arXiv subjects

Tan M. Nguyen

Publications and source records attributed to Tan M. Nguyen.

At least 37 records · Page 2Linked to original sources

arXiv2026

Tight Clusters Make Specialized Experts

Sparse Mixture-of-Experts (MoE) architectures have emerged as a promising approach to decoupling model capacity from computational cost. At the core of the MoE model is the router, which learns the underlying clustering structure of the input distribution in order to send input tokens to appropriate experts. However, latent clusters may be unidentifiable in high dimension, which causes slow convergence, susceptibility to data contamination, and overall degraded representations as the router is unable to perform appropriate token-expert matching. We examine the router through the lens of clustering optimization and derive optimal feature weights that maximally identify the latent clusters. We use these weights to compute the token-expert routing assignments in an adaptively transformed space that promotes well-separated clusters, which helps identify the best-matched expert for each token. In particular, for each expert cluster, we compute a set of weights that scales features according to whether that expert clusters tightly along that feature. We term this novel router the Adaptive Clustering (AC) router. Our AC router enables the MoE model to obtain three connected benefits: 1) faster convergence, 2) better robustness to data corruption, and 3) overall performance improvement, as experts are specialized in semantically distinct regions of the input space. We empirically demonstrate the advantages of our AC router over baseline routing methods when applied on a variety of MoE backbones for language modeling and image recognition tasks in both clean and corrupted settings.

cs.LG↗

arXiv2026

Revisiting Transformers with Insights from Image Filtering and Boosting

The self-attention mechanism, a cornerstone of Transformer-based state-of-the-art deep learning architectures, is largely heuristic-driven and fundamentally challenging to interpret. Establishing a robust theoretical foundation to explain its remarkable success and limitations has therefore become an increasingly prominent focus in recent research. Some notable directions have explored understanding self-attention through the lens of image denoising and nonparametric regression. While promising, existing frameworks still lack a deeper mechanistic interpretation of various architectural components that enhance self-attention, both in its original formulation and subsequent variants. In this work, we aim to advance this understanding by developing a unifying image processing framework, capable of explaining not only the self-attention computation itself but also the role of components such as positional encoding and residual connections, including numerous later variants. We also pinpoint potential distinctions between the two concepts building upon our framework, and make effort to close this gap. We introduce two independent architectural modifications within transformers. While our primary objective is interpretability, we empirically observe that image processing-inspired modifications can also lead to notably improved accuracy and robustness against data contamination and adversaries across language and vision tasks as well as better long sequence understanding.

cs.CV↗

arXiv2025

MMA: A Momentum Mamba Architecture for Human Activity Recognition with Inertial Sensors

Human activity recognition (HAR) from inertial sensors is essential for ubiquitous computing, mobile health, and ambient intelligence. Conventional deep models such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and transformers have advanced HAR but remain limited by vanishing or exloding gradients, high computational cost, and difficulty in capturing long-range dependencies. Structured state-space models (SSMs) like Mamba address these challenges with linear complexity and effective temporal modeling, yet they are restricted to first-order dynamics without stable longterm memory mechanisms. We introduce Momentum Mamba, a momentum-augmented SSM that incorporates second-order dynamics to improve stability of information flow across time steps, robustness, and long-sequence modeling. Two extensions further expand its capacity: Complex Momentum Mamba for frequency-selective memory scaling. Experiments on multiple HAR benchmarks demonstrate consistent gains over vanilla Mamba and Transformer baselines in accuracy, robustness, and convergence speed. With only moderate increases in training cost, momentum-augmented SSMs offer a favorable accuracy-efficiency balance, establishing them as a scalable paradigm for HAR and a promising principal framework for broader sequence modeling applications.

cs.HC↗

arXiv2025

Dynamical Properties of Tokens in Self-Attention and Effects of Positional Encoding

This paper investigates the dynamical properties of tokens in pre-trained Transformer models and explores their application to improving Transformers. To this end, we analyze the dynamical system governing the continuous-time limit of the pre-trained model and characterize the asymptotic behavior of its solutions. Specifically, we characterize when tokens move closer to or farther from one another over time, depending on the model parameters. We provide sufficient conditions, based on these parameters, to identify scenarios where tokens either converge to zero or diverge to infinity. Unlike prior works, our conditions are broader in scope and more applicable to real-world models. Furthermore, we investigate how different forms of positional encoding -- specifically absolute and rotary -- affect these dynamical regimes. Empirical evidence reveals that the convergence scenario adversely impacts model performance. Motivated by these insights, we propose simple refinements to Transformer architectures that mitigate convergence behavior in models with absolute or rotary positional encoding. These findings support theoretical foundations and design principles for improving Transformer models.

