Incorporating symbolic reasoning into machine learning algorithms is a promising approach to improve performance on learning tasks that require logical reasoning. We study the problem of generating a programmatic variant of referring expressions that we call referring relational programs. In particular, given a symbolic representation of an image and a target object in that image, the goal is to generate a relational program that uniquely identifies the target object in terms of its attributes and its relations to other objects in the image. We propose a neurosymbolic program synthesis algorithm that combines a policy neural network with enumerative search to generate such relational programs. The policy neural network employs a program interpreter that provides immediate feedback on the consequences of the decisions made by the policy, and also takes into account the uncertainty in the symbolic representation of the image. We evaluate our algorithm on challenging benchmarks based on the CLEVR dataset, and demonstrate that our approach significantly outperforms several baselines.

Inspired by the proliferation of data-analysis tasks, recent research in program synthesis has had a strong focus on enabling users to specify data-analysis programs through intuitive specifications, like examples and natural language. However, with the ever-increasing threat to privacy through data analysis, we believe it is imperative to reimagine program synthesis technology in the presence of formal privacy constraints. In this paper, we study the problem of automatically synthesizing randomized, differentially private programs, where the user can provide the synthesizer with a constraint on the privacy of the desired algorithm. We base our technique on a linear dependent type system that can track the resources consumed by a program, and hence its privacy cost. We develop a novel type-directed synthesis algorithm that constructs randomized differentially private programs. We apply our technique to the problems of synthesizing database-like queries as well as recursive differential privacy mechanisms from the literature.

We propose trace abstraction modulo probability, a proof technique for verifying high-probability accuracy guarantees of probabilistic programs. Our proofs overapproximate the set of program traces using failure automata, finite-state automata that upper bound the probability of failing to satisfy a target specification. We automate proof construction by reducing probabilistic reasoning to logical reasoning: we use program synthesis methods to select axioms for sampling instructions, and then apply Craig interpolation to prove that traces fail the target specification with only a small probability. Our method handles programs with unknown inputs, parameterized distributions, infinite state spaces, and parameterized specifications. We evaluate our technique on a range of randomized algorithms drawn from the differential privacy literature and beyond. To our knowledge, our approach is the first to automatically establish accuracy properties of these algorithms.

Formal specifications of library functions play a critical role in a number of program analysis and development tasks. We present Bach, a technique for discovering likely relational specifications from data describing input-output behavior of a set of functions comprising a library or a program. Relational specifications correlate different executions of different functions; for instance, commutativity, transitivity, equivalence of two functions, etc. Bach combines novel insights from program synthesis and databases to discover a rich array of specifications. We apply Bach to learn specifications from data generated for a number of standard libraries. Our experimental evaluation demonstrates Bach's ability to learn useful and deep specifications in a small amount of time.

By abstracting away the complexity of distributed systems, large-scale data processing platforms—MapReduce, Hadoop, Spark, Dryad, etc.—have provided developers with simple means for harnessing the power of the cloud. In this paper, we ask whether we can automatically synthesize MapReduce-style distributed programs from input–output examples. Our ultimate goal is to enable end users to specify large-scale data analyses through the simple interface of examples. We thus present a new algorithm and tool for synthesizing programs composed of efficient data-parallel operations that can execute on cloud computing infrastructure. We evaluate our tool on a range of real-world big-data analysis tasks and general computations. Our results demonstrate the efficiency of our approach and the small number of examples it requires to synthesize correct, scalable programs.