Incorporating Domain Differential Equations into Graph Convolutional Networks to Lower Generalization Discrepancy

Ensuring both accuracy and robustness in time series prediction is critical to many applications, ranging from urban planning to pandemic management. With sufficient training data where all spatiotemporal patterns are well-represented, existing deep-learning models can make reasonably accurate predictions. However, existing methods fail when the training data are drawn from different circumstances (e.g., traffic patterns on regular days) compared to test data (e.g., traffic patterns after a natural disaster). Such challenges are usually classified under domain generalization. In this work, we show that one way to address this challenge in the context of spatiotemporal prediction is by incorporating domain differential equations into Graph Convolutional Networks (GCNs). We theoretically derive conditions where GCNs incorporating such domain differential equations are robust to mismatched training and testing data compared to baseline domain agnostic models. To support our theory, we propose two domain-differential-equation-informed networks called Reaction-Diffusion Graph Convolutional Network (RDGCN), which incorporates differential equations for traffic speed evolution, and Susceptible-Infectious-Recovered Graph Convolutional Network (SIRGCN), which incorporates a disease propagation model. Both RDGCN and SIRGCN are based on reliable and interpretable domain differential equations that allow the models to generalize to unseen patterns. We experimentally show that RDGCN and SIRGCN are more robust with mismatched testing data than the state-of-the-art deep learning methods.

Robust Conformal Prediction under Distribution Shift via Physics-Informed Structural Causal Model

Uncertainty is critical to reliable decision-making with machine learning. Conformal prediction (CP) handles uncertainty by predicting a set on a test input, hoping the set to cover the true label with at least $(1-\alpha)$ confidence. This coverage can be guaranteed on test data even if the marginal distributions $P_X$ differ between calibration and test datasets. However, as it is common in practice, when the conditional distribution $P_{Y|X}$ is different on calibration and test data, the coverage is not guaranteed and it is essential to measure and minimize the coverage loss under distributional shift at \textit{all} possible confidence levels. To address these issues, we upper bound the coverage difference at all levels using the cumulative density functions of calibration and test conformal scores and Wasserstein distance. Inspired by the invariance of physics across data distributions, we propose a physics-informed structural causal model (PI-SCM) to reduce the upper bound. We validated that PI-SCM can improve coverage robustness along confidence level and test domain on a traffic speed prediction task and an epidemic spread task with multiple real-world datasets.

FourCastNeXt: Improving FourCastNet Training with Limited Compute

Recently, the FourCastNet Neural Earth System Model (NESM) has shown impressive results on predicting various atmospheric variables, trained on the ERA5 reanalysis dataset. While FourCastNet enjoys quasi-linear time and memory complexity in sequence length compared to quadratic complexity in vanilla transformers, training FourCastNet on ERA5 from scratch still requires large amount of compute resources, which is expensive or even inaccessible to most researchers. In this work, we will show improved methods that can train FourCastNet using only 1% of the compute required by the baseline, while maintaining model performance or par or even better than the baseline.

Distance Guided Generative Adversarial Network for Explainable Binary Classifications

Despite the potential benefits of data augmentation for mitigating the data insufficiency, traditional augmentation methods primarily rely on the prior intra-domain knowledge. On the other hand, advanced generative adversarial networks (GANs) generate inter-domain samples with limited variety. These previous methods make limited contributions to describing the decision boundaries for binary classification. In this paper, we propose a distance guided GAN (DisGAN) which controls the variation degrees of generated samples in the hyperplane space. Specifically, we instantiate the idea of DisGAN by combining two ways. The first way is vertical distance GAN (VerDisGAN) where the inter-domain generation is conditioned on the vertical distances. The second way is horizontal distance GAN (HorDisGAN) where the intra-domain generation is conditioned on the horizontal distances. Furthermore, VerDisGAN can produce the class-specific regions by mapping the source images to the hyperplane. Experimental results show that DisGAN consistently outperforms the GAN-based augmentation methods with explainable binary classification. The proposed method can apply to different classification architectures and has potential to extend to multi-class classification.

A Parameterized Generative Adversarial Network Using Cyclic Projection for Explainable Medical Image Classification

Although current data augmentation methods are successful to alleviate the data insufficiency, conventional augmentation are primarily intra-domain while advanced generative adversarial networks (GANs) generate images remaining uncertain, particularly in small-scale datasets. In this paper, we propose a parameterized GAN (ParaGAN) that effectively controls the changes of synthetic samples among domains and highlights the attention regions for downstream classification. Specifically, ParaGAN incorporates projection distance parameters in cyclic projection and projects the source images to the decision boundary to obtain the class-difference maps. Our experiments show that ParaGAN can consistently outperform the existing augmentation methods with explainable classification on two small-scale medical datasets.

