arXiv subjects

Thao Do

Publications and source records attributed to Thao Do.

At least 19 recordsLinked to original sources

arXiv2026

FIBER: A Differentially Private Optimizer with Filter-Aware Innovation Bias Correction

Differentially private (DP) training protects individual examples by adding noise to gradients, but the injected noise interacts nontrivially with adaptive optimizers. Recent DP methods temporally filter privatized gradients to reduce variance; however, filtering also changes the DP noise statistics seen by AdamW's second-moment accumulator. As a result, bias corrections derived for unfiltered DP noise, such as subtracting sigma_w squared, can become miscalibrated when filtering is present. We propose FiBeR, a DP optimizer designed for temporally filtered privatized gradients. FiBeR (i) performs denoising in innovation space by filtering the residual stream and integrating it to form the filtered gradient estimate, (ii) decouples the two-point observation geometry from the innovation gain to enable independent tuning, and (iii) introduces a filter-aware second-moment calibration that subtracts the attenuated DP noise contribution A(omega) sigma_w squared, where A(omega) is derived in closed form for the innovation filter and can be computed for general stable linear filters. Across vision and language benchmarks, FiBeR consistently demonstrates substantial improvements in the performance of DP optimizers, surpassing state-of-the-art results under equivalent privacy constraints on multiple tasks.

cs.LG↗

arXiv2026

SAT: Selective Aggregation Transformer for Image Super-Resolution

Transformer-based approaches have revolutionized image super-resolution by modeling long-range dependencies. However, the quadratic computational complexity of vanilla self-attention mechanisms poses significant challenges, often leading to compromises between efficiency and global context exploitation. Recent window-based attention methods mitigate this by localizing computations, but they often yield restricted receptive fields. To mitigate these limitations, we propose Selective Aggregation Transformer (SAT). This novel transformer efficiently captures long-range dependencies, leading to an enlarged model receptive field by selectively aggregating key-value matrices (reducing the number of tokens by 97\%) via our Density-driven Token Aggregation algorithm while maintaining the full resolution of the query matrix. This design significantly reduces computational costs, resulting in lower complexity and enabling scalable global interactions without compromising reconstruction fidelity. SAT identifies and represents each cluster with a single aggregation token, utilizing density and isolation metrics to ensure that critical high-frequency details are preserved. Experimental results demonstrate that SAT outperforms the state-of-the-art method PFT by up to 0.22dB, while the total number of FLOPs can be reduced by up to 27\%.

cs.CV↗

arXiv2026

LooComp: Leverage Leave-One-Out Strategy to Encoder-only Transformer for Efficient Query-aware Context Compression

Efficient context compression is crucial for improving the accuracy and scalability of question answering. For the efficiency of Retrieval Augmented Generation, context should be delivered fast, compact, and precise to ensure clue sufficiency and budget-friendly LLM reader cost. We propose a margin-based framework for query-driven context pruning, which identifies sentences that are critical for answering a query by measuring changes in clue richness when they are omitted. The model is trained with a composite ranking loss that enforces large margins for critical sentences while keeping non-critical ones near neutral. Built on a lightweight encoder-only Transformer, our approach generally achieves strong exact-match and F1 scores with high-throughput inference and lower memory requirements than those of major baselines. In addition to efficiency, our method yields effective compression ratios without degrading answering performance, demonstrating its potential as a lightweight and practical alternative for retrieval-augmented tasks.

cs.CL↗

arXiv2026

Knowing When to Answer: Adaptive Confidence Refinement for Reliable Audio-Visual Question Answering

We present a formal problem formulation for \textit{Reliable} Audio-Visual Question Answering ($\mathcal{R}$-AVQA), where we prefer abstention over answering incorrectly. While recent AVQA models have high accuracy, their ability to identify when they are likely wrong and their consequent abstention from answering remain underexplored areas of research. To fill this gap, we explore several approaches and then propose Adaptive Confidence Refinement (ACR), a lightweight method to further enhance the performance of $\mathcal{R}$-AVQA. Our key insight is that the Maximum Softmax Probability (MSP) is Bayes-optimal only under strong calibration, a condition usually not met in deep neural networks, particularly in multimodal models. Instead of replacing MSP, our ACR maintains it as a primary confidence signal and applies input-adaptive residual corrections when MSP is deemed unreliable. ACR introduces two learned heads: i) a Residual Risk Head that predicts low-magnitude correctness residuals that MSP does not capture, and ii) a Confidence Gating Head to determine MSP trustworthiness. Our experiments and theoretical analysis show that ACR consistently outperforms existing methods on in- and out-of-disrtibution, and data bias settings across three different AVQA architectures, establishing a solid foundation for $\mathcal{R}$-AVQA task. The code and checkpoints will be available upon acceptance \href{https://github.com/PhuTran1005/R-AVQA}{at here}

cs.LG↗

arXiv2025

VDInstruct: Zero-Shot Key Information Extraction via Content-Aware Vision Tokenization

