We set λ = 0 .05 in the experiment. We then reconstruct the image signal by ˆ f = T ˆ x.

Recent developments in support for constructing knowledge graphs have led to a rapid rise in their creation both on the Web and within organisations. Added to existing sources of data, including relational databases, APIs, etc., there is a strong demand for techniques to query these diverse sources of knowledge. While formal query languages, such as SPARQL, exist for querying some knowledge graphs, users are required to know which knowledge graphs they need to query and the unique resource identifiers of the resources they need. Although alternative techniques in neural information retrieval embed the content of knowledge graphs in vector spaces, they fail to provide the representation and query expressivity needed (e.g. inability to handle non-trivial aggregation functions such as regression). We believe that a lingua franca, i.e. a formalism, that enables such representational flexibility will increase the ability of intelligent automated agents to combine diverse data sources by inference. Our work proposes a flexible representation (alists) to support intelligent federated querying of diverse knowledge sources. Our contribution includes (1) a formalism that abstracts the representation of queries from the specific query language of a knowledge graph; (2) a representation to dynamically curate data and functions (operations) to perform non-trivial inference over diverse knowledge sources; (3) a demonstration of the expressiveness of alists to represent the diversity of representational formalisms, including SPARQL queries, and more generally first-order logic expressions.

Deep convolutional networks have spectacular applications to classification and regression (LeCun et al., 2015), but they are a black box which are hard to analyze mathematically because of their architecture Despite its simplicity, it applies to complex image classification and reaches a higher accuracy than AlexNet (Krizhevsky et al., 2012) over ImageNet ILSVRC2012. It is implemented with a deep convolutional network architecture. Dictionary learning for classification was introduced in Mairal et al. (2009) and implemented with deep A major issue is to compute the sparse code with a small network. We introduce a new architecture based on homotopy continuation, which leads to exponential convergence. The ALIST A (Liu et al., 2019) sparse code is incorporated in We explain the implementation and mathematical properties of each element of the sparse scattering network.