Generalized Sliced Distances for Probability Distributions

Probability metrics have become an indispensable part of modern statistics and machine learning, and they play a quintessential role in various applications, including statistical hypothesis testing and generative modeling. However, in a practical setting, the convergence behavior of the algorithms built upon these distances have not been well established, except for a few specific cases. In this paper, we introduce a broad family of probability metrics, coined as Generalized Sliced Probability Metrics (GSPMs), that are deeply rooted in the generalized Radon transform. We first verify that GSPMs are metrics. Then, we identify a subset of GSPMs that are equivalent to maximum mean discrepancy (MMD) with novel positive definite kernels, which come with a unique geometric interpretation. Finally, by exploiting this connection, we consider GSPM-based gradient flows for generative modeling applications and show that under mild assumptions, the gradient flow converges to the global optimum. We illustrate the utility of our approach on both real and synthetic problems.

Deep Reinforcement Learning with Modulated Hebbian plus Q Network Architecture

This paper introduces the modulated Hebbian plus Q network architecture (MOHQA) for solving challenging partially observable Markov decision processes (POMDPs) deep reinforcement learning problems with sparse rewards and confounding observations. The proposed architecture combines a deep Q-network (DQN), and a modulated Hebbian network with neural eligibility traces (MOHN). Bio-inspired neural traces are used to bridge temporal delays between actions and rewards. The purpose is to discover distal cause-effect relationships where confounding observations and sparse rewards cause standard RL algorithms to fail. Each of the two modules of the network (DQN and MOHN) is responsible for different aspects of learning. DQN learns low level features and control, while MOHN contributes to the high-level decisions by bridging rewards with past actions. The strength of the approach is to support a DQN standard framework when temporal difference errors are difficult to compute due to non-observable states. The system is tested on a set of generalized decision making problems encoded as decision tree graphs that deliver delayed rewards after key decision points and confounding observations. The simulations show that the proposed approach helps solve problems that are currently challenging for state-of-the-art deep reinforcement learning algorithms.

Learning a Domain-Invariant Embedding for Unsupervised Domain Adaptation Using Class-Conditioned Distribution Alignment

We address the problem of unsupervised domain adaptation (UDA) by learning a cross-domain agnostic embedding space, where the distance between the probability distributions of the two source and target visual domains is minimized. We use the output space of a shared cross-domain deep encoder to model the embedding space anduse the Sliced-Wasserstein Distance (SWD) to measure and minimize the distance between the embedded distributions of two source and target domains to enforce the embedding to be domain-agnostic.Additionally, we use the source domain labeled data to train a deep classifier from the embedding space to the label space to enforce the embedding space to be discriminative.As a result of this training scheme, we provide an effective solution to train the deep classification network on the source domain such that it will generalize well on the target domain, where only unlabeled training data is accessible. To mitigate the challenge of class matching, we also align corresponding classes in the embedding space by using high confidence pseudo-labels for the target domain, i.e. assigning the class for which the source classifier has a high prediction probability. We provide theoretical justification as well as experimental results on UDA benchmark tasks to demonstrate that our method is effective and leads to state-of-the-art performance.

Neural Networks, Hypersurfaces, and Radon Transforms

Connections between integration along hypersufaces, Radon transforms, and neural networks are exploited to highlight an integral geometric mathematical interpretation of neural networks. By analyzing the properties of neural networks as operators on probability distributions for observed data, we show that the distribution of outputs for any node in a neural network can be interpreted as a nonlinear projection along hypersurfaces defined by level surfaces over the input data space. We utilize these descriptions to provide new interpretation for phenomena such as nonlinearity, pooling, activation functions, and adversarial examples in neural network-based learning problems.

Universal Litmus Patterns: Revealing Backdoor Attacks in CNNs

The unprecedented success of deep neural networks in various applications have made these networks a prime target for adversarial exploitation. In this paper, we introduce a benchmark technique for detecting backdoor attacks (aka Trojan attacks) on deep convolutional neural networks (CNNs). We introduce the concept of Universal Litmus Patterns (ULPs), which enable one to reveal backdoor attacks by feeding these universal patterns to the network and analyzing the output (i.e., classifying as `clean' or `corrupted'). This detection is fast because it requires only a few forward passes through a CNN. We demonstrate the effectiveness of ULPs for detecting backdoor attacks on thousands of networks trained on three benchmark datasets, namely the German Traffic Sign Recognition Benchmark (GTSRB), MNIST, and CIFAR10.

