Multi-layered Network Exploration via Random Walks: From Offline Optimization to Online Learning

Multi-layered network exploration (MuLaNE) problem is an important problem abstracted from many applications. In MuLaNE, there are multiple network layers where each node has an importance weight and each layer is explored by a random walk. The MuLaNE task is to allocate total random walk budget $B$ into each network layer so that the total weights of the unique nodes visited by random walks are maximized. We systematically study this problem from offline optimization to online learning. For the offline optimization setting where the network structure and node weights are known, we provide greedy based constant-ratio approximation algorithms for overlapping networks, and greedy or dynamic-programming based optimal solutions for non-overlapping networks. For the online learning setting, neither the network structure nor the node weights are known initially. We adapt the combinatorial multi-armed bandit framework and design algorithms to learn random walk related parameters and node weights while optimizing the budget allocation in multiple rounds, and prove that they achieve logarithmic regret bounds. Finally, we conduct experiments on a real-world social network dataset to validate our theoretical results.

Incorporating NODE with Pre-trained Neural Differential Operator for Learning Dynamics

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential equations, learns the dynamics directly from the samples on the trajectory and shows great promise in the scientific field. However, the training of NODE highly depends on the numerical solver, which can amplify numerical noise and be unstable, especially for ill-conditioned dynamical systems. In this paper, to reduce the reliance on the numerical solver, we propose to enhance the supervised signal in learning dynamics. Specifically, beyond learning directly from the trajectory samples, we pre-train a neural differential operator (NDO) to output an estimation of the derivatives to serve as an additional supervised signal. The NDO is pre-trained on a class of symbolic functions, and it learns the mapping between the trajectory samples of these functions to their derivatives. We provide theoretical guarantee on that the output of NDO can well approximate the ground truth derivatives by proper tuning the complexity of the library. To leverage both the trajectory signal and the estimated derivatives from NDO, we propose an algorithm called NDO-NODE, in which the loss function contains two terms: the fitness on the true trajectory samples and the fitness on the estimated derivatives that are output by the pre-trained NDO. Experiments on various of dynamics show that our proposed NDO-NODE can consistently improve the forecasting accuracy.

PcDGAN: A Continuous Conditional Diverse Generative Adversarial Network For Inverse Design

Engineering design tasks often require synthesizing new designs that meet desired performance requirements. The conventional design process, which requires iterative optimization and performance evaluation, is slow and dependent on initial designs. Past work has used conditional generative adversarial networks (cGANs) to enable direct design synthesis for given target performances. However, most existing cGANs are restricted to categorical conditions. Recent work on Continuous conditional GAN (CcGAN) tries to address this problem, but still faces two challenges: 1) it performs poorly on non-uniform performance distributions, and 2) the generated designs may not cover the entire design space. We propose a new model, named Performance Conditioned Diverse Generative Adversarial Network (PcDGAN), which introduces a singular vicinal loss combined with a Determinantal Point Processes (DPP) based loss function to enhance diversity. PcDGAN uses a new self-reinforcing score called the Lambert Log Exponential Transition Score (LLETS) for improved conditioning. Experiments on synthetic problems and a real-world airfoil design problem demonstrate that PcDGAN outperforms state-of-the-art GAN models and improves the conditioning likelihood by 69% in an airfoil generation task and up to 78% in synthetic conditional generation tasks and achieves greater design space coverage. The proposed method enables efficient design synthesis and design space exploration with applications ranging from CAD model generation to metamaterial selection.

Network Inference and Influence Maximization from Samples

Influence maximization is the task of selecting a small number of seed nodes in a social network to maximize the spread of the influence from these seeds, and it has been widely investigated in the past two decades. In the canonical setting, the whole social network as well as its diffusion parameters is given as input. In this paper, we consider the more realistic sampling setting where the network is unknown and we only have a set of passively observed cascades that record the set of activated nodes at each diffusion step. We study the task of influence maximization from these cascade samples (IMS), and present constant approximation algorithms for this task under mild conditions on the seed set distribution. To achieve the optimization goal, we also provide a novel solution to the network inference problem, that is, learning diffusion parameters and the network structure from the cascade data. Comparing with prior solutions, our network inference algorithm requires weaker assumptions and does not rely on maximum-likelihood estimation and convex programming. Our IMS algorithms enhance the learning-and-then-optimization approach by allowing a constant approximation ratio even when the diffusion parameters are hard to learn, and we do not need any assumption related to the network structure or diffusion parameters.

DINs: Deep Interactive Networks for Neurofibroma Segmentation in Neurofibromatosis Type 1 on Whole-Body MRI

Neurofibromatosis type 1 (NF1) is an autosomal dominant tumor predisposition syndrome that involves the central and peripheral nervous systems. Accurate detection and segmentation of neurofibromas are essential for assessing tumor burden and longitudinal tumor size changes. Automatic convolutional neural networks (CNNs) are sensitive and vulnerable as tumors' variable anatomical location and heterogeneous appearance on MRI. In this study, we propose deep interactive networks (DINs) to address the above limitations. User interactions guide the model to recognize complicated tumors and quickly adapt to heterogeneous tumors. We introduce a simple but effective Exponential Distance Transform (ExpDT) that converts user interactions into guide maps regarded as the spatial and appearance prior. Comparing with popular Euclidean and geodesic distances, ExpDT is more robust to various image sizes, which reserves the distribution of interactive inputs. Furthermore, to enhance the tumor-related features, we design a deep interactive module to propagate the guides into deeper layers. We train and evaluate DINs on three MRI data sets from NF1 patients. The experiment results yield significant improvements of 44% and 14% in DSC comparing with automated and other interactive methods, respectively. We also experimentally demonstrate the efficiency of DINs in reducing user burden when comparing with conventional interactive methods. The source code of our method is available at \url{https://github.com/Jarvis73/DINs}.

