arXiv subjects

Jie Han

Publications and source records attributed to Jie Han.

At least 73 records · Page 4Linked to original sources

arXiv2023

A Survey on Approximate Multiplier Designs for Energy Efficiency: From Algorithms to Circuits

Given the stringent requirements of energy efficiency for Internet-of-Things edge devices, approximate multipliers, as a basic component of many processors and accelerators, have been constantly proposed and studied for decades, especially in error-resilient applications. The computation error and energy efficiency largely depend on how and where the approximation is introduced into a design. Thus, this article aims to provide a comprehensive review of the approximation techniques in multiplier designs ranging from algorithms and architectures to circuits. We have implemented representative approximate multiplier designs in each category to understand the impact of the design techniques on accuracy and efficiency. The designs can then be effectively deployed in high-level applications, such as machine learning, to gain energy efficiency at the cost of slight accuracy loss.

cs.AR↗

arXiv2023

Decoupled Rationalization with Asymmetric Learning Rates: A Flexible Lipschitz Restraint

A self-explaining rationalization model is generally constructed by a cooperative game where a generator selects the most human-intelligible pieces from the input text as rationales, followed by a predictor that makes predictions based on the selected rationales. However, such a cooperative game may incur the degeneration problem where the predictor overfits to the uninformative pieces generated by a not yet well-trained generator and in turn, leads the generator to converge to a sub-optimal model that tends to select senseless pieces. In this paper, we theoretically bridge degeneration with the predictor's Lipschitz continuity. Then, we empirically propose a simple but effective method named DR, which can naturally and flexibly restrain the Lipschitz constant of the predictor, to address the problem of degeneration. The main idea of DR is to decouple the generator and predictor to allocate them with asymmetric learning rates. A series of experiments conducted on two widely used benchmarks have verified the effectiveness of the proposed method. Codes: \href{https://github.com/jugechengzi/Rationalization-DR}{https://github.com/jugechengzi/Rationalization-DR}.

cs.LG↗

arXiv2023

On powers of Hamilton cycles in Ramsey-Turán Theory

We prove that for $r\in \mathbb{N}$ with $r\geq 2$ and $μ>0$, there exist $α>0$ and $n_{0}$ such that for every $n\geq n_{0}$, every $n$-vertex graph $G$ with $δ(G)\geq \left(1-\frac{1}{r}+μ\right)n$ and $α(G)\leq αn$ contains an $r$-th power of a Hamilton cycle. We also show that the minimum degree condition is asymptotically sharp for $r=2, 3$ and the $r=2$ case was recently conjectured by Staden and Treglown.

math.CO↗

arXiv2023

Transversal Hamilton cycle in hypergraph systems

A $k$-graph system $\textbf{H}=\{H_i\}_{i\in[m]}$ is a family of not necessarily distinct $k$-graphs on the same $n$-vertex set $V$ and a $k$-graph $H$ on $V$ is said to be $\textbf{H}$-transversal provided that there exists an injection $φ: E(H)\rightarrow [m]$ such that $e\in E(H_{φ(e)})$ for all $e\in E(H)$. We show that given $k\geq3, γ>0$, sufficiently large $n$ and an $n$-vertex $k$-graph system $\textbf{H}=\{H_i\}_{i\in[n]}$, if $δ_{k-1}(H_i)\geq(1/2+γ)n$ for each $i\in[n]$, then there exists an $\textbf{H}$-transversal tight Hamilton cycle. This extends the result of Rödl, Ruciński and Szemerédi [Combinatorica, 2008] on single $k$-graphs.

math.CO↗

arXiv2023

Clique-factors in graphs with sublinear $\ell$-independence number

Given a graph $G$ and an integer $\ell\ge 2$, we denote by $α_{\ell}(G)$ the maximum size of a $K_{\ell}$-free subset of vertices in $V(G)$. A recent question of Nenadov and Pehova asks for determining the best possible minimum degree conditions forcing clique-factors in $n$-vertex graphs $G$ with $α_{\ell}(G) = o(n)$, which can be seen as a Ramsey--Turán variant of the celebrated Hajnal--Szemerédi theorem. In this paper we find the asymptotical sharp minimum degree threshold for $K_r$-factors in $n$-vertex graphs $G$ with $α_\ell(G)=n^{1-o(1)}$ for all $r\ge \ell\ge 2$.