Key Information Extraction (KIE) underpins the understanding of visual documents (e.g., receipts and contracts) by extracting precise semantic content and accurately capturing spatial structure. Yet existing multimodal large language models (MLLMs) often perform poorly on dense documents and rely on vision tokenization approaches that scale with image size, leading to redundant computation and memory inefficiency. To address these challenges, we introduce VDInstruct, an MLLM that separates spatial region detection from semantic feature extraction. Central to our model is a content-aware tokenization strategy: rather than fragmenting the entire image uniformly, it generates tokens in proportion to document complexity, preserving critical structure while eliminating wasted tokens. Leveraging a three-stage training paradigm, our model achieves state-of-the-art (SOTA) results on KIE benchmarks, matching or exceeding the accuracy of leading approaches while reducing the number of image tokens by roughly 3.6x. In zero-shot evaluations, VDInstruct surpasses strong baselines-such as DocOwl 1.5-by +5.5 F1 points, highlighting its robustness to unseen documents. These findings show that content-aware tokenization combined with explicit layout modeling offers a promising direction forward for document understanding. Data, source code, and model weights will be made publicly available.

cs.CV↗

arXiv2025

Global AI Governance: Where the Challenge is the Solution- An Interdisciplinary, Multilateral, and Vertically Coordinated Approach

Current global AI governance frameworks struggle with fragmented disciplinary collaboration, ineffective multilateral coordination, and disconnects between policy design and grassroots implementation. This study, guided by Integration and Implementation Science (IIS) initiated a structured interdisciplinary dialogue at the UN Science Summit, convening legal, NGO, and HCI experts to tackle those challenges. Drawing on the common ground of the experts: dynamism, experimentation, inclusivity, and paradoxical governance, this study, through thematic analysis and interdisciplinary comparison analysis, identifies four core principles of global AI governance. Furthermore, we translate these abstract principles into concrete action plans leveraging the distinct yet complementary perspectives of each discipline. These principles and action plans are then integrated into a five-phase, time-sequential framework including foundation building, experimental verification, collaborative optimization, global adaptation, and continuous evolution phases. This multilevel framework offers a novel and concrete pathway toward establishing interdisciplinary, multilateral, and vertically coordinated AI governance, transforming global AI governance challenges into opportunities for political actions.

cs.CY↗

arXiv2024

Reference-Based Post-OCR Processing with LLM for Precise Diacritic Text in Historical Document Recognition

Extracting fine-grained OCR text from aged documents in diacritic languages remains challenging due to unexpected artifacts, time-induced degradation, and lack of datasets. While standalone spell correction approaches have been proposed, they show limited performance for historical documents due to numerous possible OCR error combinations and differences between modern and classical corpus distributions. We propose a method utilizing available content-focused ebooks as a reference base to correct imperfect OCR-generated text, supported by large language models. This technique generates high-precision pseudo-page-to-page labels for diacritic languages, where small strokes pose significant challenges in historical conditions. The pipeline eliminates various types of noise from aged documents and addresses issues such as missing characters, words, and disordered sequences. Our post-processing method, which generated a large OCR dataset of classical Vietnamese books, achieved a mean grading score of 8.72 on a 10-point scale. This outperformed the state-of-the-art transformer-based Vietnamese spell correction model, which scored 7.03 when evaluated on a sampled subset of the dataset. We also trained a baseline OCR model to assess and compare it with well-known engines. Experimental results demonstrate the strength of our baseline model compared to widely used open-source solutions. The resulting dataset will be released publicly to support future studies.