Machine-Learning Non-Conservative Dynamics for New-Physics Detection

Energy conservation is a basic physics principle, the breakdown of which often implies new physics. This paper presents a method for data-driven "new physics" discovery. Specifically, given a trajectory governed by unknown forces, our Neural New-Physics Detector (NNPhD) aims to detect new physics by decomposing the force field into conservative and non-conservative components, which are represented by a Lagrangian Neural Network (LNN) and a universal approximator network (UAN), respectively, trained to minimize the force recovery error plus a constant $\lambda$ times the magnitude of the predicted non-conservative force. We show that a phase transition occurs at $\lambda$=1, universally for arbitrary forces. We demonstrate that NNPhD successfully discovers new physics in toy numerical experiments, rediscovering friction (1493) from a damped double pendulum, Neptune from Uranus' orbit (1846) and gravitational waves (2017) from an inspiraling orbit. We also show how NNPhD coupled with an integrator outperforms previous methods for predicting the future of a damped double pendulum.

Prior-Enhanced Few-Shot Segmentation with Meta-Prototypes

Few-shot segmentation~(FSS) performance has been extensively promoted by introducing episodic training and class-wise prototypes. However, the FSS problem remains challenging due to three limitations: (1) Models are distracted by task-unrelated information; (2) The representation ability of a single prototype is limited; (3) Class-related prototypes ignore the prior knowledge of base classes. We propose the Prior-Enhanced network with Meta-Prototypes to tackle these limitations. The prior-enhanced network leverages the support and query (pseudo-) labels in feature extraction, which guides the model to focus on the task-related features of the foreground objects, and suppress much noise due to the lack of supervised knowledge. Moreover, we introduce multiple meta-prototypes to encode hierarchical features and learn class-agnostic structural information. The hierarchical features help the model highlight the decision boundary and focus on hard pixels, and the structural information learned from base classes is treated as the prior knowledge for novel classes. Experiments show that our method achieves the mean-IoU scores of 60.79% and 41.16% on PASCAL-$5^i$ and COCO-$20^i$, outperforming the state-of-the-art method by 3.49% and 5.64% in the 5-shot setting. Moreover, comparing with 1-shot results, our method promotes 5-shot accuracy by 3.73% and 10.32% on the above two benchmarks. The source code of our method is available at https://github.com/Jarvis73/PEMP.

UAV Aided Over-the-Air Computation

Over-the-air computation (AirComp) seamlessly integrates communication and computation by exploiting the waveform superposition property of multiple-access channels. Different from the existing works that focus on transceiver design of AirComp over static networks, this paper considers an unmanned aerial vehicle (UAV) aided AirComp system, where the UAV as a flying base station aggregates data from mobile sensors. The trajectory design of the UAV provides an additional degree of freedom to improve the performance of AirComp. Our goal is to minimize the time-averaged mean-squared error (MSE) of AirComp by jointly optimizing the UAV trajectory, receive normalizing factors, and sensors' transmit power. To this end, we first propose a novel and equivalent problem transformation by introducing intermediate variables. This reformulation leads to a convex subproblem when fixing any other two blocks of variables, thereby enabling efficient algorithm design based on the principle of block coordinate descent and alternating direction method of multipliers (ADMM) techniques. In particular, we derive the optimal closed-form solutions for normalizing factors and intermediate variables optimization subproblems. We also recast the convex trajectory design subproblem into an ADMM form and obtain the closed-form expressions for each variable updating. Simulation results show that the proposed algorithm achieves a smaller time-averaged MSE while reducing the simulation time by orders of magnitude compared to state-of-the-art algorithms.

Adversarial Training with Rectified Rejection

Adversarial training (AT) is one of the most effective strategies for promoting model robustness, whereas even the state-of-the-art adversarially trained models struggle to exceed 60% robust test accuracy on CIFAR-10 without additional data, which is far from practical. A natural way to break this accuracy bottleneck is to introduce a rejection option, where confidence is a commonly used certainty proxy. However, the vanilla confidence can overestimate the model certainty if the input is wrongly classified. To this end, we propose to use true confidence (T-Con) (i.e., predicted probability of the true class) as a certainty oracle, and learn to predict T-Con by rectifying confidence. We prove that under mild conditions, a rectified confidence (R-Con) rejector and a confidence rejector can be coupled to distinguish any wrongly classified input from correctly classified ones, even under adaptive attacks. We also quantify that training R-Con to be aligned with T-Con could be an easier task than learning robust classifiers. In our experiments, we evaluate our rectified rejection (RR) module on CIFAR-10, CIFAR-10-C, and CIFAR-100 under several attacks, and demonstrate that the RR module is well compatible with different AT frameworks on improving robustness, with little extra computation.