math.CO↗

arXiv2023

Spanning trees in sparse expanders

Given integers $n\ge Δ\ge 2$, let $\mathcal{T}(n, Δ)$ be the collection of all $n$-vertex trees with maximum degree at most $Δ$. A question of Alon, Krivelevich and Sudakov in 2007 asks for determining the best possible spectral gap condition forcing an $(n, d,λ)$-graph to be $\mathcal{T}(n, Δ)$-universal, namely, it contains all members of $\mathcal{T}(n, Δ)$ as a subgraph simultaneously. In this paper we show that for sufficiently large integer $n$ and all $Δ\in \mathbb{N}$, every $(n, d,λ)$-graph with \[ λ\le\frac{d}{2Δ^{5\sqrt{\log n}}} \] is $\mathcal{T}(n, Δ)$-universal. As an immediate corollary, this implies that Alon's ingenious construction of triangle-free sparse expander is $\mathcal{T}(n, Δ)$-universal, which provides an explicit construction of such graphs and thus solves a question of Johannsen, Krivelevich and Samotij. Our main result is formulated under a much more general context, namely, the $(n,d)$-expanders. More precisely, we show that there exist absolute constants $C,c>0$ such that the following statement holds for sufficiently large integer $n$. (1).For all $Δ\in \mathbb{N}$, every $(n, Δ^{5\sqrt{\log n}})$-expander is $\mathcal{T}(n, Δ)$-universal. (2).For all $Δ\in \mathbb{N}$ with $Δ\le c\sqrt{n}$, every $(n, CΔn^{1/2})$-expander is $\mathcal{T}(n, Δ)$-universal. Both results significantly improve a result of Johannsen, Krivelevich and Samotij, and have further implications in locally sparse expanders and Maker-Breaker games that also improve previously known results drastically.

math.CO↗

arXiv2023

Spanning trees in graphs without large bipartite holes

We show that for any $\varepsilon>0$ and $Δ\in\mathbb{N}$, there exists $α>0$ such that for sufficiently large $n$, every $n$-vertex graph $G$ satisfying that $δ(G)\geq\varepsilon n$ and $e(X, Y)>0$ for every pair of disjoint vertex sets $X, Y\subseteq V(G)$ of size $αn$ contains all spanning trees with maximum degree at most $Δ$. This strengthens a result of Böttcher et al.

math.CO↗

arXiv2022

Tiling multipartite hypergraphs in Quasi-random Hypergraphs

Given $k\ge 2$ and two $k$-graphs ($k$-uniform hypergraphs) $F$ and $H$, an \emph{$F$-factor} in $H$ is a set of vertex disjoint copies of $F$ that together covers the vertex set of $H$. Lenz and Mubayi studied the $F$-factor problems in quasi-random $k$-graphs with minimum degree $Ω(n^{k-1})$. In particular, they constructed a sequence of $1/8$-dense quasi-random $3$-graphs $H(n)$ with minimum degree $Ω(n^2)$ and minimum codegree $Ω(n)$ but with no $K_{2,2,2}$-factor. We prove that if $p>1/8$ and $F$ is a $3$-partite $3$-graph with $f$ vertices, then for sufficiently large $n$, all $p$-dense quasi-random $3$-graphs of order $n$ with minimum codegree $Ω(n)$ and $f\mid n$ have $F$-factors. That is, $1/8$ is the density threshold for ensuring all $3$-partite $3$-graphs $F$-factors in quasi-random $3$-graphs given a minimum codegree condition $Ω(n)$. Moreover, we show that one can not replace the minimum codegree condition by a minimum vertex degree condition. In fact, we find that for any $p\in(0,1)$ and $n\ge n_0$, there exist $p$-dense quasi-random $3$-graphs of order $n$ with minimum degree $Ω(n^2)$ having no $K_{2,2,2}$-factor. In particular, we study the optimal density threshold of $F$-factors for each $3$-partite $3$-graph $F$ in quasi-random $3$-graphs given a minimum codegree condition $Ω(n)$.

math.CO↗

arXiv2022

Improving Adversarial Robustness with Self-Paced Hard-Class Pair Reweighting

Deep Neural Networks are vulnerable to adversarial attacks. Among many defense strategies, adversarial training with untargeted attacks is one of the most effective methods. Theoretically, adversarial perturbation in untargeted attacks can be added along arbitrary directions and the predicted labels of untargeted attacks should be unpredictable. However, we find that the naturally imbalanced inter-class semantic similarity makes those hard-class pairs become virtual targets of each other. This study investigates the impact of such closely-coupled classes on adversarial attacks and develops a self-paced reweighting strategy in adversarial training accordingly. Specifically, we propose to upweight hard-class pair losses in model optimization, which prompts learning discriminative features from hard classes. We further incorporate a term to quantify hard-class pair consistency in adversarial training, which greatly boosts model robustness. Extensive experiments show that the proposed adversarial training method achieves superior robustness performance over state-of-the-art defenses against a wide range of adversarial attacks.

