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Binh T. Nguyen

Publications and source records attributed to Binh T. Nguyen.

At least 19 recordsLinked to original sources
arXiv2026

PhoPunct: A Large-Scale Benchmark of Transformer Architectures for Vietnamese Punctuation Restoration

Vietnamese punctuation restoration is often evaluated on relatively small benchmarks, limiting conclusions about how architectural choices scale with data volume. We present a controlled benchmark on News and Novels corpora containing 22.1 million labeled tokens (19.9M News and 2.2M Novels). We evaluate 17 architectures formed from four pretrained Transformer backbones and optional bidirectional long short-term memory (Bi-LSTM) and conditional random field (CRF) layers, together with a PhoBERT-large-Bi-LSTM-CRF model, PhoPunct. Every model is trained for eight epochs with the same learning rate and without architecture-specific tuning. Under this fixed budget, adding Bi-LSTM and CRF layers does not reliably improve macro F1: in seven of eight matched domain-backbone comparisons, a plain Transformer classifier matches or outperforms its Bi-LSTM-CRF counterpart. PhoPunct obtains the best News result (61.35), whereas XLM-R with a CRF obtains the best Novels result (50.18), exceeding PhoPunct (48.97). These results show that the value of recurrent and structured-prediction heads depends on their optimization regime and motivate explicit separation between architectural improvements and improvements due to architecture-specific tuning. Our source code is available at: https://github.com/aisia-research-lab/PhoPunct

cs.CL↗
arXiv2026

The Sparse-Complement Conjecture for Two Distinct Eigenvalues

For a graph $G$, let $q(G)$ be the minimum number of distinct eigenvalues of a real symmetric matrix whose off-diagonal zero--nonzero pattern is $G$. We prove that $q(G)=2$ whenever the complement $H=\overline G$ of a graph of order $n\ge3$ has at most $n-3$ edges, resolving the sparse-complement conjecture of Fallat and Mojallal. If $H$ contains a cycle, the proof constructs a nontrivial orthogonal projector with the strong spectral property and rank at most $|E(F)|-|V(F)|+4$, where $F$ is the union of the cyclic components of $H$. The construction combines faithful stress-free Gram representations, a one-coordinate lift for each excess core edge, exact orthogonal-frame completion, and a Stiefel-manifold pendant-extension argument.

math.CO↗
arXiv2026

MemoCare: An Interactive Multimodal Mobile System for Automated Cognitive Screening

MemoCare is a React Native mobile system for automated multimodal cognitive screening in English and Vietnamese. It integrates speech, temporal and spatial orientation, touchscreen interaction, and visuoconstruction. Google Speech-to-Text transcripts are scored with deterministic, task-specific rules. GPS-grounded current and historical administrative names support location scoring, touch events verify actions, and lightweight convolutional neural networks evaluate drawings. A separate model provides visual interpretation. Software verification passed 151/151 predefined language, spatial-answer, and touch-scoring regression cases and 48/48 fixed-coordinate spatial tests across four countries. Transcript-based tests exclude speech recognition accuracy. On a locked 71-image test set, validation-selected ShuffleNetV2 x1.5 achieved 91.33% mean balanced accuracy and 78.87% exact three-criterion accuracy. Four clinician co-authors rated the workflow (pooled median 4/5 across eight criteria; item medians 3-4.5), highlighting improvements needed in speech handling, response acceptance, and result transparency. The workflow automatically produces item-level and total scores.

