arXiv subjects

Minh Le

Publications and source records attributed to Minh Le.

At least 19 recordsLinked to original sources

arXiv2026

$L^\infty$ bounds and asymptotic behavior in a doubly degenerate chemotaxis system below six dimensions

We investigate a doubly degenerate nutrient-taxis system of the form \begin{equation*} \begin{cases} u_t = \nabla \cdot (u v \nabla u) - \chi \nabla \cdot (u^\alpha v \nabla v) + \ell u v, \qquad &x \in \Omega, \ t > 0, v_t = \Delta v - u v, \qquad &x \in \Omega, \ t > 0, \end{cases} \end{equation*} subject to the homogeneous Neumann boundary conditions in a smoothly bounded convex domain $\Omega \subset \mathbb{R}^n$ with $n\in \left \{ 3,4,5 \right \}$, where $\alpha \geq 1$, $\chi>0$ and $\ell \geq 0$. For any suitably regular initial data, we establish the global existence of a weak solution that remains uniformly bounded in time, provided that $\alpha$ lies in the range $\left[1, \frac{5}{2} - \frac{n}{4}\right)$, and we also determine the large-time behavior of these solutions. Our proof relies on several novel functional inequalities, a bootstrap argument, and a Moser iteration method.

math.AP↗

arXiv2026

RoboGaze: Evaluating Robot World Models via Structured Vision-Language Analysis

Recent advances in robot world models enable synthetic video generation for embodied prediction and planning. However, evaluating these videos is challenging: visually realistic outputs often violate physical laws, temporal consistency, or task logic, while conventional metrics and monolithic Vision-Language Model (VLM) judges fail to generalize or provide precise diagnostic value. We present RoboGaze, a training-free, multi-agent VLM framework that provides structured, interpretable evaluation for generated robot-manipulation videos. Given a task instruction and video, RoboGaze operates via a three-stage pipeline: task-scene grounding, dimension-specific specialist routing, and critic-based verification. It outputs temporally localized glitch reports categorized under a novel 6-dimension, 30-type robotics-specific taxonomy. To benchmark RoboGaze, we introduce a human-validated dataset of 382 clips spanning simulated and real-world multi-view manipulation. Evaluating eight open-source and proprietary VLM backbones, RoboGaze dramatically outperforms zero-shot baselines, improving description-F1 by up to +43 points and temporal alignment (F1 x IoU) by up to +37 points, closing approximately 85% of the gap to the human ceiling. Furthermore, its critic verifier mitigates the "cry-wolf" false-positive flaw of standard VLMs, lifting clean-clip accuracy from under 25% to over 80%. RoboGaze offers a scalable, highly interpretable diagnostic tool for the rigorous evaluation of robot world models.

cs.RO↗

arXiv2026

JI-ADF: Joint-Individual Learning with Adaptive Decision Fusion for Multimodal Skin Lesion Classification

Skin lesion classification is essential for early dermatological diagnosis, yet many existing computer-aided systems rely primarily on dermoscopic images and underutilize the multimodal evidence routinely available in clinical practice. To address this gap, we propose \textbf{JI-ADF}, a trimodal deep learning framework that integrates dermoscopic images, clinical photographs, and structured patient metadata for clinically grounded skin lesion classification. The proposed architecture combines joint multimodal representation learning with modality-specific auxiliary supervision and an adaptive decision fusion mechanism that dynamically calibrates modality contributions on a per-sample basis. To enhance cross-modal reasoning while preserving modality-specific evidence, we further introduce a multimodal fusion attention (MMFA) module. We evaluate JI-ADF on the large-scale MILK10k benchmark, which reflects real-world clinical acquisition conditions and severe class imbalance. The proposed method demonstrates strong and well-balanced performance across lesion categories, improving sensitivity and Dice score while maintaining high specificity and good calibration. Extensive analyses, including modality ablation, calibration evaluation, and Grad-CAM visualization, further confirm the robustness and clinically meaningful behavior of the model. These results indicate that JI-ADF provides a reliable and practical foundation for multimodal skin lesion classification in real-world clinical settings.

cs.CV↗

arXiv2026

Scribble-Supervised Medical Image Segmentation with Dynamic Teacher Switching and Hierarchical Consistency