cs.LG↗

arXiv2025

Angular Steering: Behavior Control via Rotation in Activation Space

Controlling specific behaviors in large language models while preserving their general capabilities is a central challenge for safe and reliable artificial intelligence deployment. Current steering methods, such as vector addition and directional ablation, are constrained within a two-dimensional subspace defined by the activation and feature direction, making them sensitive to chosen parameters and potentially affecting unrelated features due to unintended interactions in activation space. We introduce Angular Steering, a novel and flexible method for behavior modulation that operates by rotating activations within a fixed two-dimensional subspace. By formulating steering as a geometric rotation toward or away from a target behavior direction, Angular Steering provides continuous, fine-grained control over behaviors such as refusal and compliance. We demonstrate this method using refusal steering emotion steering as use cases. Additionally, we propose Adaptive Angular Steering, a selective variant that rotates only activations aligned with the target feature, further enhancing stability and coherence. Angular Steering generalizes existing addition and orthogonalization techniques under a unified geometric rotation framework, simplifying parameter selection and maintaining model stability across a broader range of adjustments. Experiments across multiple model families and sizes show that Angular Steering achieves robust behavioral control while maintaining general language modeling performance, underscoring its flexibility, generalization, and robustness compared to prior approaches. Code and artifacts are available at https://github.com/lone17/angular-steering/.

cs.LG↗

arXiv2025

On Linear Mode Connectivity of Mixture-of-Experts Architectures

Linear Mode Connectivity (LMC) is a notable phenomenon in the loss landscapes of neural networks, wherein independently trained models have been observed to be connected--up to permutation symmetries--by linear paths in parameter space along which the loss remains consistently low. This observation challenges classical views of non-convex optimization and has implications for model ensembling, generalization, and our understanding of neural loss geometry. Inspired by recent studies on LMC in standard neural networks, we systematically investigate this phenomenon within Mixture-of-Experts (MoE) architectures--a class of models known for their scalability and computational efficiency, which combine traditional neural networks--referred to as experts--through a learnable gating mechanism. We begin by conducting a comprehensive analysis of both dense and sparse gating regimes, demonstrating that the symmetries inherent to MoE architectures are fully characterized by permutations acting on both the expert components and the gating function. Building on these foundational findings, we propose a matching algorithm that enables alignment between independently trained MoEs, thereby facilitating the discovery of LMC. Finally, we empirically validate the presence of LMC using our proposed algorithm across diverse MoE configurations--including dense, sparse, and shared-expert variants--under a wide range of model settings and datasets of varying scales and modalities. Our results confirm the existence of LMC in MoE architectures and offer fundamental insights into the functional landscape and optimization dynamics of deep learning models.

cs.LG↗

arXiv2025

Transformer Meets Twicing: Harnessing Unattended Residual Information

Transformer-based deep learning models have achieved state-of-the-art performance across numerous language and vision tasks. While the self-attention mechanism, a core component of transformers, has proven capable of handling complex data patterns, it has been observed that the representational capacity of the attention matrix degrades significantly across transformer layers, thereby hurting its overall performance. In this work, we leverage the connection between self-attention computations and low-pass non-local means (NLM) smoothing filters and propose the Twicing Attention, a novel attention mechanism that uses kernel twicing procedure in nonparametric regression to alleviate the low-pass behavior of associated NLM smoothing with compelling theoretical guarantees and enhanced adversarial robustness. This approach enables the extraction and reuse of meaningful information retained in the residuals following the imperfect smoothing operation at each layer. Our proposed method offers two key advantages over standard self-attention: 1) a provably slower decay of representational capacity and 2) improved robustness and accuracy across various data modalities and tasks. We empirically demonstrate the performance gains of our model over baseline transformers on multiple tasks and benchmarks, including image classification and language modeling, on both clean and corrupted data.