Zero-Shot Image Classification Using Coupled Dictionary Embedding

Zero-shot learning (ZSL) is a framework to classify images belonging to unseen classes based on solely semantic information about these unseen classes. In this paper, we propose a new ZSL algorithm using coupled dictionary learning. The core idea is that the visual features and the semantic attributes of an image can share the same sparse representation in an intermediate space. We use images from seen classes and semantic attributes from seen and unseen classes to learn two dictionaries that can represent sparsely the visual and semantic feature vectors of an image. In the ZSL testing stage and in the absence of labeled data, images from unseen classes can be mapped into the attribute space by finding the joint sparse representation using solely the visual data. The image is then classified in the attribute space given semantic descriptions of unseen classes. We also provide an attribute-aware formulation to tackle domain shift and hubness problems in ZSL. Extensive experiments are provided to demonstrate the superior performance of our approach against the state of the art ZSL algorithms on benchmark ZSL datasets.

Generative Continual Concept Learning

After learning a concept, humans are also able to continually generalize their learned concepts to new domains by observing only a few labeled instances without any interference with the past learned knowledge. In contrast, learning concepts efficiently in a continual learning setting remains an open challenge for current Artificial Intelligence algorithms as persistent model retraining is necessary. Inspired by the Parallel Distributed Processing learning and the Complementary Learning Systems theories, we develop a computational model that is able to expand its previously learned concepts efficiently to new domains using a few labeled samples. We couple the new form of a concept to its past learned forms in an embedding space for effective continual learning. Doing so, a generative distribution is learned such that it is shared across the tasks in the embedding space and models the abstract concepts. This procedure enables the model to generate pseudo-data points to replay the past experience to tackle catastrophic forgetting.

Divide-and-Conquer Adversarial Detection

The vulnerabilities of deep neural networks against adversarial examples have become a major concern for deploying these models in sensitive domains. Devising a definitive defense against such attacks is proven to be challenging, and the methods relying on detecting adversarial samples have been shown to be only effective when the attacker is oblivious to the detection mechanism, i.e., in non-adaptive attacks. In this paper, we propose an effective and practical method for detecting adaptive/dynamic adversaries. In short, we train adversary-robust auxiliary detectors to discriminate in-class natural examples from adversarially crafted out-of-class examples. To identify a potential adversary, we first obtain the estimated class of the input using the classification system, and then use the corresponding detector to verify whether the input is a natural example of that class, or is an adversarially manipulated example. Experimental results on MNIST and CIFAR10 dataset show that our method could withstand adaptive PGD attacks. Furthermore, we demonstrate that with our novel training scheme our models learn significant more robust representation than ordinary adversarial training.

On Sampling Random Features From Empirical Leverage Scores: Implementation and Theoretical Guarantees

Random features provide a practical framework for large-scale kernel approximation and supervised learning. It has been shown that data-dependent sampling of random features using leverage scores can significantly reduce the number of features required to achieve optimal learning bounds. Leverage scores introduce an optimized distribution for features based on an infinite-dimensional integral operator (depending on input distribution), which is impractical to sample from. Focusing on empirical leverage scores in this paper, we establish an out-of-sample performance bound, revealing an interesting trade-off between the approximated kernel and the eigenvalue decay of another kernel in the domain of random features defined based on data distribution. Our experiments verify that the empirical algorithm consistently outperforms vanilla Monte Carlo sampling, and with a minor modification the method is even competitive to supervised data-dependent kernel learning, without using the output (label) information.

Complementary Learning for Overcoming Catastrophic Forgetting Using Experience Replay

Despite huge success, deep networks are unable to learn effectively in sequential multitask learning settings as they forget the past learned tasks after learning new tasks. Inspired from complementary learning systems theory, we address this challenge by learning a generative model that couples the current task to the past learned tasks through a discriminative embedding space. We learn an abstract level generative distribution in the embedding that allows the generation of data points to represent the experience. We sample from this distribution and utilize experience replay to avoid forgetting and simultaneously accumulate new knowledge to the abstract distribution in order to couple the current task with past experience. We demonstrate theoretically and empirically that our framework learns a distribution in the embedding that is shared across all task and as a result tackles catastrophic forgetting.