arXiv subjects

Hung Le

Publications and source records attributed to Hung Le.

At least 37 records · Page 2Linked to original sources

arXiv2026

Fatness and Flatness

Fat minors are the metric analog of graph minors that are tailored to the analysis of metric (edge-weighted) graphs and, more generally, metric spaces having a suitable notion of shortest paths. Despite a large interest in this notion, not much is known about the structure of metric graphs excluding a fixed fat minor. We prove that if a metric graph $G$ excludes a fixed graph $H$ as a $δ$-fat minor, for some $δ>0$, then $G$ enjoys the metric analog of flatness (aka uniform quasi-wideness) - a structural property from the field of Sparsity. In essence, our flatness result says that for any $α\geq β$ large enough compared to $δ$, in every large enough set $A$ in $G$ one can find a sizable subset $B$ that becomes $α$-scattered after removing a bounded number of balls of radius $β$. We call this property drill-flatness. Notably, the proof only relies on excluding shallow fat minors: every branch set has radius at most $2α$. As a corollary, we prove that metric graphs that exclude a fixed $δ$-fat minor have bounded $\varepsilon$-scatter dimension if we consider only $\varepsilon$-scatters at distances large enough compared to $δ$. By combining this with the results of Abbasi et al. [FOCS 2023], we infer that the $k$-Center problem on instances excluding $H$ as a $δ$-fat minor admits an approximation algorithm that finds a solution of cost at most $(1+\varepsilon)\cdot\mathsf{OPT}+{\cal O}(δ/\varepsilon^2)$ in time ${\cal O}_{H,\varepsilon}(n^{{\cal O}(1)})$. This is one of the first algorithmic results for general fat-minor-free metrics. We also study drill-flatness in hereditary classes of (unweighted) graphs, where we obtain a characterization equating drill-flatness with excluding shallow induced minors. This is an induced analog of the equivalence between flatness and nowhere denseness - one of central results of Sparsity.

math.CO↗

arXiv2026

Expert-Guided Forecast Editing for Time-Series Foundation Models

Time-series foundation models can forecast across heterogeneous domains without task-specific training, but their forecasts are fixed once produced and cannot directly incorporate task-specific expert feedback. We study expert-guided forecast editing: a frozen foundation model generates candidate future trajectories, and an expensive expert evaluator scores them to guide forecast revision. Under a tight query budget, two natural strategies sit at opposite ends: best-of-$N$ purely exploits the foundation model's predictive distribution, while optimization approaches mostly explore the forecast horizon as an unstructured high-dimensional vector. Each extreme is individually sub-optimal. We introduce \textbf{DEFT}, an expert-guided forecast editing framework that balances the two by first exploiting the foundation model's predictive samples in a decomposed trend--seasonal space, then exploring around them via component-wise refinement. DEFT queries the expert only on complete trajectories, then reuses scores for the trend and seasonal components that appeared in the queried recombinations. This lets each expert query provide structured component-level feedback while keeping the foundation model frozen. We compare DEFT against direct search approaches, including best-of-$N$, cross-entropy methods, and Bayesian optimization, under matched expert-query budgets. Across two forecasting benchmarks consisting of 78 datasets, three time-series foundation models, four feedback types, and seven query budgets, DEFT consistently improves the effectiveness of expert guidance. A molecular-dynamics case study further suggests that the same principle extends to more physically grounded feedback, supporting the hypothesis that sparse test-time guidance should be spent balancing prior exploitation with structured exploration.

cs.LG↗

arXiv2026

Technical Design Review of Duke Robotics Club's Oogway & Crush: AUVs for RoboSub 2026

