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.

Using World Models for Pseudo-Rehearsal in Continual Learning

The utility of learning a dynamics/world model of the environment in reinforcement learning has been shown in a many ways. When using neural networks, however, these models suffer catastrophic forgetting when learned in a lifelong or continual fashion. Current solutions to the continual learning problem require experience to be segmented and labeled as discrete tasks, however, in continuous experience it is generally unclear what a sufficient segmentation of tasks would be. Here we propose a method to continually learn these internal world models through the interleaving of internally generated rollouts from past experiences (i.e., pseudo-rehearsal). We show this method can sequentially learn unsupervised temporal prediction, without task labels, in a disparate set of Atari games. Empirically, this interleaving of the internally generated rollouts with the external environment's observations leads to an average 4.5x reduction in temporal prediction loss compared to non-interleaved learning. Similarly, we show that the representations of this internal model remain stable across learned environments. Here, an agent trained using an initial version of the internal model can perform equally well when using a subsequent version that has successfully incorporated experience from multiple new environments.

Attention-Based Structural-Plasticity

Catastrophic forgetting/interference is a critical problem for lifelong learning machines, which impedes the agents from maintaining their previously learned knowledge while learning new tasks. Neural networks, in particular, suffer plenty from the catastrophic forgetting phenomenon. Recently there has been several efforts towards overcoming catastrophic forgetting in neural networks. Here, we propose a biologically inspired method toward overcoming catastrophic forgetting. Specifically, we define an attention-based selective plasticity of synapses based on the cholinergic neuromodulatory system in the brain. We define synaptic importance parameters in addition to synaptic weights and then use Hebbian learning in parallel with backpropagation algorithm to learn synaptic importances in an online and seamless manner. We test our proposed method on benchmark tasks including the Permuted MNIST and the Split MNIST problems and show competitive performance compared to the state-of-the-art methods.

Neuromodulated Goal-Driven Perception in Uncertain Domains

In uncertain domains, the goals are often unknown and need to be predicted by the organism or system. In this paper, contrastive excitation backprop (c-EB) was used in a goal-driven perception task with pairs of noisy MNIST digits, where the system had to increase attention to one of the two digits corresponding to a goal (i.e., even, odd, low value, or high value) and decrease attention to the distractor digit or noisy background pixels. Because the valid goal was unknown, an online learning model based on the cholinergic and noradrenergic neuromodulatory systems was used to predict a noisy goal (expected uncertainty) and re-adapt when the goal changed (unexpected uncertainty). This neurobiologically plausible model demonstrates how neuromodulatory systems can predict goals in uncertain domains and how attentional mechanisms can enhance the perception of that goal.

Generalized Sliced Wasserstein Distances

The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community. The SW distance, specifically, was shown to have similar properties to the Wasserstein distance, while being much simpler to compute, and is therefore used in various applications including generative modeling and general supervised/unsupervised learning. In this paper, we first clarify the mathematical connection between the SW distance and the Radon transform. We then utilize the generalized Radon transform to define a new family of distances for probability measures, which we call generalized sliced-Wasserstein (GSW) distances. We also show that, similar to the SW distance, the GSW distance can be extended to a maximum GSW (max-GSW) distance. We then provide the conditions under which GSW and max-GSW distances are indeed distances. Finally, we compare the numerical performance of the proposed distances on several generative modeling tasks, including SW flows and SW auto-encoders.

Discovering Molecular Functional Groups Using Graph Convolutional Neural Networks

Functional groups (FGs) serve as a foundation for analyzing chemical properties of organic molecules. Automatic discovery of FGs will impact various fields of research, including medicinal chemistry, by reducing the amount of lab experiments required for discovery or synthesis of new molecules. Here, we investigate methods based on graph convolutional neural networks (GCNNs) for localizing FGs that contribute to specific chemical properties. Molecules are modeled as undirected graphs with atoms as nodes and bonds as edges. Using this graph structure, we trained GCNNs in a supervised way on experimentally-validated molecular training sets to predict specific chemical properties, e.g., toxicity. Upon learning a GCNN, we analyzed its activation patterns to automatically identify FGs using four different methods: gradient-based saliency maps, Class Activation Mapping (CAM), gradient-weighted CAM (Grad-CAM), and Excitation Back-Propagation. We evaluated the contrastive power of these methods with respect to the specificity of the identified molecular substructures and their relevance for chemical functions. Grad- CAM had the highest contrastive power and generated qualitatively the best FGs. This work paves the way for automatic analysis and design of new molecules.

Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model

In this paper we study generative modeling via autoencoders while using the elegant geometric properties of the optimal transport (OT) problem and the Wasserstein distances. We introduce Sliced-Wasserstein Autoencoders (SWAE), which are generative models that enable one to shape the distribution of the latent space into any samplable probability distribution without the need for training an adversarial network or defining a closed-form for the distribution. In short, we regularize the autoencoder loss with the sliced-Wasserstein distance between the distribution of the encoded training samples and a predefined samplable distribution. We show that the proposed formulation has an efficient numerical solution that provides similar capabilities to Wasserstein Autoencoders (WAE) and Variational Autoencoders (VAE), while benefiting from an embarrassingly simple implementation.

Multi-Agent Distributed Lifelong Learning for Collective Knowledge Acquisition

Lifelong machine learning methods acquire knowledge over a series of consecutive tasks, continually building upon their experience. Current lifelong learning algorithms rely upon a single learning agent that has centralized access to all data. In this paper, we extend the idea of lifelong learning from a single agent to a network of multiple agents that collectively learn a series of tasks. Each agent faces some (potentially unique) set of tasks; the key idea is that knowledge learned from these tasks may benefit other agents trying to learn different (but related) tasks. Our Collective Lifelong Learning Algorithm (CoLLA) provides an efficient way for a network of agents to share their learned knowledge in a distributed and decentralized manner, while preserving the privacy of the locally observed data. Note that a decentralized scheme is a subclass of distributed algorithms where a central server does not exist and in addition to data, computations are also distributed among the agents. We provide theoretical guarantees for robust performance of the algorithm and empirically demonstrate that CoLLA outperforms existing approaches for distributed multi-task learning on a variety of data sets.

Image to Image Translation for Domain Adaptation

We propose a general framework for unsupervised domain adaptation, which allows deep neural networks trained on a source domain to be tested on a different target domain without requiring any training annotations in the target domain. This is achieved by adding extra networks and losses that help regularize the features extracted by the backbone encoder network. To this end we propose the novel use of the recently proposed unpaired image-toimage translation framework to constrain the features extracted by the encoder network. Specifically, we require that the features extracted are able to reconstruct the images in both domains. In addition we require that the distribution of features extracted from images in the two domains are indistinguishable. Many recent works can be seen as specific cases of our general framework. We apply our method for domain adaptation between MNIST, USPS, and SVHN datasets, and Amazon, Webcam and DSLR Office datasets in classification tasks, and also between GTA5 and Cityscapes datasets for a segmentation task. We demonstrate state of the art performance on each of these datasets.