arXiv subjects

Tuan Tran

Publications and source records attributed to Tuan Tran.

At least 19 recordsLinked to original sources

arXiv2026

Three trees suffice for a constant stretch in minor-free graphs

In this short note, we show that $H$-minor-free graphs have a tree cover with $3$ trees and constant stretch for any fixed graph $H$. The number of trees matches the recent lower bound by Chen, Tan, and Xu who showed that a toroidal grid requires at least $3$ trees for constant stretch. Our result is obtained by establishing a connection between tree covers and Assouad--Nagata dimension and then invoking the recent dimension bound for minor-free metrics by Liu.

cs.DS↗

arXiv2026

A Picture Says Thousands of Words - Harnessing Dermal Exposure Data from Images through Hybrid Deep Learning for Enhanced Safety Assessment

This study developed a hybrid computer vision method to quantify exposed skin from images for dermal exposure assessment. Using 170 indoor-painting images, Mask R-CNN first identified human subjects and removed background interference; a color-based algorithm then segmented exposed skin. The resulting exposed-skin-to-body pixel ratios showed approximately 80% agreement with human estimates. The approach demonstrates a scalable way to extract semi-quantitative exposure information from images, with future extensions to body-part recognition, PPE detection, and video-based exposure analysis.

cs.CV↗

arXiv2026

Beating the Ahlswede--Khachatrian bound for the Erd\H{o}s--Frankl--Pach problem

In the 1980s, Erd\H{o}s and, independently, Frankl and Pach conjectured that, for sufficiently large $n$, every $(d+1)$-uniform family on $\{1,\ldots,n\}$ with VC-dimension $d$ has size at most $\binom{n-1}{d}$, the size of a star. Ahlswede and Khachatrian disproved this conjecture in 1997 by giving a family of size $\binom{n-1}{d}+\binom{n-4}{d-2}$. This value has since been widely believed to be best possible, and Mubayi and Zhao explicitly conjectured its optimality in 2007. Very recently, Wang, Xu and Zhang proved their conjecture for $d=2$ and $n\ge 7$, providing further support for this belief. Surprisingly, we show that the Mubayi-Zhao conjecture is false for every $d\ge 3$ by constructing families larger than the Ahlswede--Khachatrian bound. Our constructions suggest that the answer to the Erd\H{o}s--Frankl--Pach problem depends delicately on both $n$ and $d$.

math.CO↗

arXiv2026

Tower heights for color-avoiding Ramsey numbers of monotone paths

Ramsey numbers of monotone paths in ordered hypergraphs form a natural higher-uniformity extension of the classical Erd\H{o}s--Szekeres theorems, and their tower height was determined by Moshkovitz and Shapira. A color-avoiding variant, initiated by Loh and further developed by Gowers and Long and by Mulrenin, Pohoata, and Zakharov, asks for monotone paths whose edges use only a bounded number of colors rather than a single color. For integers $q>p$, let $A_k(n;q,p)$ be the least integer $N$ such that every $q$-coloring of the ordered complete $k$-uniform hypergraph on $\{1,\ldots,N\}$ contains a monotone path of length $n$ whose edges use at most $p$ colors. We prove that, for every fixed $p$ and all sufficiently large $q$, the exact tower height of $A_k(n;q,p)$ is $\lceil (k-1)/p\rceil$. Thus the number of colors allowed on the path affects the Ramsey number at the level of tower height: allowing $p$ colors lowers the height from $k-1$ in the monochromatic problem to $\lceil (k-1)/p\rceil$. This answers questions of Mulrenin, Pohoata, and Zakharov. The upper bound follows from a simple block-compression argument. The main contribution is the matching lower bound, for which we develop a novel variant of the stepping-up method. A surprising feature of the proof is the appearance of the Morse--Hedlund theorem, a foundational result in symbolic dynamics and combinatorics on words. We establish and use a finite version of this theorem, which may be of independent interest.