The Duke Robotics Club presents Oogway and Crush, our AUVs for RoboSub 2026. This year's strategy expands on our previously narrowed scope, targeting all four of RoboSub's design goals for the first time: movement, vision, manipulation, and acoustic tracking. This expansion is based on sustained reliability investment across all three subsystems. Mechanically, Crush gained two additional thrusters and a CFD-optimized case, providing pitch stability. Electrically, we addressed accumulated failure points by repairing unreliable connections and upgraded thruster control hardware. We also redesigned our acoustics system, adding a new custom PCB with higher-order filters, significantly improving pinger detection reliability. On the software side, improvements to state estimation, sonar-based object detection, vision-driven task planning, and IVC enable more capable and coordinated autonomous runs. Paired with investments in our testing infrastructure to maximize our limited pool time, we can now attempt a broader set of tasks while maintaining the reliability our competition strategy demands.

cs.RO↗

arXiv2026

Planar Embedding of Okamura-Seymour Quasimetrics in Polynomial Time with an Application to Distributed SSSP

A quasi-metric $(T,δ_T)$ is an Okamura-Seymour quasimetric if there exists an edge-weighted planar embedded directed graph $G = (V,E,w)$ such that $T$ is a set of terminals on the outerface of $G$ and $δ_G(t,t') = δ_T(t,t')$ for every pair $(t,t')\in T\times T$. If $(T,δ_T)$ is an Okamura-Seymour quasimetric, then $G$ is a planar embedding of $(T,δ_T)$. In a recent pioneering work, Chen and Tan gave a polynomial-time algorithm to test if a given quasi-metric $(T,δ_T)$ is an Okamura-Seymour quasimetric. A key step in their proof is existential, which suffices for an efficient testing algorithm but does not imply an efficient embedding algorithm. Our paper closes this gap by giving an algorithmic implementation of their existential step via linear programming. As a result, we obtain the first polynomial-time algorithm for finding a planar embedding of any given Okamura-Seymour quasimetric $(T,δ_T)$. As an application, we show how to use our planar embedding of Okamura-Seymour quasimetrics to compute a $(1+ε)$-approximate single-source shortest path (SSSP) in planar directed graphs in the distributed CONGEST model in $\widetilde{O}(D)$ rounds for any fixed $ε\in (0,1)$, nearly matching a simple lower bound of $Ω(D)$ and resolving a fundamental problem in this area. The best-known algorithm for this problem has round complexity $\widetilde{O}(D^2)$.

cs.DS↗

arXiv2026

Spectral Text Fusion: A Frequency-Aware Approach to Multimodal Time-Series Forecasting

Multimodal time series forecasting is crucial in real-world applications, where decisions depend on both numerical data and contextual signals. The core challenge is to effectively combine temporal numerical patterns with the context embedded in other modalities, such as text. While most existing methods align textual features with time-series patterns one step at a time, they neglect the multiscale temporal influences of contextual information such as time-series cycles and dynamic shifts. This mismatch between local alignment and global textual context can be addressed by spectral decomposition, which separates time series into frequency components capturing both short-term changes and long-term trends. In this paper, we propose SpecTF, a simple yet effective framework that integrates the effect of textual data on time series in the frequency domain. Our method extracts textual embeddings, projects them into the frequency domain, and fuses them with the time series' spectral components using a lightweight cross-attention mechanism. This adaptively reweights frequency bands based on textual relevance before mapping the results back to the temporal domain for predictions. Experimental results demonstrate that SpecTF significantly outperforms state-of-the-art models across diverse multi-modal time series datasets while utilizing considerably fewer parameters. Code is available at https://github.com/hiepnh137/SpecTF.

cs.LG↗

arXiv2026

Spectral Retrieval-Augmented Time-Series Forecasting

Time series forecasting leverages historical patterns to predict future values, but traditional methods face challenges when dealing with complex, non-stationary patterns that are difficult to memorize during training. Retrieval-augmented approaches have emerged as promising solutions by retrieving similar historical patterns to enhance predictions. However, existing retrieval methods suffer from two fundamental limitations: spectral blindness, which overlooks critical frequency-domain characteristics that capture underlying periodic structures, and temporal recency, which treats all historical data equally without emphasizing recent, more relevant patterns. In this paper, we propose SpecReTF, a novel retrieval method that addresses these issues by converting time series into windowed frequency representations, measuring similarity with a combined metric that captures both amplitude and phase information. To balance recency and historical context, we apply an exponential moving average weighting scheme that emphasizes recent windows. Extensive experiments on benchmark datasets demonstrate that SpecReTF outperforms time-domain retrieval methods, achieving superior forecasting accuracy across diverse, non-stationary time series.

