arXiv subjects

Hyunwoo Lee

Publications and source records attributed to Hyunwoo Lee.

At least 55 records · Page 3Linked to original sources

arXiv2025

Robust Weight Initialization for Tanh Neural Networks with Fixed Point Analysis

As a neural network's depth increases, it can improve generalization performance. However, training deep networks is challenging due to gradient and signal propagation issues. To address these challenges, extensive theoretical research and various methods have been introduced. Despite these advances, effective weight initialization methods for tanh neural networks remain insufficiently investigated. This paper presents a novel weight initialization method for neural networks with tanh activation function. Based on an analysis of the fixed points of the function $\tanh(ax)$, the proposed method aims to determine values of $a$ that mitigate activation saturation. A series of experiments on various classification datasets and physics-informed neural networks demonstrates that the proposed method outperforms Xavier initialization methods~(with or without normalization) in terms of robustness across different network sizes, data efficiency, and convergence speed. Code is available at https://github.com/1HyunwooLee/Tanh-Init

cs.LG↗

arXiv2025

Can TDD Be Employed in LEO SatCom Systems? Challenges and Potential Approaches

Frequency-division duplexing (FDD) remains the de facto standard in modern low Earth orbit (LEO) satellite communication (SatCom) systems, such as SpaceX's Starlink, OneWeb, and Amazon's Project Kuiper. While time-division duplexing (TDD) is often regarded as superior in today's terrestrial networks, its viability in future LEO SatCom systems remains unclear. This article details how the long propagation delays and high orbital velocities exhibited by LEO SatCom systems impedes the adoption of TDD, due to challenges involving the frame structure and synchronization. We then present potential approaches to overcome these challenges, which vary in terms of resource efficiency and operational/device complexity and thus would likely be application-specific. We conclude by assessing the performance of these proposed approaches, putting into perspective the tradeoff between complexity and performance gains over FDD. Overall, this article aims to motivate future investigation into the prospects of TDD in LEO SatCom systems and solutions to enable such, with the goal of enhancing future systems and unifying them with terrestrial networks.

eess.SP↗

arXiv2025

Reconstructing hypergraph matching polynomials

By utilizing the recently developed hypergraph analogue of Godsil's identity by the second author, we prove that for all $n \geq k \geq 2$, one can reconstruct the matching polynomial of an $n$-vertex $k$-uniform hypergraph from the multiset of all induced sub-hypergraphs on $\lfloor \frac{k-1}{k}n \rfloor + 1$ vertices. This generalizes the well-known result of Godsil on graphs in 1981 to every uniform hypergraph. As a corollary, we show that for every graph $F$, one can reconstruct the number of $F$-factors in a graph under analogous conditions. We also constructed examples that imply the number $\lfloor \frac{k-1}{k}n \rfloor + 1$ is the best possible for all $n\geq k \geq 2$ with $n$ divisible by $k$.

math.CO↗

arXiv2024

Automated Body Composition Analysis Using DAFS Express on 2D MRI Slices at L3 Vertebral Level

Body composition analysis is vital in assessing health conditions such as obesity, sarcopenia, and metabolic syndromes. MRI provides detailed images of skeletal muscle (SKM), visceral adipose tissue (VAT), and subcutaneous adipose tissue (SAT), but their manual segmentation is labor-intensive and limits clinical applicability. This study validates an automated tool for MRI-based 2D body composition analysis- (Data Analysis Facilitation Suite (DAFS) Express), comparing its automated measurements with expert manual segmentations using UK Biobank data. A cohort of 399 participants from the UK Biobank dataset was selected, yielding 423 single L3 slices for analysis. DAFS Express performed automated segmentations of SKM, VAT, and SAT, which were then manually corrected by expert raters for validation. Evaluation metrics included Jaccard coefficients, Dice scores, Intraclass Correlation Coefficients (ICCs), and Bland-Altman Plots to assess segmentation agreement and reliability. High agreements were observed between automated and manual segmentations with mean Jaccard scores: SKM 99.03%, VAT 95.25%, and SAT 99.57%; and mean Dice scores: SKM 99.51%, VAT 97.41%, and SAT 99.78%. Cross-sectional area comparisons showed consistent measurements with automated methods closely matching manual measurements for SKM and SAT, and slightly higher values for VAT (SKM: Auto 132.51 cm^2, Manual 132.36 cm^2; VAT: Auto 137.07 cm^2, Manual 134.46 cm^2; SAT: Auto 203.39 cm^2, Manual 202.85 cm^2). ICCs confirmed strong reliability (SKM: 0.998, VAT: 0.994, SAT: 0.994). Bland-Altman plots revealed minimal biases, and boxplots illustrated distribution similarities across SKM, VAT, and SAT areas. On average DAFS Express took 18 seconds per DICOM. This underscores its potential to streamline image analysis processes in research and clinical settings, enhancing diagnostic accuracy and efficiency.

