arXiv subjects

Huy Nguyen

Publications and source records attributed to Huy Nguyen.

At least 55 records · Page 3Linked to original sources

arXiv2025

On Expert Estimation in Hierarchical Mixture of Experts: Beyond Softmax Gating Functions

With the growing prominence of the Mixture of Experts (MoE) architecture in developing large-scale foundation models, we investigate the Hierarchical Mixture of Experts (HMoE), a specialized variant of MoE that excels in handling complex inputs and improving performance on targeted tasks. Our analysis highlights the advantages of using the Laplace gating function over the traditional Softmax gating within the HMoE frameworks. We theoretically demonstrate that applying the Laplace gating function at both levels of the HMoE model helps eliminate undesirable parameter interactions caused by the Softmax gating and, therefore, accelerates the expert convergence as well as enhances the expert specialization. Empirical validation across diverse scenarios supports these theoretical claims. This includes large-scale multimodal tasks, image classification, and latent domain discovery and prediction tasks, where our modified HMoE models show great performance improvements compared to the conventional HMoE models.

stat.ML↗

arXiv2025

Understanding Expert Structures on Minimax Parameter Estimation in Contaminated Mixture of Experts

We conduct the convergence analysis of parameter estimation in the contaminated mixture of experts. This model is motivated from the prompt learning problem where ones utilize prompts, which can be formulated as experts, to fine-tune a large-scale pre-trained model for learning downstream tasks. There are two fundamental challenges emerging from the analysis: (i) the proportion in the mixture of the pre-trained model and the prompt may converge to zero during the training, leading to the prompt vanishing issue; (ii) the algebraic interaction among parameters of the pre-trained model and the prompt can occur via some partial differential equations and decelerate the prompt learning. In response, we introduce a distinguishability condition to control the previous parameter interaction. Additionally, we also investigate various types of expert structure to understand their effects on the convergence behavior of parameter estimation. In each scenario, we provide comprehensive convergence rates of parameter estimation along with the corresponding minimax lower bounds. Finally, we run several numerical experiments to empirically justify our theoretical findings.

cs.LG↗

arXiv2025

Statistical Advantages of Perturbing Cosine Router in Mixture of Experts

The cosine router in Mixture of Experts (MoE) has recently emerged as an attractive alternative to the conventional linear router. Indeed, the cosine router demonstrates favorable performance in image and language tasks and exhibits better ability to mitigate the representation collapse issue, which often leads to parameter redundancy and limited representation potentials. Despite its empirical success, a comprehensive analysis of the cosine router in MoE has been lacking. Considering the least square estimation of the cosine routing MoE, we demonstrate that due to the intrinsic interaction of the model parameters in the cosine router via some partial differential equations, regardless of the structures of the experts, the estimation rates of experts and model parameters can be as slow as $\mathcal{O}(1/\log^τ(n))$ where $τ> 0$ is some constant and $n$ is the sample size. Surprisingly, these pessimistic non-polynomial convergence rates can be circumvented by the widely used technique in practice to stabilize the cosine router -- simply adding noises to the $\ell^2$-norms in the cosine router, which we refer to as \textit{perturbed cosine router}. Under the strongly identifiable settings of the expert functions, we prove that the estimation rates for both the experts and model parameters under the perturbed cosine routing MoE are significantly improved to polynomial rates. Finally, we conduct extensive simulation studies in both synthetic and real data settings to empirically validate our theoretical results.

stat.ML↗

arXiv2025

Convergence Rates for Softmax Gating Mixture of Experts

Mixture of experts (MoE) has recently emerged as an effective framework to advance the efficiency and scalability of machine learning models by softly dividing complex tasks among multiple specialized sub-models termed experts. Central to the success of MoE is an adaptive softmax gating mechanism which takes responsibility for determining the relevance of each expert to a given input and then dynamically assigning experts their respective weights. Despite its widespread use in practice, a comprehensive study on the effects of the softmax gating on the MoE has been lacking in the literature. To bridge this gap in this paper, we perform a convergence analysis of parameter estimation and expert estimation under the MoE equipped with the standard softmax gating or its variants, including a dense-to-sparse gating and a hierarchical softmax gating, respectively. Furthermore, our theories also provide useful insights into the design of sample-efficient expert structures. In particular, we demonstrate that it requires polynomially many data points to estimate experts satisfying our proposed \emph{strong identifiability} condition, namely a commonly used two-layer feed-forward network. In stark contrast, estimating linear experts, which violate the strong identifiability condition, necessitates exponentially many data points as a result of intrinsic parameter interactions expressed in the language of partial differential equations. All the theoretical results are substantiated with a rigorous guarantee.