cs.LG↗

arXiv2026

Does Text Actually Help? Uncovering and Resolving Text Collapse in Multimodal Time Series Forecasting

Multimodal time series forecasting, which pairs numerical sequences with domain-relevant textual reports, promises to inject world knowledge into forecasting pipelines. However, we uncover a critical failure mode in existing frameworks that we term text collapse: the text branch converges to a content-independent transformation, contributing negligible discriminative signal regardless of the input description. We argue that text collapse is a consequence of a fundamental asymmetry in time series forecasting: the numerical input is strongly autocorrelated with the output, making the numerical backbone inherently dominant, while the text branch, despite carrying complementary and often critical information, is insufficiently utilized, leading to its systematic underexploitation. To address this, we propose \textbf{REST-TS} (\textbf{R}esidual-\textbf{E}xclusive \textbf{S}upervision for \textbf{T}ext in \textbf{T}ime \textbf{S}eries), which turns the asymmetry into a design principle: the numerical backbone produces its own independent numerical forecast, and the text branch is exclusively supervised to predict the structured components of the residual, the prediction gap that numbers cannot explain. Because no numerical pathway can reduce these losses, the text branch must extract genuine content from the input description. Evaluated across diverse real-world domains and backbone architectures, REST-TS achieves state-of-the-art performance and consistently demonstrates greater text-branch utilization than existing frameworks, providing strong empirical evidence that supervising the text branch on the residual compels it to extract genuine content from the input.

cs.LG↗

arXiv2026

Rethinking Sparse Mixture of Experts from a Unified Perspective

Sparse Mixture of Experts (SMoE) models scale the capacity of models while maintaining constant computational overhead. SMoE methods fall into two categories: Token Choice, which routes each token to a fixed number of experts, and Expert Choice, which assigns a fixed number of tokens to each expert. However, the use of fixed budgets for tokens or experts causes both approaches to select irrelevant token-expert pairs or overlook critical assignments, which degrades overall performance. To fill that gap, we rethink SMoE from a unified perspective through the lens of linear programming, which provides a general formulation for SMoE models. Furthermore, we introduce Unified Sparse Mixture of Experts (USMoE), a novel framework comprising a unified mechanism and a unified score to overcome these limitations. We provide both theoretical justification and empirical evidence demonstrating USMoE's effectiveness. Extensive evaluations across diverse data settings (clean and corrupted), multiple domains (including texts and vision tasks), and different learning approaches (training-free and training-based) show that USMoE not only delivers significant performance improvements over existing SMoE methods, but also enables more flexible expert selection budgets, reducing inference costs without compromising model performance. Our implementation is publicly available at https://github.com/giangdip2410/USMoE.

cs.CL↗

arXiv2026

Eigenvectors of Experts are Training-free Non-collapsing Routers

Sparse Mixture of Experts (SMoE) architectures improve the training efficiency of Large Language Models (LLMs) by routing input tokens to a selected subset of specialized experts. Despite their remarkable success, both training and inference in SMoE models suffer from the expert collapse issue (Chi et al., 2022), which degrades model performance. Prior studies primarily focus on improving the router; however, such methods rely on training from scratch or fine-tuning, which requires high computational and data-processing costs. Furthermore, we demonstrate that, despite these efforts, the issue persists when advancing well-pretrained SMoE models, as evidenced by both theoretical and empirical results. To fill that gap, we analyze the advanced SMoE models and observe that the eigenvectors of expert weight matrices encode rich semantic information, pointing to an effective alternative to conventional routing strategies. Building on this insight, we propose Singular Value Decomposition SMoE (SSMoE), a novel and training-free framework that leverages spectral properties of the expert weights to address the collapse issue and enhance model performance. Extensive experiments across diverse language and vision tasks, under both clean and corrupt data settings, demonstrate the strong generalization and robustness of SSMoE. Our findings highlight how a deeper understanding of model internals can guide the development of more effective SMoE architectures. Our implementation is publicly available at https://github.com/giangdip2410/SSMoE.

