Learning value functions off-policy is at the core of modern Reinforcement Learning (RL). Traditional off-policy actor-critic algorithms, however, only approximate the true policy gradient, since the gradient $\nabla_{\theta} Q^{\pi_{\theta}}(s,a)$ of the action-value function with respect to the policy parameters is often ignored. We introduce a class of value functions called Parameter-based Value Functions (PVFs) whose inputs include the policy parameters. PVFs can evaluate the performance of any policy given a state, a state-action pair, or a distribution over the RL agent's initial states. We show how PVFs yield exact policy gradient theorems. We derive off-policy actor-critic algorithms based on PVFs trained using Monte Carlo or Temporal Difference methods. Preliminary experimental results indicate that PVFs can effectively evaluate deterministic linear and nonlinear policies, outperforming state-of-the-art algorithms in the continuous control environment Swimmer-v3. Finally, we show how recurrent neural networks can be trained through PVFs to solve supervised and RL problems involving partial observability and long time lags between relevant events. This provides an alternative to backpropagation through time.

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.

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.

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.

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.

Building machine learning models from decentralized datasets located in different centers with federated learning (FL) is a promising approach to circumvent local data scarcity while preserving privacy. However, the prominent Cox proportional hazards (PH) model, used for survival analysis, does not fit the FL framework, as its loss function is non-separable with respect to the samples. The na\"ive method to bypass this non-separability consists in calculating the losses per center, and minimizing their sum as an approximation of the true loss. We show that the resulting model may suffer from important performance loss in some adverse settings. Instead, we leverage the discrete-time extension of the Cox PH model to formulate survival analysis as a classification problem with a separable loss function. Using this approach, we train survival models using standard FL techniques on synthetic data, as well as real-world datasets from The Cancer Genome Atlas (TCGA), showing similar performance to a Cox PH model trained on aggregated data. Compared to previous works, the proposed method is more communication-efficient, more generic, and more amenable to using privacy-preserving techniques.

The increased use of convolutional neural networks for face recognition in science, governance, and broader society has created an acute need for methods that can show how these 'black box' decisions are made. To be interpretable and useful to humans, such a method should convey a model's learned classification strategy in a way that is robust to random initializations or spurious correlations in input data. To this end, we applied the decompositional pixel-wise attribution method of layer-wise relevance propagation (LRP) to resolve the decisions of several classes of VGG-16 models trained for face recognition. We then quantified how these relevance measures vary with and generalize across key model parameters, such as the pretraining dataset (ImageNet or VGGFace), the finetuning task (gender or identity classification), and random initializations of model weights. Using relevance-based image masking, we find that relevance maps for face classification prove generally stable across random initializations, and can generalize across finetuning tasks. However, there is markedly less generalization across pretraining datasets, indicating that ImageNet- and VGGFace-trained models sample face information differently even as they achieve comparably high classification performance. Fine-grained analyses of relevance maps across models revealed asymmetries in generalization that point to specific benefits of choice parameters, and suggest that it may be possible to find an underlying set of important face image pixels that drive decisions across convolutional neural networks and tasks. Finally, we evaluated model decision weighting against human measures of similarity, providing a novel framework for interpreting face recognition decisions across human and machine.

Stochastic network modeling is often limited by high computational costs to generate a large number of networks enough for meaningful statistical evaluation. In this study, Deep Convolutional Generative Adversarial Networks (DCGANs) were applied to quickly reproduce drainage networks from the already generated network samples without repetitive long modeling of the stochastic network model, Gibb's model. In particular, we developed a novel connectivity-informed method that converts the drainage network images to the directional information of flow on each node of the drainage network, and then transform it into multiple binary layers where the connectivity constraints between nodes in the drainage network are stored. DCGANs trained with three different types of training samples were compared; 1) original drainage network images, 2) their corresponding directional information only, and 3) the connectivity-informed directional information. Comparison of generated images demonstrated that the novel connectivity-informed method outperformed the other two methods by training DCGANs more effectively and better reproducing accurate drainage networks due to its compact representation of the network complexity and connectivity. This work highlights that DCGANs can be applicable for high contrast images common in earth and material sciences where the network, fractures, and other high contrast features are important.