, Relabeler further performs label correction by estimating the most probable clean label for each instance based on both its input features and observed noisy label. Extensive experiments across multiple datasets, noise types, and noise rates demonstrate that Relabeler consistently outperforms state-of-the-art baselines, achieving up to 58% improvement in label correction precision and 6% improvement in downstream task performance.

cs.LG↗

arXiv2026

CUPID in the Model Zoo: Online Matchmaking for Selecting Your Dream LLM

Users increasingly face the challenge of selecting an appropriate LLM for a given task from a rapidly growing pool of LLMs, each with distinct but often opaque latent properties. Compounding this challenge, users may lack the vocabulary or awareness to explicitly articulate the characteristics they value in an LLM's responses or deployment. We propose an interaction-efficient active learning framework in which a dueling bandit algorithm iteratively selects pairs of LLMs, collects user feedback about their responses, and updates its belief about the user's latent preferences. We introduce a novel belief-aware upper confidence bound strategy that balances exploration of the model pool with exploitation of inferred preferences, enabling efficient alignment between user needs and LLM capabilities under user-specified cost and time budgets. Through diverse experiments on LLMs and human studies, we experimentally verify that our model can efficiently match well-aligned LLMs to users at a lower cost.

cs.LG↗

arXiv2026

Temperley-Lieb Immanants of Ribbon Decomposition Matrices

Ribbon decomposition matrices give determinantal formulas for skew Schur functions that include as special cases the classical Jacobi-Trudi, Giambelli, and Lascoux-Pragacz formulas. We prove that certain elements of Lusztig's dual canonical basis, called Temperley-Lieb immanants, are Schur-positive when evaluated on ribbon decomposition matrices. We conjecture that this positivity holds for all elements of the dual canonical basis. This is known in the special case of Jacobi-Trudi matrices by a result of Haiman.

math.CO↗

arXiv2026

Structured Exploration and Exploitation of Label Functions for Automated Data Annotation

High-quality labeled data is critical for training reliable machine learning and deep learning models, yet manual annotation remains costly and error-prone. Programmatic labeling addresses this challenge by using label functions (LFs), i.e., heuristic rules that automatically generate weak labels for training datasets. However, existing automated LF generation methods either rely on large language models (LLMs) to synthesize surface-level heuristics or employ model-based synthesis over hand-crafted primitives. These approaches often result in limited coverage and unreliable label quality. In this paper, we introduce EXPONA, an automated framework for programmatic labeling that formulates LF generation as a principled process balancing diversity and reliability. EXPONA systematically explores multi-level LFs, spanning surface, structural, and semantic perspectives. EXPONA further applies reliability-aware mechanisms to suppress noisy or redundant heuristics while preserving complementary signals. To evaluate EXPONA, we conducted extensive experiments on eleven classification datasets across diverse domains. Experimental results show that EXPONA consistently outperformed state-of-the-art automated LF generation methods. Specifically, EXPONA achieved nearly complete label coverage (up to 98.9%), improved weak label quality by up to 87%, and yielded downstream performance gains of up to 46% in weighted F1. These results indicate that EXPONA's combination of multi-level LF exploration and reliability-aware filtering enabled more consistent label quality and downstream performance across diverse tasks by balancing coverage and precision in the generated LF set.

cs.LG↗

arXiv2026

LLM Routing as Reasoning: A MaxSAT View

Routing a query through an appropriate LLM is challenging, particularly when user preferences are expressed in natural language and model attributes are only partially observable. We propose a constraint-based interpretation of language-conditioned LLM routing, formulating it as a weighted MaxSAT/MaxSMT problem in which natural language feedback induces hard and soft constraints over model attributes. Under this view, routing corresponds to selecting models that approximately maximize satisfaction of feedback-conditioned clauses. Empirical analysis on a 25-model benchmark shows that language feedback produces near-feasible recommendation sets, while no-feedback scenarios reveal systematic priors. Our results suggest that LLM routing can be understood as structured constraint optimization under language-conditioned preferences.

cs.AI↗

arXiv2026

iML: Executable, Problem-Grounded, and Broadly Exploratory Code-Driven AutoML

Automated Machine Learning (AutoML) has improved access to machine learning, yet existing techniques often remain limited in flexibility, transparency, and execution reliability. Code-driven AutoML offers a promising direction by synthesizing executable code for preprocessing, model training, and evaluation. However, current LLM-based approaches frequently generate code that is plausible in text yet brittle in execution, insufficiently grounded in the actual dataset, or restricted to narrow solution paths. In this paper, we introduce iML, a multi-agent code-driven AutoML framework designed around three requirements: executability, problem grounding, and broad exploration of valid solutions. iML first analyzes the task and profiles the data, then synthesizes a structured blueprint that guides modular code generation across multiple implementation tracks, including traditional ML,pretrained adaptation, and custom neural architectures. To improve reliability, iML enforces interface checking, dynamic execution, and iterative debugging during integration. We evaluate iML on MLE-BENCH and the newly introduced iML-BENCH, covering diverse Kaggle-style tasks. On MLE-BENCH, iML attains a 90% valid submission rate and a 45% medal rate, and an APS of 0.82, improving the average standardized performance score (APS) over the LLM-based baselines by 52%-273%. On iML-BENCH, it achieves the highest APS and demonstrates robust performance even when task descriptions are substantially stripped. These results establish iML as a reliable and competitive framework for code-driven AutoML.