cs.MM↗
arXiv2026

Birth-Death Structural Learning for 3D Gaussian Splatting

3D Gaussian Splatting (3DGS) has become a standard representation for real-time novel-view synthesis. Yet, its quality-efficiency trade-off still relies heavily on adaptive density control. Existing cloning, splitting, and pruning rules use proxy signals, such as position gradients, opacity, and image-space error. Although effective in practice, these signals do not directly answer the structural question behind density control: where should new Gaussians be allocated to reduce the multi-view reconstruction loss, and which existing primitives can be pruned with minimal penalty. To address this, we propose first-variation birth-death control for 3DGS, a principled approach that replaces heuristic structural decisions with a variational score derived from the reconstruction loss. At each structural update, we freeze the current Gaussian population, attach auxiliary mass coordinates to each primitive, and differentiate the multiview loss with respect to these coordinates. We demonstrate that this score is a coordinate of the first variation of the Splat Regression Model, giving a rigorous local descent surrogate for birth-death moves: high-score Gaussians are selected as birth sites, while low-score, low-opacity Gaussians are selected for removal. Across standard 3DGS benchmarks, integrating this score into 3DGS-MCMC yields state-of-the-art reconstruction quality and outperforms existing methods, delivering the most significant gains under tight Gaussian budgets. Ultimately, our work provides compelling evidence that gradient-based variational metrics offer a principled alternative to proxy heuristics in 3DGS.

cs.CV↗
arXiv2026

Adaptive Restart under Unknown KL Geometry in Stochastic Weakly-Convex Optimization

KL geometry accelerates restart schedules in stochastic weakly-convex optimization, but the schedule depends jointly on an unknown and potentially nonunique geometric description. We introduce CARP-KL, a certified portfolio that adapts over valid KL descriptions while using the same primitive stochastic-subgradient oracle for both optimization and candidate selection. Over declared polynomial parameter ranges, CARP-KL competes with every affordable valid description and preserves the known-description polynomial Moreau-stationarity rate up to logarithmic factors, without objective values, an exact proximal map, direct Moreau-gradient access, or a bounded-domain assumption. Controlled experiments quantify the finite-budget price of this universality. The portfolio repeatedly contains strong candidates, while certification consumes a substantial share of the oracle budget and finite-sample ranking limits their recovery. A common conservative gap bound further reduces the portfolio from $O(\log^3 T)$ to $O(\log^2 T)$ candidates with an explicit scale-mismatch penalty. The theory and diagnostics together establish certified unknown-geometry adaptation and pinpoint selection as the principal practical frontier of the current construction.

math.OC↗
arXiv2026

ERCLIP: Small-Data Adaptation of CLIP for Free-Length Image-Text Retrieval

CLIP's 77-token text encoder truncates detailed image descriptions. We present ERCLIP, a small-data adaptation of CLIP for long-caption image--text retrieval. During training, a long caption is split into sentences that the CLIP text encoder encodes independently; the sentence embeddings are fused by mean pooling or a gated residual Transformer scorer and receive their own contrastive loss. At inference ERCLIP is an unmodified CLIP dual encoder: test captions are still read through the 77-token window, and only training sees the full caption. We find that this fine-tuning erodes CLIP's zero-shot classification, most when the fusion output is not a combination of CLIP embeddings, and add a frozen-CLIP preservation loss on the image and short-caption embeddings. With 20k pairs and one epoch, ERCLIP improves long-caption R@1 over CLIP by 6.5--11.2 points, closing 62--77% of the gap to LongCLIP with 2% of its long captions. Preservation recovers 1.5--2.1 ImageNet zero-shot points (30--42% of the loss) and adds up to 2.4 points of COCO image-to-text R@1, at no inference cost.

cs.IR↗
arXiv2026

Wasserstein Robust Classification Error: Surrogate Loss Misalignment and Distributional Attacks

Wasserstein distributionally robust optimization (WDRO) provides a framework for evaluating model robustness through the worst-case expectation in the Wasserstein ball around a reference distribution. We prove that ordering hypotheses by increasing WDRO risk is equivalent to ordering them by decreasing robust accuracy if and only if the loss function is a positive multiple of the zero-one loss plus a label-dependent offset. For a class of loss functions including cross-entropy, we show that a hypothesis with perfect robust accuracy can conversely have a higher WDRO risk than another hypothesis with near zero robust accuracy. To evaluate robust accuracy directly, we develop Wasserstein distributional attacks (WDA), which add a weight generation stage after candidate support search to optimize the allocation of empirical mass under the Wasserstein constraint, rather than assigning each data point's full mass to one returned attack point as existing methods do. We further introduce a support-search algorithm for WDA that finds nearby misclassified inputs. On CIFAR-10, CIFAR-100, and ImageNet, WDA using our search algorithm achieves the lowest adversarial accuracy in most tested settings. Our code is available at https://github.com/OLab-Repo/WDA.

