We develop an approach to estimate the probability that a program sampled from a large language model is correct. Given a natural language description of a programming problem, our method samples both candidate programs as well as candidate predicates specifying how the program should behave. This allows learning a model that forms a well-calibrated probabilistic prediction of program correctness. Our system also infers which predicates are useful to explain the behavior of the generated code, and humans preferred these in a human study over raw language model outputs. Our method is simple, easy to implement, and maintains state of the art generation accuracy results.

A core tension in models of concept learning is that the model must carefully balance the tractability of inference against the expressivity of the hypothesis class. Humans, however, can efficiently learn a broad range of concepts. We introduce a model of inductive learning that seeks to be human-like in that sense. It implements a Bayesian reasoning process where a language model first proposes candidate hypotheses expressed in natural language, which are then re-weighed by a prior and a likelihood. By estimating the prior from human data, we can predict human judgments on learning problems involving numbers and sets, spanning concepts that are generative, discriminative, propositional, and higher-order.

Toward combining inductive reasoning with perception abilities, we develop techniques for neurosymbolic program synthesis where perceptual input is first parsed by neural nets into a low-dimensional interpretable representation, which is then processed by a synthesized program. We explore several techniques for relaxing the problem and jointly learning all modules end-to-end with gradient descent: multitask learning; amortized inference; overparameterization; and a differentiable strategy for penalizing lengthy programs. Collectedly this toolbox improves the stability of gradient-guided program search, and suggests ways of learning both how to perceive input as discrete abstractions, and how to symbolically process those abstractions as programs.

This paper introduces corpus-guided top-down synthesis as a mechanism for synthesizing library functions that capture common functionality from a corpus of programs in a domain specific language (DSL). The algorithm builds abstractions directly from initial DSL primitives, using syntactic pattern matching of intermediate abstractions to intelligently prune the search space and guide the algorithm towards abstractions that maximally capture shared structures in the corpus. We present an implementation of the approach in a tool called Stitch and evaluate it against the state-of-the-art deductive library learning algorithm from DreamCoder. Our evaluation shows that Stitch is 3-4 orders of magnitude faster and uses 2 orders of magnitude less memory while maintaining comparable or better library quality (as measured by compressivity). We also demonstrate Stitch's scalability on corpora containing hundreds of complex programs that are intractable with prior deductive approaches and show empirically that it is robust to terminating the search procedure early -- further allowing it to scale to challenging datasets by means of early stopping.

Many approaches to program synthesis perform a search within an enormous space of programs to find one that satisfies a given specification. Prior works have used neural models to guide combinatorial search algorithms, but such approaches still explore a huge portion of the search space and quickly become intractable as the size of the desired program increases. To tame the search space blowup, we propose training a neural model to learn a hands-on search policy for bottom-up synthesis, instead of relying on a combinatorial search algorithm. Our approach, called CrossBeam, uses the neural model to choose how to combine previously-explored programs into new programs, taking into account the search history and partial program executions. Motivated by work in structured prediction on learning to search, CrossBeam is trained on-policy using data extracted from its own bottom-up searches on training tasks. We evaluate CrossBeam in two very different domains, string manipulation and logic programming. We observe that CrossBeam learns to search efficiently, exploring much smaller portions of the program space compared to the state-of-the-art.

Writing software is tedious, error-prone, and accessible only to a small share of the population - yet coding grows increasingly important as the digital world plays larger and larger roles in peoples' lives. Program synthesis seeks to make coding more reliable and accessible by developing methods for automatically constructing programs Gulwani et al. (2017). For example, the FlashFill system Gulwani et al. (2017) in Microsoft Excel makes coding more accessible by allowing nontechnical users to synthesize spreadsheet programs by giving inputoutput examples, while the TF-coder system Shi et al. (2020a) seeks to make coding neural networks more reliable by synthesizing TensorFlow code from input-outputs. Where these systems have been most successful is when they pair a specialized domain-specific language (DSL) to a domain-specific search algorithm for synthesizing programs in that DSL. A recent trend - both in industry Kalyan et al. (2018) and academia Devlin et al. (2017) - is to employ machine learning methods to learn to quickly search for a program in the DSL Balog et al. (2017); Devlin et al. (2017); Lee et al. (2018); Zhang et al.

Modeling complex phenomena typically involves the use of both discrete and continuous variables. Such a setting applies across a wide range of problems, from identifying trends in time-series data to performing effective compositional scene understanding in images. Here, we propose Hybrid Memoised Wake-Sleep (HMWS), an algorithm for effective inference in such hybrid discrete-continuous models. Prior approaches to learning suffer as they need to perform repeated expensive inner-loop discrete inference. We build on a recent approach, Memoised Wake-Sleep (MWS), which alleviates part of the problem by memoising discrete variables, and extend it to allow for a principled and effective way to handle continuous variables by learning a separate recognition model used for importance-sampling based approximate inference and marginalization. We evaluate HMWS in the GP-kernel learning and 3D scene understanding domains, and show that it outperforms current state-of-the-art inference methods.

Inductive program synthesis, or inferring programs from examples of desired behavior, offers a general paradigm for building interpretable, robust, and generalizable machine learning systems. Effective program synthesis depends on two key ingredients: a strong library of functions from which to build programs, and an efficient search strategy for finding programs that solve a given task. We introduce LAPS (Language for Abstraction and Program Search), a technique for using natural language annotations to guide joint learning of libraries and neurally-guided search models for synthesis. When integrated into a state-of-the-art library learning system (DreamCoder), LAPS produces higher-quality libraries and improves search efficiency and generalization on three domains -- string editing, image composition, and abstract reasoning about scenes -- even when no natural language hints are available at test time.

Humans flexibly solve new problems that differ qualitatively from those they were trained on. This ability to generalize is supported by learned concepts that capture structure common across different problems. Here we develop a naturalistic drawing task to study how humans rapidly acquire structured prior knowledge. The task requires drawing visual objects that share underlying structure, based on a set of composable geometric rules. We show that people spontaneously learn abstract drawing procedures that support generalization, and propose a model of how learners can discover these reusable drawing programs. Trained in the same setting as humans, and constrained to produce efficient motor actions, this model discovers new drawing routines that transfer to test objects and resemble learned features of human sequences. These results suggest that two principles guiding motor program induction in the model - abstraction (general programs that ignore object-specific details) and compositionality (recombining previously learned programs) - are key for explaining how humans learn structured internal representations that guide flexible reasoning and learning.

Program synthesis techniques construct or infer programs from user-provided specifications, such as input-output examples. Yet most specifications, especially those given by end-users, leave the synthesis problem radically ill-posed, because many programs may simultaneously satisfy the specification. Prior work resolves this ambiguity by using various inductive biases, such as a preference for simpler programs. This work introduces a new inductive bias derived by modeling the program synthesis task as rational communication, drawing insights from recursive reasoning models of pragmatics. Given a specification, we score a candidate program both on its consistency with the specification, and also whether a rational speaker would chose this particular specification to communicate that program. We develop efficient algorithms for such an approach when learning from input-output examples, and build a pragmatic program synthesizer over a simple grid-like layout domain. A user study finds that end-user participants communicate more effectively with the pragmatic program synthesizer over a non-pragmatic one.