cs.CL↗

arXiv2021

QuickBrowser: A Unified Model to Detect and Read Simple Object in Real-time

There are many real-life use cases such as barcode scanning or billboard reading where people need to detect objects and read the object contents. Commonly existing methods are first trying to localize object regions, then determine layout and lastly classify content units. However, for simple fixed structured objects like license plates, this approach becomes overkill and lengthy to run. This work aims to solve this detect-and-read problem in a lightweight way by integrating multi-digit recognition into a one-stage object detection model. Our unified method not only eliminates the duplication in feature extraction (one for localizing, one again for classifying) but also provides useful contextual information around object regions for classification. Additionally, our choice of backbones and modifications in architecture, loss function, data augmentation and training make the method robust, efficient and speedy. Secondly, we made a public benchmark dataset of diverse real-life 1D barcodes for a reliable evaluation, which we collected, annotated and checked carefully. Eventually, experimental results prove the method's efficiency on the barcode problem by outperforming industrial tools in both detecting and decoding rates with a real-time fps at a VGA-similar resolution. It also did a great job expectedly on the license-plate recognition task (on the AOLP dataset) by outperforming the current state-of-the-art method significantly in terms of recognition rate and inference time.

cs.CV↗

arXiv2020

Smart Inference for Multidigit Convolutional Neural Network based Barcode Decoding

Barcodes are ubiquitous and have been used in most of critical daily activities for decades. However, most of traditional decoders require well-founded barcode under a relatively standard condition. While wilder conditioned barcodes such as underexposed, occluded, blurry, wrinkled and rotated are commonly captured in reality, those traditional decoders show weakness of recognizing. Several works attempted to solve those challenging barcodes, but many limitations still exist. This work aims to solve the decoding problem using deep convolutional neural network with the possibility of running on portable devices. Firstly, we proposed a special modification of inference based on the feature of having checksum and test-time augmentation, named as Smart Inference (SI) in prediction phase of a trained model. SI considerably boosts accuracy and reduces the false prediction for trained models. Secondly, we have created a large practical evaluation dataset of real captured 1D barcode under various challenging conditions to test our methods vigorously, which is publicly available for other researchers. The experiments' results demonstrated the SI effectiveness with the highest accuracy of 95.85% which outperformed many existing decoders on the evaluation set. Finally, we successfully minimized the best model by knowledge distillation to a shallow model which is shown to have high accuracy (90.85%) with good inference speed of 34.2 ms per image on a real edge device.

cs.CV↗

arXiv2020

Dissecting Catastrophic Forgetting in Continual Learning by Deep Visualization

Interpreting the behaviors of Deep Neural Networks (usually considered as a black box) is critical especially when they are now being widely adopted over diverse aspects of human life. Taking the advancements from Explainable Artificial Intelligent, this paper proposes a novel technique called Auto DeepVis to dissect catastrophic forgetting in continual learning. A new method to deal with catastrophic forgetting named critical freezing is also introduced upon investigating the dilemma by Auto DeepVis. Experiments on a captioning model meticulously present how catastrophic forgetting happens, particularly showing which components are forgetting or changing. The effectiveness of our technique is then assessed; and more precisely, critical freezing claims the best performance on both previous and coming tasks over baselines, proving the capability of the investigation. Our techniques could not only be supplementary to existing solutions for completely eradicating catastrophic forgetting for life-long learning but also explainable.

cs.LG↗

arXiv2018

Extending Erdős- Beck's theorem to higher dimensions

Erdős-Beck theorem states that $n$ points in the plane with at most $n-x$ points collinear define at least $c xn$ lines for some positive constant $c$. In this paper, we will present two ways to extend this result to higher dimensions. Our result has application to point-hyperplane incidences and potential application to the point covering problem.

math.CO↗

arXiv2018

Zarankiewicz's problem for semi-algebraic hypergraphs

Zarankiewicz's problem asks for the largest possible number of edges in a graph that does not contain a $K_{u,u}$ subgraph for a fixed positive integer $u$. Recently, Fox, Pach, Sheffer, Sulk and Zahl considered this problem for semi-algebraic graphs, where vertices are points in $\mathbb{R}^d$ and edges are defined by some semi-algebraic relations. In this paper, we extend this idea to semi-algebraic hypergraphs. For each $k\geq 2$, we find an upper bound on the number of hyperedges in a $k$-uniform $k$-partite semi-algebraic hypergraph without $K_{u_1,\dots,u_k}$ for fixed positive integers $u_1,\dots, u_k$. When $k=2$, this bound matches the one of Fox et.al. and when $k=3$, it is $$O\left((mnp)^{\frac{2d}{2d+1}+\varepsilon}+m(np)^{\frac{d}{d+1}+\varepsilon}+n(mp)^{\frac{d}{d+1}+\varepsilon}+p(mn)^{\frac{d}{d+1}+\varepsilon}+mn+np+pm\right),$$ where $m,n,p$ are the sizes of the parts of the tripartite hypergraph and $\varepsilon$ is an arbitrarily small positive constant. We then present applications of this result to a variant of the unit area problem, the unit minor problem and intersection hypergraphs.

