Pattern Matching in AI Compilers and its Formalization (Extended Version)

PyPM is a Python-based domain specific language (DSL) for building rewrite-based optimization passes on machine learning computation graphs. Users define individual optimizations by writing (a) patterns that match subgraphs of a computation graph and (b) corresponding rules which replace a matched subgraph with an optimized kernel. PyPM is distinguished from the many other DSLs for defining rewriting passes by its complex and novel pattern language which borrows concepts from logic programming. PyPM patterns can be recursive, nondeterminstic, and can require checking domain-specific constraints such as the shapes of tensors. The PyPM implementation is thus similarly complicated, consisting of thousands of lines of C++ code. In this paper, we present our work on building PyPM, as well as formalizing and distilling and this complexity to an understandable mathematical core. We have developed a formal core calculus expressing the main operations of the PyPM pattern language. We define both a declarative semantics - describing which patterns match which terms - and an algorithmic semantics - an idealized version of the PyPM pattern interpreter - and prove their equivalence. The development is fully mechanized in the Coq proof assistant.

Evaluating approaches for supervised semantic labeling

Relational data sources are still one of the most popular ways to store enterprise or Web data, however, the issue with relational schema is the lack of a well-defined semantic description. A common ontology provides a way to represent the meaning of a relational schema and can facilitate the integration of heterogeneous data sources within a domain. Semantic labeling is achieved by mapping attributes from the data sources to the classes and properties in the ontology. We formulate this problem as a multi-class classification problem where previously labeled data sources are used to learn rules for labeling new data sources. The majority of existing approaches for semantic labeling have focused on data integration challenges such as naming conflicts and semantic heterogeneity. In addition, machine learning approaches typically have issues around class imbalance, lack of labeled instances and relative importance of attributes. To address these issues, we develop a new machine learning model with engineered features as well as two deep learning models which do not require extensive feature engineering. We evaluate our new approaches with the state-of-the-art.