In recent years, deep discrete representation learning (DRL) has achieved significant success across various domains. Most DRL frameworks (e.g., the widely used VQ-VAE and its variants) have primarily focused on generative settings, where the quality of a representation is implicitly gauged by the fidelity of its generation. In fact, the goodness of a discrete representation remain ambiguously defined across the literature. In this work, we adopt a practical approach that examines DRL from a task-driven perspective. We propose a unified framework that explores the usefulness of discrete features in relation to downstream tasks, with generation naturally viewed as one possible application. In this context, the properties of discrete representations as well as the way they benefit certain tasks are also relatively understudied. We therefore provide an additional theoretical analysis of the trade-off between representational capacity and sample complexity, shedding light on how discrete representation utilization impacts task performance. Finally, we demonstrate the flexibility and effectiveness of our framework across diverse applications.

Concept erasure has emerged as a promising technique for mitigating the risk of harmful content generation in diffusion models by selectively unlearning undesirable concepts. The common principle of previous works to remove a specific concept is to map it to a fixed generic concept, such as a neutral concept or just an empty text prompt. In this paper, we demonstrate that this fixed-target strategy is suboptimal, as it fails to account for the impact of erasing one concept on the others. To address this limitation, we model the concept space as a graph and empirically analyze the effects of erasing one concept on the remaining concepts. Our analysis uncovers intriguing geometric properties of the concept space, where the influence of erasing a concept is confined to a local region. Building on this insight, we propose the Adaptive Guided Erasure (AGE) method, which dynamically selects optimal target concepts tailored to each undesirable concept, minimizing unintended side effects. Experimental results show that AGE significantly outperforms state-of-the-art erasure methods on preserving unrelated concepts while maintaining effective erasure performance. Our code is published at {https://github.com/tuananhbui89/Adaptive-Guided-Erasure}.

Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are intractable without assumptions about structural dependencies or model classes. While existing learning methods are fundamentally based on likelihood maximization, here we offer a new view of the parameter learning problem through the lens of optimal transport. This perspective licenses a general framework that operates on any directed graphs without making unrealistic assumptions on the posterior over the latent variables or resorting to variational approximations. We develop a theoretical framework and support it with extensive empirical evidence demonstrating the versatility and robustness of our approach. Across experiments, we show that not only can our method effectively recover the ground-truth parameters but it also performs comparably or better than competing baselines on downstream applications.

Learning deep discrete latent presentations offers a promise of better symbolic and summarized abstractions that are more useful to subsequent downstream tasks. Inspired by the seminal Vector Quantized Variational Auto-Encoder (VQ-VAE), most of work in learning deep discrete representations has mainly focused on improving the original VQ-VAE form and none of them has studied learning deep discrete representations from the generative viewpoint. In this work, we study learning deep discrete representations from the generative viewpoint. Specifically, we endow discrete distributions over sequences of codewords and learn a deterministic decoder that transports the distribution over the sequences of codewords to the data distribution via minimizing a WS distance between them. We develop further theories to connect it with the clustering viewpoint of WS distance, allowing us to have a better and more controllable clustering solution. Finally, we empirically evaluate our method on several well-known benchmarks, where it achieves better qualitative and quantitative performances than the other VQ-VAE variants in terms of the codebook utilization and image reconstruction/generation.