math.CO↗

arXiv2026

TextSeal: A Localized LLM Watermark for Provenance & Distillation Protection

We introduce TextSeal, a state-of-the-art watermark for large language models. Building on Gumbel-max sampling, TextSeal introduces dual-key generation to restore output diversity, along with entropy-weighted scoring and multi-region localization for improved detection. It supports serving optimizations such as speculative decoding and multi-token prediction, and does not add any inference overhead. TextSeal strictly dominates baselines like SynthID-text in detection strength and is robust to dilution, maintaining confident localized detection even in heavily mixed human/AI documents. The scheme is theoretically distortion-free, and evaluation across reasoning benchmarks confirms that it preserves downstream performance; while a multilingual human evaluation (6000 A/B comparisons, 5 languages) shows no perceptible quality difference. Beyond its use for provenance detection, TextSeal is also ``radioactive'': its watermark signal transfers through model distillation, enabling detection of unauthorized use.

cs.CR↗

arXiv2026

Learning to Watermark in the Latent Space of Generative Models

Existing approaches for watermarking AI-generated images often rely on post-hoc methods applied in pixel space, introducing computational overhead and potential visual artifacts. In this work, we explore latent space watermarking and introduce DistSeal, a unified approach for latent watermarking that works across both diffusion and autoregressive models. Our approach works by training post-hoc watermarking models in the latent space of generative models. We demonstrate that these latent watermarkers can be effectively distilled either into the generative model itself or into the latent decoder, enabling in-model watermarking. The resulting latent watermarks achieve competitive robustness while offering similar imperceptibility and up to 20x speedup compared to pixel-space baselines. Our experiments further reveal that distilling latent watermarkers outperforms distilling pixel-space ones, providing a solution that is both more efficient and more robust.

cs.CV↗

arXiv2025

The anti-concentration phenomenon with respect to random permutations

The anti-concentration phenomenon in probability theory has been intensively studied in recent years, with applications across many areas of mathematics. In most existing works, the ambient probability space is a product space generated by independent random variables. In this paper, we initiate a systematic study of anti-concentration when the ambient space is the symmetric group, equipped with the uniform measure. Concretely, we focus on the random sum $S_{\pi} = \sum_{i=1}^{n} w_i\, v_{\pi(i)}$, where $w=(w_1,\dots,w_n)$ and $v=(v_1,\dots,v_n)$ are fixed vectors and $\pi$ is a uniformly random permutation. The paper contains several new results, addressing both discrete and continuous anti-concentration phenomena. On the discrete side, we establish a near-optimal structural characterization of the vectors $w$ and $v$ under the assumption that the concentration probability $\sup_x P(S_{\pi}=x)$ is polynomially large. On the continuous side, we study the small-ball event $|S_{\pi}-L|\le \delta$. Our results exhibit sub-gaussian decay in $L$. Our results have applications in various areas. First, we use our inverse theorems to derive and strengthen a number of previous anti-concentration bounds. In particular, we show that if both $w$ and $v$ have distinct entries, then $\sup_x P(S_{\pi}=x) \le n^{-5/2+o(1)}$. Next, we apply our new results to study random polynomials, and prove that the number of extremal points of random permutation polynomials is bounded by $O(\log n)$, extending results of S{\"o}ze~\cite{Soze1, Soze2}. In the final application, we prove that random matrices whose rows are independent random permutations of a fixed non-degenerate vector are nonsingular with high probability.

