arXiv subjects

Huy Tran

Publications and source records attributed to Huy Tran.

At least 37 records · Page 2Linked to original sources

arXiv2022

The Generalized Elastic Net for least squares regression with network-aligned signal and correlated design

We propose a novel $\ell_1+\ell_2$-penalty, which we refer to as the Generalized Elastic Net, for regression problems where the feature vectors are indexed by vertices of a given graph and the true signal is believed to be smooth or piecewise constant with respect to this graph. Under the assumption of correlated Gaussian design, we derive upper bounds for the prediction and estimation errors, which are graph-dependent and consist of a parametric rate for the unpenalized portion of the regression vector and another term that depends on our network alignment assumption. We also provide a coordinate descent procedure based on the Lagrange dual objective to compute this estimator for large-scale problems. Finally, we compare our proposed estimator to existing regularized estimators on a number of real and synthetic datasets and discuss its potential limitations.

stat.ME↗

arXiv2022

Is Multi-Task Learning an Upper Bound for Continual Learning?

Continual and multi-task learning are common machine learning approaches to learning from multiple tasks. The existing works in the literature often assume multi-task learning as a sensible performance upper bound for various continual learning algorithms. While this assumption is empirically verified for different continual learning benchmarks, it is not rigorously justified. Moreover, it is imaginable that when learning from multiple tasks, a small subset of these tasks could behave as adversarial tasks reducing the overall learning performance in a multi-task setting. In contrast, continual learning approaches can avoid the performance drop caused by such adversarial tasks to preserve their performance on the rest of the tasks, leading to better performance than a multi-task learner. This paper proposes a novel continual self-supervised learning setting, where each task corresponds to learning an invariant representation for a specific class of data augmentations. In this setting, we show that continual learning often beats multi-task learning on various benchmark datasets, including MNIST, CIFAR-10, and CIFAR-100.

cs.LG↗

arXiv2022

WayFAST: Navigation with Predictive Traversability in the Field

We present a self-supervised approach for learning to predict traversable paths for wheeled mobile robots that require good traction to navigate. Our algorithm, termed WayFAST (Waypoint Free Autonomous Systems for Traversability), uses RGB and depth data, along with navigation experience, to autonomously generate traversable paths in outdoor unstructured environments. Our key inspiration is that traction can be estimated for rolling robots using kinodynamic models. Using traction estimates provided by an online receding horizon estimator, we are able to train a traversability prediction neural network in a self-supervised manner, without requiring heuristics utilized by previous methods. We demonstrate the effectiveness of WayFAST through extensive field testing in varying environments, ranging from sandy dry beaches to forest canopies and snow covered grass fields. Our results clearly demonstrate that WayFAST can learn to avoid geometric obstacles as well as untraversable terrain, such as snow, which would be difficult to avoid with sensors that provide only geometric data, such as LiDAR. Furthermore, we show that our training pipeline based on online traction estimates is more data-efficient than other heuristic-based methods.

cs.RO↗

arXiv2022

Fine-Grained Visual Classification using Self Assessment Classifier

Extracting discriminative features plays a crucial role in the fine-grained visual classification task. Most of the existing methods focus on developing attention or augmentation mechanisms to achieve this goal. However, addressing the ambiguity in the top-k prediction classes is not fully investigated. In this paper, we introduce a Self Assessment Classifier, which simultaneously leverages the representation of the image and top-k prediction classes to reassess the classification results. Our method is inspired by continual learning with coarse-grained and fine-grained classifiers to increase the discrimination of features in the backbone and produce attention maps of informative areas on the image. In practice, our method works as an auxiliary branch and can be easily integrated into different architectures. We show that by effectively addressing the ambiguity in the top-k prediction classes, our method achieves new state-of-the-art results on CUB200-2011, Stanford Dog, and FGVC Aircraft datasets. Furthermore, our method also consistently improves the accuracy of different existing fine-grained classifiers with a unified setup.

cs.CV↗

arXiv2022

Coarse-to-Fine Reasoning for Visual Question Answering

Bridging the semantic gap between image and question is an important step to improve the accuracy of the Visual Question Answering (VQA) task. However, most of the existing VQA methods focus on attention mechanisms or visual relations for reasoning the answer, while the features at different semantic levels are not fully utilized. In this paper, we present a new reasoning framework to fill the gap between visual features and semantic clues in the VQA task. Our method first extracts the features and predicates from the image and question. We then propose a new reasoning framework to effectively jointly learn these features and predicates in a coarse-to-fine manner. The intensively experimental results on three large-scale VQA datasets show that our proposed approach achieves superior accuracy comparing with other state-of-the-art methods. Furthermore, our reasoning framework also provides an explainable way to understand the decision of the deep neural network when predicting the answer.

