Smart Choices and the Selection Monad

Describing systems in terms of choices and of the resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized by optimization techniques and, increasingly, by machine learning methods. We study this approach from a programming-language perspective. We define two small languages that support decision-making abstractions: one with choices and rewards, and the other additionally with probabilities. We give both operational and denotational semantics. The operational semantics combine the usual semantics of standard constructs with optimization over a space of possible executions. The denotational semantics, which are compositional and can also be viewed as an implementation by translation to a simpler language, rely on the selection monad. We establish that the two semantics coincide in both cases.

A Simple Differentiable Programming Language

Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the mathematical notion of derivative is not always entirely clear---discrepancies can arise, sometimes inadvertently. In order to study automatic differentiation in such programming contexts, we define a small but expressive programming language that includes a construct for reverse-mode differentiation. We give operational and denotational semantics for this language. The operational semantics employs popular implementation techniques, while the denotational semantics employs notions of differentiation familiar from real analysis. We establish that these semantics coincide.

Learning a Natural Language Interface with Neural Programmer

Learning a natural language interface for database tables is a challenging task that involves deep language understanding and multi-step reasoning. The task is often approached by mapping natural language queries to logical forms or programs that provide the desired response when executed on the database. To our knowledge, this paper presents the first weakly supervised, end-to-end neural network model to induce such programs on a real-world dataset. We enhance the objective function of Neural Programmer, a neural network with built-in discrete operations, and apply it on WikiTableQuestions, a natural language question-answering dataset. The model is trained end-to-end with weak supervision of question-answer pairs, and does not require domain-specific grammars, rules, or annotations that are key elements in previous approaches to program induction. The main experimental result in this paper is that a single Neural Programmer model achieves 34.2% accuracy using only 10,000 examples with weak supervision. An ensemble of 15 models, with a trivial combination technique, achieves 37.7% accuracy, which is competitive to the current state-of-the-art accuracy of 37.1% obtained by a traditional natural language semantic parser.