cs.CV↗

arXiv2024

Transversal cycles and paths in tournaments

Thomason [$\textit{Trans. Amer. Math. Soc.}$ 296.1 (1986)] proved that every sufficiently large tournament contains Hamilton paths and cycles with all possible orientations, except possibly the consistently oriented Hamilton cycle. This paper establishes $\textit{transversal}$ generalizations of these classical results. For a collection $\mathbf{T}=\{T_1,\dots,T_m\}$ of not-necessarily distinct tournaments on the common vertex set $V$, an $m$-edge directed subgraph $\mathcal{D}$ with the vertices in $V$ is called a transversal if there exists an bijection $φ\colon E(\mathcal{D})\to [m]$ such that $e\in E(T_{φ(e)})$ for all $e\in E(\mathcal{D})$. We prove that for sufficiently large $n$, there exist transversal Hamilton cycles of all possible orientations possibly except the consistently oriented one. We also obtain a similar result for the transversal Hamilton paths of all possible orientations. These results generalize the classical theorem of Thomason, and our approach provides another proof of this theorem.

math.CO↗

arXiv2024

Random matchings in linear hypergraphs

For a given hypergraph $H$ and a vertex $v\in V(H)$, consider a random matching $M$ chosen uniformly from the set of all matchings in $H.$ In $1995,$ Kahn conjectured that if $H$ is a $d$-regular linear $k$-uniform hypergraph, the probability that $M$ does not cover $v$ is $(1 + o_d(1))d^{-1/k}$ for all vertices $v\in V(H).$ This conjecture was proved for $k = 2$ by Kahn and Kim in $1998.$ In this paper, we disprove this conjecture for all $k \geq 3.$ For infinitely many values of $d,$ we construct $d$-regular linear $k$-uniform hypergraph $H$ containing two vertices $v_1$ and $v_2$ such that $\mathcal{P}(v_1 \notin M) = 1 - \frac{(1 + o_d(1))}{d^{k-2}}$ and $\mathcal{P}(v_2 \notin M) = \frac{(1 + o_d(1))}{d+1}.$ The gap between $\mathcal{P}(v_1 \notin M)$ and $\mathcal{P}(v_2 \notin M)$ in this $H$ is best possible. In the course of proving this, we also prove a hypergraph analog of Godsil's result on matching polynomials and paths in graphs, which is of independent interest.

math.CO↗

arXiv2024

Hamilton transversals in tournaments

It is well-known that every tournament contains a Hamilton path, and every strongly connected tournament contains a Hamilton cycle. This paper establishes transversal generalizations of these classical results. For a collection $\mathbf{T}=\{T_1,\dots,T_m\}$ of not-necessarily distinct tournaments on a common vertex set $V$, an $m$-edge directed graph $\mathcal{D}$ with vertices in $V$ is called a $\mathbf{T}$-transversal if there exists a bijection $ϕ\colon E(\mathcal{D})\to [m]$ such that $e\in E(T_{ϕ(e)})$ for all $e\in E(\mathcal{D})$. We prove that for sufficiently large $m$ with $m=|V|-1$, there exists a $\mathbf{T}$-transversal Hamilton path. Moreover, if $m=|V|$ and at least $m-1$ of the tournaments $T_1,\ldots,T_m$ are assumed to be strongly connected, then there is a $\mathbf{T}$-transversal Hamilton cycle. In our proof, we utilize a novel way of partitioning tournaments which we dub $\mathbf{H}$-partition.

math.CO↗

arXiv2024

SLM as Guardian: Pioneering AI Safety with Small Language Models

Most prior safety research of large language models (LLMs) has focused on enhancing the alignment of LLMs to better suit the safety requirements of humans. However, internalizing such safeguard features into larger models brought challenges of higher training cost and unintended degradation of helpfulness. To overcome such challenges, a modular approach employing a smaller LLM to detect harmful user queries is regarded as a convenient solution in designing LLM-based system with safety requirements. In this paper, we leverage a smaller LLM for both harmful query detection and safeguard response generation. We introduce our safety requirements and the taxonomy of harmfulness categories, and then propose a multi-task learning mechanism fusing the two tasks into a single model. We demonstrate the effectiveness of our approach, providing on par or surpassing harmful query detection and safeguard response performance compared to the publicly available LLMs.