cs.CV↗

arXiv2021

Light-weight Deformable Registration using Adversarial Learning with Distilling Knowledge

Deformable registration is a crucial step in many medical procedures such as image-guided surgery and radiation therapy. Most recent learning-based methods focus on improving the accuracy by optimizing the non-linear spatial correspondence between the input images. Therefore, these methods are computationally expensive and require modern graphic cards for real-time deployment. In this paper, we introduce a new Light-weight Deformable Registration network that significantly reduces the computational cost while achieving competitive accuracy. In particular, we propose a new adversarial learning with distilling knowledge algorithm that successfully leverages meaningful information from the effective but expensive teacher network to the student network. We design the student network such as it is light-weight and well suitable for deployment on a typical CPU. The extensively experimental results on different public datasets show that our proposed method achieves state-of-the-art accuracy while significantly faster than recent methods. We further show that the use of our adversarial learning algorithm is essential for a time-efficiency deformable registration method. Finally, our source code and trained models are available at: https://github.com/aioz-ai/LDR_ALDK.

eess.IV↗

arXiv2021

Regularity of SLE in $(t,κ)$ and refined GRR estimates

Schramm-Loewner evolution (SLE$_κ$) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by $\sqrtκ$ times Brownian motion. This yields a (half-plane) valued random field $γ= γ(t, κ; ω)$. (Hölder) regularity of in $γ(\cdot,κ;ω$), a.k.a. SLE trace, has been considered by many authors, starting with Rohde-Schramm (2005). Subsequently, Johansson Viklund, Rohde, and Wong (2014) showed a.s. Hölder continuity of this random field for $κ< 8(2-\sqrt{3})$. In this paper, we improve their result to joint Hölder continuity up to $κ< 8/3$. Moreover, we show that the SLE$_κ$ trace $γ(\cdot,κ)$ (as a continuous path) is stochastically continuous in $κ$ at all $κ\neq 8$. Our proofs rely on a novel variation of the Garsia-Rodemich-Rumsey (GRR) inequality, which is of independent interest.

math.PR↗

arXiv2020

Multiple interaction learning with question-type prior knowledge for constraining answer search space in visual question answering

Different approaches have been proposed to Visual Question Answering (VQA). However, few works are aware of the behaviors of varying joint modality methods over question type prior knowledge extracted from data in constraining answer search space, of which information gives a reliable cue to reason about answers for questions asked in input images. In this paper, we propose a novel VQA model that utilizes the question-type prior information to improve VQA by leveraging the multiple interactions between different joint modality methods based on their behaviors in answering questions from different types. The solid experiments on two benchmark datasets, i.e., VQA 2.0 and TDIUC, indicate that the proposed method yields the best performance with the most competitive approaches.

cs.CV↗

arXiv2020

The continuum self-similar tree

We introduce the continuum self-similar tree (CSST) and characterize it topologically. We apply this to answer a question of Curien about the topology of the continuum random tree (CRT). We also give a topological characterization of other trees with branch points of finite or infinite valences.

math.GT↗

arXiv2020

A support theorem for SLE curves

For all $κ> 0$, we show that the support of SLE$_κ$ curves is the closure in the sup-norm of the set of Loewner curves driven by nice (e.g. smooth) functions. It follows that the support is the closure of the set of simple curves starting at $0$.

math.PR↗

arXiv2019

Compact Trilinear Interaction for Visual Question Answering

In Visual Question Answering (VQA), answers have a great correlation with question meaning and visual contents. Thus, to selectively utilize image, question and answer information, we propose a novel trilinear interaction model which simultaneously learns high level associations between these three inputs. In addition, to overcome the interaction complexity, we introduce a multimodal tensor-based PARALIND decomposition which efficiently parameterizes trilinear interaction between the three inputs. Moreover, knowledge distillation is first time applied in Free-form Opened-ended VQA. It is not only for reducing the computational cost and required memory but also for transferring knowledge from trilinear interaction model to bilinear interaction model. The extensive experiments on benchmarking datasets TDIUC, VQA-2.0, and Visual7W show that the proposed compact trilinear interaction model achieves state-of-the-art results when using a single model on all three datasets.

cs.CV↗

arXiv2018

Remarks on Loewner Chains Driven by Finite Variation Functions

To explore the relation between properties of Loewner chains and properties of their driving functions, we study Loewner chains driven by functions $U$ of finite total variation. Under some appropriate conditions, we show existence of the simple trace $γ$ and establish continuity of the map $U$ to $γ$ with respect to uniform topology on $γ$ and the total variation topology on $U$. In the spirit of work of Wong and Tran-Lind, we also obtain conditions on the driving function that ensures the trace to be continuously differentiable.