math.CO↗

arXiv2025

Pixel Seal: Adversarial-only training for invisible image and video watermarking

Invisible watermarking is essential for tracing the provenance of digital content. However, training state-of-the-art models remains notoriously difficult, with current approaches often struggling to balance robustness against true imperceptibility. This work introduces Pixel Seal, which sets a new state-of-the-art for image and video watermarking. We first identify three fundamental issues of existing methods: (i) the reliance on proxy perceptual losses such as MSE and LPIPS that fail to mimic human perception and result in visible watermark artifacts; (ii) the optimization instability caused by conflicting objectives, which necessitates exhaustive hyperparameter tuning; and (iii) reduced robustness and imperceptibility of watermarks when scaling models to high-resolution images and videos. To overcome these issues, we first propose an adversarial-only training paradigm that eliminates unreliable pixel-wise imperceptibility losses. Second, we introduce a three-stage training schedule that stabilizes convergence by decoupling robustness and imperceptibility. Third, we address the resolution gap via high-resolution adaptation, employing JND-based attenuation and training-time inference simulation to eliminate upscaling artifacts. We thoroughly evaluate the robustness and imperceptibility of Pixel Seal on different image types and across a wide range of transformations, and show clear improvements over the state-of-the-art. We finally demonstrate that the model efficiently adapts to video via temporal watermark pooling, positioning Pixel Seal as a practical and scalable solution for reliable provenance in real-world image and video settings.

cs.CV↗

arXiv2025

How Good is Post-Hoc Watermarking With Language Model Rephrasing?

Generation-time text watermarking embeds statistical signals into text for traceability of AI-generated content. We explore *post-hoc watermarking* where an LLM rewrites existing text while applying generation-time watermarking, to protect copyrighted documents, or detect their use in training or RAG via watermark radioactivity. Unlike generation-time approaches, which is constrained by how LLMs are served, this setting offers additional degrees of freedom for both generation and detection. We investigate how allocating compute (through larger rephrasing models, beam search, multi-candidate generation, or entropy filtering at detection) affects the quality-detectability trade-off. Our strategies achieve strong detectability and semantic fidelity on open-ended text such as books. Among our findings, the simple Gumbel-max scheme surprisingly outperforms more recent alternatives under nucleus sampling, and most methods benefit significantly from beam search. However, most approaches struggle when watermarking verifiable text such as code, where we counterintuitively find that smaller models outperform larger ones. This study reveals both the potential and limitations of post-hoc watermarking, laying groundwork for practical applications and future research.

cs.CR↗

arXiv2025

Transferable Black-Box One-Shot Forging of Watermarks via Image Preference Models

Recent years have seen a surge in interest in digital content watermarking techniques, driven by the proliferation of generative models and increased legal pressure. With an ever-growing percentage of AI-generated content available online, watermarking plays an increasingly important role in ensuring content authenticity and attribution at scale. There have been many works assessing the robustness of watermarking to removal attacks, yet, watermark forging, the scenario when a watermark is stolen from genuine content and applied to malicious content, remains underexplored. In this work, we investigate watermark forging in the context of widely used post-hoc image watermarking. Our contributions are as follows. First, we introduce a preference model to assess whether an image is watermarked. The model is trained using a ranking loss on purely procedurally generated images without any need for real watermarks. Second, we demonstrate the model's capability to remove and forge watermarks by optimizing the input image through backpropagation. This technique requires only a single watermarked image and works without knowledge of the watermarking model, making our attack much simpler and more practical than attacks introduced in related work. Third, we evaluate our proposed method on a variety of post-hoc image watermarking models, demonstrating that our approach can effectively forge watermarks, questioning the security of current watermarking approaches. Our code and further resources are publicly available.

cs.LG↗

arXiv2025

Geometric Image Synchronization with Deep Watermarking

Synchronization is the task of estimating and inverting geometric transformations (e.g., crop, rotation) applied to an image. This work introduces SyncSeal, a bespoke watermarking method for robust image synchronization, which can be applied on top of existing watermarking methods to enhance their robustness against geometric transformations. It relies on an embedder network that imperceptibly alters images and an extractor network that predicts the geometric transformation to which the image was subjected. Both networks are end-to-end trained to minimize the error between the predicted and ground-truth parameters of the transformation, combined with a discriminator to maintain high perceptual quality. We experimentally validate our method on a wide variety of geometric and valuemetric transformations, demonstrating its effectiveness in accurately synchronizing images. We further show that our synchronization can effectively upgrade existing watermarking methods to withstand geometric transformations to which they were previously vulnerable.