math.CO↗

arXiv2018

A General Incidence Bound in ${\mathbb R}^d$ and Related Problems

We derive a general upper bound for the number of incidences with $k$-dimensional varieties in ${\mathbb R}^d$. The leading term of this new bound generalizes previous bounds for the special cases of $k=1, k=d-1,$ and $k= d/2$, to every $1\le k <d$. We derive lower bounds showing that this leading term is tight in various cases. We derive a bound for incidences with transverse varieties, generalizing a result of Solymosi and Tao. Finally, we derive a bound for incidences with hyperplanes in ${\mathbb C}^d$, which is also tight in some cases. (In both ${\mathbb R}^d$ and ${\mathbb C}^d$, the bounds are tight up to sub-polynomial factors.) To prove our incidence bounds, we define the \emph{dimension ratio} of an incidence problem. This ratio provides an intuitive approach for deriving incidence bounds and isolating the main difficulties in each proof. We rely on the dimension ratio both in ${\mathbb R}^d$ and in ${\mathbb C}^d$, and also in some of our lower bounds.

math.CO↗

arXiv2018

Representation Complexity of Semi-algebraic Graphs

The representation complexity of a bipartite graph $G=(P,Q)$ is the minimum size $\sum_{i=1}^s (|A_i|+|B_i|)$ over all possible ways to write $G$ as a (not necessarily disjoint) union of complete bipartite subgraphs $G=\cup_{i=1}^s A_i\times B_i$ where $A_i\subset P, B_i\subset Q$ for $i=1,\dots, s$. In this paper we prove that if $G$ is \emph{semi-algebraic}, i.e. when $P$ is a set of $m$ points in $\mathbb{R}^{d_1}$, $Q$ is a set of $n$ points in $\mathbb{R}^{d_2}$ and the edges are defined by some semi-algebraic relations, the representation complexity of $G$ is $O( m^{\frac{d_1d_2-d_2}{d_1d_2-1}+\varepsilon} n^{\frac{d_1d_2-d_1}{d_1d_2-1}+\varepsilon}+m^{1+\varepsilon}+n^{1+\varepsilon})$ for arbitrarily small positive $\varepsilon$. This generalizes results by Apfelbaum-Sharir and Solomon-Sharir. As a consequence, when $G$ is $K_{u,u}$-free for some positive integer $u$, its number of edges is $O(u m^{\frac{d_1d_2-d_2}{d_1d_2-1}+\varepsilon} n^{\frac{d_1d_2-d_1}{d_1d_2-1}+\varepsilon}+ u m^{1+\varepsilon}+u n^{1+\varepsilon})$. This bound is stronger than that of Fox, Pach, Sheffer, Suk and Zahl when the first term dominates and $u$ grows with $m,n$. Another consequence is that we can find a large complete bipartite subgraph in a semi-algebraic graph when the number of edges is large. Similar results hold for semi-algebraic hypergraphs.

math.CO↗

arXiv2017

The k-planar crossing number of random graphs and random regular graphs

We give an explicit extension of Spencer's result on the biplanar crossing number of the Erdos-Renyi random graph $G(n,p)$. In particular, we show that the k-planar crossing number of $G(n,p)$ is almost surely $Ω((n^2p)^2)$. Along the same lines, we prove that for any fixed $k$, the $k$-planar crossing number of various models of random $d$-regular graphs is $Ω((dn)^2)$ for $d > c_0$ for some constant $c_0=c_0(k)$.

math.CO↗

arXiv2014

Sets Characterized by Missing Sums and Differences in Dilating Polytopes

A sum-dominant set is a finite set $A$ of integers such that $|A+A| > |A-A|$. As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to be rare in some sense. In 2006, however, Martin and O'Bryant showed that the proportion of sum-dominant subsets of $\{0,\dots,n\}$ is bounded below by a positive constant as $n\to\infty$. Hegarty then extended their work and showed that for any prescribed $s,d\in\mathbb{N}_0$, the proportion $ρ^{s,d}_n$ of subsets of $\{0,\dots,n\}$ that are missing exactly $s$ sums in $\{0,\dots,2n\}$ and exactly $2d$ differences in $\{-n,\dots,n\}$ also remains positive in the limit. We consider the following question: are such sets, characterized by their sums and differences, similarly ubiquitous in higher dimensional spaces? We generalize the integers in a growing interval to the lattice points in a dilating polytope. Specifically, let $P$ be a polytope in $\mathbb{R}^D$ with vertices in $\mathbb{Z}^D$, and let $ρ_n^{s,d}$ now denote the proportion of subsets of $L(nP)$ that are missing exactly $s$ sums in $L(nP)+L(nP)$ and exactly $2d$ differences in $L(nP)-L(nP)$. As it turns out, the geometry of $P$ has a significant effect on the limiting behavior of $ρ_n^{s,d}$. We define a geometric characteristic of polytopes called local point symmetry, and show that $ρ_n^{s,d}$ is bounded below by a positive constant as $n\to\infty$ if and only if $P$ is locally point symmetric. We further show that the proportion of subsets in $L(nP)$ that are missing exactly $s$ sums and at least $2d$ differences remains positive in the limit, independent of the geometry of $P$. A direct corollary of these results is that if $P$ is additionally point symmetric, the proportion of sum-dominant subsets of $L(nP)$ also remains positive in the limit.