cs.LG↗
arXiv2026

How Finite-Rank Bottlenecks Shape the Low-Rank Adaptation Landscape

Low-rank adaptation (LoRA) has become the standard method for parameter-efficient fine-tuning of large pretrained models, yet theoretical explanations for why low-rank updates suffice remain incomplete. Most existing analyses rely on the Neural Tangent Kernel (NTK) regime, which linearizes the network around the pretrained weights. In this work, we take a different approach that requires no linearization: our key observation is that, once the backbone is frozen, the loss sees each adapted weight matrix only through a finite-rank linear map induced by the frozen activations. Trace-norm regularization then forces the optimizer to pick a low-rank matrix among all matrices that produce the same observed output. This yields global minimizers whose ranks are controlled by the rank of this map, which we call the \emph{bottleneck rank}, rather than the sample size. For multi-head attention, we obtain tighter rank upper bounds by exploiting two additional invariances: row-wise softmax is insensitive to additive row constants in the score matrix, and value updates are observable only after attention weighting and frozen output projection. For the factorized LoRA objective with weight decay, we prove a complementary result on the nonconvex side: after an arbitrarily small generic positive semidefinite perturbation, every first-order stationary point is rank-deficient once the LoRA rank exceeds a threshold determined by the bottleneck rank. Finally, we show that global minimizers of the perturbed objective are near-optimal for the original trace-norm problem, and we provide uniform generalization bounds governed by the spectral structure of the frozen features.

cs.LG↗
arXiv2026

Curvature, Scaling, and Complexity in Riemannian Projection-Free Optimization

Projection-free methods replace projections by linear minimization oracles, making their convergence fundamentally sensitive to the geometry of the feasible region. We develop a geometric framework for this dependence in Riemannian Frank--Wolfe optimization. A power-type double-geodesic modulus quantifies the intrinsic geometry of the feasible set, and an exact transfer principle shows that this modulus induces a Frank--Wolfe scaling margin modulated by the differential of the Riemannian logarithm map. The resulting factorization separates the contributions of feasible-set geometry and ambient Riemannian distortion. Rauch comparison provides explicit curvature-dependent certificates for this distortion, while on the positive-definite cone equipped with the affine-invariant metric the logarithm differential admits an exact spectral characterization in terms of relative eigenvalue spread. Combined with a quadratic error bound, the power-type geometry yields the convergence rate $O(t^{-p/(p-1)})$ for the gap-feedback short-step policy. For every fixed $p>3$, a compact feasible set in a hyperbolic plane attains the matching rate $Θ(t^{-p/(p-1)})$ under the same policy. The geometry-derived exponent $p/(p-1)$ is therefore sharp for the gap-feedback short-step policy over the geometry-controlled class considered here.

math.OC↗
arXiv2026

Certificate-Coupled DCA for the Trust-Region Subproblem: Early Structural Escape and Progressive Global Certification

