Yohan Jung

Yohan Jung, Jinkyoo Park

Convolutional deep sets are the architecture of a deep neural network (DNN) that can model stationary stochastic process. This architecture uses the kernel smoother and the DNN to construct the translation equivariant functional representations, and thus reflects the inductive bias of the stationarity into DNN. However, since this architecture employs the kernel smoother known as the non-parametric model, it may produce ambiguous representations when the number of data points is not given sufficiently. To remedy this issue, we introduce Bayesian convolutional deep sets that construct the random translation equivariant functional representations with stationary prior. Furthermore, we present how to impose the task-dependent prior for each dataset because a wrongly imposed prior forms an even worse representation than that of the kernel smoother. We validate the proposed architecture and its training on various experiments with time-series and image datasets.

Subarnaduti Paul, Yohan Jung, Mohammad Emtiyaz Khan et al.

Continual learning remains a major challenge for modern deep networks, partly because commonly used optimizers lack inherent mechanisms for continual adaptation. One such natural mechanism is fast and slow adaptation to balance stability and plasticity. This mechanism has deep roots in neuroscience and biology, but there is no consensus on how to best incorporate it in commonly used optimizers. Here, we show that this can be easily done via the VCL framework, where past posteriors are used as priors in the future. Our key idea is to incorporate slow adaptation via merging of past posteriors to slow down the drift in the knowledge as learning progresses. The merged posterior is then used as the prior in the VCL update to implement the fast-weight updates. These steps can be seamlessly implemented in the IVON optimizer, whose form and costs are nearly identical to that of Adam. We call this new optimizer the Continual IVON (CoVON) optimizer and show that it not only consistently improves over existing VCL optimizers, but also performs better than other weight-regularization strategies across domain-incremental learning, continual pre-training, and fine-tuning of large language models.

Sungjun Lim, Jeyoon Yeom, Sooyon Kim et al.

Bayesian neural networks (BNNs) estimate the posterior distribution of model parameters and utilize posterior samples for Bayesian Model Averaging (BMA) in prediction. However, despite the crucial role of flatness in the loss landscape in improving the generalization of neural networks, its impact on BMA has been largely overlooked. In this work, we explore how posterior flatness influences BMA generalization and empirically demonstrate that (1) most approximate Bayesian inference methods fail to yield a flat posterior and (2) BMA predictions, without considering posterior flatness, are less effective at improving generalization. To address this, we propose Flat Posterior-aware Bayesian Model Averaging (FP-BMA), a novel training objective that explicitly encourages flat posteriors in a principled Bayesian manner. We also introduce a Flat Posterior-aware Bayesian Transfer Learning scheme that enhances generalization in downstream tasks. Empirically, we show that FP-BMA successfully captures flat posteriors, improving generalization performance.

Yohan Jung, Kyungwoo Song, Jinkyoo Park

A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of parameters for the SM kernel typically induces an over-fitting, particularly when a gradient-based optimization is used. Also, a longer training time is required. To improve the training, we propose an approximate Bayesian inference for the SM kernel. Specifically, we employ the variational distribution of the spectral points to approximate SM kernel with a random Fourier feature. We optimize the variational parameters by applying a sampling-based variational inference to the derived evidence lower bound (ELBO) estimator constructed from the approximate kernel. To improve the inference, we further propose two additional strategies: (1) a sampling strategy of spectral points to estimate the ELBO estimator reliably and thus its associated gradient, and (2) an approximate natural gradient to accelerate the convergence of the parameters. The proposed inference combined with two strategies accelerates the convergence of the parameters and leads to better optimal parameters.

Kyungwoo Song, Yohan Jung, Dongjun Kim et al.

\textit{Attention} computes the dependency between representations, and it encourages the model to focus on the important selective features. Attention-based models, such as Transformer and graph attention network (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.

Yohan Jung, Jinkyoo Park

Hidden Markov Model (HMM) combined with Gaussian Process (GP) emission can be effectively used to estimate the hidden state with a sequence of complex input-output relational observations. Especially when the spectral mixture (SM) kernel is used for GP emission, we call this model as a hybrid HMM-GPSM. This model can effectively model the sequence of time-series data. However, because of a large number of parameters for the SM kernel, this model can not effectively be trained with a large volume of data having (1) long sequence for state transition and 2) a large number of time-series dataset in each sequence. This paper proposes a scalable learning method for HMM-GPSM. To effectively train the model with a long sequence, the proposed method employs a Stochastic Variational Inference (SVI) approach. Also, to effectively process a large number of data point each time-series data, we approximate the SM kernel using Reparametrized Random Fourier Feature (R-RFF). The combination of these two techniques significantly reduces the training time. We validate the proposed learning method in terms of its hidden-sate estimation accuracy and computation time using large-scale synthetic and real data sets with missing values.