Hoang M. Nguyen

Xuefeng Gao, Hoang M. Nguyen, Lingjiong Zhu

Score-based generative models (SGMs) is a recent class of deep generative models with state-of-the-art performance in many applications. In this paper, we establish convergence guarantees for a general class of SGMs in 2-Wasserstein distance, assuming accurate score estimates and smooth log-concave data distribution. We specialize our result to several concrete SGMs with specific choices of forward processes modelled by stochastic differential equations, and obtain an upper bound on the iteration complexity for each model, which demonstrates the impacts of different choices of the forward processes. We also provide a lower bound when the data distribution is Gaussian. Numerically, we experiment SGMs with different forward processes, some of which are newly proposed in this paper, for unconditional image generation on CIFAR-10. We find that the experimental results are in good agreement with our theoretical predictions on the iteration complexity, and the models with our newly proposed forward processes can outperform existing models.

Mert Gurbuzbalaban, Hoang M. Nguyen, Xicheng Zhang et al.

Standard first-order Langevin algorithms such as the unadjusted Langevin algorithm (ULA) are obtained by discretizing the Langevin diffusion and are widely used for sampling in machine learning because they scale to high dimensions and large datasets. However, they face two key limitations: (i) they require differentiable log-densities, excluding targets with non-differentiable components; and (ii) they generally fail to sample heavy-tailed targets. We propose anchored Langevin dynamics, a unified approach that accommodates non-differentiable targets and certain classes of heavy-tailed distributions. The method replaces the original potential with a smooth reference potential and modifies the Langevin diffusion via multiplicative scaling. We establish non-asymptotic guarantees in the 2-Wasserstein distance to the target distribution and provide an equivalent formulation derived via a random time change of the Langevin diffusion. We provide numerical experiments to illustrate the theory and practical performance of our proposed approach.

Hoang M. Nguyen, Satya N. Shukla, Qiang Zhang et al.

Self-supervised learning has been a powerful approach for learning meaningful representations from unlabeled data across various domains, reducing the reliance on large labeled datasets. Inspired by BERT's success in capturing deep bidirectional contexts in natural language processing, similar frameworks have been adapted to other modalities such as audio, with models like BEATs extending the bidirectional training paradigm to audio signals using vector quantization (VQ). However, these frameworks face challenges, notably their dependence on a single codebook for quantization, which may not capture the complex, multifaceted nature of signals. In addition, inefficiencies in codebook utilization lead to underutilized code vectors. To address these limitations, we introduce BRIDLE (Bidirectional Residual Quantization Interleaved Discrete Learning Encoder), a self-supervised encoder pretraining framework that incorporates residual quantization (RQ) into the bidirectional training process, and is generalized for pretraining with audio, image, and video. Using multiple hierarchical codebooks, RQ enables fine-grained discretization in the latent space, enhancing representation quality. BRIDLE involves an interleaved training procedure between the encoder and tokenizer. We evaluate BRIDLE on audio understanding tasks using classification benchmarks, achieving state-of-the-art results, and demonstrate competitive performance on image classification and video classification tasks, showing consistent improvements over traditional VQ methods in downstream performance.