We study the nonconvex trust-region subproblem by a certificate-coupled difference-of-convex algorithm that incorporates spectral information before exact first-order stationarity is attained. The method maintains a persistent randomized Krylov subspace together with the DCA iterates. Near stationarity, a sufficiently negative shifted Rayleigh quotient yields an explicit feasible correction with a quantitative decrease in the objective value; otherwise, completion of a prescribed Lanczos depth provides, with high probability, an approximate positive-semidefiniteness certificate. The same Krylov subspace also provides a certified upper bound on the largest eigenvalue for selecting the DC curvature parameter at subsequent accuracy stages. We prove a uniform negative-curvature correction result over the trust region, covering the near-orthogonal hard-case regime, together with finite-termination and work bounds at fixed tolerances and a quantitative objective-gap certificate. Under a progressive accuracy schedule, the certified objective values converge to the global optimum and the iterates converge in distance to the global solution set, while the Krylov subspace is retained across corrections and accuracy stages. Numerical experiments illustrate the phenomena established by the analysis: negative-curvature corrections can occur before the corresponding post-convergence spectral corrections, the quantitative decrease bound is satisfied in all tested near-orthogonal instances, and retaining the Krylov subspace reduces the median number of spectral matrix-vector products by approximately a factor of $2.6$ relative to restarting the spectral process in the controlled comparison.

math.OC↗
arXiv2026

Uniform High-Frequency Localization on Quantum Graphs

We study uniform high-frequency localization for the Laplacian on compact metric graphs through the least $L^2$-mass that eigenfunctions must place in a prescribed measurable observation set. We first identify this asymptotic localization constant with the minimum of a linear functional over the attainable edge-intensity set; in the generic standard-Kirchhoff setting, this set is governed by the regular Gauss image of the secular manifold. Primitive cycles and exterior-to-exterior paths consequently determine the positivity threshold, but not, in general, the positive numerical value. We introduce a boundary-aware singular-completion cone and prove that it contains all regular secular edge-energy vectors for trees, unicyclic graphs, and closed graphs of cycle rank two. We then construct a cycle-rank-two graph with two Dirichlet leaves for which this completion principle fails. An exact rational separator, combined with a validated Krawczyk enclosure, yields a nonsingular scalar secular state lying outside every boundary-compatible singular sector. A positive radial derivative identity and recurrence in the compact orbit closure convert this local separation into an exact high-frequency eigensequence for a single fixed metric. For a suitable measurable observation set, the true high-frequency localization constant $C_\infty(ω;\ell)$ and its singular-completion counterpart $C_{\mathrm{sing}}(ω;\ell)$ satisfy $$C_\infty(ω;\ell)<1/2<C_{\mathrm{sing}}(ω;\ell)$$. Thus, singular completion captures the quantitative localization geometry in several low-complexity classes but does not, in general, determine the high-frequency variational problem on a fixed quantum graph.

math.SP↗
arXiv2026

HANCLIP: A Family of Hyperbolic Angular Negation Vision Language Models

Vision-language models (VLMs) achieve strong cross-modal alignment but remain brittle to negation, often relying on shallow word associations rather than compositional reasoning. Fine-tuning on negation-specific data can also compromise their general purpose capabilities through catastrophic forgetting. We introduce HANCLIP (Hyperbolic, Angular, and Negation), a geometry-aware framework that improves negation sensitivity while preserving the structure of the pretrained joint embedding space. HANCLIP combines a hyperbolic contrastive objective, which models hierarchical relations and semantic asymmetries, with an angular triplet loss that separates negated descriptions from their affirmative counterparts. Using only 20,000 image-text quadruplets, HANCLIP consistently improves performance across CLIP, LongCLIP, and SmartCLIP backbones on the NegBench benchmark, while maintaining or improving zero-shot classification and image-text retrieval performance. These results show that lightweight, geometry-guided objectives can enhance negation understanding without large-scale retraining.

cs.CV↗
arXiv2026

Uniform Eigenfunction Observability under Mixed Reflection Monodromy

We study uniform observability for Laplace eigenfunctions with mixed boundary conditions whose reflection signs do not define a scalar character. For the DDN/NND sectors of the equilateral rhombus, the resulting $\mathbb Z_2$ monodromy is resolved by a degree-two branched arithmetic translation surface of genus two. On an explicit class of admissible open sets, every exact mixed-sector eigenfunction satisfies a local $L^2$ lower bound uniform in the eigenvalue, multiplicity, and choice within the eigenspace. The proof combines exact unfolding, semiclassical defect measures, and the Veech dichotomy to exclude concentration near the saddle/conic network and inside periodic cylinders. We also obtain a reflection-overlap observability result for the full rhombus and isolate the remaining saddle-network obstruction for arbitrary open observation sets.