Scribble-supervised methods have emerged to mitigate the prohibitive annotation burden in medical image segmentation. However, the inherent sparsity of these annotations introduces significant ambiguity, which results in noisy pseudo-label propagation and hinders the learning of robust anatomical boundaries. To address this challenge, we propose SDT-Net, a novel dual-teacher, single-student framework designed to maximize supervision quality from these weak signals. Our method features a Dynamic Teacher Switching (DTS) module to adaptively select the most reliable teacher. This selected teacher then guides the student via two synergistic mechanisms: high-confidence pseudo-labels, refined by a Pick Reliable Pixels (PRP) mechanism, and multi-level feature alignment, enforced by a Hierarchical Consistency (HiCo) module. Extensive experiments on the ACDC and MSCMRseg datasets demonstrate that SDT-Net achieves state-of-the-art performance, producing more accurate and anatomically plausible segmentation.

cs.CV↗

arXiv2026

A Sharp Global Boundedness Result for Keller--Segel--(Navier--)Stokes Systems with Rapid Diffusion and Saturated Sensitivities

We investigate the Keller--Segel--(Navier--)Stokes system posed in a smooth bounded domain $\Omega \subset \mathbb{R}^N$ with $N = 2,3$: \begin{equation*} \begin{cases} n_t + u \cdot \nabla n = \Delta n - \nabla \cdot \big( n S(n)\nabla c \big), \\[2mm] u \cdot \nabla c = \Delta c - c + n, \\[2mm] u_t + \kappa (u \cdot \nabla) u = \Delta u - \nabla P + n \nabla \phi, \\[2mm] \nabla \cdot u = 0, \end{cases} \end{equation*} where $\kappa \in \left \{0,1 \right \} $, the given gravitational potential $\phi \in W^{2, \infty}(\Omega)$, and the chemotactic sensitivity function $S \in C^2([0,\infty))$. Under no-flux boundary conditions for $n$ and $c$, together with the Dirichlet boundary condition for $u$, we show that, provided the initial data satisfy suitable regularity assumptions, the following results hold: \begin{itemize} \item If $N = 2$, $\kappa = 1$, and the sensitivity function satisfies $\lim_{\xi \to \infty} S(\xi) = 0$, then the Keller--Segel--Navier--Stokes system admits a global classical solution that remains uniformly bounded in time. \item If $N = 3$, $\kappa = 0$, and $S$ satisfies \[ |S(\xi)| \le K_S (\xi + 1)^{-\alpha} \quad \text{for all } \xi \ge 0, \] with some constants $K_S > 0$ and $\alpha > \frac{1}{3}$, then the Keller--Segel--Stokes system possesses a global bounded classical solution. \end{itemize} Our results are optimal, since it is well established that, in the absence of fluid effects, blow-up can occur when $S \equiv \mathrm{const}$ in two dimensions, or when $\alpha < \tfrac{1}{3}$ in three dimensions.

math.AP↗

arXiv2026

On the Extreme Variance of Certified Local Robustness Across Model Seeds

Robustness verification of neural networks, referring to formally proving that neural networks satisfy robustness properties, is of crucial importance in safety-critical applications, where model failures can result in loss of human life or million-dollar damages. However, the dependability of verification results may be questioned due to sources of randomness in machine learning, and although this has been widely investigated for accuracy, its impact on robustness verification remains unknown. In this paper, we demonstrate a concerning result: Models that differ only in random seeds during training exhibit extreme variance in their certified robustness, with a standard deviation that is statistically larger than the marginal robustness improvements reported in recent machine learning papers. In addition, we also show that certified robustness generalization to unseen data varies significantly across datasets, falling short of the dependability expectations for safety-critical tasks. Our findings are major concerns because: (i) machine learning results in certified robustness are likely unconvincing due to extreme variance in certified robustness, and (ii) a ``lucky'' model seed in a test set cannot be guaranteed to maintain its higher certified robustness under a different test set. In light of these results, we urge researchers to increase the reporting of confidence intervals for certified robustness, and we urge those verifying neural networks to be more comprehensive in verification by using large-scale, diverse, and unseen data.

cs.LG↗

arXiv2025

Global boundedness, absorbing sets and mass persistene in two-dimensional chemotaxis-Navier-Stokes systems with weakly singular sensitivity and sub-logistic sources