stat.ML↗

arXiv2025

RAPID: Retrieval-Augmented Parallel Inference Drafting for Text-Based Video Event Retrieval

Retrieving events from videos using text queries has become increasingly challenging due to the rapid growth of multimedia content. Existing methods for text-based video event retrieval often focus heavily on object-level descriptions, overlooking the crucial role of contextual information. This limitation is especially apparent when queries lack sufficient context, such as missing location details or ambiguous background elements. To address these challenges, we propose a novel system called RAPID (Retrieval-Augmented Parallel Inference Drafting), which leverages advancements in Large Language Models (LLMs) and prompt-based learning to semantically correct and enrich user queries with relevant contextual information. These enriched queries are then processed through parallel retrieval, followed by an evaluation step to select the most relevant results based on their alignment with the original query. Through extensive experiments on our custom-developed dataset, we demonstrate that RAPID significantly outperforms traditional retrieval methods, particularly for contextually incomplete queries. Our system was validated for both speed and accuracy through participation in the Ho Chi Minh City AI Challenge 2024, where it successfully retrieved events from over 300 hours of video. Further evaluation comparing RAPID with the baseline proposed by the competition organizers demonstrated its superior effectiveness, highlighting the strength and robustness of our approach.

cs.CL↗

arXiv2025

Mixture of Experts Meets Prompt-Based Continual Learning

Exploiting the power of pre-trained models, prompt-based approaches stand out compared to other continual learning solutions in effectively preventing catastrophic forgetting, even with very few learnable parameters and without the need for a memory buffer. While existing prompt-based continual learning methods excel in leveraging prompts for state-of-the-art performance, they often lack a theoretical explanation for the effectiveness of prompting. This paper conducts a theoretical analysis to unravel how prompts bestow such advantages in continual learning, thus offering a new perspective on prompt design. We first show that the attention block of pre-trained models like Vision Transformers inherently encodes a special mixture of experts architecture, characterized by linear experts and quadratic gating score functions. This realization drives us to provide a novel view on prefix tuning, reframing it as the addition of new task-specific experts, thereby inspiring the design of a novel gating mechanism termed Non-linear Residual Gates (NoRGa). Through the incorporation of non-linear activation and residual connection, NoRGa enhances continual learning performance while preserving parameter efficiency. The effectiveness of NoRGa is substantiated both theoretically and empirically across diverse benchmarks and pretraining paradigms. Our code is publicly available at https://github.com/Minhchuyentoancbn/MoE_PromptCL

cs.LG↗

arXiv2024

Revisiting the Role of Texture in 3D Person Re-identification

This study introduces a new framework for 3D person re-identification (re-ID) that leverages readily available high-resolution texture data in 3D reconstruction to improve the performance and explainability of the person re-ID task. We propose a method to emphasize texture in 3D person re-ID models by incorporating UVTexture mapping, which better differentiates human subjects. Our approach uniquely combines UVTexture and its heatmaps with 3D models to visualize and explain the person re-ID process. In particular, the visualization and explanation are achieved through activation maps and attribute-based attention maps, which highlight the important regions and features contributing to the person re-ID decision. Our contributions include: (1) a novel technique for emphasizing texture in 3D models using UVTexture processing, (2) an innovative method for explicating person re-ID matches through a combination of 3D models and UVTexture mapping, and (3) achieving state-of-the-art performance in 3D person re-ID. We ensure the reproducibility of our results by making all data, codes, and models publicly available.

cs.CV↗

arXiv2024

Sigmoid Gating is More Sample Efficient than Softmax Gating in Mixture of Experts