math.SP↗
arXiv2026

Arithmetic Scar Accessibility and Generic Schrodinger Control on Metric Graphs

We study internal exact controllability of the free Schrödinger equation on finite compact metric graphs with Kirchhoff conditions at interior vertices and a fixed Dirichlet-Neumann assignment at exterior vertices. For a prescribed primitive cycle or exterior-to-exterior path, we identify an arithmetic criterion ensuring that the corresponding scar is accessible by exact high-frequency eigenfunctions of a fixed target metric. The criterion is formulated by intersecting the regular scar stratum of the secular set with the orbit-closure torus of the target length vector, and it can hold for resonant metrics beyond the rationally independent class. Under an intrinsic Diophantine condition on the orbit-closure flow, the construction is quantitative: along an exact eigensequence the mass outside the prescribed support decays polynomially, yielding a polynomial degeneration law for finite-frequency observation when that support is uncontrolled. Rationally independent metrics have full phase-orbit closure and therefore make every primitive obstruction accessible. Combining this spectral result with the known graph-theoretic characterization and sufficiency of the Graph Geometric Control Condition (GGCC), we prove that, for every rationally independent and hence for Lebesgue-almost every metric, GGCC is necessary and sufficient for exact controllability at every positive time in the free setting.

math.OC↗
arXiv2026

Uniform Non-Localization under Robin Boundary Perturbations: Spectral Splitting and Bounded Eigenspace Complexity

We study the high-energy spectral effect of Robin boundary perturbations on complete Laplace eigenspaces and its consequences for eigenfunction non-localization. Highly degenerate Neumann levels generally split under Robin perturbation, but this splitting need not produce a simple spectrum: distinct modal classes may still contribute to the same Robin eigenvalue. We prove that, for every fixed positive Robin parameter, the number of modal classes contributing to any one eigenvalue is uniformly bounded over the spectrum on the equilateral triangle and on every rectangle with rational squared aspect ratio. On the equilateral triangle, for all sufficiently small Robin parameters, the Neumann complete-eigenspace observation estimate persists with a constant uniform both in the eigenvalue and in the boundary parameter. For an arbitrary fixed positive Robin parameter, a high-frequency shell-splitting analysis gives a spectrum-wide bound on the number of modal classes contributing to any one Robin eigenvalue. In the nonsquare rectangular case, the corresponding splitting is governed by a strongly convex profile on weighted quadratic shells. Since each modal class has uniformly boundedplane-wave complexity, the spectral complexity bound implies observation on every measurable set of positive measure through a multidimensional Turán--Nazarov inequality, without a frequency-separation assumption. Thus, spectral simplicity is not required for complete-eigenspace non-localization: uniformly bounded spectral coincidence complexity is sufficient.

math.SP↗
arXiv2026

PRISM: A Multi-Dimensional Benchmark for Evaluating LLM Peer Reviewers

The rapid growth in submissions to machine learning venues has strained the scientific peer-review system and intensified interest in LLM-based automated peer reviewers. However, how good these systems are actually, especially compared to human reviewers at catching scientific gaps, remains poorly understood. In this work, we introduce PRISM (Peer Review Intelligence via Structured Multi-dimensional assessment), a benchmarking framework that evaluates review quality across four dimensions: Depth of Analysis, Novelty Assessment,Flaw Identification & Major Issues Prioritization, and Multi-dimensional Constructiveness. Unlike most existing evaluations based on surface-level metrics like ROUGE and BLEU, or unconstrained LLM-as-a-judge prompting that conflates fluency with rigor, PRISM grounds each dimension in argument mining, retrieval-augmented verification, and consensus-based scoring. We apply PRISM to benchmark five leading automated reviewer systems and human reviewers on a stratified corpus of reviews from ICLR, ICML, and NeurIPS. The results reveal that LLMs can match or beat human reviewers on individual dimensions: comparable depth of analysis, stronger novelty verification, and highly accurate critique prioritization. However, no single system consistently matches the balanced performance of the human baseline across all dimensions at once. Each exhibits a distinct specialization profile with characteristic blind spots -- failure modes that aggregate metrics miss entirely. The implication is that LLM reviewers are best understood as targeted supplements to human review, effective within specific dimensions, but unreliable as standalone replacements. Our demo and key results can be found at https://khanhthanhdev.github.io/prism-page/.