cs.LG↗

arXiv2025

BRIDGE: Budget-aware Reasoning via Intermediate Distillation with Guided Examples

Distilling knowledge from large proprietary models (e.g., GPT-4) to tiny deployable models (less than 1B parameters) faces a critical capacity-budget trap: the 1000x capacity gap between teachers and students prevents effective direct transfer, while API costs prohibit extensive data collection. We introduce BRIDGE (Budget-Aware Reasoning via Intermediate Distillation), a two-phase framework that resolves these constraints through strategic intermediation and budget asymmetry. In Phase 1, a mid-sized Teacher Assistant (TA; e.g., about 7B) learns from the black-box teacher on a strictly limited subset of data (e.g., 3-5%), selected via a zero-API-cost pipeline that balances entropic difficulty and semantic diversity using only local TA inference. In Phase 2, we exploit this asymmetry-teacher queries are expensive, whereas TA inference is free to amplify supervision: the refined TA generates synthetic rationales for the full dataset to train the tiny student. Crucially, we apply an instruction-tuning curriculum to establish behavioral alignment in the tiny student before transferring reasoning. Our theoretical analysis shows that BRIDGE yields tighter generalization bounds than direct distillation when data is abundant. Experiments across medical, legal, and financial benchmarks demonstrate consistent improvements: BRIDGE delivers student performance gains of 28-41%, closing the capability gap with proprietary teachers by 12-16% while using 10x fewer teacher queries. Notably, BRIDGE defies the conventional cost-performance frontier, surpassing direct distillation baselines that use 100% of the budget while consuming only 5% of the resources.

cs.LG↗

arXiv2025

Model-Agnostic Correctness Assessment for LLM-Generated Code via Dynamic Internal Representation Selection

Large Language Models (LLMs) have demonstrated impressive capabilities in code generation and are increasingly integrated into the software development process. However, ensuring the correctness of LLM-generated code remains a critical concern. Prior work has shown that the internal representations of LLMs encode meaningful signals for assessing code correctness. Nevertheless, the existing methods rely on representations from pre-selected/fixed layers and token positions, which could limit its generalizability across diverse model architectures and tasks. In this work, we introduce AUTOPROBE, a novel model-agnostic approach that dynamically selects the most informative internal representations for code correctness assessment. AUTOPROBE employs an attention-based mechanism to learn importance scores for hidden states, enabling it to focus on the most relevant features. These weighted representations are then aggregated and passed to a probing classifier to predict code correctness across multiple dimensions, including compilability, functionality, and security. To evaluate the performance of AUTOPROBE, we conduct extensive experiments across multiple benchmarks and code LLMs. Our experimental results show that AUTOPROBE consistently outperforms the baselines. For security assessment, AUTOPROBE surpasses the state-of-the-art white-box approach by 18%. For compilability and functionality assessment, AUTOPROBE demonstrates its highest robustness to code complexity, with the performance higher than the other approaches by up to 19% and 111%, respectively. These findings highlight that dynamically selecting important internal signals enables AUTOPROBE to serve as a robust and generalizable solution for assessing the correctness of code generated by various LLMs.

cs.SE↗

arXiv2025

A generalization of RSK to $d$-complete posets

The hook length formula for $d$-complete posets expresses the number of linear extensions of a $d$-complete poset $P$ in terms of hooks of $P$. It generalizes the usual hook length formula for standard Young tableaux, as well as hook length formulas for shifted Young tableaux and trees. We give a new proof of the hook length formula for $d$-complete posets which is elementary and purely combinatorial. Our approach is to define a generalization of the Robinson-Schensted-Knuth bijection for $d$-complete posets, which may be of independent interest.

math.CO↗

arXiv2025

CABENCH: Benchmarking Composable AI for Solving Complex Tasks through Composing Ready-to-Use Models

Composable AI offers a scalable and effective paradigm for tackling complex AI tasks by decomposing them into sub-tasks and solving each sub-task using ready-to-use well-trained models. However, systematically evaluating methods under this setting remains largely unexplored. In this paper, we introduce CABENCH, the first public benchmark comprising 70 realistic composable AI tasks, along with a curated pool of 700 models across multiple modalities and domains. We also propose an evaluation framework to enable end-to-end assessment of composable AI solutions. To establish initial baselines, we provide human-designed reference solutions and compare their performance with two LLM-based approaches. Our results illustrate the promise of composable AI in addressing complex real-world problems while highlighting the need for methods that can fully unlock its potential by automatically generating effective execution pipelines.