math.NT↗

arXiv2014

A Generalization of Fibonacci Far-Difference Representations and Gaussian Behavior

A natural generalization of base B expansions is Zeckendorf's Theorem: every integer can be uniquely written as a sum of non-consecutive Fibonacci numbers $\{F_n\}$, with $F_{n+1} = F_n + F_{n-1}$ and $F_1=1, F_2=2$. If instead we allow the coefficients of the Fibonacci numbers in the decomposition to be zero or $\pm 1$, the resulting expression is known as the far-difference representation. Alpert proved that a far-difference representation exists and is unique under certain restraints that generalize non-consecutiveness, specifically that two adjacent summands of the same sign must be at least 4 indices apart and those of opposite signs must be at least 3 indices apart. We prove that a far-difference representation can be created using sets of Skipponacci numbers, which are generated by recurrence relations of the form $S^{(k)}_{n+1} = S^{(k)}_{n} + S^{(k)}_{n-k}$ for $k \ge 0$. Every integer can be written uniquely as a sum of the $\pm S^{(k)}_n $'s such that every two terms of the same sign differ in index by at least 2k+2, and every two terms of opposite signs differ in index by at least k+2. Additionally, we prove that the number of positive and negative terms in given Skipponacci decompositions converges to a Gaussian, with a computable correlation coefficient that is a rational function of the smallest root of the characteristic polynomial of the recurrence. The proof uses recursion to obtain the generating function for having a fixed number of summands, which we prove converges to the generating function of a Gaussian. We next explore the distribution of gaps between summands, and show that for any k the probability of finding a gap of length $j \ge 2k+2$ decays geometrically, with decay ratio equal to the largest root of the given k-Skipponacci recurrence. We conclude by finding sequences that have an (s,d) far-difference representation for any positive integers s,d.

math.NT↗

arXiv2014

Sums and differences of correlated random sets

Many fundamental questions in additive number theory (such as Goldbach's conjecture, Fermat's last theorem, and the Twin Primes conjecture) can be expressed in the language of sum and difference sets. As a typical pair of elements contributes one sum and two differences, we expect that $|A-A| > |A+A|$ for a finite set $A$. However, in 2006 Martin and O'Bryant showed that a positive proportion of subsets of $\{0, \dots, n\}$ are sum-dominant, and Zhao later showed that this proportion converges to a positive limit as $n \to \infty$. Related problems, such as constructing explicit families of sum-dominant sets, computing the value of the limiting proportion, and investigating the behavior as the probability of including a given element in $A$ to go to zero, have been analyzed extensively. We consider many of these problems in a more general setting. Instead of just one set $A$, we study sums and differences of pairs of \emph{correlated} sets $(A,B)$. Specifically, we place each element $a \in \{0,\dots, n\}$ in $A$ with probability $p$, while $a$ goes in $B$ with probability $ρ_1$ if $a \in A$ and probability $ρ_2$ if $a \not \in A$. If $|A+B| > |(A-B) \cup (B-A)|$, we call the pair $(A,B)$ a \emph{sum-dominant $(p,ρ_1, ρ_2)$-pair}. We prove that for any fixed $\vecρ=(p, ρ_1, ρ_2)$ in $(0,1)^3$, $(A,B)$ is a sum-dominant $(p,ρ_1, ρ_2)$-pair with positive probability, and show that this probability approaches a limit $P(\vecρ)$. Furthermore, we show that the limit function $P(\vecρ)$ is continuous. We also investigate what happens as $p$ decays with $n$, generalizing results of Hegarty-Miller on phase transitions. Finally, we find the smallest sizes of MSTD pairs.

math.NT↗