Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by a regularized version that is less accurate but easy to differentiate. In this work we characterize the differential properties of the original Sinkhorn distance, proving that it enjoys the same smoothness as its regularized version and we explicitly provide an efficient algorithm to compute its gradient. We show that this result benefits both theory and applications: on one hand, high order smoothness confers statistical guarantees to learning with Wasserstein approximations. On the other hand, the gradient formula allows us to efficiently solve learning and optimization problems in practice. Promising preliminary experiments complement our analysis.

While variational dropout approaches have been shown to be effective for network sparsification, they are still suboptimal in the sense that they set the dropout rate for each neuron without consideration of the input data. With such input-independent dropout, each neuron is evolved to be generic across inputs, which makes it difficult to sparsify networks without accuracy loss. To overcome this limitation, we propose adaptive variational dropout whose probabilities are drawn from sparsity-inducing beta-Bernoulli prior. It allows each neuron to be evolved either to be generic or specific for certain inputs, or dropped altogether. Such input-adaptive sparsity- inducing dropout allows the resulting network to tolerate larger degree of sparsity without losing its expressive power by removing redundancies among features. We validate our dependent variational beta-Bernoulli dropout on multiple public datasets, on which it obtains significantly more compact networks than baseline methods, with consistent accuracy improvements over the base networks.

This paper presents a new class of gradient methods for distributed machine learning that adaptively skip the gradient calculations to learn with reduced communication and computation. Simple rules are designed to detect slowly-varying gradients and, therefore, trigger the reuse of outdated gradients. The resultant gradient-based algorithms are termed Lazily Aggregated Gradient --- justifying our acronym LAG used henceforth. Theoretically, the merits of this contribution are: i) the convergence rate is the same as batch gradient descent in strongly-convex, convex, and nonconvex smooth cases; and, ii) if the distributed datasets are heterogeneous (quantified by certain measurable constants), the communication rounds needed to achieve a targeted accuracy are reduced thanks to the adaptive reuse of lagged gradients. Numerical experiments on both synthetic and real data corroborate a significant communication reduction compared to alternatives.

This paper presents Amnestic Forgery, an ontology for metaphor semantics, based on MetaNet, which is inspired by the theory of Conceptual Metaphor. Amnestic Forgery reuses and extends the Framester schema, as an ideal ontology design framework to deal with both semiotic and referential aspects of frames, roles, mappings, and eventually blending. The description of the resource is supplied by a discussion of its applications, with examples taken from metaphor generation, and the referential problems of metaphoric mappings. Both schema and data are available from the Framester SPARQL endpoint.

Functional design of objects is slow and still largely an artisanal activity, with few Computer-Aided Design (CAD) tools existing to aid the exploration of the design solution space. In order to accelerate object design, we introduce an automatic method for generating object shapes with desired functionalities. We employ the concept of shape arithmetic, where shapes are manipulated in an arithmetic fashion inside a latent space representation learned by a neural network. We propose a functionality arithmetic, with the aim of conceiving new objects with desired functionalities from other objects with known functionalities. This is done by first extracting the descriptions of forms providing these functionalities, and then manipulating them using shape arithmetic functions. Form-to-function mappings are extracted by identifying the common features between objects belonging to the same class, inside which all objects provide the same functionality.

Needless to say, mathematics has become the reliable foundation of modern natural science, including several branches of theoretical computer science, by justifying theorems with proofs. The importance of correct proofs leads to the study of software called proof assistants [Nipkow et al. 2002; Norell 2009; The Coq Development Team 2017], which allow users to state theorems and their proofs formally in the form of certain programming languages and automatically check that the proofs correctly prove the theorems. The realm of the areas that rely on theorem proving is expanding beyond mathematics; for example, it is being applied for system verification [Klein et al. 2009; Leroy 2009], where one states the correctness of a system as a theorem and justifies it in the form of proofs. Automated theorem proving (ATP) [Bibel 2013; Fitting 2012; Pfenning 2004] is a set of techniques that prove logical formulas automatically. We are concerned with the following form of ATP called automated proof synthesis (APS): Given a logical formula P, if P holds, return a proof M of P. In the light of the importance of theorem proving, APS serves as a useful tool for activities based on formal reasoning. For example, from the perspective of the aforementioned system verification, APS serves for automating system verification; indeed, various methods for (semi)automated static program verification [Barnett et al. 2005; Chalin et al. 2007; Filliâtre and Paskevich 2013] can be seen as APS procedures. We also remark another important application of APS: automated program synthesis. An APS algorithm can be seen as an automated program synthesis procedure via the Curry-Howard isomorphism [Sørensen and Urzyczyn 2006], in which M can be seen as a program and P can be seen as a specification. Not only is APS interesting from the practical viewpoint, it is also interesting from the theoretical perspective in that it investigates the algorithmic aspect of theorem proving.

We propose a new way of deriving policy gradient updates for reinforcement learning. Our technique, based on Fourier analysis, recasts integrals that arise with expected policy gradients as convolutions and turns them into multiplications. The obtained analytical solutions allow us to capture the low variance benefits of EPG in a broad range of settings. For the critic, we treat trigonometric and radial basis functions, two function families with the universal approximation property. The choice of policy can be almost arbitrary, including mixtures or hybrid continuous-discrete probability distributions. Moreover, we derive a general family of sample-based estimators for stochastic policy gradients, which unifies existing results on sample-based approximation. We believe that this technique has the potential to shape the next generation of policy gradient approaches, powered by analytical results.

Many works in collaborative robotics and human-robot interaction focuses on identifying and predicting human behaviour while considering the information about the robot itself as given. This can be the case when sensors and the robot are calibrated in relation to each other and often the reconfiguration of the system is not possible, or extra manual work is required. We present a deep learning based approach to remove the constraint of having the need for the robot and the vision sensor to be fixed and calibrated in relation to each other. The system learns the visual cues of the robot body and is able to localise it, as well as estimate the position of robot joints in 3D space by just using a 2D color image. The method uses a cascaded convolutional neural network, and we present the structure of the network, describe our own collected dataset, explain the network training and achieved results. A fully trained system shows promising results in providing an accurate mask of where the robot is located and a good estimate of its joints positions in 3D. The accuracy is not good enough for visual servoing applications yet, however, it can be sufficient for general safety and some collaborative tasks not requiring very high precision. The main benefit of our method is the possibility of the vision sensor to move freely. This allows it to be mounted on moving objects, for example, a body of the person or a mobile robot working in the same environment as the robots are operating in.

Mao H. (2017, Representing attribute reduction and concepts in concept lattice using graphs. Soft Computing 21(24):7293--7311) claims to make contributions to the study of reduction of attributes in concept lattices by using graph theory. We show that her results are either trivial or already well-known and all three algorithms proposed in the paper are incorrect.

A parasitic fungus that turns carpenter ants into'zombies' is learning to adapt to the changing climate. The fungus is known to infect carpenter ants and cause them to clamp onto hanging vegetation, where they dangle for months to spew spores. But, researchers have found that zombie ants don't always bite onto the same part of the plant. According to a new study, this is because the choice of leaves or twigs boils down to the local climate – and, as conditions continue to change, the fungi have been forced to adapt. A parasitic fungus that turns carpenter ants into'zombies' is learning to adapt to the changing climate.