Towards neural-network-guided program synthesis and verification

We propose a novel framework of program and invariant synthesis called neural network-guided synthesis. We first show that, by suitably designing and training neural networks, we can extract logical formulas over integers from the weights and biases of the trained neural networks. Based on the idea, we have implemented a tool to synthesize formulas from positive/negative examples and implication constraints, and obtained promising experimental results. We also discuss an application of our method for improving the qualifier discovery in the framework of ICE-learning-based CHC solving, which can in turn be applied to program verification and inductive invariant synthesis. Another potential application is to a neural-network-guided variation of Solar-Lezama’s program synthesis by sketching.

We present a method for example-guided synthesis of functional programs over recursive data structures. Given a set of input-output examples, our method synthesizes a program in a functional language with higher-order combinators like map and fold. The synthesized program is guaranteed to be the simplest program in the language to fit the examples. Our approach combines three technical ideas: inductive generalization, deduction, and enumerative search. First, we generalize the input-output examples into hypotheses about the structure of the target program. For each hypothesis, we use deduction to infer new input/output examples for the missing subexpressions. This leads to a new subproblem where the goal is to synthesize expressions within each hypothesis. Since not every hypothesis can be realized into a program that fits the examples, we use a combination of best-first enumeration and deduction to search for a hypothesis that meets our needs. We have implemented our method in a tool called λ2, and we evaluate this tool on a large set of synthesis problems involving lists, trees, and nested data structures. The experiments demonstrate the scalability and broad scope of λ2. A highlight is the synthesis of a program believed to be the world's earliest functional pearl.

In program synthesis there is a well-known trade-off between concise and strong specifications: if a specification is too verbose, it might be harder to write than the program; if it is too weak, the synthesised program might not match the user’s intent. In this work we explore the use of annotations for restricting memory access permissions in program synthesis, and show that they can make specifications much stronger while remaining surprisingly concise. Specifically, we enhance Synthetic Separation Logic (SSL), a framework for synthesis of heap-manipulating programs, with the logical mechanism of read-only borrows.We observe that this minimalistic and conservative SSL extension benefits the synthesis in several ways, making it more (a) expressive (stronger correctness guarantees are achieved with a modest annotation overhead), (b) effective (it produces more concise and easier-to-read programs), (c) efficient (faster synthesis), and (d) robust (synthesis efficiency is less affected by the choice of the search heuristic). We explain the intuition and provide formal treatment for read-only borrows. We substantiate the claims (a)–(d) by describing our quantitative evaluation of the borrowing-aware synthesis implementation on a series of standard benchmark specifications for various heap-manipulating programs.

Artificial neural networks (ANN) have been widely used in the field of data classification. Normally, training of neural network is applied with the traditional back propagation technique. As, this approach has various drawbacks, training of neural network is done with Particle Swarm Optimization (PSO). PSO has been widely used to solve the diverse kind of optimization problems. Population initialization performs a significant role in meta-heuristic algorithms. This paper describes a new initialization population approach Log Logistic termed as PSOLL-NN to create the initialization of the swarm. The proposed algorithm has been tested for weight optimization of feed forward neural network; and compared with back propagation Algorithm (BPA), standard PSO (PSO-NN), PSO initialized with Halton Sequence (PSOH-NN), Torus sequence (PSOT-NN) and Sobol sequence (PSOS-NN). The experimental results show that the proposed technique performed exceptionally better than the other traditional techniques. Moreover, the outcome of our work presents a foresight that how the proposed initialization technique can be used as an efficient alternative to standard training approaches for the data classification problems.

In this paper we introduce a planning approach based on a method of deductive program synthesis. The program synthesis system we rely upon takes first-order specifications and from these derives recursive programs automatically. It uses a set of transformation rules whose applications are guided by an overall strategy. Additionally several heuristics are involved which considerably reduce the search space. We show by means of an example taken from the blocks world how even recursive plans can be obtained with this method. Some modifications of the synthesis strategy and heuristics are discussed, which are necessary to obtain a powerful and automatic planning system. Finally it is shown how subplans can be introduced and generated separately.