cs.AI↗

arXiv2025

Chute Move Posets are Lattices

For each permutation $w$, we consider the set $\mathrm{PD}(w)$ of reduced pipe dreams for $w$, partially ordered so that cover relations correspond to (generalized) chute moves. Settling a conjecture of Rubey from 2012, we prove that $\mathrm{PD}(w)$ is a lattice. To establish this result, we provide a global description of the partial order on $\mathrm{PD}(w)$ by showing that $\mathrm{PD}(w)$ is isomorphic to a poset consisting of objects called Lehmer tableaux. In addition, we prove that $\mathrm{PD}(w)$ is a semidistributive polygonal lattice whose polygons are all diamonds or pentagons.

math.CO↗

arXiv2025

Correlations in random cluster model at $q=1$

Let $\mu$ be a measure that samples a subset of a finite ground set, and let $\mathcal{A}_e$ be the event that element $e$ is sampled. The measure $\mu$ is negatively correlated if for any pair of elements $e, f$ one has $\mu(\mathcal{A}_e \cap \mathcal{A}_f) - \mu(\mathcal{A}_e) \mu(\mathcal{A}_f) \leq 0$. A measure is positively correlated if the direction of the inequality is reversed. For the random cluster model on graphs positive correlation between edges is known for $q \geq 1$ due to the FKG inequality, while the negative correlation is only conjectured for $0 \leq q \leq 1$. The main result of this paper is to give a combinatorial formula for the difference in question at $q=1$. Previously, such a formula was known in the uniform spanning tree case, which is a limit of the random cluster model at $q=0$.

math.CO↗

arXiv2025

VDInstruct: Zero-Shot Key Information Extraction via Content-Aware Vision Tokenization

Key Information Extraction (KIE) underpins the understanding of visual documents (e.g., receipts and contracts) by extracting precise semantic content and accurately capturing spatial structure. Yet existing multimodal large language models (MLLMs) often perform poorly on dense documents and rely on vision tokenization approaches that scale with image size, leading to redundant computation and memory inefficiency. To address these challenges, we introduce VDInstruct, an MLLM that separates spatial region detection from semantic feature extraction. Central to our model is a content-aware tokenization strategy: rather than fragmenting the entire image uniformly, it generates tokens in proportion to document complexity, preserving critical structure while eliminating wasted tokens. Leveraging a three-stage training paradigm, our model achieves state-of-the-art (SOTA) results on KIE benchmarks, matching or exceeding the accuracy of leading approaches while reducing the number of image tokens by roughly 3.6x. In zero-shot evaluations, VDInstruct surpasses strong baselines-such as DocOwl 1.5-by +5.5 F1 points, highlighting its robustness to unseen documents. These findings show that content-aware tokenization combined with explicit layout modeling offers a promising direction forward for document understanding. Data, source code, and model weights will be made publicly available.

cs.CV↗

arXiv2025

Shuffle Tableaux, Littlewood--Richardson Coefficients, and Schur Log-Concavity

We give a new formula for the Littlewood--Richardson coefficients in terms of peelable tableaux compatible with shuffle tableaux, in the same fashion as Remmel--Whitney rule. This gives an efficient way to compute generalized Littlewood--Richardson coefficients for Temperley--Lieb immanants of Jacobi--Trudi matrices. We will also show that our rule behaves well with Bender--Knuth involutions, recovering the symmetry of Littlewood--Richardson coefficients. As an application, we use our rule to prove a special case of a Schur log-concavity conjecture by Lam--Postnikov--Pylyavskyy.

math.CO↗

arXiv2025

Improving Adaptive Moment Optimization via Preconditioner Diagonalization

Modern adaptive optimization methods, such as Adam and its variants, have emerged as the most widely used tools in deep learning over recent years. These algorithms offer automatic mechanisms for dynamically adjusting the update step based on estimates of gradient statistics. Compared to traditional algorithms like Stochastic Gradient Descent, these adaptive methods are typically more robust to model scale and hyperparameter tuning. However, the gradient statistics employed by these methods often do not leverage sufficient gradient covariance information, leading to suboptimal updates in certain directions of the parameter space and potentially slower convergence. In this work, we keep track of such covariance statistics in the form of a structured preconditioner matrix. Unlike other works, our approach does not apply direct approximations to estimate this matrix. We instead implement an invertible transformation that maps the preconditioner matrix into a new space where it becomes approximately diagonal. This enables a diagonal approximation of the preconditioner matrix in the transformed space, offering several computational advantages. Empirical results show that our approach can substantially enhance the convergence speed of modern adaptive optimizers. Notably, for large language models like LLaMA, we can achieve a speedup of 2x compared to the baseline Adam. Additionally, our method can be integrated with memory-efficient optimizers like Adafactor to manage computational overhead.

cs.LG↗