cs.LG↗

arXiv2025

The Blessing and Curse of Dimensionality in Safety Alignment

The focus on safety alignment in large language models (LLMs) has increased significantly due to their widespread adoption across different domains. The scale of LLMs play a contributing role in their success, and the growth in parameter count follows larger hidden dimensions. In this paper, we hypothesize that while the increase in dimensions has been a key advantage, it may lead to emergent problems as well. These problems emerge as the linear structures in the activation space can be exploited, in the form of activation engineering, to circumvent its safety alignment. Through detailed visualizations of linear subspaces associated with different concepts, such as safety, across various model scales, we show that the curse of high-dimensional representations uniquely impacts LLMs. Further substantiating our claim, we demonstrate that projecting the representations of the model onto a lower dimensional subspace can preserve sufficient information for alignment while avoiding those linear structures. Empirical results confirm that such dimensional reduction significantly reduces susceptibility to jailbreaking through representation engineering. Building on our empirical validations, we provide theoretical insights into these linear jailbreaking methods relative to a model's hidden dimensions. Broadly speaking, our work posits that the high dimensions of a model's internal representations can be both a blessing and a curse in safety alignment.

cs.AI↗

arXiv2025

Tree-Sliced Wasserstein Distance: A Geometric Perspective

Many variants of Optimal Transport (OT) have been developed to address its heavy computation. Among them, notably, Sliced Wasserstein (SW) is widely used for application domains by projecting the OT problem onto one-dimensional lines, and leveraging the closed-form expression of the univariate OT to reduce the computational burden. However, projecting measures onto low-dimensional spaces can lead to a loss of topological information. To mitigate this issue, in this work, we propose to replace one-dimensional lines with a more intricate structure, called tree systems. This structure is metrizable by a tree metric, which yields a closed-form expression for OT problems on tree systems. We provide an extensive theoretical analysis to formally define tree systems with their topological properties, introduce the concept of splitting maps, which operate as the projection mechanism onto these structures, then finally propose a novel variant of Radon transform for tree systems and verify its injectivity. This framework leads to an efficient metric between measures, termed Tree-Sliced Wasserstein distance on Systems of Lines (TSW-SL). By conducting a variety of experiments on gradient flows, image style transfer, and generative models, we illustrate that our proposed approach performs favorably compared to SW and its variants.

cs.LG↗

arXiv2025

Tree-Sliced Wasserstein Distance with Nonlinear Projection

Tree-Sliced methods have recently emerged as an alternative to the traditional Sliced Wasserstein (SW) distance, replacing one-dimensional lines with tree-based metric spaces and incorporating a splitting mechanism for projecting measures. This approach enhances the ability to capture the topological structures of integration domains in Sliced Optimal Transport while maintaining low computational costs. Building on this foundation, we propose a novel nonlinear projectional framework for the Tree-Sliced Wasserstein (TSW) distance, substituting the linear projections in earlier versions with general projections, while ensuring the injectivity of the associated Radon Transform and preserving the well-definedness of the resulting metric. By designing appropriate projections, we construct efficient metrics for measures on both Euclidean spaces and spheres. Finally, we validate our proposed metric through extensive numerical experiments for Euclidean and spherical datasets. Applications include gradient flows, self-supervised learning, and generative models, where our methods demonstrate significant improvements over recent SW and TSW variants.

cs.LG↗

arXiv2025

Spherical Tree-Sliced Wasserstein Distance

Sliced Optimal Transport (OT) simplifies the OT problem in high-dimensional spaces by projecting supports of input measures onto one-dimensional lines and then exploiting the closed-form expression of the univariate OT to reduce the computational burden of OT. Recently, the Tree-Sliced method has been introduced to replace these lines with more intricate structures, known as tree systems. This approach enhances the ability to capture topological information of integration domains in Sliced OT while maintaining low computational cost. Inspired by this approach, in this paper, we present an adaptation of tree systems on OT problems for measures supported on a sphere. As a counterpart to the Radon transform variant on tree systems, we propose a novel spherical Radon transform with a new integration domain called spherical trees. By leveraging this transform and exploiting the spherical tree structures, we derive closed-form expressions for OT problems on the sphere. Consequently, we obtain an efficient metric for measures on the sphere, named Spherical Tree-Sliced Wasserstein (STSW) distance. We provide an extensive theoretical analysis to demonstrate the topology of spherical trees and the well-definedness and injectivity of our Radon transform variant, which leads to an orthogonally invariant distance between spherical measures. Finally, we conduct a wide range of numerical experiments, including gradient flows and self-supervised learning, to assess the performance of our proposed metric, comparing it to recent benchmarks.

