18 papers
Conformal Prediction for Distribution-to-Distribution Regression
Trung-Khang Tran, Tuan A. Hoang, Viet-Hoang Tran +1
Conformal Prediction (CP) provides a model-agnostic framework for constructing finite-sample prediction sets with coverage guarantees and has become a tool for reliable decision-ma…
Implicit Assumptions About Tasks in Continual Learning
Kathrin Korte, Christian Metzner, Akshay Bedhotiya +3
Continual learning is the study of how a model accumulates knowledge from data received over time, rather than all at once. In practice, this is typically achieved by dividing a da…
A one-dimensional coherent domain with non-Prüfer integral closure
Viet-Hoang Tran, Thieu N. Vo, Tan M. Nguyen
In a question recorded in 1978, Vasconcelos asked whether the integral closure of a one-dimensional coherent local domain in its fraction field is Prüfer. We construct such a domai…
Dimensions of a ring and its formal power series ring
Viet-Hoang Tran, Thieu N. Vo, Tan M. Nguyen
Understanding the relation between and is a classical problem in commutative algebra. For a Noetherian ring , one has , but the gene…
A Reduced Non-McCoy Ring with the Annihilator Condition and
Viet-Hoang Tran, Tan M. Nguyen
It has been asked whether a reduced non-McCoy ring can satisfy both the annihilator condition and for some . In this work, we prove that such rings exist exactly…
On the Krull dimensions of rings of integer-valued polynomials and polynomial rings
Viet-Hoang Tran, Tan M. Nguyen
It was conjectured that every integral domain satisfies . We disprove this conjecture and, more strongly, classify all pairs for which…
Alternating Divisoriality of Prime Ideals along Infinite Chains of Bézout Domains
Viet-Hoang Tran, Tan M. Nguyen
A question posed in the literature asks whether the divisoriality of a prime can alternate indefinitely along an ascending chain of overrings of a Prüfer domain or a descending cha…
Bouvier's Conjecture and Dimension Sequences of Unique Factorization Domains
Viet-Hoang Tran, Thieu N. Vo, Tan M. Nguyen
We prove Bouvier's conjecture. More generally, an integer sequence with is realized by a unique factorization domain (UFD) with $\dim R[X_1,\ldo…
The Erdős-Hajnal Property for the six-vertex Graph with Edge Set
Viet-Hoang Tran, Tan M. Nguyen
We prove that the six-vertex graph with edge set has the Erdős-Hajnal property. The proof adapts the iterative-sparsification method of Nguyen, Scott, an…
Polynomial extensions do not preserve the strong finite type property
Viet-Hoang Tran, Phan Thanh Toan, Thieu N. Vo +1
Arnold introduced the strong finite type (SFT) property in 1973 while studying the dimension of power series rings. For several classes of rings, polynomial extension is known to p…
The Noetherian Case of Bayart's Power-Series Question
Viet-Hoang Tran, Dung V. Nguyen, Quang X. Nguyen +2
Let be a commutative Noetherian ring. We prove that if the one-variable formal power-series ring is a unique factorization domain, then so is the two-variable formal p…
Geometric and Stochastic Analysis of Discontinuities in Sparse Mixture-of-Experts
Tho Tran Huu, Huu-Tuan Nguyen, Thien-Hai Nguyen +4
Sparse Mixture-of-Experts (SMoE) architectures are now widely deployed in state-of-the-art language and vision models, where conditional routing allows scaling to very large networ…
Conservation Laws for Modern Neural Architectures
Viet-Hoang Tran, Vinh Khanh Bui, Tan Lai Ngoc +3
Understanding gradient descent dynamics is key to explaining the success of over-parameterized models, where implicit bias manifests through conservation laws in gradient flow. Whi…
Quasi-Equivariant Metanetworks
Viet-Hoang Tran, An Nguyen, Benoît Guérand +2
Metanetworks are neural architectures designed to operate directly on pretrained weights to perform downstream tasks. However, the parameter space serves only as a proxy for the un…
Approximation rates of quantum neural networks for periodic functions via Jackson's inequality
Ariel Neufeld, Philipp Schmocker, Viet Khoa Tran
Quantum neural networks (QNNs) are an analog of classical neural networks in the world of quantum computing, which are represented by a unitary matrix with trainable parameters. In…
Contrastive Consolidation of Top-Down Modulations Achieves Sparsely Supervised Continual Learning
Viet Anh Khoa Tran, Emre Neftci, Willem A. M. Wybo
Biological brains learn continually from a stream of unlabeled data, while integrating specialized information from sparsely labeled examples without compromising their ability to…
Does Joint Training Really Help Cascaded Speech Translation?
Viet Anh Khoa Tran, David Thulke, Yingbo Gao +2
Currently, in speech translation, the straightforward approach - cascading a recognition system with a translation system - delivers state-of-the-art results. However, fundamental…
On Sampling-Based Training Criteria for Neural Language Modeling
Yingbo Gao, David Thulke, Alexander Gerstenberger +3
As the vocabulary size of modern word-based language models becomes ever larger, many sampling-based training criteria are proposed and investigated. The essence of these sampling…