cs.CV↗

arXiv2025

Relative discrepancy of hypergraphs

Given $k$-uniform hypergraphs $G$ and $H$ on $n$ vertices with densities $p$ and $q$, their relative discrepancy is defined as $\hbox{disc}(G,H)=\max\big||E(G')\cap E(H')|-pq\binom{n}{k}\big|$, where the maximum ranges over all pairs $G',H'$ with $G'\cong G$, $H'\cong H$, and $V(G')=V(H')$. Let $\hbox{bs}(k)$ denote the smallest integer $m \ge 2$ such that any collection of $m$ $k$-uniform hypergraphs on $n$ vertices with moderate densities contains a pair $G,H$ for which $\hbox{disc}(G,H) = \Omega(n^{(k+1)/2})$. In this paper, we answer several questions raised by Bollob\'as and Scott, providing both upper and lower bounds for $\hbox{bs}(k)$. Consequently, we determine the exact value of $\hbox{bs}(k)$ for $2\le k\le 13$, and show $\hbox{bs}(k)=O(k^{0.525})$, substantially improving the previous bound $\hbox{bs}(k)\le k+1$ due to Bollob\'as-Scott. The case $k=2$ recovers a result of Bollob\'as-Scott, which generalises classical theorems of Erd\H{o}s-Spencer, and Erd\H{o}s-Goldberg-Pach-Spencer. The case $k=3$ also follows from the results of Bollob\'as-Scott and Kwan-Sudakov-Tran. Our proof combines linear algebra, Fourier analysis, and extremal hypergraph theory.

math.CO↗

arXiv2025

Seamless Interaction: Dyadic Audiovisual Motion Modeling and Large-Scale Dataset

Human communication involves a complex interplay of verbal and nonverbal signals, essential for conveying meaning and achieving interpersonal goals. To develop socially intelligent AI technologies, it is crucial to develop models that can both comprehend and generate dyadic behavioral dynamics. To this end, we introduce the Seamless Interaction Dataset, a large-scale collection of over 4,000 hours of face-to-face interaction footage from over 4,000 participants in diverse contexts. This dataset enables the development of AI technologies that understand dyadic embodied dynamics, unlocking breakthroughs in virtual agents, telepresence experiences, and multimodal content analysis tools. We also develop a suite of models that utilize the dataset to generate dyadic motion gestures and facial expressions aligned with human speech. These models can take as input both the speech and visual behavior of their interlocutors. We present a variant with speech from an LLM model and integrations with 2D and 3D rendering methods, bringing us closer to interactive virtual agents. Additionally, we describe controllable variants of our motion models that can adapt emotional responses and expressivity levels, as well as generating more semantically-relevant gestures. Finally, we discuss methods for assessing the quality of these dyadic motion models, which are demonstrating the potential for more intuitive and responsive human-AI interactions.

cs.CV↗

arXiv2025

FLAME: Towards Federated Fine-Tuning Large Language Models Through Adaptive SMoE

Existing resource-adaptive LoRA federated fine-tuning methods enable clients to fine-tune models using compressed versions of global LoRA matrices, in order to accommodate various compute resources across clients. This compression requirement will lead to suboptimal performance due to information loss. To address this, we propose FLAME, a novel federated learning framework based on the Sparse Mixture-of-Experts (SMoE) architecture. Unlike prior approaches, FLAME retains full (uncompressed) global LoRA matrices and achieves client-side adaptability by varying the number of activated experts per client. However, incorporating SMoE into federated learning introduces unique challenges, specifically, the mismatch in output magnitude from partial expert activation and the imbalance in expert training quality across clients. FLAME tackles these challenges through a lightweight rescaling mechanism and an activation-aware aggregation scheme. Empirical results across diverse computational settings demonstrate that FLAME consistently outperforms existing methods, providing a robust and effective solution for resource-adaptive federated learning.

