arXiv subjects

Hien Dang

Publications and source records attributed to Hien Dang.

8 recordsLinked to original sources

arXiv2026

Prediction-Only Distillation in Linear and Logistic Regression

Self-distillation (SD) is typically studied when the student is retrained on the teacher's original training inputs. In many practical deployments, however, the labeled training data are no longer available, and one has access only to the trained predictor and fresh unlabeled covariates. We study SD in this prediction-only regime through a fresh-X prediction-mixed scheme: a pure-distilled student is trained on fresh covariates pseudo-labeled by the teacher, and the final predictor is an affine combination of the teacher and student predictions. For ridge regression under proportional asymptotics, we derive deterministic equivalents for the optimally mixed prediction risk under general anisotropic covariance and deterministic signal. We show that this risk is strictly smaller than the teacher risk for almost every pair of teacher and student regularization levels, including when the fresh covariates are out-of-distribution and even when their covariance is isotropic. We further show that the optimal mixing weight cannot be identified from unlabeled data alone, but can be consistently estimated in a single post-training step using a small independent labeled calibration set, without additional model fitting. Finally, for binary logistic regression, we show that prediction mixing can outperform both the teacher and the pure-distilled classifier.

math.ST↗

arXiv2026

Optimal Unconstrained Self-Distillation in Ridge Regression: Strict Improvements, Precise Asymptotics, and One-Shot Tuning

Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth labels and the teacher's own predictions using the same architecture and training data. Although SD has been empirically shown to often improve generalization, its formal guarantees remain limited. We study SD for ridge regression in unconstrained setting in which the mixing weight $\xi$ may be outside the unit interval. Conditioned on the training data and without any distributional assumptions, we prove that for any squared prediction risk (including out-of-distribution), the optimally mixed student strictly improves upon the ridge teacher for every regularization level $\lambda > 0$ at which the teacher ridge risk $R(\lambda)$ is nonstationary (i.e., $R'(\lambda) \neq 0$). We obtain a closed-form expression for the optimal mixing weight $\xi^\star(\lambda)$ for any value of $\lambda$ and show that it obeys the sign rule: $\operatorname{sign}(\xi^\star(\lambda))=-\operatorname{sign}(R'(\lambda))$. In particular, $\xi^\star(\lambda)$ can be negative, which is the case in over-regularized regimes. To quantify the risk improvement due to SD, we derive exact deterministic equivalents for the optimal SD risk in the proportional asymptotics regime (where the sample and feature sizes $n$ and $p$ both diverge but their aspect ratio $p/n$ converges) under general anisotropic covariance and deterministic signals. Our asymptotic analysis extends standard second-order ridge deterministic equivalents to their fourth-order analogs using block linearization, which may be of independent interest. From a practical standpoint, we propose a consistent one-shot tuning method to estimate $\xi^\star$ without grid search, sample splitting, or refitting. Experiments on real-world datasets and pretrained neural network features support our theory and the one-shot tuning method.

math.ST↗

arXiv2025

On the Mechanisms of Collaborative Learning in VAE Recommenders

Variational Autoencoders (VAEs) are a powerful alternative to matrix factorization for recommendation. A common technique in VAE-based collaborative filtering (CF) consists in applying binary input masking to user interaction vectors, which improves performance but remains underexplored theoretically. In this work, we analyze how collaboration arises in VAE-based CF and show it is governed by \emph{latent proximity}: we derive a latent sharing radius that informs when an SGD update on one user strictly reduces the loss on another user, with influence decaying as the latent Wasserstein distance increases. We further study the induced geometry: with clean inputs, VAE-based CF primarily exploits \emph{local} collaboration between input-similar users and under-utilizes \emph{global} collaboration between far-but-related users. We compare two mechanisms that encourage \emph{global} mixing and characterize their trade-offs: \ding{172} $\beta$-KL regularization directly tightens the information bottleneck, promoting posterior overlap but risking representational collapse if too large; \ding{173} input masking induces stochastic \emph{geometric} contractions and expansions, which can bring distant users onto the same latent neighborhood but also introduce neighborhood drift. To preserve user identity while enabling global consistency, we propose an anchor regularizer that aligns user posteriors with item embeddings, stabilizing users under masking and facilitating signal sharing across related items. Our analyses are validated on the Netflix, MovieLens-20M, and Million Song datasets. We also successfully deployed our proposed algorithm on an Amazon streaming platform following a successful online experiment.

cs.LG↗

arXiv2025

DoRAN: Stabilizing Weight-Decomposed Low-Rank Adaptation via Noise Injection and Auxiliary Networks

Parameter-efficient fine-tuning (PEFT) methods have become the standard paradigm for adapting large-scale models. Among these techniques, Weight-Decomposed Low-Rank Adaptation (DoRA) has been shown to improve both the learning capacity and training stability of the Low-Rank Adaptation (LoRA) method by explicitly decomposing pre-trained weights into magnitude and directional components. In this work, we propose DoRAN, a new technique designed to stabilize training and boost the sample efficiency of DoRA. Our framework introduces two key components: (i) the injection of learnable noise into the denominator of DoRA weight decomposition, which serves as an adaptive regularizer to mitigate instabilities and improve the estimation rate of low-rank matrices; and (ii) the replacement of static low-rank matrices with auxiliary networks that generate them dynamically, enabling parameter coupling between the query and value projection matrices, leading to improved sample efficiency both theoretically and empirically. Comprehensive experiments on vision and language benchmarks show that DoRAN consistently outperforms LoRA, DoRA, and other PEFT baselines, underscoring the effectiveness of combining noise-based regularization with network-based parameter generation.