cs.LG↗

arXiv2026

Reviving Error Correction in Modern Deep Time-Series Forecasting

Modern deep-learning models have achieved remarkable success in time-series forecasting. Yet, their performance degrades in long-term prediction due to error accumulation in autoregressive inference, where predictions are recursively used as inputs. While classical error correction mechanisms (ECMs) have long been used in statistical methods, their applicability to deep learning models remains limited or ineffective. In this work, we revisit the error accumulation problem in deep time-series forecasting and investigate the role and necessity of ECMs in this new context. We propose a simple, architecture-agnostic error correction model that can be integrated with any existing forecaster without requiring retraining. By explicitly decomposing predictions into trend and seasonal components and training the corrector to adjust each separately, we introduce the Universal Error Corrector with Seasonal-Trend Decomposition (UEC-STD), which significantly improves correction accuracy and robustness across 4 backbones and 10 datasets. Our findings provide a practical tool for enhancing forecasts while offering new insights into mitigating autoregressive errors in deep time-series models. Code is available at https://github.com/DA2I2-SLM/UEC-STD.

cs.LG↗

arXiv2026

Continual Fine-Tuning of Large Language Models via Program Memory

Parameter-Efficient Fine-Tuning (PEFT), particularly Low-Rank Adaptation (LoRA), has become a standard approach for adapting Large Language Models (LLMs) under limited compute. However, in continual settings where models are updated sequentially with small datasets, conventional LoRA updates struggle to balance rapid adaptation and knowledge retention. Existing methods typically treat the low-rank space as a homogeneous update region, lacking mechanisms to regulate how short-term updates are consolidated over time. We propose a continual LoRA framework with \textbf{Pro}gram memory, inspired by \textbf{C}omplementary \textbf{L}earning Systems in neuroscience. Our approach, dubbed \textbf{ProCL}, organizes LoRA adapters into structured program memory slots that are dynamically retrieved through input-conditioned attention. This enables rapid and localized adaptation, encouraging similar inputs to reuse shared adapter regions while reserving unused capacity for future data. The slots are then combined with the underlying adapter, which maintains a distributed representation that gradually accumulates knowledge across tasks to balance plasticity and stability. Our method operates entirely within the LoRA parameterization and incurs no additional inference cost. Experiments on diverse benchmarks demonstrate improved retention and reduced catastrophic forgetting over other continual LoRA strategies.

cs.LG↗

arXiv2026

Charting the Diameter Computation Landscape on Intersection Graphs in the Plane

Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in 2D, the problem is solvable in truly subquadratic time, while for other objects, including unit segments and equilateral triangles in 2D or unit balls and axis-parallel unit cubes in 3D, there is no truly subquadratic time algorithm under the Orthogonal Vector (OV) hypothesis. We undertake a comprehensive study of computing the diameter of geometric intersection graphs for various types of objects. We discover many new irregularities, showing that the landscape is extremely nuanced: the source of hardness is a combination of the object type, the true diameter value, and how the objects intersect with each other. Our highlighted results for the 2D case include: 1. The diameter of non-degenerate, axis-aligned line segments can be computed in truly subquadratic time. Previous hardness result for line segments applies only to degenerate instances. On the other hand, for the degenerate case, we show that a truly subquadratic time algorithm exists when the true diameter is constant. 2. An almost-linear-time algorithm for unit-square graphs of constant diameter. Previous algorithms rely on succinct representation assuming bounded VC-dimension; for such a strategy $Ω(n^{7/4})$ time is an inherent barrier. 3. An $\tilde{O}(n^{4/3})$-time algorithm to decide if the diameter of a unit-disk graph is at most 2. This improves upon the recent algorithm with running time $\tilde{O}(n^{2-1/9})$. 4. Deciding if the diameter of intersection graphs of fat triangles or line segments is at most 2 is truly subquadratic-hard under fine-grained complexity assumptions. Previous lower bounds only hold when deciding if diameter is at most 3.