cs.CL↗

arXiv2024

Improved weight initialization for deep and narrow feedforward neural network

Appropriate weight initialization settings, along with the ReLU activation function, have become cornerstones of modern deep learning, enabling the training and deployment of highly effective and efficient neural network models across diverse areas of artificial intelligence. The problem of \textquotedblleft dying ReLU," where ReLU neurons become inactive and yield zero output, presents a significant challenge in the training of deep neural networks with ReLU activation function. Theoretical research and various methods have been introduced to address the problem. However, even with these methods and research, training remains challenging for extremely deep and narrow feedforward networks with ReLU activation function. In this paper, we propose a novel weight initialization method to address this issue. We establish several properties of our initial weight matrix and demonstrate how these properties enable the effective propagation of signal vectors. Through a series of experiments and comparisons with existing methods, we demonstrate the effectiveness of the novel initialization method.

cs.LG↗

arXiv2024

Dense triangle-free $(n, d, λ)$-graphs for all orders

In 1994, Alon construct a triangle-free $(n,d,λ)$-graph with $d = Ω(n^{2/3})$ and $λ= O(d^{1/2})$ for an exponentially increasing sequence of integers $n$. Using his ingenious construction, we deduce that there exist triangle-free $(n,d,λ)$-graphs with $d = Ω(n^{2/3})$ and $λ= O( (d \log n)^{1/2} )$ for all sufficiently large $n$.

math.CO↗

arXiv2023

On rainbow Turán Densities of Trees

For a given collection $\mathcal{G} = (G_1,\dots, G_k)$ of graphs on a common vertex set $V$, which we call a \emph{graph system}, a graph $H$ on a vertex set $V(H) \subseteq V$ is called a \emph{rainbow subgraph} of $\mathcal{G}$ if there exists an injective function $ψ:E(H) \rightarrow [k]$ such that $e \in G_{ψ(e)}$ for each $e\in E(H)$. The maximum value of $\min_{i}\{|E(G_i)|\}$ over $n$-vertex graph systems $\mathcal{G}$ having no rainbow subgraph isomorphic to $H$ is called the rainbow Turán number $\mathrm{ex}_k^{\ast}(n, H)$ of $H$. In this article, we study the rainbow Turán density $π_k^{\ast}(T) = \lim_{n \rightarrow \infty} \frac{\mathrm{ex}_k^{\ast}(n, T)}{\binom{n}{2}}$ of a tree $T$. While the classical Turán density $π(H)$ of a graph $H$ lies in the set $\{1-\frac{1}{t} : t\in \mathbb{N}\}$, the rainbow Turán density exhibits different behaviors as it can even be an irrational number. Nevertheless, we conjecture that the rainbow Turán density is always an algebraic number. We provide evidence for this conjecture by proving that the rainbow Turán density of a tree is an algebraic number. To show this, we identify the structure of extremal graphs for rainbow trees. Moreover, we further determine all tuples $(α_1,\dots, α_k)$ such that every graph system $(G_1,\dots,G_k)$ satisfying $|E(G_i)|>(α_i+o(1))\binom{n}{2}$ contains all rainbow $k$-edge trees. In the course of proving these results, we also develop the theory on the limit of graph systems.

math.CO↗

arXiv2023

Covering multigraphs with bipartite graphs

Hansel's lemma states that $\sum_{H\in \mathcal{H}}|H| \geq n \log_2 n$ holds where $\mathcal{H}$ is a collection of bipartite graphs covering all the edges of $K_n$. We generalize this lemma to the corresponding multigraph covering problem and the graphon covering problem. We also prove an upper bound on $\sum_{H\in \mathcal{H}}|H|$ which shows that our generalization is asymptotically tight in some sense.

math.CO↗

arXiv2022

Predicting Time-to-conversion for Dementia of Alzheimer's Type using Multi-modal Deep Survival Analysis

Dementia of Alzheimer's Type (DAT) is a complex disorder influenced by numerous factors, but it is unclear how each factor contributes to disease progression. An in-depth examination of these factors may yield an accurate estimate of time-to-conversion to DAT for patients at various disease stages. We used 401 subjects with 63 features from MRI, genetic, and CDC (Cognitive tests, Demographic, and CSF) data modalities in the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. We used a deep learning-based survival analysis model that extends the classic Cox regression model to predict time-to-conversion to DAT. Our findings showed that genetic features contributed the least to survival analysis, while CDC features contributed the most. Combining MRI and genetic features improved survival prediction over using either modality alone, but adding CDC to any combination of features only worked as well as using only CDC features. Consequently, our study demonstrated that using the current clinical procedure, which includes gathering cognitive test results, can outperform survival analysis results produced using costly genetic or CSF data.