This paper studies the following chemotaxis-fluid system in a two-dimensional bounded domain $\Omega$: \begin{equation*} \begin{cases} n_t + u \cdot \nabla n &= \Delta n - \chi \nabla \cdot \left (n \frac{\nabla c}{c^k} \right ) + r n - \frac{\mu n^2}{\log^\eta(n+e)}, c_t + u \cdot \nabla c &= \Delta c - \alpha c + \beta n, u_t + u \cdot \nabla u &= \Delta u - \nabla P + n \nabla \phi + f, \nabla \cdot u &= 0, \end{cases} \end{equation*} where $r, \mu, \alpha, \beta, \chi$ are positive parameters, $k, \eta \in (0,1)$, $\phi \in W^{2,\infty}(\Omega)$, and $f \in C^1\left(\bar{\Omega}\times [0, \infty)\right) \cap L^\infty\left(\Omega \times (0, \infty)\right)$. We show that, under suitable conditions on the initial data and with no-flux/no-flux/Dirichlet boundary conditions, this system admits a globally bounded classical solution. Furthermore, the system possesses an absorbing set in the topology of $C^0(\bar{\Omega}) \times W^{1, \infty}(\Omega) \times C^0(\bar{\Omega}; \mathbb{R}^2)$. Finally, we establish the persistence of the total mass of solutions, indicating that the population does not face extinction as a whole.

math.AP↗

arXiv2025

One-Prompt Strikes Back: Sparse Mixture of Experts for Prompt-based Continual Learning

Prompt-based methods have recently gained prominence in Continual Learning (CL) due to their strong performance and memory efficiency. A prevalent strategy in this paradigm assigns a dedicated subset of prompts to each task, which, while effective, incurs substantial computational overhead and causes memory requirements to scale linearly with the number of tasks. Conversely, approaches employing a single shared prompt across tasks offer greater efficiency but often suffer from degraded performance due to knowledge interference. To reconcile this trade-off, we propose SMoPE, a novel framework that integrates the benefits of both task-specific and shared prompt strategies. Inspired by recent findings on the relationship between Prefix Tuning and Mixture of Experts (MoE), SMoPE organizes a shared prompt into multiple "prompt experts" within a sparse MoE architecture. For each input, only a select subset of relevant experts is activated, effectively mitigating interference. To facilitate expert selection, we introduce a prompt-attention score aggregation mechanism that computes a unified proxy score for each expert, enabling dynamic and sparse activation. Additionally, we propose an adaptive noise mechanism to encourage balanced expert utilization while preserving knowledge from prior tasks. To further enhance expert specialization, we design a prototype-based loss function that leverages prefix keys as implicit memory representations. Extensive experiments across multiple CL benchmarks demonstrate that SMoPE consistently outperforms task-specific prompt methods and achieves performance competitive with state-of-the-art approaches, all while significantly reducing parameter counts and computational costs.

cs.LG↗

arXiv2025

LEAF: A Robust Expert-Based Framework for Few-Shot Continual Event Detection

Few-shot Continual Event Detection (FCED) poses the dual challenges of learning from limited data and mitigating catastrophic forgetting across sequential tasks. Existing approaches often suffer from severe forgetting due to the full fine-tuning of a shared base model, which leads to knowledge interference between tasks. Moreover, they frequently rely on data augmentation strategies that can introduce unnatural or semantically distorted inputs. To address these limitations, we propose LEAF, a novel and robust expert-based framework for FCED. LEAF integrates a specialized mixture of experts architecture into the base model, where each expert is parameterized with low-rank adaptation (LoRA) matrices. A semantic-aware expert selection mechanism dynamically routes instances to the most relevant experts, enabling expert specialization and reducing knowledge interference. To improve generalization in limited-data settings, LEAF incorporates a contrastive learning objective guided by label descriptions, which capture high-level semantic information about event types. Furthermore, to prevent overfitting on the memory buffer, our framework employs a knowledge distillation strategy that transfers knowledge from previous models to the current one. Extensive experiments on multiple FCED benchmarks demonstrate that LEAF consistently achieves state-of-the-art performance.

cs.LG↗

arXiv2025

Graph-Theoretic Consistency for Robust and Topology-Aware Semi-Supervised Histopathology Segmentation

Semi-supervised semantic segmentation (SSSS) is vital in computational pathology, where dense annotations are costly and limited. Existing methods often rely on pixel-level consistency, which propagates noisy pseudo-labels and produces fragmented or topologically invalid masks. We propose Topology Graph Consistency (TGC), a framework that integrates graph-theoretic constraints by aligning Laplacian spectra, component counts, and adjacency statistics between prediction graphs and references. This enforces global topology and improves segmentation accuracy. Experiments on GlaS and CRAG demonstrate that TGC achieves state-of-the-art performance under 5-10% supervision and significantly narrows the gap to full supervision.