cs.CL↗
arXiv2026

Logarithmic-Free Moment and Generalization Bounds for Uniformly Stable Algorithms

Uniform stability is a classical tool for controlling the generalization error of a learning algorithm. Bousquet, Klochkov, and Zhivotovskiy (2020) showed that the problem can be reduced to a moment inequality for a sum of weakly interacting functions of independent random variables. Their bound contains an additional factor $\log n$, and they asked whether this factor can be removed. We answer this upper-bound question affirmatively. More specifically, let $Z=(Z_1,\ldots,Z_n)$ have independent coordinates and let $g_i(Z)$ satisfy $\mathbb E[g_i(Z)\mid Z_{-i}]=0, \ \left| \mathbb E[g_i(Z)\mid Z_i]\right|\le M, \ \text{for every } i = 1, \dots, n, $ where $Z_{-i}$ denotes all coordinates except $Z_i$. Assume additionally that changing any coordinate $Z_j$, $j\neq i$, changes $g_i$ by at most $β$, we prove that, for every $p\ge2$, for every $p\ge2$, $$ \left\| \sum_{i=1}^n g_i(Z)\right\|_p \le 16pnβ+M\sqrt{2pn}. $$ This removes the $\log n$ factor from the previous bound and matches the lower bound of Bousquet, Klochkov, and Zhivotovskiy up to universal constants in the range covered by their construction. Our proof first establishes the required estimate on the Rademacher cube, then transfers it to arbitrary product distributions by a two-copy randomization argument.

stat.ML↗
arXiv2026

Inertia-Sensitive Kreiss Bounds for $J$-Selfadjoint Matrices

Let $A \in \mathbb{C}^{n \times n}$ have spectrum in the closed unit disk. Its maximal power growth $\operatorname{Power}(A) := \sup_{k \ge 0} \Vert{}A^k\Vert{}$ measures transient amplification, whereas the Kreiss constant $\operatorname{Kreiss}(A) := \sup_{\vert{}z\vert{}>1} (\vert{}z\vert{}-1) \Vert{}(zI-A)^{-1}\Vert{}$ measures the corresponding resolvent growth outside the disk. The classical finite-dimensional Kreiss theorem gives $\operatorname{Power}(A) \le en \operatorname{Kreiss}(A)$, and the linear dependence on $n$ is unavoidable for general matrices. We show that, for matrices selfadjoint with respect to an indefinite metric, the ambient dimension $n$ can be replaced by an effective dimension determined by the minimal polynomial and the inertia of the metric. Specifically, if $A^*J = JA$, where $J$ is a fundamental symmetry with inertia $(n-q,q)$, then $\operatorname{Power}(A) \le e \min\{d(A), 2q+1, 2(n-q)+1\} \operatorname{Kreiss}(A)$, where $d(A)$ is the degree of the minimal polynomial. Our proof requires no assumption on diagonalizability or reality on the spectrum. Instead, we associate each cyclic orbit with a finite-rank selfadjoint Hankel operator and transfer its rank and inertia to a coefficient estimate. Examples based on scaled nilpotent shifts show that the linear dependence on the smaller inertia index is asymptotically sharp, even when this index is negligible relative to the matrix size and $d(A)=n$. We also obtain scaled-disk decay estimates and weighted-norm extensions to arbitrary nonsingular Hermitian metrics.

math.FA↗