cs.LG↗

arXiv2022

On a rainbow extremal problem for color-critical graphs

There has been extensive studies on the following question: given $k$ graphs $G_1,\dots, G_k$ over a common vertex set of size $n$, what conditions on $G_i$ ensures a `colorful' copy of $H$, i.e., a copy of $H$ containing at most one edge from each $G_i$? A lower bound on $\sum_{i\in [k]} e(G_i)$ enforcing a colorful copy of a given graph $H$ was considered by Keevash, Saks, Sudakov, and Verstraëte. They defined $\operatorname{ex}_k(n,H)$ to be the maximum total number of edges of the graphs $G_1,\dots, G_k$ on a common vertex set of size $n$ having no colorful copy of $H$. They completely determined $\operatorname{ex}_k(n,K_r)$ for large $n$ by showing that, depending on the value of $k$, one of the two natural constructions is always the extremal construction. Moreover, they conjectured the same holds for every color-critical graphs and proved it for 3-color-critical graphs. We prove their conjecture for 4-color-critical graphs and for almost all $r$-color-critical graphs when $r > 4$. Moreover, we show that for every non-color-critical non-bipartite graphs, none of the two natural constructions is extremal for certain values of $k$. This answers a question of Keevash, Saks, Sudakov, and Verstraëte.

math.CO↗

arXiv2022

On 1-subdivisions of transitive tournaments

The oriented Ramsey number $\vec{r}(H)$ for an acyclic digraph $H$ is the minimum integer $n$ such that any $n$-vertex tournament contains a copy of $H$ as a subgraph. We prove that the $1$-subdivision of the $k$-vertex transitive tournament $H_k$ satisfies $\vec{r}(H_k)= O(k^2\log\log k)$. This is tight up to multiplicative $\log\log k$-term. We also show that if $T$ is an $n$-vertex tournament with $Δ^+(T)-δ^+(T)= O(n/k) - k^2$, then $T$ contains a $1$-subdivision of $\vec{K}_k$, a complete $k$-vertex digraph with all possible $k(k-1)$ arcs. This is also tight up to multiplicative constant.

math.CO↗

arXiv2022

Machine Learning Based Multimodal Neuroimaging Genomics Dementia Score for Predicting Future Conversion to Alzheimer's Disease

Background: The increasing availability of databases containing both magnetic resonance imaging (MRI) and genetic data allows researchers to utilize multimodal data to better understand the characteristics of dementia of Alzheimer's type (DAT). Objective: The goal of this study was to develop and analyze novel biomarkers that can help predict the development and progression of DAT. Methods: We used feature selection and ensemble learning classifier to develop an image/genotype-based DAT score that represents a subject's likelihood of developing DAT in the future. Three feature types were used: MRI only, genetic only, and combined multimodal data. We used a novel data stratification method to better represent different stages of DAT. Using a pre-defined 0.5 threshold on DAT scores, we predicted whether or not a subject would develop DAT in the future. Results: Our results on Alzheimer's Disease Neuroimaging Initiative (ADNI) database showed that dementia scores using genetic data could better predict future DAT progression for currently normal control subjects (Accuracy=0.857) compared to MRI (Accuracy=0.143), while MRI can better characterize subjects with stable mild cognitive impairment (Accuracy=0.614) compared to genetics (Accuracy=0.356). Combining MRI and genetic data showed improved classification performance in the remaining stratified groups. Conclusion: MRI and genetic data can contribute to DAT prediction in different ways. MRI data reflects anatomical changes in the brain, while genetic data can detect the risk of DAT progression prior to the symptomatic onset. Combining information from multimodal data in the right way can improve prediction performance.

cs.LG↗

arXiv2022

Modelling Agent-Skipping Attacks in Message Forwarding Protocols

Message forwarding protocols are protocols in which a chain of agents handles transmission of a message. Each agent forwards the received message to the next agent in the chain. For example, TLS middleboxes act as intermediary agents in TLS, adding functionality such as filtering or compressing data. In such protocols, an attacker may attempt to bypass one or more intermediary agents. Such an agent-skipping attack can the violate security requirements of the protocol. Using the multiset rewriting model in the symbolic setting, we construct a comprehensive framework of such path protocols. In particular, we introduce a set of security goals related to path integrity: the notion that a message faithfully travels through participants in the order intended by the initiating agent. We perform a security analysis of several such protocols, highlighting key attacks on modern protocols.

cs.CR↗

arXiv2021

Optimal solutions and ranks in the max-cut SDP

The max-cut problem is a classical graph theory problem which is NP-complete. The best polynomial time approximation scheme relies on \emph{semidefinite programming} (SDP). We study the conditions under which graphs of certain classes have rank~1 solutions to the max-cut SDP. We apply these findings to look at how solutions to the max-cut SDP behave under simple combinatorial constructions. Our results determine when solutions to the max-cut SDP for cycle graphs are rank~1. We find the solutions to the max-cut SDP of the vertex~sum of two graphs. We then characterize the SDP solutions upon joining two triangle graphs by an edge~sum.

math.OC↗