We study a class of neuro-symbolic generative models in which neural networks are used both for inference and as priors over symbolic, data-generating programs. As generative models, these programs capture compositional structures in a naturally explainable form. To tackle the challenge of performing program induction as an ‘inner-loop’ to learning, we propose the Memoised Wake-Sleep (MWS) algorithm, which extends Wake Sleep by explicitly storing and reusing the best programs discovered by the inference network throughout training. We use MWS to learn accurate, explainable models in three challenging domains: stroke-based character modelling, cellular automata, and few-shot learning in a novel dataset of real-world string concepts.

Expert problem-solving is driven by powerful languages for thinking about problems and their solutions. Acquiring expertise means learning these languages -- systems of concepts, alongside the skills to use them. We present DreamCoder, a system that learns to solve problems by writing programs. It builds expertise by creating programming languages for expressing domain concepts, together with neural networks to guide the search for programs within these languages. A ``wake-sleep'' learning algorithm alternately extends the language with new symbolic abstractions and trains the neural network on imagined and replayed problems. DreamCoder solves both classic inductive programming tasks and creative tasks such as drawing pictures and building scenes. It rediscovers the basics of modern functional programming, vector algebra and classical physics, including Newton's and Coulomb's laws. Concepts are built compositionally from those learned earlier, yielding multi-layered symbolic representations that are interpretable and transferrable to new tasks, while still growing scalably and flexibly with experience.

The overall goal of neuro-symbolic computation is to integrate high-level reasoning with low-level perception. We argue 1) that neuro-symbolic computation should integrate neural networks with the two most prominent methods for reasoning, that is, logic and probability, and 2) that neuro-symbolic integrated methods should have the pure neural, logical and probabilistic methods as special cases. We examine the state-of-the-art with regard to these claims and briefly position our own contribution DeepProbLog in this perspective.

We introduce DeepProbLog, a probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques can be adapted for the new language. Our experiments demonstrate that DeepProbLog supports both symbolic and subsymbolic representations and inference, 1) program induction, 2) probabilistic (logic) programming, and 3) (deep) learning from examples. To the best of our knowledge, this work is the first to propose a framework where general-purpose neural networks and expressive probabilistic-logical modeling and reasoning are integrated in a way that exploits the full expressiveness and strengths of both worlds and can be trained end-to-end based on examples.      

Synthesizing user-intended programs from a small number of input-output examples is a challenging problem with several important applications like spreadsheet manipulation, data wrangling and code refactoring. Existing synthesis systems either completely rely on deductive logic techniques that are extensively hand-engineered or on purely statistical models that need massive amounts of data, and in general fail to provide real-time synthesis on challenging benchmarks. In this work, we propose Neural Guided Deductive Search (NGDS), a hybrid synthesis technique that combines the best of both symbolic logic techniques and statistical models. Thus, it produces programs that satisfy the provided specifications by construction and generalize well on unseen examples, similar to data-driven systems. Our technique effectively utilizes the deductive search framework to reduce the learning problem of the neural component to a simple supervised learning setup. Further, this allows us to both train on sparingly available real-world data and still leverage powerful recurrent neural network encoders. We demonstrate the effectiveness of our method by evaluating on real-world customer scenarios by synthesizing accurate programs with up to 12× speed-up compared to state-of-the-art systems.

Motivation: Biological data and knowledge bases increasingly rely on Semantic Web technologies and the use of knowledge graphs for data integration, retrieval and federated queries. In the past years, feature learning methods that are applicable to graph-structured data are becoming available, but have not yet widely been applied and evaluated on structured biological knowledge. Results: We develop a novel method for feature learning on biological knowledge graphs. Our method combines symbolic methods, in particular knowledge representation using symbolic logic and automated reasoning, with neural networks to generate embeddings of nodes that encode for related information within knowledge graphs. Through the use of symbolic logic, these embeddings contain both explicit and implicit information. We apply these embeddings to the prediction of edges in the knowledge graph representing problems of function prediction, finding candidate genes of diseases, protein-protein interactions, or drug target relations, and demonstrate performance that matches and sometimes outperforms traditional approaches based on manually crafted features. Our method can be applied to any biological knowledge graph, and will thereby open up the increasing amount of Semantic Web based knowledge bases in biology to use in machine learning and data analytics. Availability and Implementation: https://github.com/bio-ontology-research-group/walking-rdf-and-owl

We develop a framework for combining differentiable programming languages with neural networks. Using this framework we create end-toend trainable systems that learn to write interpretable algorithms with perceptual components. We explore the benefits of inductive biases for strong generalization and modularity that come from the program-like structure of our models. In particular, modularity allows us to learn a library of (neural) functions which grows and improves as more tasks are solved. Empirically, we show that this leads to lifelong learning systems that transfer knowledge to new tasks more effectively than baselines

Given that in practice training data is scarce for all but a small set of problems, a core question is how to incorporate prior knowledge into a model. In this paper, we consider the case of prior procedural knowledge for neural networks, such as knowing how a program should traverse a sequence, but not what local actions should be performed at each step. To this end, we present an end-to-end differentiable interpreter for the programming language Forth which enables programmers to write program sketches with slots that can be filled with behaviour trained from program input-output data. We can optimise this behaviour directly through gradient descent techniques on user-specified objectives, and also integrate the program into any larger neural computation graph. We show empirically that our interpreter is able to effectively leverage different levels of prior program structure and learn complex behaviours such as sequence sorting and addition. When connected to outputs of an LSTM and trained jointly, our interpreter achieves state-of-the-art accuracy for end-to-end reasoning about quantities expressed in natural language stories.      

Recent years have seen the proposal of a number of neural architectures for the problem of Program Induction. Given a set of input-output examples, these architectures are able to learn mappings that generalize to new test inputs. While achieving impressive results, these approaches have a number of important limitations: (a) they are computationally expensive and hard to train, (b) a model has to be trained for each task (program) separately, and (c) it is hard to interpret or verify the correctness of the learnt mapping (as it is defined by a neural network). In this paper, we propose a novel technique, Neuro-Symbolic Program Synthesis, to overcome the above-mentioned problems. Once trained, our approach can automatically construct computer programs in a domain-specific language that are consistent with a set of input-output examples provided at test time. Our method is based on two novel neural modules. The first module, called the cross correlation I/O network, given a set of input-output examples, produces a continuous representation of the set of I/O examples. The second module, the Recursive-Reverse-Recursive Neural Network (R3NN), given the continuous representation of the examples, synthesizes a program by incrementally expanding partial programs. We demonstrate the effectiveness of our approach by applying it to the rich and complex domain of regular expression based string transformations. Experiments show that the R3NN model is not only able to construct programs from new input-output examples, but it is also able to construct new programs for tasks that it had never observed before during training.