The softmax gating function is arguably the most popular choice in mixture of experts modeling. Despite its widespread use in practice, the softmax gating may lead to unnecessary competition among experts, potentially causing the undesirable phenomenon of representation collapse due to its inherent structure. In response, the sigmoid gating function has been recently proposed as an alternative and has been demonstrated empirically to achieve superior performance. However, a rigorous examination of the sigmoid gating function is lacking in current literature. In this paper, we verify theoretically that the sigmoid gating, in fact, enjoys a higher sample efficiency than the softmax gating for the statistical task of expert estimation. Towards that goal, we consider a regression framework in which the unknown regression function is modeled as a mixture of experts, and study the rates of convergence of the least squares estimator under the over-specified case in which the number of fitted experts is larger than the true value. We show that two gating regimes naturally arise and, in each of them, we formulate an identifiability condition for the expert functions and derive the corresponding convergence rates. In both cases, we find that experts formulated as feed-forward networks with commonly used activation such as ReLU and GELU enjoy faster convergence rates under the sigmoid gating than those under softmax gating. Furthermore, given the same choice of experts, we demonstrate that the sigmoid gating function requires a smaller sample size than its softmax counterpart to attain the same error of expert estimation and, therefore, is more sample efficient.

stat.ML↗

arXiv2024

Deep-Wide Learning Assistance for Insect Pest Classification

Accurate insect pest recognition plays a critical role in agriculture. It is a challenging problem due to the intricate characteristics of insects. In this paper, we present DeWi, novel learning assistance for insect pest classification. With a one-stage and alternating training strategy, DeWi simultaneously improves several Convolutional Neural Networks in two perspectives: discrimination (by optimizing a triplet margin loss in a supervised training manner) and generalization (via data augmentation). From that, DeWi can learn discriminative and in-depth features of insect pests (deep) yet still generalize well to a large number of insect categories (wide). Experimental results show that DeWi achieves the highest performances on two insect pest classification benchmarks (76.44\% accuracy on the IP102 dataset and 99.79\% accuracy on the D0 dataset, respectively). In addition, extensive evaluations and ablation studies are conducted to thoroughly investigate our DeWi and demonstrate its superiority. Our source code is available at https://github.com/toannguyen1904/DeWi.

cs.CV↗

arXiv2024

A General Theory for Softmax Gating Multinomial Logistic Mixture of Experts

Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been previous attempts to comprehend the behavior of that model under the regression settings through the convergence analysis of maximum likelihood estimation in the Gaussian MoE model, such analysis under the setting of a classification problem has remained missing in the literature. We close this gap by establishing the convergence rates of density estimation and parameter estimation in the softmax gating multinomial logistic MoE model. Notably, when part of the expert parameters vanish, these rates are shown to be slower than polynomial rates owing to an inherent interaction between the softmax gating and expert functions via partial differential equations. To address this issue, we propose using a novel class of modified softmax gating functions which transform the input before delivering them to the gating functions. As a result, the previous interaction disappears and the parameter estimation rates are significantly improved.

stat.ML↗

arXiv2024

Is Temperature Sample Efficient for Softmax Gaussian Mixture of Experts?

Dense-to-sparse gating mixture of experts (MoE) has recently become an effective alternative to a well-known sparse MoE. Rather than fixing the number of activated experts as in the latter model, which could limit the investigation of potential experts, the former model utilizes the temperature to control the softmax weight distribution and the sparsity of the MoE during training in order to stabilize the expert specialization. Nevertheless, while there are previous attempts to theoretically comprehend the sparse MoE, a comprehensive analysis of the dense-to-sparse gating MoE has remained elusive. Therefore, we aim to explore the impacts of the dense-to-sparse gate on the maximum likelihood estimation under the Gaussian MoE in this paper. We demonstrate that due to interactions between the temperature and other model parameters via some partial differential equations, the convergence rates of parameter estimations are slower than any polynomial rates, and could be as slow as $\mathcal{O}(1/\log(n))$, where $n$ denotes the sample size. To address this issue, we propose using a novel activation dense-to-sparse gate, which routes the output of a linear layer to an activation function before delivering them to the softmax function. By imposing linearly independence conditions on the activation function and its derivatives, we show that the parameter estimation rates are significantly improved to polynomial rates. Finally, we conduct a simulation study to empirically validate our theoretical results.