cs.CG↗

arXiv2026

A Separator for Minor-Free Graphs Beyond the Flow Barrier

In 1990, Alon, Seymour, and Thomas gave the first balanced separator of size $O(h^{3/2}\sqrt{n})$ for any $K_h$-minor-free graph, which has had numerous algorithmic applications. They conjectured that the size of the balanced separator can be reduced to $O(h\sqrt{n})$, which is asymptotically tight. Two decades later, Kawarabayashi and Reed constructed a separator of size $O(h\sqrt{n} + f(h))$ based on the graph minor structure theorem, where $f(h)$ is an extremely fast-growing function typically seen in the structure theorem. Recently, Spalding-Jamieson constructed a separator of size $O(h\log h \log\log h \sqrt{n})$; the technique is rooted in concurrent flow-sparsest cut duality. Spalding-Jamieson's separator comes very close to $O(h\log h \sqrt{n})$, which is the barrier for techniques based on the flow-cut duality. In this work, we first observe that plugging in the recent padded decomposition by Filtser and Conroy into the flow-based algorithm of Korhonen and Lokshtanov yields a balanced separator of size $O(h\log h \sqrt{n})$, matching the flow barrier. This result motivates the question of whether the flow barrier can be broken, which would be a stepping stone toward resolving the conjecture of Alon, Seymour, and Thomas. The main result of our work is a positive answer to this question: we construct a balanced separator of size $O(h \sqrt{\log h} \sqrt{n})$. Surprisingly, perhaps, our algorithm is still based on the iterative framework of Alon, Seymour, and Thomas, although a key component of their algorithm within this framework, called the neighborhood bound, was shown to be tight. Our new idea is to incorporate a low-diameter decomposition into the framework, which allows us to reduce the neighborhood bound by a factor of $h$, at the cost of a factor $\log h$. As a result, we improve the $\sqrt{h}$ factor to $\sqrt{\log h}$ in the final separator's size.

cs.DS↗

arXiv2026

Empowering Multi-Turn Tool-Integrated Agentic Reasoning with Group Turn Policy Optimization

Training Large Language Models (LLMs) for multi-turn Tool-Integrated Reasoning (TIR) - where models iteratively reason, generate code, and verify through execution - remains challenging for existing reinforcement learning (RL) approaches. Current RL methods, exemplified by Group Relative Policy Optimization (GRPO), suffer from coarse-grained, trajectory-level rewards that provide insufficient learning signals for complex multi-turn interactions, leading to training stagnation. To address this issue, we propose Group Turn Policy Optimization (GTPO), a novel RL algorithm specifically designed for training LLMs on multi-turn TIR tasks. GTPO introduces three key innovations: (1) turn-level reward assignment that provides fine-grained feedback for individual turns, (2) return-based advantage estimation where normalized discounted returns are calculated as advantages, and (3) self-supervised reward shaping that exploits self-supervision signals from generated code to densify sparse binary outcome-based rewards. Our comprehensive evaluation demonstrates that GTPO outperforms GRPO by 3.0% across diverse math reasoning benchmarks, establishing its effectiveness. GTPO also improves GRPO by 3.9% on commonsense reasoning and program synthesis tasks, demonstrating its generalizability to non-math domains. Importantly, GTPO incurs negligible overhead, ensuring its practicality for real-world scenarios.

cs.LG↗

arXiv2026

SPaCe: Unlocking Sample-Efficient Large Language Models Training With Self-Pace Curriculum Learning