cs.LG↗

arXiv2025

Distance-Based Tree-Sliced Wasserstein Distance

To overcome computational challenges of Optimal Transport (OT), several variants of Sliced Wasserstein (SW) has been developed in the literature. These approaches exploit the closed-form expression of the univariate OT by projecting measures onto (one-dimensional) lines. However, projecting measures onto low-dimensional spaces can lead to a loss of topological information. Tree-Sliced Wasserstein distance on Systems of Lines (TSW-SL) has emerged as a promising alternative that replaces these lines with a more advanced structure called tree systems. The tree structures enhance the ability to capture topological information of the metric while preserving computational efficiency. However, at the core of TSW-SL, the splitting maps, which serve as the mechanism for pushing forward measures onto tree systems, focus solely on the position of the measure supports while disregarding the projecting domains. Moreover, the specific splitting map used in TSW-SL leads to a metric that is not invariant under Euclidean transformations, a typically expected property for OT on Euclidean space. In this work, we propose a novel class of splitting maps that generalizes the existing one studied in TSW-SL enabling the use of all positional information from input measures, resulting in a novel Distance-based Tree-Sliced Wasserstein (Db-TSW) distance. In addition, we introduce a simple tree sampling process better suited for Db-TSW, leading to an efficient GPU-friendly implementation for tree systems, similar to the original SW. We also provide a comprehensive theoretical analysis of proposed class of splitting maps to verify the injectivity of the corresponding Radon Transform, and demonstrate that Db-TSW is an Euclidean invariant metric. We empirically show that Db-TSW significantly improves accuracy compared to recent SW variants while maintaining low computational cost via a wide range of experiments.

cs.LG↗

arXiv2025

MoLEx: Mixture of Layer Experts for Finetuning with Sparse Upcycling

Large-scale pre-training of deep models, followed by fine-tuning them, has become the cornerstone of natural language processing (NLP). The prevalence of data coupled with computational resources has led to large models with a considerable number of parameters. While the massive size of these models has led to remarkable success in many NLP tasks, a detriment is the expense required to retrain all the base model's parameters for the adaptation to each task or domain. Parameter Efficient Fine-Tuning (PEFT) provides an effective solution for this challenge by minimizing the number of parameters required to be fine-tuned while maintaining the quality of the model. While existing methods have achieved impressive results, they mainly focus on adapting a subset of parameters, weight reparameterization, and prompt engineering. In this paper, we study layers as extractors of different types of linguistic information that are valuable when used in conjunction. We then propose the Mixture of Layer Experts (MoLEx), a novel sparse mixture of experts (SMoE) whose experts are layers in the pre-trained model. It performs a conditional computation of a mixture of layers during fine-tuning to provide the model with more structural knowledge about the data. By providing an avenue for information exchange between layers, MoLEx enables the model to make a more well-informed prediction for the downstream task, leading to better fine-tuning results with the same number of effective parameters. As experts can be processed in parallel, MoLEx introduces minimal additional computational overhead. We empirically corroborate the advantages of MoLEx when combined with popular PEFT baseline methods on a variety of downstream fine-tuning tasks, including the popular GLUE benchmark as well as the End-to-End Challenge (E2E). The code is publicly available at https://github.com/rachtsy/molex.

cs.CL↗

arXiv2025

Monomial Matrix Group Equivariant Neural Functional Networks

Neural functional networks (NFNs) have recently gained significant attention due to their diverse applications, ranging from predicting network generalization and network editing to classifying implicit neural representation. Previous NFN designs often depend on permutation symmetries in neural networks' weights, which traditionally arise from the unordered arrangement of neurons in hidden layers. However, these designs do not take into account the weight scaling symmetries of $\ReLU$ networks, and the weight sign flipping symmetries of $\sin$ or $\Tanh$ networks. In this paper, we extend the study of the group action on the network weights from the group of permutation matrices to the group of monomial matrices by incorporating scaling/sign-flipping symmetries. Particularly, we encode these scaling/sign-flipping symmetries by designing our corresponding equivariant and invariant layers. We name our new family of NFNs the Monomial Matrix Group Equivariant Neural Functional Networks (Monomial-NFN). Because of the expansion of the symmetries, Monomial-NFN has much fewer independent trainable parameters compared to the baseline NFNs in the literature, thus enhancing the model's efficiency. Moreover, for fully connected and convolutional neural networks, we theoretically prove that all groups that leave these networks invariant while acting on their weight spaces are some subgroups of the monomial matrix group. We provide empirical evidence to demonstrate the advantages of our model over existing baselines, achieving competitive performance and efficiency.