stat.ML↗

arXiv2024

On Least Square Estimation in Softmax Gating Mixture of Experts

Mixture of experts (MoE) model is a statistical machine learning design that aggregates multiple expert networks using a softmax gating function in order to form a more intricate and expressive model. Despite being commonly used in several applications owing to their scalability, the mathematical and statistical properties of MoE models are complex and difficult to analyze. As a result, previous theoretical works have primarily focused on probabilistic MoE models by imposing the impractical assumption that the data are generated from a Gaussian MoE model. In this work, we investigate the performance of the least squares estimators (LSE) under a deterministic MoE model where the data are sampled according to a regression model, a setting that has remained largely unexplored. We establish a condition called strong identifiability to characterize the convergence behavior of various types of expert functions. We demonstrate that the rates for estimating strongly identifiable experts, namely the widely used feed-forward networks with activation functions $\mathrm{sigmoid}(\cdot)$ and $\tanh(\cdot)$, are substantially faster than those of polynomial experts, which we show to exhibit a surprising slow estimation rate. Our findings have important practical implications for expert selection.

stat.ML↗

arXiv2024

On Parameter Estimation in Deviated Gaussian Mixture of Experts

We consider the parameter estimation problem in the deviated Gaussian mixture of experts in which the data are generated from $(1 - λ^{\ast}) g_0(Y| X)+ λ^{\ast} \sum_{i = 1}^{k_{\ast}} p_{i}^{\ast} f(Y|(a_{i}^{\ast})^{\top}X+b_i^{\ast},σ_{i}^{\ast})$, where $X, Y$ are respectively a covariate vector and a response variable, $g_{0}(Y|X)$ is a known function, $λ^{\ast} \in [0, 1]$ is true but unknown mixing proportion, and $(p_{i}^{\ast}, a_{i}^{\ast}, b_{i}^{\ast}, σ_{i}^{\ast})$ for $1 \leq i \leq k^{\ast}$ are unknown parameters of the Gaussian mixture of experts. This problem arises from the goodness-of-fit test when we would like to test whether the data are generated from $g_{0}(Y|X)$ (null hypothesis) or they are generated from the whole mixture (alternative hypothesis). Based on the algebraic structure of the expert functions and the distinguishability between $g_0$ and the mixture part, we construct novel Voronoi-based loss functions to capture the convergence rates of maximum likelihood estimation (MLE) for our models. We further demonstrate that our proposed loss functions characterize the local convergence rates of parameter estimation more accurately than the generalized Wasserstein, a loss function being commonly used for estimating parameters in the Gaussian mixture of experts.

stat.ML↗

arXiv2024

AG-ReID.v2: Bridging Aerial and Ground Views for Person Re-identification

Aerial-ground person re-identification (Re-ID) presents unique challenges in computer vision, stemming from the distinct differences in viewpoints, poses, and resolutions between high-altitude aerial and ground-based cameras. Existing research predominantly focuses on ground-to-ground matching, with aerial matching less explored due to a dearth of comprehensive datasets. To address this, we introduce AG-ReID.v2, a dataset specifically designed for person Re-ID in mixed aerial and ground scenarios. This dataset comprises 100,502 images of 1,615 unique individuals, each annotated with matching IDs and 15 soft attribute labels. Data were collected from diverse perspectives using a UAV, stationary CCTV, and smart glasses-integrated camera, providing a rich variety of intra-identity variations. Additionally, we have developed an explainable attention network tailored for this dataset. This network features a three-stream architecture that efficiently processes pairwise image distances, emphasizes key top-down features, and adapts to variations in appearance due to altitude differences. Comparative evaluations demonstrate the superiority of our approach over existing baselines. We plan to release the dataset and algorithm source code publicly, aiming to advance research in this specialized field of computer vision. For access, please visit https://github.com/huynguyen792/AG-ReID.v2.

cs.CV↗

arXiv2024

Gaussian process surrogate models for the properties of micro-tearing modes in spherical tokamaks

Spherical tokamaks (STs) have many desirable features that make them a suitable choice for fusion power plants. To understand their confinement properties, accurate calculation of turbulent micro-instabilities is necessary for tokamak design. Presented is a novel surrogate model for Micro-tearing modes (MTMs), the micro-instability thought to be dominant in high beta STs. Direct numerical calculation of micro-instabilities is computationally expensive and is a significant bottleneck in integrated plasma modelling. The considerable number of geometric and thermodynamic parameters, the interactions that influence these coefficients and the resolutions needed to accurately resolve these modes, makes direct numerical simulation for parameter space exploration computationally extremely challenging. However, this and the dearth of accurate reduced physics models for MTMs makes it suitable for surrogate modelling using Gaussian Process Regression, a modern machine learning technique. This paper outlines the further development of a data-driven reduced-order model across a spherical tokamak reactor-relevant parameter space utilising Gaussian Process Regression (GPR) and classification; techniques from machine learning. To build the original simple GP model these two components were used in an active learning loop to maximise the efficiency of data acquisition thus minimising computational cost. The `simple' GP was seen to show a plateau of fidelity with more data and to be under-confident, particular in areas of parameter space close to marginal stability. It is postulated that the presence of multiple sub-types of MTM could be the root cause, with the underlying function being less smooth than expected. An expansion of the model using clustering algorithms to find optimal sub models using a mixture of experts approach is shown to greatly improve the variances in the outputs of the GP model.

