The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire reasonable solutions from noisy datasets. However, this framework severely limits expressions for solutions, e.g., no function symbols are allowed, and the shapes of clauses are fixed. As a result, the framework cannot deal with structured examples. Therefore we propose a new framework to learn logic programs from noisy and structured examples, including the following contributions. First, we propose an adaptive clause search method by looking through structured space, which is defined by the generality of the clauses, to yield an efficient search space for differentiable solvers. Second, we propose for ground atoms an enumeration algorithm, which determines a necessary and sufficient set of ground atoms to perform differentiable inference functions. Finally, we propose a new method to compose logic programs softly, enabling the system to deal with complex programs consisting of several clauses. Our experiments show that our new framework can learn logic programs from noisy and structured examples, such as sequences or trees. Our framework can be scaled to deal with complex programs that consist of several clauses with function symbols.

Computing the similarity between two data points plays a vital role in many machine learning algorithms. Metric learning has the aim of learning a good metric automatically from data. Most existing studies on metric learning for tree-structured data have adopted the approach of learning the tree edit distance. However, the edit distance is not amenable for big data analysis because it incurs high computation cost. In this paper, we propose a new metric learning approach for tree-structured data with pq-grams. The pq-gram distance is a distance for ordered labeled trees, and has much lower computation cost than the tree edit distance. In order to perform metric learning based on pq-grams, we propose a new differentiable parameterized distance, weighted pq-gram distance. We also propose a way to learn the proposed distance based on Large Margin Nearest Neighbors (LMNN), which is a well-studied and practical metric learning scheme. We formulate the metric learning problem as an optimization problem and use the gradient descent technique to perform metric learning. We empirically show that the proposed approach not only achieves competitive results with the state-of-the-art edit distance-based methods in various classification problems, but also solves the classification problems much more rapidly than the edit distance-based methods.

The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire reasonable solutions from noisy datasets. However, this framework severely limits expressions for solutions, e.g., no function symbols are allowed, and the shapes of clauses are fixed. As a result, the framework cannot deal with structured examples. Therefore we propose a new framework to learn logic programs from noisy and structured examples, including the following contributions. First, we propose an adaptive clause search method by looking through structured space, which is defined by the generality of the clauses, to yield an efficient search space for differentiable solvers. Second, we propose for ground atoms an enumeration algorithm, which determines a necessary and sufficient set of ground atoms to perform differentiable inference functions. Finally, we propose a new method to compose logic programs softly, enabling the system to deal with complex programs consisting of several clauses. Our experiments show that our new framework can learn logic programs from noisy and structured examples, such as sequences or trees. Our framework can be scaled to deal with complex programs that consist of several clauses with function symbols.

Recently, Probabilistic Circuits such as Sum-Product Networks have received growing attention, as they can represent complex features but still provide tractable inference. Although quite successful, unfortunately, they lack the capability of handling control structures, such as for and while loops. In this work, we introduce Sum-Product Loop Language (SPLL), a novel programming language that is capable of tractable inference on complex probabilistic code that includes loops. SPLL has dual semantics: every program has generative semantics familiar to most programmers and probabilistic semantics that assign a probability to each possible result. This way, the programmer can describe how to generate samples almost like in any standard programming language. The language takes care of computing the probability values of all results for free at run time. We demonstrate that SPLL inherits the beneficial properties of PCs, namely tractability and differentiability, while generalizing to other distributions and programs, and retains substantial computational similarities.