Explaining and reasoning about processes which underlie observed black-box phenomena enables the discovery of causal mechanisms, derivation of suitable abstract representations and the formulation of more robust predictions. We propose to learn high level functional programs in order to represent abstract models which capture the invariant structure in the observed data. We introduce the @math -machine (program-induction machine) -- an architecture able to induce interpretable LISP-like programs from observed data traces. We propose an optimisation procedure for program learning based on backpropagation, gradient descent and A* search. We apply the proposed method to three problems: system identification of dynamical systems, explaining the behaviour of a DQN agent and learning by demonstration in a human-robot interaction scenario. Our experimental results show that the @math -machine can efficiently induce interpretable programs from individual data traces.
Determining how many input output examples or execution traces are required in order to generalise well is still an open research problem. However, in this paper, we focus attention more on the explanatory power afforded by programs rather than on the broader problems of generalisation in the space of programs. While these characteristics are of course related, we take a view similar to that of @cite_0 , arguing that it is possible to build from locally valid program fragments which provide useful insight into the black-box processes generating the data. By combining gradient descent and A* search the @math -machine is able to learn informative and interpretable high-level LISP-like programs, even just from a single observation trace.
@cite_0
2079632486
The property of locality in program behavior has been studied and modelled extensively because of its application to memory design, code optimization, multiprogramming etc. We propose a k order Markov chain based scheme to model the sequence of time intervals between successive references to the same address in memory during program execution. Each unique address in a program is modelled separately. To validate our model, which we call the Inter-Reference Gap (IRG) model, we show substantial improvements in three different areas where it is applied. (1) We improve upon the miss ratio for the Least Recently Used (LRU) memory replacement algorithm by up to 37 . (2) We achieve up to 22 space-time product improvement over the Working Set (WS) algorithm for dynamic memory management. (3) A new trace compression technique is proposed which compresses up to 2.5 with zero error in WS simulations and up to 3.7 error in the LRU simulations. All these results are obtained experimentally, via trace driven simulations over a wide range of cache traces, page reference traces, object traces and database traces.