Journal of Parallel and Distributed Computing 104, 19-35.

Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation program, in a general-purpose programming language. Examples of such computations on models include model analysis, relatively general-purpose model-reduction maps, and the initial phases of model implementation, all of which should preserve or approximate the mathematical semantics of a complex biological model. Multiscale modeling benefits from both the expressive power of declarative modeling languages and the application of model reduction methods to link models across scale. Based on previous work, here we define declarative modeling of complex biological systems by defining the semantics of an increasingly powerful series of declarative modeling languages including reaction-like dynamics of parameterized and extended objects, we define semantics-preserving implementation and semantics-approximating model reduction transformations, and we outline a "meta-hierarchy" for organizing declarative models and the mathematical methods that can fruitfully manipulate them.

In this paper we introduce the notion of Demand-Weighted Completeness, allowing estimation of the completeness of a knowledge base with respect to how it is used. Defining an entity by its classes, we employ usage data to predict the distribution over relations for that entity. For example, instances of person in a knowledge base may require a birth date, name and nationality to be considered complete. These predicted relation distributions enable detection of important gaps in the knowledge base, and define the required facts for unseen entities. Such characterisation of the knowledge base can also quantify how usage and completeness change over time. We demonstrate a method to measure Demand-Weighted Completeness, and show that a simple neural network model performs well at this prediction task.

Partially-observable Markov decision processes (POMDPs) with discounted-sum payoff are a standard framework to model a wide range of problems related to decision making under uncertainty. Traditionally, the goal has been to obtain policies that optimize the expectation of the discounted-sum payoff. A key drawback of the expectation measure is that even low probability events with extreme payoff can significantly affect the expectation, and thus the obtained policies are not necessarily risk-averse. An alternate approach is to optimize the probability that the payoff is above a certain threshold, which allows obtaining risk-averse policies, but ignores optimization of the expectation. We consider the expectation optimization with probabilistic guarantee (EOPG) problem, where the goal is to optimize the expectation ensuring that the payoff is above a given threshold with at least a specified probability. We present several results on the EOPG problem, including the first algorithm to solve it.

In this work we address the problem of fast and scalable learning of neuro-symbolic representations for general biological knowledge. Based on a recently published comprehensive biological knowledge graph (Alshahrani, 2017) that was used for demonstrating neuro-symbolic representation learning, we show how to train fast (under 1 minute) log-linear neural embeddings of the entities. We utilize these representations as inputs for machine learning classifiers to enable important tasks such as biological link prediction. Classifiers are trained by concatenating learned entity embeddings to represent entity relations, and training classifiers on the concatenated embeddings to discern true relations from automatically generated negative examples. Our simple embedding methodology greatly improves on classification error compared to previously published state-of-the-art results, yielding a maximum increase of $+0.28$ F-measure and $+0.22$ ROC AUC scores for the most difficult biological link prediction problem. Finally, our embedding approach is orders of magnitude faster to train ($\leq$ 1 minute vs. hours), much more economical in terms of embedding dimensions ($d=50$ vs. $d=512$), and naturally encodes the directionality of the asymmetric biological relations, that can be controlled by the order with which we concatenate the embeddings.

In the last years, deep learning algorithms have highly revolutionized several areas including speech, image and natural language processing. The specific field of Machine Translation (MT) has not remained invariant. Integration of deep learning in MT varies from re-modeling existing features into standard statistical systems to the development of a new architecture. Among the different neural networks, research works use feedforward neural networks, recurrent neural networks and the encoder-decoder schema. These architectures are able to tackle challenges as having low-resources or morphology variations. This manuscript focuses on describing how these neural networks have been integrated to enhance different aspects and models from statistical MT, including language modeling, word alignment, translation, reordering, and rescoring. Then, we report the new neural MT approach together with a description of the foundational related works and recent approaches on using subword, characters and training with multilingual languages, among others. Finally, we include an analysis of the corresponding challenges and future work in using deep learning in MT.

In an influential paper (“Rule Learning by Seven-Month-Old Infants”), Marcus, Vijayan, Rao and Vishton claimed that connectionist models cannot account for human success at learning tasks that involved generalization of abstract knowledge such as grammatical rules. This claim triggered a heated debate, centered mostly around variants of the Simple Recurrent Network model. In our work, we revisit this unresolved debate and analyze the underlying issues from a different perspective. We argue that, in order to simulate human-like learning of grammatical rules, a neural network model should not be used as a tabula rasa, but rather, the initial wiring of the neural connections and the experience acquired prior to the actual task should be incorporated into the model. We present two methods that aim to provide such initial state: a manipulation of the initial connections of the network in a cognitively plausible manner (concretely, by implementing a “delay-line” memory), and a pre-training algorithm that incrementally challenges the network with novel stimuli. We implement such techniques in an Echo State Network (ESN), and we show that only when combining both techniques the ESN is able to learn truly general identity rules. Finally, we discuss the relation between these cognitively motivated techniques and recent advances in Deep Learning.

We investigate how neural networks can learn and process languages with hierarchical, compositional semantics. To this end, we define the artificial task of processing nested arithmetic expressions, and study whether different types of neural networks can learn to compute their meaning. We find that recursive neural networks can implement a generalising solution to this problem, and we visualise this solution by breaking it up in three steps: project, sum and squash. As a next step, we investigate recurrent neural networks, and show that a gated recurrent unit, that processes its input incrementally, also performs very well on this task: the network learns to predict the outcome of the arithmetic expressions with high accuracy, although performance deteriorates somewhat with increasing length. To develop an understanding of what the recurrent network encodes, visualisation techniques alone do not suffice. Therefore, we develop an approach where we formulate and test multiple hypotheses on the information encoded and processed by the network. For each hypothesis, we derive predictions about features of the hidden state representations at each time step, and train 'diagnostic classifiers' to test those predictions. Our results indicate that the networks follow a strategy similar to our hypothesised 'cumulative strategy', which explains the high accuracy of the network on novel expressions, the generalisation to longer expressions than seen in training, and the mild deterioration with increasing length. This in turn shows that diagnostic classifiers can be a useful technique for opening up the black box of neural networks. We argue that diagnostic classification, unlike most visualisation techniques, does scale up from small networks in a toy domain, to larger and deeper recurrent networks dealing with real-life data, and may therefore contribute to a better understanding of the internal dynamics of current state-of-the-art models in natural language processing.

We describe two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs. The selection graph neural network (GNN) replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The aggregation GNN diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a synthetic source localization application. Performance is evaluated for a text category classification problem using word proximity networks. Multinode aggregation GNNs are consistently the best performing GNN architecture.

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between Gaussian processes with a recursive kernel definition and random wide fully connected feedforward networks with more than one hidden layer. We show that, under broad conditions, as we make the architecture increasingly wide, the implied random function converges in distribution to a Gaussian process, formalising and extending existing results by Neal (1996) to deep networks. To evaluate convergence rates empirically, we use maximum mean discrepancy. We then exhibit situations where existing Bayesian deep networks are close to Gaussian processes in terms of the key quantities of interest. Any Gaussian process has a flat representation. Since this behaviour may be undesirable in certain situations we discuss ways in which it might be prevented.