math.CV↗

arXiv2017

Loewner Equation driven by complex-valued functions

Consider the Loewner equation associated to the upper-half plane. Normally this equation is driven by a real-valued function. In this paper, we show that when the driving function is complex-valued with small $1/2$-Hölder norm, the corresponding hull is a quasi-arc, hence is a simple curve. We also study how the hull changes with respect to complex parameters and make a connection between Loewner equation and complex dynamics.

math.CV↗

arXiv2016

Precision of readout at the hunchback gene: analyzing short transcription time traces in living fly embryos

The simultaneous expression of the hunchback gene in the numerous nuclei of the developing fly embryo gives us a unique opportunity to study how transcription is regulated in living organisms. A recently developed MS2-MCP technique for imaging nascent messenger RNA in living Drosophila embryos allows us to quantify the dynamics of the developmental transcription process. The initial measurement of the morphogens by the hunchback promoter takes place during very short cell cycles, not only giving each nucleus little time for a precise readout, but also resulting in short time traces of transcription. Additionally, the relationship between the measured signal and the promoter state depends on the molecular design of the reporting probe. We develop an analysis approach based on tailor made autocorrelation functions that overcomes the short trace problems and quantifies the dynamics of transcription initiation. Based on live imaging data, we identify signatures of bursty transcription initiation from the hunchback promoter. We show that the precision of the expression of the hunchback gene to measure its position along the anterior-posterior axis is low both at the boundary and in the anterior even at cycle 13, suggesting additional post-transcriptional averaging mechanisms to provide the precision observed in fixed embryos.

q-bio.MN↗

arXiv2016

On the regularity of SLE trace

We revisit regularity of SLE trace, for all $κ\neq 8$, and establish Besov regularity under the usual half-space capacity parametrization. With an embedding theorem of Garsia--Rodemich--Rumsey type, we obtain finite moments (and hence almost surely) optimal variation regularity with index $\min (1 + κ/ 8, 2) $, improving on previous works of Werness, and also (optimal) Hölder regularity à la Johansson Viklund and Lawler.

math.PR↗

arXiv2014

Regularity of Loewner Curves

The Loewner equation encrypts a growing simple curve in the plane into a real-valued driving function. We show that if the driving function $λ$ is in $C^β$ with $β>2$ (or real analytic) then the Loewner curve is in $C^{β+ \frac{1}{2}}$ (respectively analytic). This is a converse to a result by Earle and Epstein and extends a result of Wong.

math.CV↗

arXiv2014

Automated Mapping of UML Activity Diagrams to Formal Specifications for Supporting Containment Checking

Business analysts and domain experts are often sketching the behaviors of a software system using high-level models that are technology- and platform-independent. The developers will refine and enrich these high-level models with technical details. As a consequence, the refined models can deviate from the original models over time, especially when the two kinds of models evolve independently. In this context, we focus on behavior models; that is, we aim to ensure that the refined, low-level behavior models conform to the corresponding high-level behavior models. Based on existing formal verification techniques, we propose containment checking as a means to assess whether the system's behaviors described by the low-level models satisfy what has been specified in the high-level counterparts. One of the major obstacles is how to lessen the burden of creating formal specifications of the behavior models as well as consistency constraints, which is a tedious and error-prone task when done manually. Our approach presented in this paper aims at alleviating the aforementioned challenges by considering the behavior models as verification inputs and devising automated mappings of behavior models onto formal properties and descriptions that can be directly used by model checkers. We discuss various challenges in our approach and show the applicability of our approach in illustrative scenarios.

cs.SE↗

arXiv2013

Convergence of an algorithm simulating Loewner curves

The development of Schramm--Loewner evolution (SLE) as the scaling limits of discrete models from statistical physics makes direct simulation of SLE an important task. The most common method, suggested by Marshall and Rohde \cite{MR05}, is to sample Brownian motion at discrete times, interpolate appropriately in between and solve explicitly the Loewner equation with this approximation. This algorithm always produces piecewise smooth non self-intersecting curves whereas SLE$_κ$ has been proven to be simple for $κ\in[0,4]$, self-touching for $κ\in(4,8)$ and space-filling for $κ\geq 8$. In this paper we show that this sequence of curves converges to SLE$_κ$ for all $κ\neq 8$ by giving a condition on deterministic driving functions to ensure the sup-norm convergence of simulated curves when we use this algorithm.

math.CV↗