Humans have a remarkable capacity to reason about abstract relational structures, an ability that may support some of the most impressive, human-unique cognitive feats. Because equality (or identity) is a simple and ubiquitous relational operator, equality reasoning has been a key case study for the broader question of abstract relational reasoning. This paper revisits the question of whether equality can be learned by neural networks that do not encode explicit symbolic structure. Earlier work arrived at a negative answer to this question, but that result holds only for a particular class of hand-crafted feature representations. In our experiments, we assess out-of-sample generalization of equality using both arbitrary representations and representations that have been pretrained on separate tasks to imbue them with abstract structure. In this setting, even simple neural networks are able to learn basic equality with relatively little training data. In a second case study, we show that sequential equality problems (learning ABA sequences) can be solved with only positive training instances. Finally, we consider a more complex, hierarchical equality problem, but this requires vastly more data. However, using a pretrained equality network as a modular component of this larger task leads to good performance with no task-specific training. Overall, these findings indicate that neural models are able to solve equality-based reasoning tasks, suggesting that essential aspects of symbolic reasoning can emerge from data-driven, non-symbolic learning processes.

In February 2020, the European Commission (EC) published a white paper entitled, On Artificial Intelligence - A European approach to excellence and trust. This paper outlines the EC's policy options for the promotion and adoption of artificial intelligence (AI) in the European Union. The Montreal AI Ethics Institute (MAIEI) reviewed this paper and published a response addressing the EC's plans to build an "ecosystem of excellence" and an "ecosystem of trust," as well as the safety and liability implications of AI, the internet of things (IoT), and robotics. MAIEI provides 15 recommendations in relation to the sections outlined above, including: 1) focus efforts on the research and innovation community, member states, and the private sector; 2) create alignment between trading partners' policies and EU policies; 3) analyze the gaps in the ecosystem between theoretical frameworks and approaches to building trustworthy AI; 4) focus on coordination and policy alignment; 5) focus on mechanisms that promote private and secure sharing of data; 6) create a network of AI research excellence centres to strengthen the research and innovation community; 7) promote knowledge transfer and develop AI expertise through Digital Innovation Hubs; 8) add nuance to the discussion regarding the opacity of AI systems; 9) create a process for individuals to appeal an AI system's decision or output; 10) implement new rules and strengthen existing regulations; 11) ban the use of facial recognition technology; 12) hold all AI systems to similar standards and compulsory requirements; 13) ensure biometric identification systems fulfill the purpose for which they are implemented; 14) implement a voluntary labelling system for systems that are not considered high-risk; 15) appoint individuals to the oversight process who understand AI systems well and are able to communicate potential risks.

Continually solving new, unsolved tasks is the key to learning diverse behaviors. Through reinforcement learning (RL), we have made massive strides towards solving tasks that have a single goal. However, in the multi-task domain, where an agent needs to reach multiple goals, the choice of training goals can largely affect sample efficiency. When biological agents learn, there is often an organized and meaningful order to which learning happens. Inspired by this, we propose setting up an automatic curriculum for goals that the agent needs to solve. Our key insight is that if we can sample goals at the frontier of the set of goals that an agent is able to reach, it will provide a significantly stronger learning signal compared to randomly sampled goals. To operationalize this idea, we introduce a goal proposal module that prioritizes goals that maximize the epistemic uncertainty of the Q-function of the policy. This simple technique samples goals that are neither too hard nor too easy for the agent to solve, hence enabling continual improvement. We evaluate our method across 13 multi-goal robotic tasks and 5 navigation tasks, and demonstrate performance gains over current state-of-the-art methods.

Network densification and millimeter-wave technologies are key enablers to fulfill the capacity and data rate requirements of the fifth generation (5G) of mobile networks. In this context, designing low-complexity policies with local observations, yet able to adapt the user association with respect to the global network state and to the network dynamics is a challenge. In fact, the frameworks proposed in literature require continuous access to global network information and to recompute the association when the radio environment changes. With the complexity associated to such an approach, these solutions are not well suited to dense 5G networks. In this paper, we address this issue by designing a scalable and flexible algorithm for user association based on multi-agent reinforcement learning. In this approach, users act as independent agents that, based on their local observations only, learn to autonomously coordinate their actions in order to optimize the network sum-rate. Since there is no direct information exchange among the agents, we also limit the signaling overhead. Simulation results show that the proposed algorithm is able to adapt to (fast) changes of radio environment, thus providing large sum-rate gain in comparison to state-of-the-art solutions.

Efficient exploration is one of the main challenges in reinforcement learning (RL). Most existing sample-efficient algorithms assume the existence of a single reward function during exploration. In many practical scenarios, however, there is not a single underlying reward function to guide the exploration, for instance, when an agent needs to learn many skills simultaneously, or multiple conflicting objectives need to be balanced. To address these challenges, we propose the \textit{task-agnostic RL} framework: In the exploration phase, the agent first collects trajectories by exploring the MDP without the guidance of a reward function. After exploration, it aims at finding near-optimal policies for $N$ tasks, given the collected trajectories augmented with \textit{sampled rewards} for each task. We present an efficient task-agnostic RL algorithm, \textsc{UCBZero}, that finds $\epsilon$-optimal policies for $N$ arbitrary tasks after at most $\tilde O(\log(N)H^5SA/\epsilon^2)$ exploration episodes. We also provide an $\Omega(\log (N)H^2SA/\epsilon^2)$ lower bound, showing that the $\log$ dependency on $N$ is unavoidable. Furthermore, we provide an $N$-independent sample complexity bound of \textsc{UCBZero} in the statistically easier setting when the ground truth reward functions are known.

