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.

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.

Sharing forecasts of network timeseries data, such as cellular or electricity load patterns, can improve independent control applications ranging from traffic scheduling to power generation. Typically, forecasts are designed without knowledge of a downstream controller's task objective, and thus simply optimize for mean prediction error. However, such task-agnostic representations are often too large to stream over a communication network and do not emphasize salient temporal features for cooperative control. This paper presents a solution to learn succinct, highly-compressed forecasts that are co-designed with a modular controller's task objective. Our simulations with real cellular, Internet-of-Things (IoT), and electricity load data show we can improve a model predictive controller's performance by at least 25% while transmitting 80% less data than the competing method.

Since out-of-distribution generalization is a generally ill-posed problem, various proxy targets (e.g., calibration, adversarial robustness, algorithmic corruptions, invariance across shifts) were studied across different research programs resulting in different recommendations. While sharing the same aspirational goal, these approaches have never been tested under the same experimental conditions on real data. In this paper, we take a unified view of previous work, highlighting message discrepancies that we address empirically, and providing recommendations on how to measure the robustness of a model and how to improve it. To this end, we collect 172 publicly available dataset pairs for training and out-of-distribution evaluation of accuracy, calibration error, adversarial attacks, environment invariance, and synthetic corruptions.

For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? While MARL algorithms may be implemented for potentially harmful applications, we do not believe this work uniquely enables such applications. If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] In the supplemental material (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A] (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? Our allocation proposal network and Q network are illustrated in Figures 7 and 8. Low-level action utility functions and mixing networks are similar to those described in Iqbal et al. [10] with the only 13 difference being a replacement of the RNN layers with standard fully connected layers.