cs.CV↗

arXiv2022

On powers of tight Hamilton cycles in randomly perturbed hypergraphs

For integers $k \geq 3$ and $r\geq 2$, we show that for every $α> 0$, there exists $\varepsilon > 0$ such that the union of $k$-uniform hypergraph on $n$ vertices with minimum codegree at least $αn$ and a binomial random $k$-uniform hypergraph $G^{(k)}(n,p)$ with $p\geq n^{-{\binom{k+r-2}{k-1}}^{-1}-\varepsilon}$ on the same vertex set contains the $r^{th}$ power of a tight Hamilton cycle with high probability. Moreover, a construction shows that one cannot take $\varepsilon > Cα$, where $C=C(k,r)$ is a constant. Thus the bound on $p$ is optimal up to the value of $\varepsilon$ and this answers a question of Bedenknecht, Han, Kohayakawa, and Mota.

math.CO↗

arXiv2022

Matching of given sizes in hypergraphs

For all integers $k,d$ such that $k \geq 3$ and $k/2\leq d \leq k-1$, let $n$ be a sufficiently large integer {\rm(}which may not be divisible by $k${\rm)} and let $s\le \lfloor n/k\rfloor-1$. We show that if $H$ is a $k$-uniform hypergraph on $n$ vertices with $δ_{d}(H)>\binom{n-d}{k-d}-\binom{n-d-s+1}{k-d}$, then $H$ contains a matching of size $s$. This improves a recent result of Lu, Yu, and Yuan and also answers a question of Kühn, Osthus, and Townsend. In many cases, our result can be strengthened to $s\leq \lfloor n/k\rfloor$, which then covers the entire possible range of $s$. On the other hand, there are examples showing that the result does not hold for certain $n, k, d$ and $s= \lfloor n/k\rfloor$.

math.CO↗

arXiv2022

Semantic Compression with Side Information: A Rate-Distortion Perspective

We consider the semantic rate-distortion problem motivated by task-oriented video compression. The semantic information corresponding to the task, which is not observable to the encoder, shows impacts on the observations through a joint probability distribution. The similarities among intra-frame segments and inter-frames in video compression are formulated as side information available at both the encoder and the decoder. The decoder is interested in recovering the observation and making an inference of the semantic information under certain distortion constraints. We establish the information-theoretic limits for the tradeoff between compression rates and distortions by fully characterizing the rate-distortion function. We further evaluate the rate-distortion function under specific Markov conditions for three scenarios: i) both the task and the observation are binary sources; ii) the task is a binary classification of an integer observation as even and odd; iii) Gaussian correlated task and observation. We also illustrate through numerical results that recovering only the semantic information can reduce the coding rate comparing to recovering the source observation.

cs.IT↗

arXiv2022

$H$-factors in graphs with small independence number

Let $H$ be an $h$-vertex graph. The vertex arboricity $ar(H)$ of $H$ is the least integer $r$ such that $V(H)$ can be partitioned into $r$ parts and each part induces a forest in $H$. We show that for sufficiently large $n\in h\mathbb{N}$, every $n$-vertex graph $G$ with $δ(G)\geq \max\left\{\left(1-\frac{2}{f(H)}+o(1)\right)n, \left(\frac{1}{2}+o(1)\right)n\right\}$ and $α(G)=o(n)$ contains an $H$-factor, where $f(H)=2ar(H)$ or $2ar(H)-1$. The result can be viewed an analogue of the Alon--Yuster theorem \cite{MR1376050} in Ramsey--Turán theory, which generalises the results of Balogh--Molla--Sharifzadeh~\cite{MR3570984} and Knierm--Su~\cite{MR4193066} on clique factors. In particular the degree conditions are asymptotically sharp for infinitely many graphs $H$ which are not cliques.