physics.plasm-ph↗

arXiv2024

Statistical Perspective of Top-K Sparse Softmax Gating Mixture of Experts

Top-K sparse softmax gating mixture of experts has been widely used for scaling up massive deep-learning architectures without increasing the computational cost. Despite its popularity in real-world applications, the theoretical understanding of that gating function has remained an open problem. The main challenge comes from the structure of the top-K sparse softmax gating function, which partitions the input space into multiple regions with distinct behaviors. By focusing on a Gaussian mixture of experts, we establish theoretical results on the effects of the top-K sparse softmax gating function on both density and parameter estimations. Our results hinge upon defining novel loss functions among parameters to capture different behaviors of the input regions. When the true number of experts $k_{\ast}$ is known, we demonstrate that the convergence rates of density and parameter estimations are both parametric on the sample size. However, when $k_{\ast}$ becomes unknown and the true model is over-specified by a Gaussian mixture of $k$ experts where $k > k_{\ast}$, our findings suggest that the number of experts selected from the top-K sparse softmax gating function must exceed the total cardinality of a certain number of Voronoi cells associated with the true parameters to guarantee the convergence of the density estimation. Moreover, while the density estimation rate remains parametric under this setting, the parameter estimation rates become substantially slow due to an intrinsic interaction between the softmax gating and expert functions.

stat.ML↗

arXiv2024

Towards Convergence Rates for Parameter Estimation in Gaussian-gated Mixture of Experts

Originally introduced as a neural network for ensemble learning, mixture of experts (MoE) has recently become a fundamental building block of highly successful modern deep neural networks for heterogeneous data analysis in several applications of machine learning and statistics. Despite its popularity in practice, a satisfactory level of theoretical understanding of the MoE model is far from complete. To shed new light on this problem, we provide a convergence analysis for maximum likelihood estimation (MLE) in the Gaussian-gated MoE model. The main challenge of that analysis comes from the inclusion of covariates in the Gaussian gating functions and expert networks, which leads to their intrinsic interaction via some partial differential equations with respect to their parameters. We tackle these issues by designing novel Voronoi loss functions among parameters to accurately capture the heterogeneity of parameter estimation rates. Our findings reveal that the MLE has distinct behaviors under two complement settings of location parameters of the Gaussian gating functions, namely when all these parameters are non-zero versus when at least one among them vanishes. Notably, these behaviors can be characterized by the solvability of two different systems of polynomial equations. Finally, we conduct a simulation study to empirically verify our theoretical results.

stat.ML↗

arXiv2024

Encoding Version History Context for Better Code Representation

With the exponential growth of AI tools that generate source code, understanding software has become crucial. When developers comprehend a program, they may refer to additional contexts to look for information, e.g. program documentation or historical code versions. Therefore, we argue that encoding this additional contextual information could also benefit code representation for deep learning. Recent papers incorporate contextual data (e.g. call hierarchy) into vector representation to address program comprehension problems. This motivates further studies to explore additional contexts, such as version history, to enhance models' understanding of programs. That is, insights from version history enable recognition of patterns in code evolution over time, recurring issues, and the effectiveness of past solutions. Our paper presents preliminary evidence of the potential benefit of encoding contextual information from the version history to predict code clones and perform code classification. We experiment with two representative deep learning models, ASTNN and CodeBERT, to investigate whether combining additional contexts with different aggregations may benefit downstream activities. The experimental result affirms the positive impact of combining version history into source code representation in all scenarios; however, to ensure the technique performs consistently, we need to conduct a holistic investigation on a larger code base using different combinations of contexts, aggregation, and models. Therefore, we propose a research agenda aimed at exploring various aspects of encoding additional context to improve code representation and its optimal utilisation in specific situations.

cs.SE↗