cs.LG↗

arXiv2025

Why Domain Generalization Fail? A View of Necessity and Sufficiency

Despite a strong theoretical foundation, empirical experiments reveal that existing domain generalization (DG) algorithms often fail to consistently outperform the ERM baseline. We argue that this issue arises because most DG studies focus on establishing theoretical guarantees for generalization under unrealistic assumptions, such as the availability of sufficient, diverse (or even infinite) domains or access to target domain knowledge. As a result, the extent to which domain generalization is achievable in scenarios with limited domains remains largely unexplored. This paper seeks to address this gap by examining generalization through the lens of the conditions necessary for its existence and learnability. Specifically, we systematically establish a set of necessary and sufficient conditions for generalization. Our analysis highlights that existing DG methods primarily act as regularization mechanisms focused on satisfying sufficient conditions, while often neglecting necessary ones. However, sufficient conditions cannot be verified in settings with limited training domains. In such cases, regularization targeting sufficient conditions aims to maximize the likelihood of generalization, whereas regularization targeting necessary conditions ensures its existence. Using this analysis, we reveal the shortcomings of existing DG algorithms by showing that, while they promote sufficient conditions, they inadvertently violate necessary conditions. To validate our theoretical insights, we propose a practical method that promotes the sufficient condition while maintaining the necessary conditions through a novel subspace representation alignment strategy. This approach highlights the advantages of preserving the necessary conditions on well-established DG benchmarks.

cs.LG↗

arXiv2024

Neural Collapse for Cross-entropy Class-Imbalanced Learning with Unconstrained ReLU Feature Model

The current paradigm of training deep neural networks for classification tasks includes minimizing the empirical risk that pushes the training loss value towards zero, even after the training error has been vanished. In this terminal phase of training, it has been observed that the last-layer features collapse to their class-means and these class-means converge to the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is termed as Neural Collapse (NC). To theoretically understand this phenomenon, recent works employ a simplified unconstrained feature model to prove that NC emerges at the global solutions of the training problem. However, when the training dataset is class-imbalanced, some NC properties will no longer be true. For example, the class-means geometry will skew away from the simplex ETF when the loss converges. In this paper, we generalize NC to imbalanced regime for cross-entropy loss under the unconstrained ReLU feature model. We prove that, while the within-class features collapse property still holds in this setting, the class-means will converge to a structure consisting of orthogonal vectors with different lengths. Furthermore, we find that the classifier weights are aligned to the scaled and centered class-means with scaling factors depend on the number of training samples of each class, which generalizes NC in the class-balanced setting. We empirically prove our results through experiments on practical architectures and dataset.

cs.LG↗

arXiv2023

Beyond Vanilla Variational Autoencoders: Detecting Posterior Collapse in Conditional and Hierarchical Variational Autoencoders

The posterior collapse phenomenon in variational autoencoder (VAE), where the variational posterior distribution closely matches the prior distribution, can hinder the quality of the learned latent variables. As a consequence of posterior collapse, the latent variables extracted by the encoder in VAE preserve less information from the input data and thus fail to produce meaningful representations as input to the reconstruction process in the decoder. While this phenomenon has been an actively addressed topic related to VAE performance, the theory for posterior collapse remains underdeveloped, especially beyond the standard VAE. In this work, we advance the theoretical understanding of posterior collapse to two important and prevalent yet less studied classes of VAE: conditional VAE and hierarchical VAE. Specifically, via a non-trivial theoretical analysis of linear conditional VAE and hierarchical VAE with two levels of latent, we prove that the cause of posterior collapses in these models includes the correlation between the input and output of the conditional VAE and the effect of learnable encoder variance in the hierarchical VAE. We empirically validate our theoretical findings for linear conditional and hierarchical VAE and demonstrate that these results are also predictive for non-linear cases with extensive experiments.

stat.ML↗

arXiv2023

Neural Collapse in Deep Linear Networks: From Balanced to Imbalanced Data

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural properties in their last-layer features and classifiers across canonical datasets when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means, and those class-means are the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is known as Neural Collapse (NC). Recent papers have theoretically shown that NC emerges in the global minimizers of training problems with the simplified "unconstrained feature model". In this context, we take a step further and prove the NC occurrences in deep linear networks for the popular mean squared error (MSE) and cross entropy (CE) losses, showing that global solutions exhibit NC properties across the linear layers. Furthermore, we extend our study to imbalanced data for MSE loss and present the first geometric analysis of NC under bias-free setting. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of orthogonal vectors, whose lengths depend on the amount of data in their corresponding classes. Finally, we empirically validate our theoretical analyses on synthetic and practical network architectures with both balanced and imbalanced scenarios.

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