Local Convolution Enhanced Global Fourier Neural Operator For Multiscale Dynamic Spaces Prediction

Neural operators extend the capabilities of traditional neural networks by allowing them to handle mappings between function spaces for the purpose of solving partial differential equations (PDEs). One of the most notable methods is the Fourier Neural Operator (FNO), which is inspired by Green's function method and approximate operator kernel directly in the frequency domain. In this work, we focus on predicting multiscale dynamic spaces, which is equivalent to solving multiscale PDEs. Multiscale PDEs are characterized by rapid coefficient changes and solution space oscillations, which are crucial for modeling atmospheric convection and ocean circulation. To solve this problem, models should have the ability to capture rapid changes and process them at various scales. However, the FNO only approximates kernels in the low-frequency domain, which is insufficient when solving multiscale PDEs. To address this challenge, we propose a novel hierarchical neural operator that integrates improved Fourier layers with attention mechanisms, aiming to capture all details and handle them at various scales. These mechanisms complement each other in the frequency domain and encourage the model to solve multiscale problems. We perform experiments on dynamic spaces governed by forward and reverse problems of multiscale elliptic equations, Navier-Stokes equations and some other physical scenarios, and reach superior performance in existing PDE benchmarks, especially equations characterized by rapid coefficient variations.

Neurogenesis Dynamics-inspired Spiking Neural Network Training Acceleration

Biologically inspired Spiking Neural Networks (SNNs) have attracted significant attention for their ability to provide extremely energy-efficient machine intelligence through event-driven operation and sparse activities. As artificial intelligence (AI) becomes ever more democratized, there is an increasing need to execute SNN models on edge devices. Existing works adopt weight pruning to reduce SNN model size and accelerate inference. However, these methods mainly focus on how to obtain a sparse model for efficient inference, rather than training efficiency. To overcome these drawbacks, in this paper, we propose a Neurogenesis Dynamics-inspired Spiking Neural Network training acceleration framework, NDSNN. Our framework is computational efficient and trains a model from scratch with dynamic sparsity without sacrificing model fidelity. Specifically, we design a new drop-and-grow strategy with decreasing number of non-zero weights, to maintain extreme high sparsity and high accuracy. We evaluate NDSNN using VGG-16 and ResNet-19 on CIFAR-10, CIFAR-100 and TinyImageNet. Experimental results show that NDSNN achieves up to 20.52\% improvement in accuracy on Tiny-ImageNet using ResNet-19 (with a sparsity of 99\%) as compared to other SOTA methods (e.g., Lottery Ticket Hypothesis (LTH), SET-SNN, RigL-SNN). In addition, the training cost of NDSNN is only 40.89\% of the LTH training cost on ResNet-19 and 31.35\% of the LTH training cost on VGG-16 on CIFAR-10.

Quantum Deep Hedging

Quantum machine learning has the potential for a transformative impact across industry sectors and in particular in finance. In our work we look at the problem of hedging where deep reinforcement learning offers a powerful framework for real markets. We develop quantum reinforcement learning methods based on policy-search and distributional actor-critic algorithms that use quantum neural network architectures with orthogonal and compound layers for the policy and value functions. We prove that the quantum neural networks we use are trainable, and we perform extensive simulations that show that quantum models can reduce the number of trainable parameters while achieving comparable performance and that the distributional approach obtains better performance than other standard approaches, both classical and quantum. We successfully implement the proposed models on a trapped-ion quantum processor, utilizing circuits with up to $16$ qubits, and observe performance that agrees well with noiseless simulation. Our quantum techniques are general and can be applied to other reinforcement learning problems beyond hedging.

Around the world in 60 words: A generative vocabulary test for online research

Conducting experiments with diverse participants in their native languages can uncover insights into culture, cognition, and language that may not be revealed otherwise. However, conducting these experiments online makes it difficult to validate self-reported language proficiency. Furthermore, existing proficiency tests are small and cover only a few languages. We present an automated pipeline to generate vocabulary tests using text from Wikipedia. Our pipeline samples rare nouns and creates pseudowords with the same low-level statistics. Six behavioral experiments (N=236) in six countries and eight languages show that (a) our test can distinguish between native speakers of closely related languages, (b) the test is reliable ($r=0.82$), and (c) performance strongly correlates with existing tests (LexTale) and self-reports. We further show that test accuracy is negatively correlated with the linguistic distance between the tested and the native language. Our test, available in eight languages, can easily be extended to other languages.