cs.LG↗

arXiv2025

The edge-statistics conjecture for hypergraphs

Let $r,k,\ell$ be integers such that $0\le\ell\le\binom{k}{r}$. Given a large $r$-uniform hypergraph $G$, we consider the fraction of $k$-vertex subsets which span exactly $\ell$ edges. If $\ell$ is 0 or $\binom{k}{r}$, this fraction can be exactly 1 (by taking $G$ to be empty or complete), but for all other values of $\ell$, one might suspect that this fraction is always significantly smaller than 1. In this paper we prove an essentially optimal result along these lines: if $\ell$ is not 0 or $\binom{k}{r}$, then this fraction is at most $(1/e) + \varepsilon$, assuming $k$ is sufficiently large in terms of $r$ and $\varepsilon>0$, and $G$ is sufficiently large in terms of $k$. Previously, this was only known for a very limited range of values of $r,k,\ell$ (due to Kwan-Sudakov-Tran, Fox-Sauermann, and Martinsson-Mousset-Noever-Truji\'{c}). Our result answers a question of Alon-Hefetz-Krivelevich-Tyomkyn, who suggested this as a hypergraph generalisation of their "edge-statistics conjecture". We also prove a much stronger bound when $\ell$ is far from 0 and $\binom{k}{r}$.

math.CO↗

arXiv2025

On the order of intersecting hypergraphs

Determining the maximum number of edges in an intersecting hypergraph on a fixed ground set under additional constraints is one of the central topics in extremal combinatorics. In contrast, there are few results on analogous problems concerning the maximum order of such hypergraphs. In this paper, we systematically study these vertex analogues.

math.CO↗

arXiv2024

LCFO: Long Context and Long Form Output Dataset and Benchmarking

This paper presents the Long Context and Form Output (LCFO) benchmark, a novel evaluation framework for assessing gradual summarization and summary expansion capabilities across diverse domains. LCFO consists of long input documents (5k words average length), each of which comes with three summaries of different lengths (20%, 10%, and 5% of the input text), as well as approximately 15 questions and answers (QA) related to the input content. Notably, LCFO also provides alignments between specific QA pairs and corresponding summaries in 7 domains. The primary motivation behind providing summaries of different lengths is to establish a controllable framework for generating long texts from shorter inputs, i.e. summary expansion. To establish an evaluation metric framework for summarization and summary expansion, we provide human evaluation scores for human-generated outputs, as well as results from various state-of-the-art large language models (LLMs). GPT-4o-mini achieves best human scores among automatic systems in both summarization and summary expansion tasks (~ +10% and +20%, respectively). It even surpasses human output quality in the case of short summaries (~ +7%). Overall automatic metrics achieve low correlations with human evaluation scores (~ 0.4) but moderate correlation on specific evaluation aspects such as fluency and attribution (~ 0.6).

cs.CL↗

arXiv2024

Large Concept Models: Language Modeling in a Sentence Representation Space

LLMs have revolutionized the field of artificial intelligence and have emerged as the de-facto tool for many tasks. The current established technology of LLMs is to process input and generate output at the token level. This is in sharp contrast to humans who operate at multiple levels of abstraction, well beyond single words, to analyze information and to generate creative content. In this paper, we present an attempt at an architecture which operates on an explicit higher-level semantic representation, which we name a concept. Concepts are language- and modality-agnostic and represent a higher level idea or action in a flow. Hence, we build a "Large Concept Model". In this study, as proof of feasibility, we assume that a concept corresponds to a sentence, and use an existing sentence embedding space, SONAR, which supports up to 200 languages in both text and speech modalities. The Large Concept Model is trained to perform autoregressive sentence prediction in an embedding space. We explore multiple approaches, namely MSE regression, variants of diffusion-based generation, and models operating in a quantized SONAR space. These explorations are performed using 1.6B parameter models and training data in the order of 1.3T tokens. We then scale one architecture to a model size of 7B parameters and training data of about 2.7T tokens. We perform an experimental evaluation on several generative tasks, namely summarization and a new task of summary expansion. Finally, we show that our model exhibits impressive zero-shot generalization performance to many languages, outperforming existing LLMs of the same size. The training code of our models is freely available.

cs.CL↗