Large language models (LLMs) have shown strong reasoning capabilities when fine-tuned with reinforcement learning (RL). However, such methods require extensive data and compute, making them impractical under many realistic training budgets. Many existing pipelines sample training examples uniformly across steps or epochs, ignoring differences in difficulty, redundancy, and learning value, which slows learning and wastes computation. We propose \textbf{SPaCe}, a self-paced learning framework that enables efficient learning based on the capability of the model being trained through optimizing which data to use and when. First, we apply \emph{cluster-based data reduction} to partition training data by semantics and difficulty, extracting a compact yet diverse subset that reduces redundancy. Then, a \textit{multi-armed bandit} treats data clusters as arms, allocating training samples based on the model's solve rates and learning progress. Experiments across multiple reasoning benchmarks show that SPaCe achieves comparable or better accuracy than state-of-the-art baselines while using up to $100\times$ fewer samples. Ablation studies and analyses further highlight the importance of both data clustering and adaptive selection. Our results demonstrate that carefully curated, performance-driven training curricula can unlock strong reasoning abilities in LLMs with minimal resources.

cs.LG↗

arXiv2026

Hear Both Sides: Efficient Multi-Agent Debate via Diversity-Aware Message Retention

Multi-Agent Debate has emerged as a promising framework for improving the reasoning quality of large language models through iterative inter-agent communication. However, broadcasting all agent messages at every round introduces noise and redundancy that can degrade debate quality and waste computational resources. Current approaches rely on uncertainty estimation to filter low-confidence responses before broadcasting, but this approach is unreliable due to miscalibrated confidence scores and sensitivity to threshold selection. To address this, we propose Diversity-Aware Retention (DAR), a lightweight debate framework that, at each debate round, selects the subset of agent responses that maximally disagree with each other and with the majority vote before broadcasting. Through an explicit index-based retention mechanism, DAR preserves the original messages without modification, ensuring that retained disagreements remain authentic. Experiments on diverse reasoning and question answering benchmarks demonstrate that our selective message propagation consistently improves debate performance, particularly as the number of agents scales, where noise accumulation is most severe. Our results highlight that what agents hear is as important as what agents say in multi-agent reasoning systems. Code is publicly available at https://github.com/DA2I2-SLM/DAR.

cs.CL↗

arXiv2026

Coarse Balanced Separators in Fat-Minor-Free Graphs

Fat minors are a coarse analogue of graph minors where the subgraphs modeling vertices and edges of the embedded graph are required to be distant from each other, instead of just being disjoint. In this paper, we give a coarse analogue of the classic theorem that an $n$-vertex graph excluding a fixed minor admits a balanced separator of size $O(\sqrt{n})$. Specifically, we prove that for every integer $d$, real $\varepsilon>0$, and graph $H$, there exist constants $c$ and $r$ such that every $n$-vertex graph $G$ excluding $H$ as a $d$-fat minor admits a set $S \subseteq V(G)$ that is a balanced separator of $G$ and can be covered by $c n^{\frac{1}{2}+\varepsilon}$ balls of radius $r$ in $G$. Our proof also works in the weighted setting where the balance of the separator is measured with respect to any weight function on the vertices, and is effective: we obtain a randomized polynomial-time algorithm to compute either such a balanced separator, or a $d$-fat model of $H$ in $G$.

math.CO↗

arXiv2026

Distance Is All You Need: Radial Dispersion for Uncertainty Estimation in Large Language Models

Detecting uncertainty in large language models (LLMs) is essential for building reliable systems, yet many existing approaches are overly complex and depend on brittle semantic clustering or access to model internals. We introduce Radial Dispersion Score (RDS), a simple, training-free, fully model-agnostic uncertainty metric that measures the radial dispersion of sampled generations in embedding space. Specifically, given $N$ sampled generations embedded on the unit hypersphere, RDS computes the total l1 distance from the empirical centroid, i.e., the mean embedding, providing a direct geometric signal of semantic variability. A lightweight probability-weighted variant further incorporates the model's own token probabilities when available, outperforming nine recent state-of-the-art baselines. Moreover, RDS naturally extends to effective per-sample uncertainty estimates that complement probability- and consistency-based methods while remaining lightweight for practical use. Across four challenging free-form question-answering datasets and four LLMs, our metrics achieve state-of-the-art hallucination detection performance, while remaining robust and scalable with respect to sample size and embedding choice. These results highlight the practical value of RDS and its contribution toward improving the trustworthiness of LLMs. Code is publicly available at https://github.com/manhitv/RDS.

cs.LG↗