Hierarchically Clustered Representation Learning

The joint optimization of representation learning and clustering in the embedding space has experienced a breakthrough in recent years. In spite of the advance, clustering with representation learning has been limited to flat-level categories, which often involves cohesive clustering with a focus on instance relations. To overcome the limitations of flat clustering, we introduce hierarchically-clustered representation learning (HCRL), which simultaneously optimizes representation learning and hierarchical clustering in the embedding space. Compared with a few prior works, HCRL firstly attempts to consider a generation of deep embeddings from every component of the hierarchy, not just leaf components. In addition to obtaining hierarchically clustered embeddings, we can reconstruct data by the various abstraction levels, infer the intrinsic hierarchical structure, and learn the level-proportion features. We conducted evaluations with image and text domains, and our quantitative analyses showed competent likelihoods and the best accuracies compared with the baselines.Comment: 10 pages, 7 figures, Under review as a conference pape

Bivariate Beta-LSTM

Long Short-Term Memory (LSTM) infers the long term dependency through a cell state maintained by the input and the forget gate structures, which models a gate output as a value in [0,1] through a sigmoid function. However, due to the graduality of the sigmoid function, the sigmoid gate is not flexible in representing multi-modality or skewness. Besides, the previous models lack modeling on the correlation between the gates, which would be a new method to adopt inductive bias for a relationship between previous and current input. This paper proposes a new gate structure with the bivariate Beta distribution. The proposed gate structure enables probabilistic modeling on the gates within the LSTM cell so that the modelers can customize the cell state flow with priors and distributions. Moreover, we theoretically show the higher upper bound of the gradient compared to the sigmoid function, and we empirically observed that the bivariate Beta distribution gate structure provides higher gradient values in training. We demonstrate the effectiveness of bivariate Beta gate structure on the sentence classification, image classification, polyphonic music modeling, and image caption generation.Comment: AAAI 202

Frequency Domain-based Dataset Distillation

This paper presents FreD, a novel parameterization method for dataset distillation, which utilizes the frequency domain to distill a small-sized synthetic dataset from a large-sized original dataset. Unlike conventional approaches that focus on the spatial domain, FreD employs frequency-based transforms to optimize the frequency representations of each data instance. By leveraging the concentration of spatial domain information on specific frequency components, FreD intelligently selects a subset of frequency dimensions for optimization, leading to a significant reduction in the required budget for synthesizing an instance. Through the selection of frequency dimensions based on the explained variance, FreD demonstrates both theoretical and empirical evidence of its ability to operate efficiently within a limited budget, while better preserving the information of the original dataset compared to conventional parameterization methods. Furthermore, based on the orthogonal compatibility of FreD with existing methods, we confirm that FreD consistently improves the performances of existing distillation methods over the evaluation scenarios with different benchmark datasets. We release the code at https://github.com/sdh0818/FreD.Comment: Accepted at NeurIPS 202

Implicit Kernel Attention

\textit{Attention} computes the dependency between representations, and it encourages the model to focus on the important selective features. Attention-based models, such as Transformers and graph attention networks (GAT) are widely utilized for sequential data and graph-structured data. This paper suggests a new interpretation and generalized structure of the attention in Transformer and GAT. For the attention in Transformer and GAT, we derive that the attention is a product of two parts: 1) the RBF kernel to measure the similarity of two instances and 2) the exponential of $L^{2}$ norm to compute the importance of individual instances. From this decomposition, we generalize the attention in three ways. First, we propose implicit kernel attention with an implicit kernel function, instead of manual kernel selection. Second, we generalize $L^{2}$ norm as the $L^{p}$ norm. Third, we extend our attention to structured multi-head attention. Our generalized attention shows better performance on classification, translation, and regression tasks

Generalized Gumbel-Softmax Gradient Estimator for Various Discrete Random Variables

Estimating the gradients of stochastic nodes is one of the crucial research questions in the deep generative modeling community, which enables the gradient descent optimization on neural network parameters. This estimation problem becomes further complex when we regard the stochastic nodes to be discrete because pathwise derivative techniques cannot be applied. Hence, the stochastic gradient estimation of discrete distributions requires either a score function method or continuous relaxation of the discrete random variables. This paper proposes a general version of the Gumbel-Softmax estimator with continuous relaxation, and this estimator is able to relax the discreteness of probability distributions including more diverse types, other than categorical and Bernoulli. In detail, we utilize the truncation of discrete random variables and the Gumbel-Softmax trick with a linear transformation for the relaxed reparameterization. The proposed approach enables the relaxed discrete random variable to be reparameterized and to backpropagated through a large scale stochastic computational graph. Our experiments consist of (1) synthetic data analyses, which show the efficacy of our methods; and (2) applications on VAE and topic model, which demonstrate the value of the proposed estimation in practices