Phase retrieval, the problem of recovering lost phase information from measured intensity alone, is an inverse problem that is widely faced in various imaging modalities ranging from astronomy to nanoscale imaging. The current process of phase recovery is iterative in nature. As a result, the image formation is time-consuming and computationally expensive, precluding real-time imaging. Here, we use 3D nanoscale X-ray imaging as a representative example to develop a deep learning model to address this phase retrieval problem. We introduce 3D-CDI-NN, a deep convolutional neural network and differential programming framework trained to predict 3D structure and strain solely from input 3D X-ray coherent scattering data. Our networks are designed to be "physics-aware" in multiple aspects; in that the physics of x-ray scattering process is explicitly enforced in the training of the network, and the training data are drawn from atomistic simulations that are representative of the physics of the material. We further refine the neural network prediction through a physics-based optimization procedure to enable maximum accuracy at lowest computational cost. 3D-CDI-NN can invert a 3D coherent diffraction pattern to real-space structure and strain hundreds of times faster than traditional iterative phase retrieval methods, with negligible loss in accuracy. Our integrated machine learning and differential programming solution to the phase retrieval problem is broadly applicable across inverse problems in other application areas.

We present Wasserstein Embedding for Graph Learning (WEGL), a novel and fast framework for embedding entire graphs in a vector space, in which various machine learning models are applicable for graph-level prediction tasks. We leverage new insights on defining similarity between graphs as a function of the similarity between their node embedding distributions. Specifically, we use the Wasserstein distance to measure the dissimilarity between node embeddings of different graphs. Different from prior work, we avoid pairwise calculation of distances between graphs and reduce the computational complexity from quadratic to linear in the number of graphs. WEGL calculates Monge maps from a reference distribution to each node embedding and, based on these maps, creates a fixed-sized vector representation of the graph. We evaluate our new graph embedding approach on various benchmark graph-property prediction tasks, showing state-of-the-art classification performance, while having superior computational efficiency.

We present MCRapper, an algorithm for efficient computation of Monte-Carlo Empirical Rademacher Averages (MCERA) for families of functions exhibiting poset (e.g., lattice) structure, such as those that arise in many pattern mining tasks. The MCERA allows us to compute upper bounds to the maximum deviation of sample means from their expectations, thus it can be used to find both statistically-significant functions (i.e., patterns) when the available data is seen as a sample from an unknown distribution, and approximations of collections of high-expectation functions (e.g., frequent patterns) when the available data is a small sample from a large dataset. This feature is a strong improvement over previously proposed solutions that could only achieve one of the two. MCRapper uses upper bounds to the discrepancy of the functions to efficiently explore and prune the search space, a technique borrowed from pattern mining itself. To show the practical use of MCRapper, we employ it to develop an algorithm TFP-R for the task of True Frequent Pattern (TFP) mining. TFP-R gives guarantees on the probability of including any false positives (precision) and exhibits higher statistical power (recall) than existing methods offering the same guarantees. We evaluate MCRapper and TFP-R and show that they outperform the state-of-the-art for their respective tasks.

It is fundamental to measure model complexity of deep neural networks. The existing literature on model complexity mainly focuses on neural networks with piecewise linear activation functions. Model complexity of neural networks with general curve activation functions remains an open problem. To tackle the challenge, in this paper, we first propose the linear approximation neural network (LANN for short), a piecewise linear framework to approximate a given deep model with curve activation function. LANN constructs individual piecewise linear approximation for the activation function of each neuron, and minimizes the number of linear regions to satisfy a required approximation degree. Then, we analyze the upper bound of the number of linear regions formed by LANNs, and derive the complexity measure based on the upper bound. To examine the usefulness of the complexity measure, we experimentally explore the training process of neural networks and detect overfitting. Our results demonstrate that the occurrence of overfitting is positively correlated with the increase of model complexity during training. We find that the $L^1$ and $L^2$ regularizations suppress the increase of model complexity. Finally, we propose two approaches to prevent overfitting by directly constraining model complexity, namely neuron pruning and customized $L^1$ regularization.

We present a methodology for integrating functional data into deep densely connected feed-forward neural networks. The model is defined for scalar responses with multiple functional and scalar covariates. A by-product of the method is a set of dynamic functional weights that can be visualized during the optimization process. This visualization leads to greater interpretability of the relationship between the covariates and the response relative to conventional neural networks. The model is shown to perform well in a number of contexts including prediction of new data and recovery of the true underlying functional weights; these results were confirmed through real applications and simulation studies. A forthcoming R package is developed on top of a popular deep learning library (Keras) allowing for general use of the approach.