eess.IV↗

arXiv2025

Subliminal Learning: Language models transmit behavioral traits via hidden signals in data

We study subliminal learning, a surprising phenomenon where language models transmit behavioral traits via semantically unrelated data. In our main experiments, a "teacher" model with some trait T (such as liking owls or being misaligned) generates a dataset consisting solely of number sequences. Remarkably, a "student" model trained on this dataset learns T. This occurs even when the data is filtered to remove references to T. We observe the same effect when training on code or reasoning traces generated by the same teacher model. However, we do not observe the effect when the teacher and student have different base models. To help explain our findings, we prove a theoretical result showing that subliminal learning occurs in all neural networks under certain conditions, and demonstrate subliminal learning in a simple MLP classifier. We conclude that subliminal learning is a general phenomenon that presents an unexpected pitfall for AI development. Distillation could propagate unintended traits, even when developers try to prevent this via data filtering.

cs.LG↗

arXiv2025

An improvement toward global boundedness in a fully parabolic chemotaxis with singular sensitivity in any dimension

This paper deals with the problem of global solvability and boundedness of classical solutions to a fully parabolic chemotaxis system with singular sensitivity in any dimensional setting. In particular, We show that the system \begin{equation*} \begin{cases} u_t = \Delta u - \chi \nabla \cdot \left( \dfrac{u}{v} \nabla v \right), \\ v_t = \Delta v - v + u, \end{cases} \end{equation*} posed in a bounded domain $\Omega \subset \mathbb{R}^n$ with $n \geq 3$, admits a global bounded classical solution provided that $\chi \in (0,\chi_0)$ with $\chi_0 > \sqrt{\frac{2}{n}}$ can be determined explicitly. This result extends several existing works, which established global boundedness under the more restrictive condition $\chi < \sqrt{\frac{2}{n}}$, and shows that this threshold is not an optimal upper bound for preventing blow-up.

math.AP↗

arXiv2025

Trustworthy Chronic Disease Risk Prediction For Self-Directed Preventive Care via Medical Literature Validation

Chronic diseases are long-term, manageable, yet typically incurable conditions, highlighting the need for effective preventive strategies. Machine learning has been widely used to assess individual risk for chronic diseases. However, many models rely on medical test data (e.g. blood results, glucose levels), which limits their utility for proactive self-assessment. Additionally, to gain public trust, machine learning models should be explainable and transparent. Although some research on self-assessment machine learning models includes explainability, their explanations are not validated against established medical literature, reducing confidence in their reliability. To address these issues, we develop deep learning models that predict the risk of developing 13 chronic diseases using only personal and lifestyle factors, enabling accessible, self-directed preventive care. Importantly, we use SHAP-based explainability to identify the most influential model features and validate them against established medical literature. Our results show a strong alignment between the models' most influential features and established medical literature, reinforcing the models' trustworthiness. Critically, we find that this observation holds across 13 distinct diseases, indicating that this machine learning approach can be broadly trusted for chronic disease prediction. This work lays the foundation for developing trustworthy machine learning tools for self-directed preventive care. Future research can explore other approaches for models' trustworthiness and discuss how the models can be used ethically and responsibly.

cs.LG↗

arXiv2025

WAVE++: Capturing Within-Task Variance for Continual Relation Extraction with Adaptive Prompting

Memory-based approaches have shown strong performance in Continual Relation Extraction (CRE). However, storing examples from previous tasks increases memory usage and raises privacy concerns. Recently, prompt-based methods have emerged as a promising alternative, as they do not rely on storing past samples. Despite this progress, current prompt-based techniques face several core challenges in CRE, particularly in accurately identifying task identities and mitigating catastrophic forgetting. Existing prompt selection strategies often suffer from inaccuracies, lack robust mechanisms to prevent forgetting in shared parameters, and struggle to handle both cross-task and within-task variations. In this paper, we propose WAVE++, a novel approach inspired by the connection between prefix-tuning and mixture of experts. Specifically, we introduce task-specific prompt pools that enhance flexibility and adaptability across diverse tasks while avoiding boundary-spanning risks; this design more effectively captures both within-task and cross-task variations. To further refine relation classification, we incorporate label descriptions that provide richer, more global context, enabling the model to better distinguish among different relations. We also propose a training-free mechanism to improve task prediction during inference. Moreover, we integrate a generative model to consolidate prior knowledge within the shared parameters, thereby removing the need for explicit data storage. Extensive experiments demonstrate that WAVE++ outperforms state-of-the-art prompt-based and rehearsal-based methods, offering a more robust solution for continual relation extraction. Our code is publicly available at https://github.com/PiDinosauR2804/WAVE-CRE-PLUS-PLUS.

