Neural networks learn to detect and emulate sorting algorithms from images of their execution traces

Abstract

Context: Recent advancements in the applicability of neural networks across a variety of fields, such as computer vision, natural language processing and others, have re-sparked an interest in program induction methods. (Kitzelman [1] , Gulwani et al. [2] or Kant [3].) Problem: When performing a program induction task, it is not feasible to search across all possible programs that map an input to an output because the number of possible combinations or sequences of instructions is too high: at least an exponential growth based on the generated program length. Moreover, there does not exist a general framework to formulate such program induction tasks and current computational limitations do not allow a very wide range of machine learning applications in the field of computer programs generation.Objective: In this study, we analyze the effectiveness of execution traces as learning representations for neural network models in a program induction set-up. Our goal is to generate visualizations of program execution dynamics, specifically of sorting algorithms, and to apply machine learning techniques on them to capture their semantics and emulate their behavior using neural networks. Method:We begin by classifying images of execution traces for algorithms working on a finite array of numbers, such as various sorting and data structures algorithms. Next we experiment with detecting sub-program patterns inside the trace sequence of a larger program. The last step is to predict future steps in the execution of various sorting algorithms. More specifically, we try to emulate their behavior by observing their execution traces. We also discuss generalizations to other classes of programs, such as 1-D cellular automata. Results:Our experiments show that neural networks are capable of modeling the mechanisms underlying simple algorithms if enough execution traces are provided as data. We compare the performance of our program induction model with other similar experimental results from Graves et al. [4] and Vinyals et al. [5]. We were also able to demonstrate that sorting algorithms can be treated both as images displaying spatial patterns, as well as sequential instructions in a domain specific language, such as swapping two elements. We tested our approach on three types of increasingly harder tasks: detection, recognition and emulation. Conclusions:We demonstrate that simple algorithms can be modelled using neural networks and provide a method for representing specific classes of programs as either images or sequences of instructions in a domain-specific language, such that a neural network can learn their behavior. We consider the complexity of various set-ups to arrive at some improvements based on the data representation type. The insights from our experiments can be applied for designing better models of program induction.

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