Anindya Sarkar

Jiarui Feng, Yixin Chen, Fuhai Li et al.

The most popular design paradigm for Graph Neural Networks (GNNs) is 1-hop message passing -- aggregating information from 1-hop neighbors repeatedly. However, the expressive power of 1-hop message passing is bounded by the Weisfeiler-Lehman (1-WL) test. Recently, researchers extended 1-hop message passing to K-hop message passing by aggregating information from K-hop neighbors of nodes simultaneously. However, there is no work on analyzing the expressive power of K-hop message passing. In this work, we theoretically characterize the expressive power of K-hop message passing. Specifically, we first formally differentiate two different kernels of K-hop message passing which are often misused in previous works. We then characterize the expressive power of K-hop message passing by showing that it is more powerful than 1-WL and can distinguish almost all regular graphs. Despite the higher expressive power, we show that K-hop message passing still cannot distinguish some simple regular graphs and its expressive power is bounded by 3-WL. To further enhance its expressive power, we introduce a KP-GNN framework, which improves K-hop message passing by leveraging the peripheral subgraph information in each hop. We show that KP-GNN can distinguish many distance regular graphs which could not be distinguished by previous distance encoding or 3-WL methods. Experimental results verify the expressive power and effectiveness of KP-GNN. KP-GNN achieves competitive results across all benchmark datasets.

Quan Nguyen, Anindya Sarkar, Roman Garnett

Active search formalizes a specialized active learning setting where the goal is to collect members of a rare, valuable class. The state-of-the-art algorithm approximates the optimal Bayesian policy in a budget-aware manner, and has been shown to achieve impressive empirical performance in previous work. However, even this approximate policy has a superlinear computational complexity with respect to the size of the search problem, rendering its application impractical in large spaces or in real-time systems where decisions must be made quickly. We study the amortization of this policy by training a neural network to learn to search. To circumvent the difficulty of learning from scratch, we appeal to imitation learning techniques to mimic the behavior of the expert, expensive-to-compute policy. Our policy network, trained on synthetic data, learns a beneficial search strategy that yields nonmyopic decisions carefully balancing exploration and exploitation. Extensive experiments demonstrate our policy achieves competitive performance at real-world tasks that closely approximates the expert's at a fraction of the cost, while outperforming cheaper baselines.

Anindya Sarkar, Nikhil Kumar Gupta, Raghu Iyengar

Recent studies on the adversarial vulnerability of neural networks have shown that models trained with the objective of minimizing an upper bound on the worst-case loss over all possible adversarial perturbations improve robustness against adversarial attacks. Beside exploiting adversarial training framework, we show that by enforcing a Deep Neural Network (DNN) to be linear in transformed input and feature space improves robustness significantly. We also demonstrate that by augmenting the objective function with Local Lipschitz regularizer boost robustness of the model further. Our method outperforms most sophisticated adversarial training methods and achieves state of the art adversarial accuracy on MNIST, CIFAR10 and SVHN dataset. In this paper, we also propose a novel adversarial image generation method by leveraging Inverse Representation Learning and Linearity aspect of an adversarially trained deep neural network classifier.