A standard practice in developing image recognition models is to train a model on a specific image resolution and then deploy it. However, in real-world inference, models often encounter images different from the training sets in resolution and/or subject to natural variations such as weather changes, noise types and compression artifacts. While traditional solutions involve training multiple models for different resolutions or input variations, these methods are computationally expensive and thus do not scale in practice. To this end, we propose a novel neural network model, parallel-structured and all-component Fourier neural operator (PAC-FNO), that addresses the problem. Unlike conventional feed-forward neural networks, PAC-FNO operates in the frequency domain, allowing it to handle images of varying resolutions within a single model. We also propose a twostage algorithm for training PAC-FNO with a minimal modification to the original, downstream model. Moreover, the proposed PAC-FNO is ready to work with existing image recognition models. Extensively evaluating methods with seven image recognition benchmarks, we show that the proposed PAC-FNO improves the performance of existing baseline models on images with various resolutions by up to 77.1% and various types of natural variations in the images at inference. Deep neural networks have enabled many breakthroughs in visual recognition (Simonyan & Zisserman, 2014; He et al., 2016; Szegedy et al., 2016; Krizhevsky et al., 2017; Dosovitskiy et al., 2020; Liu et al., 2022). A common practice of developing these models is to learn a model on training images with a fixed input resolution and then deploy the model to many applications. In practice, when these models are deployed to real world, they are likely to face low-quality inputs at inference, e.g., images with resolutions different from the training data and/or those with natural input variations such as weather changes, noise types, and compression artifacts. For example, Figure 1 shows that the ConvNeXt models (Liu et al., 2022) trained on ImageNet-1k (Russakovsky et al., 2015) suffer from (top-1) accuracy degradation when their inputs are of low-quality. 'resize' baselines which is resize-and-feed using interpolation.

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for various downstream tasks, e.g., image classification, time series classification, image generation, etc. Its key part is how to model the time-derivative of the hidden state, denoted dh(t)/dt. People have habitually used conventional neural network architectures, e.g., fully-connected layers followed by non-linear activations. In this paper, however, we present a neural operator-based method to define the time-derivative term. Neural operators were initially proposed to model the differential operator of partial differential equations (PDEs). Since the time-derivative of NODEs can be understood as a special type of the differential operator, our proposed method, called branched Fourier neural operator (BFNO), makes sense. In our experiments with general downstream tasks, our method significantly outperforms existing methods.

Long-term time series forecasting (LTSF) is a challenging task that has been investigated in various domains such as finance investment, health care, traffic, and weather forecasting. In recent years, Linear-based LTSF models showed better performance, pointing out the problem of Transformer-based approaches causing temporal information loss. However, Linear-based approach has also limitations that the model is too simple to comprehensively exploit the characteristics of the dataset. To solve these limitations, we propose LTSF-DNODE, which applies a model based on linear ordinary differential equations (ODEs) and a time series decomposition method according to data statistical characteristics. We show that LTSF-DNODE outperforms the baselines on various real-world datasets. In addition, for each dataset, we explore the impacts of regularization in the neural ordinary differential equation (NODE) framework.

Score-based generative models (SGMs) are a recently proposed paradigm for deep generative tasks and now show the state-of-the-art sampling performance. It is known that the original SGM design solves the two problems of the generative trilemma: i) sampling quality, and ii) sampling diversity. However, the last problem of the trilemma was not solved, i.e., their training/sampling complexity is notoriously high. To this end, distilling SGMs into simpler models, e.g., generative adversarial networks (GANs), is gathering much attention currently. We present an enhanced distillation method, called straight-path interpolation GAN (SPI-GAN), which can be compared to the state-of-the-art shortcut-based distillation method, called denoising diffusion GAN (DD-GAN). However, our method corresponds to an extreme method that does not use any intermediate shortcut information of the reverse SDE path, in which case DD-GAN fails to obtain good results. Nevertheless, our straight-path interpolation method greatly stabilizes the overall training process. As a result, SPI-GAN is one of the best models in terms of the sampling quality/diversity/time for CIFAR-10, CelebA-HQ-256, and LSUN-Church-256.

Tabular data synthesis has received wide attention in the literature. This is because available data is often limited, incomplete, or cannot be obtained easily, and data privacy is becoming increasingly important. In this work, we present a generalized GAN framework for tabular synthesis, which combines the adversarial training of GANs and the negative log-density regularization of invertible neural networks. The proposed framework can be used for two distinctive objectives. First, we can further improve the synthesis quality, by decreasing the negative log-density of real records in the process of adversarial training. On the other hand, by increasing the negative log-density of real records, realistic fake records can be synthesized in a way that they are not too much close to real records and reduce the chance of potential information leakage. We conduct experiments with real-world datasets for classification, regression, and privacy attacks. In general, the proposed method demonstrates the best synthesis quality (in terms of task-oriented evaluation metrics, e.g., F1) when decreasing the negative log-density during the adversarial training. If increasing the negative log-density, our experimental results show that the distance between real and fake records increases, enhancing robustness against privacy attacks.

There were fierce debates on whether the non-linear embedding propagation of GCNs is appropriate to GCN-based recommender systems. It was recently found that the linear embedding propagation shows better accuracy than the non-linear embedding propagation. Since this phenomenon was discovered especially in recommender systems, it is required that we carefully analyze the linearity and non-linearity issue. In this work, therefore, we revisit the issues of i) which of the linear or non-linear propagation is better and ii) which factors of users/items decide the linearity/non-linearity of the embedding propagation. We propose a novel Hybrid Method of Linear and non-linEar collaborative filTering method (HMLET, pronounced as Hamlet). In our design, there exist both linear and non-linear propagation steps, when processing each user or item node, and our gating module chooses one of them, which results in a hybrid model of the linear and non-linear GCN-based collaborative filtering (CF). The proposed model yields the best accuracy in three public benchmark datasets. Moreover, we classify users/items into the following three classes depending on our gating modules' selections: Full-Non-Linearity (FNL), Partial-Non-Linearity (PNL), and Full-Linearity (FL). We found that there exist strong correlations between nodes' centrality and their class membership, i.e., important user/item nodes exhibit more preferences towards the non-linearity during the propagation steps. To our knowledge, we are the first who design a hybrid method and report the correlation between the graph centrality and the linearity/non-linearity of nodes. All HMLET codes and datasets are available at: https://github.com/qbxlvnf11/HMLET.

Collaborative filtering (CF) is a long-standing problem of recommender systems. Many novel methods have been proposed, ranging from classical matrix factorization to recent graph convolutional network-based approaches. After recent fierce debates, researchers started to focus on linear graph convolutional networks (GCNs) with a layer combination, which show state-of-the-art accuracy in many datasets. In this work, we extend them based on neural ordinary differential equations (NODEs), because the linear GCN concept can be interpreted as a differential equation, and present the method of Learnable-Time ODE-based Collaborative Filtering (LT-OCF). The main novelty in our method is that after redesigning linear GCNs on top of the NODE regime, i) we learn the optimal architecture rather than relying on manually designed ones, ii) we learn smooth ODE solutions that are considered suitable for CF, and iii) we test with various ODE solvers that internally build a diverse set of neural network connections. We also present a novel training method specialized to our method. In our experiments with three benchmark datasets, Gowalla, Yelp2018, and Amazon-Book, our method consistently shows better accuracy than existing methods, e.g., a recall of 0.0411 by LightGCN vs. 0.0442 by LT-OCF and an NDCG of 0.0315 by LightGCN vs. 0.0341 by LT-OCF in Amazon-Book. One more important discovery in our experiments that is worth mentioning is that our best accuracy was achieved by dense connections rather than linear connections.