Synthesis and transformation of logic programs using unfold/fold proofs

Program synthesis is the mechanized construction of software, dubbed ‘self-writing code’. Synthesis tools relieve the programmer from thinking about how the problem is to be solved; instead, the programmer only provides a description of what is to be achieved. Given a specification of what the program should do, the synthesizer generates an implementation that provably satisfies this specification. From a logical point of view, a program synthesizer is a solver for second-order existential logic. Owing to the expressiveness of second-order logic, program synthesis has an extremely broad range of applications. We survey some of these applications as well as recent trends in the algorithms that solve the program synthesis problem. In particular, we focus on an approach that has raised the profile of program synthesis and ushered in a generation of new synthesis tools, namely counter-example-guided inductive synthesis (CEGIS). We provide a description of the CEGIS architecture, followed by recent algorithmic improvements. We conjecture that the capacity of program synthesis engines will see further step change, in a manner that is transparent to the applications, which will open up an even broader range of use-cases.This article is part of the themed issue ‘Verified trustworthy software systems’.

Program verification is the task of automatically generating proofs for a program’s compliance with a given specification. Program synthesis is the task of automatically generating a program that meets a given specification. Both program verification and program synthesis can be viewed as search problems, for proofs and programs, respectively. For these search problems, we present approaches based on user-provided insights in the form of templates. Templates are hints about the syntactic forms of the invariants and programs, and help guide the search for solutions. We show how to reduce the template-based search problem to satisfiability solving, which permits the use of off-the-shelf solvers to efficiently explore the search space. Template-based approaches have allowed us to verify and synthesize programs outside the abilities of previous verifiers and synthesizers. Our approach can verify and synthesize difficult algorithmic textbook programs (e.g., sorting and dynamic programming-based algorithms) and difficult arithmetic programs.

Proposes a fuzzy neural expert system (FNES) which has a feedforward fuzzy neural network whose input layer consists of fuzzy cell groups and crisp (non-fuzzy) cell groups. Here, the truthfulness of fuzzy information and crisp information of training data is represented by fuzzy cell groups and crisp cell groups, respectively. The expert system has the following two functions: generalization of the information derived from the training data and embodiment of knowledge in the form of the fuzzy neural network; and extraction of fuzzy If-Then rules with linguistic relative importance of each proposition in an antecedent (If-part) from a trained fuzzy neural network. The paper also gives a method to extract automatically fuzzy If-Then rules from the trained neural network. To prove the effectiveness and validity of the proposed fuzzy neural expert system, a fuzzy neural expert system for medical diagnosis has been developed. >

BACKGROUND: Currently, artificial intelligence in the form of artificial neural networks is being actively implemented in a number of areas of our lives, including medicine. In particular, in otorhinolaryngology, artificial neural networks are used to analyze images obtained during endoscopic examinations of patients (e.g., videolaryngoscopy) [1–3]. The interpretation of laryngoscopic images often presents significant difficulties for practicing physicians, which reduces the frequency of detection of precancerous laryngeal diseases and contributes to the increase in the number of patients with stage III–IV laryngeal cancer [4, 5]. This underscores the significance of prompt performance and accurate interpretation of the findings of endoscopic examinations of patients with laryngeal disorders. Artificial neural networks can be employed to analyze the results of videolaryngoscopy, furnishing the physician with supplementary information that can enhance diagnostic accuracy and diminish the probability of error [6, 7]. AIM: The study aims to develop and train an artificial neural network for recognizing characteristic features of laryngeal neoplasms and variants of laryngeal normality. MATERIALS AND METHODS: The study was conducted under the grant of the Moscow Center for Innovative Technologies in Healthcare (grant No. 2112-1/22) entitled “Using Neural Networks (Artificial Intelligence Algorithms) for Control and Improving the Quality of Diagnosis and Treatment of Diseases of Laryngeal and Ear Structures through Digital Technologies”.The following methods were used during the course of the study: data collection for the creation of a photobank (dataset) of medical images obtained during videolaryngoscopy; data partitioning for the formation of datasets for individual nosologies and groups of diseases; the method of consilium; analysis of the accuracy of recognition and classification of digital endoscopic images; and training of classification neural networks. Consequently, a dataset comprising 1,471 laryngeal images in digital formats (JPEG, BMP) was assembled, labelled, and uploaded for the purpose of training the artificial neural network. Of the total number of images, 410 were classified as pertaining to laryngeal formation, while 1061 were classified as variants of normality. Subsequently, the neural network was trained and tested to identify the signs of normal and laryngeal masses. RESULTS: The results of the testing of the artificial neural network indicated the formation of an inaccuracy matrix, the calculation of the value of recognition accuracy, the calculation of the quality indicators of the model performance, and the construction of the ROC curve. The developed and trained artificial neural network demonstrated an accuracy of 86% in recognizing the signs of laryngeal masses and norms. CONCLUSIONS: This study demonstrates that a trained artificial neural network can successfully distinguish between signs of normal and laryngeal masses in endoscopic photographs. With further training of the neural network and achievement of high accuracy, this technology can be used in clinical practice as an assistant in the interpretation of laryngoscopic images and early diagnosis of laryngeal masses. It can also be employed to control and improve the quality of diagnosis and treatment of diseases of the throat, nose, and ears by primary care physicians.

