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 two problems: system identification of dynamical systems and explaining the behaviour of a DQN agent. Our 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
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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. The difficulties posed by GPGPU programming and the need to increase productivity have guided research towards directive-based high-level programs for accelerators. This effort has led to the definition of the OpenACC industry standard. It significantly simplifies writing code for graphics engines leaving the programmer the opportunity to tune the application for the target hardware and input. In this paper we address the problem of choosing the best mapping of sequential OpenACC loops to the parallel thread-space for a given program and input size. We show that auto-tuning on mapping parameters can improve performance by up to 4.8x over the default chosen by a state-of-the-art compiler. To reduce the overhead of auto-tuning we introduce a search technique that exploits similarities in behaviour across inputs using a nearest neighbour approach. This dramatically reduces the search for a good mapping (by 97 compared to random search). Finally we propose a heuristic for stopping the focused search which, averaged across 12 benchmarks and 30 input sizes each, achieves a speedup over the default of 1.26x with only 8 sampling runs. Inferring a minimal finite state machine (FSM) from a given set of traces is a fundamental problem in computer science. Although the problem is known to be NP-complete, it can be solved efficiently with SAT solvers when the given set of traces is relatively small. On the other hand, to infer an FSM equivalent to a machine which generates traces, the set of traces should be sufficiently representative and hence large. However, the existing SAT-based inference techniques do not scale well when the length and number of traces increase. In this paper, we propose a novel approach which processes lengthy traces incrementally. The experimental results indicate that it scales sufficiently well and time it takes grows slowly with the size of traces. A well known but incorrect piece of functional programming folklore is that ML expressions can be efficiently typed in polynomial time. In probing the truth of that folklore, various researchers, including Wand, Buneman, Kanellakis, and Mitchell, constructed simple counterexamples consisting of typable ML programs having length n , with principal types having O(2 cn ) distinct type variables and length O(2 2cn ). When the types associated with these ML constructions were represented as directed acyclic graphs, their sizes grew as O(2 cn ). The folklore was even more strongly contradicted by the recent result of Kanellakis and Mitchell that simply deciding whether or not an ML expression is typable is PSPACE-hard. We improve the latter result, showing that deciding ML typability is DEXPTIME-hard. As Kanellakis and Mitchell have shown containment in DEXPTIME, the problem is DEXPTIME-complete. The proof of DEXPTIME-hardness is carried out via a generic reduction: it consists of a very straightforward simulation of any deterministic one-tape Turing machine M with input k running in O ( c |k| ) time by a polynomial-sized ML formula P M,k , such that M accepts k iff P M,k is typable. The simulation of the transition function δ of the Turing Machine is realized uniquely through terms in the lambda calculus without the use of the polymorphic let construct. We use let for two purposes only: to generate an exponential amount of blank tape for the Turing Machine simulation to begin, and to compose an exponential number of applications of the ML formula simulating state transition. It is purely the expressive power of ML polymorphism to succinctly express function composition which results in a proof of DEXPTIME-hardness. We conjecture that lower bounds on deciding typability for extensions to the typed lambda calculus can be regarded precisely in terms of this expressive capacity for succinct function composition. To further understand this lower bound, we relate it to the problem of proving equality of type variables in a system of type equations generated from an ML expression with let-polymorphism. We show that given an oracle for solving this problem, deciding typability would be in PSPACE, as would be the actual computation of the principal type of the expression, were it indeed typable.