cs.CL↗

arXiv2025

Global boundedness in the higher-dimensional fully parabolic chemotaxis with weak singular sensitivity and logistic source

We consider the following chemotaxis system under homogeneous Neumann boundary conditions in a smooth, open, bounded domain $\Omega \subset \mathbb{R}^n$ with $n \geq 3$: \begin{equation*} \begin{cases} u_t = \Delta u - \chi \nabla \cdot \left( \frac{u}{v^k} \nabla v \right) + ru - \mu u^2, & \text{in } \Omega \times (0,T_{\rm max}), v_t = \Delta v - \alpha v + \beta u, & \text{in } \Omega \times (0,T_{\rm max}), \end{cases} \end{equation*} where $k \in (0,1)$, and $\chi, r, \mu, \alpha, \beta$ are positive parameters. In this paper, we demonstrate that for suitably smooth initial data, the problem admits a unique nonnegative classical solution that remains globally bounded in time when $\mu$ is sufficiently large.

math.AP↗

arXiv2025

Absence of blow-up in a fully parabolic chemotaxis system with weak singular sensitivity and logistic damping in dimension two

It is shown in this paper that blow-up does not occur in the following chemotaxis system under homogeneous Neumann boundary conditions in a smooth, open, bounded domain $\Omega \subset \mathbb{R}^2$: \begin{equation*} \begin{cases} u_t = \Delta u - \chi \nabla \cdot \left( \frac{u}{v^k} \nabla v \right) + ru - \mu u^2, \qquad &\text{in } \Omega \times (0,T_{\rm max}), v_t = \Delta v - \alpha v + \beta u, \qquad &\text{in } \Omega \times (0,T_{\rm max}), \end{cases} \end{equation*} where $ k \in (0,1) $, and $\chi, r, \mu, \alpha, \beta $ are positive parameters. Known results have already established the same conclusion for the parabolic-elliptic case. Here, we complement these findings by extending the result to the fully parabolic case.

math.AP↗

arXiv2025

On Zero-Initialized Attention: Optimal Prompt and Gating Factor Estimation

The LLaMA-Adapter has recently emerged as an efficient fine-tuning technique for LLaMA models, leveraging zero-initialized attention to stabilize training and enhance performance. However, despite its empirical success, the theoretical foundations of zero-initialized attention remain largely unexplored. In this paper, we provide a rigorous theoretical analysis, establishing a connection between zero-initialized attention and mixture-of-expert models. We prove that both linear and non-linear prompts, along with gating functions, can be optimally estimated, with non-linear prompts offering greater flexibility for future applications. Empirically, we validate our findings on the open LLM benchmarks, demonstrating that non-linear prompts outperform linear ones. Notably, even with limited training data, both prompt types consistently surpass vanilla attention, highlighting the robustness and adaptability of zero-initialized attention.

cs.LG↗

arXiv2025

RepLoRA: Reparameterizing Low-Rank Adaptation via the Perspective of Mixture of Experts

Low-rank Adaptation (LoRA) has emerged as a powerful method for fine-tuning large-scale foundation models. Despite its popularity, the theoretical understanding of LoRA has remained limited. This paper presents a theoretical analysis of LoRA by examining its connection to the Mixture of Experts models. Under this framework, we show that simple reparameterizations of the LoRA matrices can notably accelerate the low-rank matrix estimation process. In particular, we prove that reparameterization can reduce the data needed to achieve a desired estimation error from an exponential to a polynomial scale. Motivated by this insight, we propose Reparameterized Low-Rank Adaptation (RepLoRA), which incorporates lightweight MLPs to reparameterize the LoRA matrices. Extensive experiments across multiple domains demonstrate that RepLoRA consistently outperforms vanilla LoRA. Notably, with limited data, RepLoRA surpasses LoRA by a margin of up to 40.0% and achieves LoRA's performance with only 30.0% of the training data, highlighting both the theoretical and empirical robustness of our PEFT method.

cs.LG↗