cs.LG↗

arXiv2025

CAMEx: Curvature-aware Merging of Experts

Existing methods for merging experts during model training and fine-tuning predominantly rely on Euclidean geometry, which assumes a flat parameter space. This assumption can limit the model's generalization ability, especially during the pre-training phase, where the parameter manifold might exhibit more complex curvature. Curvature-aware merging methods typically require additional information and computational resources to approximate the Fisher Information Matrix, adding memory overhead. In this paper, we introduce CAMEx (Curvature-Aware Merging of Experts), a novel expert merging protocol that incorporates natural gradients to account for the non-Euclidean curvature of the parameter manifold. By leveraging natural gradients, CAMEx adapts more effectively to the structure of the parameter space, improving alignment between model updates and the manifold's geometry. This approach enhances both pre-training and fine-tuning, resulting in better optimization trajectories and improved generalization without the substantial memory overhead typically associated with curvature-aware methods. Our contributions are threefold: (1) CAMEx significantly outperforms traditional Euclidean-based expert merging techniques across various natural language processing tasks, leading to enhanced performance during pre-training and fine-tuning; (2) we introduce a dynamic merging architecture that optimizes resource utilization, achieving high performance while reducing computational costs, facilitating efficient scaling of large language models; and (3) we provide both theoretical and empirical evidence to demonstrate the efficiency of our proposed method. The code is publicly available at: https://github.com/kpup1710/CAMEx.

cs.LG↗

arXiv2024

An Attention-based Framework for Fair Contrastive Learning

Contrastive learning has proven instrumental in learning unbiased representations of data, especially in complex environments characterized by high-cardinality and high-dimensional sensitive information. However, existing approaches within this setting require predefined modelling assumptions of bias-causing interactions that limit the model's ability to learn debiased representations. In this work, we propose a new method for fair contrastive learning that employs an attention mechanism to model bias-causing interactions, enabling the learning of a fairer and semantically richer embedding space. In particular, our attention mechanism avoids bias-causing samples that confound the model and focuses on bias-reducing samples that help learn semantically meaningful representations. We verify the advantages of our method against existing baselines in fair contrastive learning and show that our approach can significantly boost bias removal from learned representations without compromising downstream accuracy.

cs.LG↗

arXiv2024

Elliptical Attention

Pairwise dot-product self-attention is key to the success of transformers that achieve state-of-the-art performance across a variety of applications in language and vision. This dot-product self-attention computes attention weights among the input tokens using Euclidean distance, which makes the model prone to representation collapse and vulnerable to contaminated samples. In this paper, we propose using a Mahalanobis distance metric for computing the attention weights to stretch the underlying feature space in directions of high contextual relevance. In particular, we define a hyper-ellipsoidal neighborhood around each query to increase the attention weights of the tokens lying in the contextually important directions. We term this novel class of attention Elliptical Attention. Our Elliptical Attention provides two benefits: 1) reducing representation collapse and 2) enhancing the model's robustness as Elliptical Attention pays more attention to contextually relevant information rather than focusing on some small subset of informative features. We empirically demonstrate the advantages of Elliptical Attention over the baseline dot-product attention and state-of-the-art attention methods on various practical tasks, including object classification, image segmentation, and language modeling across different data modalities.

cs.LG↗

arXiv2024

Unveiling the Hidden Structure of Self-Attention via Kernel Principal Component Analysis

The remarkable success of transformers in sequence modeling tasks, spanning various applications in natural language processing and computer vision, is attributed to the critical role of self-attention. Similar to the development of most deep learning models, the construction of these attention mechanisms relies on heuristics and experience. In our work, we derive self-attention from kernel principal component analysis (kernel PCA) and show that self-attention projects its query vectors onto the principal component axes of its key matrix in a feature space. We then formulate the exact formula for the value matrix in self-attention, theoretically and empirically demonstrating that this value matrix captures the eigenvectors of the Gram matrix of the key vectors in self-attention. Leveraging our kernel PCA framework, we propose Attention with Robust Principal Components (RPC-Attention), a novel class of robust attention that is resilient to data contamination. We empirically demonstrate the advantages of RPC-Attention over softmax attention on the ImageNet-1K object classification, WikiText-103 language modeling, and ADE20K image segmentation task.

cs.LG↗