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Thai Hoang Le

Publications and source records attributed to Thai Hoang Le.

11 recordsLinked to original sources

WSS-CL: Weight Saliency Soft-Guided Contrastive Learning for Efficient Machine Unlearning Image Classification

Machine unlearning, the efficient deletion of the impact of specific data in a trained model, remains a challenging problem. Current machine unlearning approaches that focus primarily on data-centric or weight-based strategies frequently encounter challenges in achieving precise unlearning, maintaining stability, and ensuring applicability across diverse domains. In this work, we introduce a new two-phase efficient machine unlearning method for image classification, in terms of weight saliency, leveraging weight saliency to focus the unlearning process on critical model parameters. Our method is called weight saliency soft-guided contrastive learning for efficient machine unlearning image classification (WSS-CL), which significantly narrows the performance gap with "exact" unlearning. First, the forgetting stage maximizes kullback-leibler divergence between output logits and aggregated pseudo-labels for efficient forgetting in logit space. Next, the adversarial fine-tuning stage introduces contrastive learning in a self-supervised manner. By using scaled feature representations, it maximizes the distance between the forgotten and retained data samples in the feature space, with the forgotten and the paired augmented samples acting as positive pairs, while the retained samples act as negative pairs in the contrastive loss computation. Experimental evaluations reveal that our proposed method yields much-improved unlearning efficacy with negligible performance loss compared to state-of-the-art approaches, indicative of its usability in supervised and self-supervised settings.

cs.LG↗

Sums of products of fractional parts

We prove upper and lower bounds for certain sums of products of fractional parts by using majoring and minorizing functions from Fourier analysis. In special cases the upper bounds are sharp if there exist counterexamples to the Littlewood conjecture in Diophantine approximation. We introduce a generalization of such counterexamples which we call strongly badly approximable matrices. And we prove a transference principle for strongly badly approximable matrices.

math.NT↗

Polynomial configurations in the primes

The Bergelson-Leibman theorem states that if P_1, ..., P_k are polynomials with integer coefficients, then any subset of the integers of positive upper density contains a polynomial configuration x+P_1(m), ..., x+P_k(m), where x,m are integers. Various generalizations of this theorem are known. Wooley and Ziegler showed that the variable m can in fact be taken to be a prime minus 1, and Tao and Ziegler showed that the Bergelson-Leibman theorem holds for subsets of the primes of positive relative upper density. Here we prove a hybrid of the latter two results, namely that the step m in the Tao-Ziegler theorem can be restricted to the set of primes minus 1.

math.NT↗

Uniform Dilations in Higher Dimensions

A theorem of Glasner says that if $X$ is an infinite subset of the torus $\mathbb{T}$, then for any $ε>0$, there exists an integer $n$ such that the dilation $nX=\{nx: x \in \mathbb{T} \}$ is $ε$-dense (i.e, it intersects any interval of length $2ε$ in $\mathbb{T}$). Alon and Peres provided a general framework for this problem, and showed quantitatively that one can restrict the dilation to be of the form $f(n)X$ where $f \in \mathbb{Z}[x]$ is not constant. Building upon the work of Alon and Peres, we study this phenomenon in higher dimensions. Let ${\bf A}(x)$ be an $L \times N$ matrix whose entries are in $\mathbb{Z}[x]$, and $X$ be an infinite subset of $\mathbb{T}^N$. Contrarily to the case $N=L=1$, it's not always true that there is an integer $n$ such that $\bA(n)X$ is $ε$-dense in a translate of a subtorus of $\mathbb{T}^{L}$. We give a necessary and sufficient condition for matrices ${\bf A}$ for which this is true. We also prove an effective version of the result.

math.NT↗

Face Alignment Using Active Shape Model And Support Vector Machine

The Active Shape Model (ASM) is one of the most popular local texture models for face alignment. It applies in many fields such as locating facial features in the image, face synthesis, etc. However, the experimental results show that the accuracy of the classical ASM for some applications is not high. This paper suggests some improvements on the classical ASM to increase the performance of the model in the application: face alignment. Four of our major improvements include: i) building a model combining Sobel filter and the 2-D profile in searching face in image; ii) applying Canny algorithm for the enhancement edge on image; iii) Support Vector Machine (SVM) is used to classify landmarks on face, in order to determine exactly location of these landmarks support for ASM; iv)automatically adjust 2-D profile in the multi-level model based on the size of the input image. The experimental results on Caltech face database and Technical University of Denmark database (imm_face) show that our proposed improvement leads to far better performance.

cs.CV↗

Face Recognition Based on SVM and 2DPCA

The paper will present a novel approach for solving face recognition problem. Our method combines 2D Principal Component Analysis (2DPCA), one of the prominent methods for extracting feature vectors, and Support Vector Machine (SVM), the most powerful discriminative method for classification. Experiments based on proposed method have been conducted on two public data sets FERET and AT&T; the results show that the proposed method could improve the classification rates.

cs.CV↗

Intersective polynomials and the primes

Intersective polynomials are polynomials in $\Z[x]$ having roots every modulus. For example, $P_1(n)=n^2$ and $P_2(n)=n^2-1$ are intersective polynomials, but $P_3(n)=n^2+1$ is not. The purpose of this note is to deduce, using results of Green-Tao \cite{gt-chen} and Lucier \cite{lucier}, that for any intersective polynomial $h$, inside any subset of positive relative density of the primes, we can find distinct primes $p_1, p_2$ such that $p_1-p_2=h(n)$ for some integer $n$. Such a conclusion also holds in the Chen primes (where by a Chen prime we mean a prime number $p$ such that $p+2$ is the product of at most 2 primes).

math.NT↗

On a question of Sárközy on gaps of product sequences

Motivated by a question of Sárközy, we study the gaps in the product sequence $\B=\A ... \A=\{b_n=a_ia_j, a_i,a_j\in \A\}$ when $\A$ has upper Banach density $α>0$. We prove that there are infinitely many gaps $b_{n+1}-b_n\ll α^{-3}$ and that for $t\ge2$ there are infinitely many $t$-gaps $b_{n+t}-b_{n}\ll t^2α^{-4}$. Furthermore we prove that these estimates are best possible. We also discuss a related question about the cardinality of the quotient set $\A/\A=\{a_i/a_j, a_i,a_j\in \A\}$ when $\A\subset\{1,..., N\}$ and $|\A|=αN$.

math.NT↗

Green-Tao theorem in function fields

We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every $k$, the irreducible polynomials in $\mathbf{F}_q[t]$ contain configurations of the form $\{f+ Pg : \d(P)<k \}, g \neq 0$.

math.NT↗