Designing spectral convolutional networks is a challenging problem in graph learning. ChebNet, one of the early attempts, approximates the spectral graph convolutions using Chebyshev polynomials.

We introduce HALO - a deep generative model utilising HAmiltonian Latent Operators to reliably disentangle content and motion information in image sequences. The content represents summary statistics of a sequence, and motion is a dynamic process that determines how information is expressed in any part of the sequence. By modelling the dynamics as a Hamiltonian motion, important desiderata are ensured: (1) the motion is reversible, (2) the symplectic, volume-preserving structure in phase space means paths are continuous and are not divergent in the latent space. Consequently, the nearness of sequence frames is realised by the nearness of their coordinates in the phase space, which proves valuable for disentanglement and long-term sequence generation. The sequence space is generally comprised of different types of dynamical motions. To ensure long-term separability and allow controlled generation, we associate every motion with a unique Hamiltonian that acts in its respective subspace. We demonstrate the utility of HALO by swapping the motion of a pair of sequences, controlled generation, and image rotations.

A central challenge in training classification models in the real-world federated system is learning with non-IID data. To cope with this, most of the existing works involve enforcing regularization in local optimization or improving the model aggregation scheme at the server. Other works also share public datasets or synthesized samples to supplement the training of under-represented classes or introduce a certain level of personalization. Though effective, they lack a deep understanding of how the data heterogeneity affects each layer of a deep classification model. In this paper, we bridge this gap by performing an experimental analysis of the representations learned by different layers. Our observations are surprising: (1) there exists a greater bias in the classifier than other layers, and (2) the classification performance can be significantly improved by post-calibrating the classifier after federated training. Motivated by the above findings, we propose a novel and simple algorithm called Classifier Calibration with Virtual Representations (CCVR), which adjusts the classifier using virtual representations sampled from an approximated gaussian mixture model. Experimental results demonstrate that CCVR achieves state-of-the-art performance on popular federated learning benchmarks including CIFAR-10, CIFAR-100, and CINIC-10. We hope that our simple yet effective method can shed some light on the future research of federated learning with non-IID data.

A central challenge in training classification models in the real-world federated system is learning with non-IID data. To cope with this, most of the existing works involve enforcing regularization in local optimization or improving the model aggregation scheme at the server. Other works also share public datasets or synthesized samples to supplement the training of under-represented classes or introduce a certain level of personalization. Though effective, they lack a deep understanding of how the data heterogeneity affects each layer of a deep classification model. In this paper, we bridge this gap by performing an experimental analysis of the representations learned by different layers. Our observations are surprising: (1) there exists a greater bias in the classifier than other layers, and (2) the classification performance can be significantly improved by post-calibrating the classifier after federated training. Motivated by the above findings, we propose a novel and simple algorithm called Classifier Calibration with Virtual Representations (CCVR), which adjusts the classifier using virtual representations sampled from an approximated gaussian mixture model. Experimental results demonstrate that CCVR achieves state-of-the-art performance on popular federated learning benchmarks including CIFAR-10, CIFAR-100, and CINIC-10. We hope that our simple yet effective method can shed some light on the future research of federated learning with non-IID data.

Aimed at adapting a generative model to a novel generation task with only a few given data samples, the capability of few-shot generation is crucial for many realworld applications with limited data, e.g., artistic domains. Instead of training from scratch, recent works tend to leverage the prior knowledge stored in previous datasets, which is quite similar to the memory mechanism of human intelligence, but few of these works directly imitate the memory-recall mechanism that humans make good use of in accomplishing creative tasks, e.g., painting and writing. Inspired by the memory mechanism of human brain, in this work, we carefully design a variational structured memory module (VSM), which can simultaneously store both episodic and semantic memories to assist existing generative models efficiently recall these memories during sample generation. Meanwhile, we introduce a bionic memory updating strategy for the conversion between episodic and semantic memories, which can also model the uncertainty during conversion. Then, we combine the developed VSM with various generative models under the Bayesian framework, and evaluate these memory-augmented generative models with few-shot generation tasks, demonstrating the effectiveness of our methods.

Domain decomposition methods are widely used and effective in the approximation of solutions to partial differential equations. Yet the optimal construction of these methods requires tedious analysis and is often available only in simplified, structured-grid settings, limiting their use for more complex problems. In this work, we generalize optimized Schwarz domain decomposition methods to unstructured-grid problems, using Graph Convolutional Neural Networks (GCNNs) and unsupervised learning to learn optimal modifications at subdomain interfaces. A key ingredient in our approach is an improved loss function, enabling effective training on relatively small problems, but robust performance on arbitrarily large problems, with computational cost linear in problem size. The performance of the learned linear solvers is compared with both classical and optimized domain decomposition algorithms, for both structured-and unstructured-grid problems.

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De novo drug design is a pivotal issue in pharmacology and a new area of focus in AI for science research. A central challenge in this field is to generate molecules with specific properties while also producing a wide range of diverse candidates. Although advanced technologies such as transformer models and reinforcement learning have been applied in drug design, their potential has not been fully realized. Therefore, we propose MolRL-MGPT, a reinforcement learning algorithm with multiple GPT agents for drug molecular generation. To promote molecular diversity, we encourage the agents to collaborate in searching for desirable molecules in diverse directions. Our algorithm has shown promising results on the GuacaMol benchmark and exhibits efficacy in designing inhibitors against SARS-CoV-2 protein targets. The codes are available at: https://github.com/HXYfighter/