Synthesizing intended programs from user-specified input-output examples, also known as Programming by Examples (PBE), is a challenging problem in program synthesis, and has been applied to a wide range of domains. A key challenge in PBE is to efficiently discover a user-intended program in the search space that can be exponentially large. In this work, we propose a method for automatic synthesis of functional programs on list manipulation, by using offline-trained Recurrent Neural Network (RNN) models to guide the program search. We adopt miniKanren, an embedded domain-specific language for flexible relational programming, as an underlying top-down deductive search engine of candidate programs that are consistent with input-output examples. Our approach targets an easy and effective integration of deep learning techniques in making better PBE systems and combines two technical ideas on generating diverse training dataset and designing rich feature embeddings of probable subproblems for synthesis generated by deductive search. The offline-learned model is then used in PBE to guide the top-down deductive search with specific strategies. To practically manipulate data structures of lists, our method synthesizes functional programs with popular higher-order combinators including $\texttt {map}$ , $\texttt {foldl}$ and $\texttt {foldr}$ . We have implemented our method and evaluated it with challenging program synthesis tasks on list manipulation. The experiments show promising results on the performance of our method compared to related state-of-the-art inductive synthesizers.

Training of neural network can be accelerated by limited numerical precision together with specialized low-precision hardware. This paper studies how low precision can impact on entire training of RNNs. We emulate low precision training for recently proposed gated recurrent unit (GRU) and use dynamic fixed point as a target numeric format. We first show that batch normalization on input sequences can help speed up training with low precision as well as high precision. We also show that the overflow rate should be carefully controlled for dynamic fixed point. We study low precision training with various rounding options including bit truncation, round to nearest, and stochastic rounding. Stochastic rounding shows superior results than the other options. The effect of fully low precision training is also analyzed by comparing partial low precision training. We show that the piecewise linear activation function with stochastic rounding can achieve comparable training results with floating point precision. Low precision multiplier and accumulator (MAC) with linear-feedback shift register (LFSR) is implemented with 28nm Synopsys PDK for energy and performance analysis. Implementation results show low precision hardware is 4.7x faster, and energy per task is up to 4.55x lower than that of floating point hardware.

In optimization and machine learning, the divide between discrete and continuous problems and methods is deep and persistent. We attempt to remove this distinction by training neural network autoencoders that embed discrete candidate solutions in continuous latent spaces. This allows us to take advantage of state-of-the-art continuous optimization methods for solving discrete optimization problems, and mitigates certain challenges in discrete optimization, such as design of bias-free search operators. In the experimental part, we consider program synthesis as the special case of combinatorial optimization. We train an autoencoder network on a large sample of programs in a problem-agnostic, unsupervised manner, and then use it with an evolutionary continuous optimization algorithm (CMA-ES) to map the points from the latent space to programs. We propose also a variant in which semantically similar programs are more likely to have similar embeddings. Assessment on a range of benchmarks in two domains indicates the viability of this approach and the usefulness of involving program semantics.

In this paper we propose a method for program synthesis from constructive proofs based on a particular proof strategy, we call dischargeable set construction. This proof-strategy allows to build proofs in which active patterns (sequences of application of rules with proper computational content) can be distinguished from correctness patterns (concerning correctness properties of the algorithm implicitly contained in the proof). The synthesis method associates with every active pattern of the proof a program schema (in an imperative language) translating only the computational content of the proof. One of the main features of our method is that it can be applied to a variety of theories formalizing ADT’s and classes of ADT’s. Here we will discuss the method and the computational content of some principles of particular interest in the context of some classes of ADT’s.

ABSTRACTA back‐propagation neural network was applied to predicting the KIC values using tensile material data and investigating the effects of crack plane orientation and temperature. The 595 KIC data of structural steels were used for training and testing the neural network model. In the trained neural network model, yield stress has relatively the most effect on KIC value among tensile material properties and KIC value was more sensitive to KIC test temperature than to crack plane orientation valid in the range of material data covered in this study. The performance of the trained artificial neural network (ANN) was evaluated by comparing output of the ANN with results of a conventional least squares fit to an assumed shape. The conventional linear or nonlinear least squares fitting methods gave very poor fitting results but the results predicted by the trained neural network were considerably satisfactory. This study shows that the neural network can be a good tool to predict KIC values according to the variation of the temperature and the crack plane orientation using tensile test results.