math.CO↗

arXiv2022

Dropout Prediction Uncertainty Estimation Using Neuron Activation Strength

Dropout has been commonly used to quantify prediction uncertainty, i.e, the variations of model predictions on a given input example. However, using dropout in practice can be expensive as it requires running dropout inferences many times. In this paper, we study how to estimate dropout prediction uncertainty in a resource-efficient manner. We demonstrate that we can use neuron activation strengths to estimate dropout prediction uncertainty under different dropout settings and on a variety of tasks using three large datasets, MovieLens, Criteo, and EMNIST. Our approach provides an inference-once method to estimate dropout prediction uncertainty as a cheap auxiliary task. We also demonstrate that using activation features from a subset of the neural network layers can be sufficient to achieve uncertainty estimation performance almost comparable to that of using activation features from all layers, thus reducing resources even further for uncertainty estimation.

cs.LG↗

arXiv2022

Cover 3-uniform hypergraphs by vertex-disjoint tight paths

Let $H$ be an $n$-vertex 3-uniform hypergraph such that every pair of vertices is in at least $n/3+o(n)$ edges. We show that $H$ contains two vertex-disjoint tight paths whose union covers the vertex set of $H$. The quantity two here is best possible and the degree condition is asymptotically best possible. This result also has an interpretation as the \emph{deficiency problems}, recently introduced by Nenadov, Sudakov and Wagner: every such $H$ can be made Hamiltonian by adding at most two vertices and all triples intersecting them.

math.CO↗

arXiv2022

Adversarial Fine-tune with Dynamically Regulated Adversary

Adversarial training is an effective method to boost model robustness to malicious, adversarial attacks. However, such improvement in model robustness often leads to a significant sacrifice of standard performance on clean images. In many real-world applications such as health diagnosis and autonomous surgical robotics, the standard performance is more valued over model robustness against such extremely malicious attacks. This leads to the question: To what extent we can boost model robustness without sacrificing standard performance? This work tackles this problem and proposes a simple yet effective transfer learning-based adversarial training strategy that disentangles the negative effects of adversarial samples on model's standard performance. In addition, we introduce a training-friendly adversarial attack algorithm, which facilitates the boost of adversarial robustness without introducing significant training complexity. Extensive experimentation indicates that the proposed method outperforms previous adversarial training algorithms towards the target: to improve model robustness while preserving model's standard performance on clean data.

cs.LG↗

arXiv2022

$F$-factors in Quasi-random Hypergraphs

Given $k\ge 2$ and two $k$-graphs ($k$-uniform hypergraphs) $F$ and $H$, an $F$-factor in $H$ is a set of vertex-disjoint copies of $F$ that together covers the vertex set of $H$. Lenz and Mubayi [J. Combin. Theory Ser. B, 2016] studied the $F$-factor problem in quasi-random $k$-graphs with minimum degree $Ω(n^{k-1})$. They posed the problem of characterizing the $k$-graphs $F$ such that every sufficiently large quasi-random $k$-graph with constant edge density and minimum degree $Ω(n^{k-1})$ contains an $F$-factor, and in particular, they showed that all linear $k$-graphs satisfy this property. In this paper we prove a general theorem on $F$-factors which reduces the $F$-factor problem of Lenz and Mubayi to a natural sub-problem, that is, the $F$-cover problem. By using this result, we answer the question of Lenz and Mubayi for those $F$ which are $k$-partite $k$-graphs, and for all 3-graphs $F$, separately. Our characterization result on 3-graphs is motivated by the recent work of Reiher, Rödl and Schacht [J. Lond. Math. Soc., 2018] that classifies the 3-graphs with vanishing Turán density in quasi-random $k$-graphs.

math.CO↗

arXiv2021

Structural Entropy of the Stochastic Block Models

With the rapid expansion of graphs and networks and the growing magnitude of data from all areas of science, effective treatment and compression schemes of context-dependent data is extremely desirable. A particularly interesting direction is to compress the data while keeping the "structural information" only and ignoring the concrete labelings. Under this direction, Choi and Szpankowski introduced the structures (unlabeled graphs) which allowed them to compute the structural entropy of the Erdős--Rényi random graph model. Moreover, they also provided an asymptotically optimal compression algorithm that (asymptotically) achieves this entropy limit and runs in expectation in linear time. In this paper, we consider the Stochastic Block Models with an arbitrary number of parts. Indeed, we define a partitioned structural entropy for Stochastic Block Models, which generalizes the structural entropy for unlabeled graphs and encodes the partition information as well. We then compute the partitioned structural entropy of the Stochastic Block Models, and provide a compression scheme that asymptotically achieves this entropy limit.

cs.IT↗