TABLE OF LINKS TABLE OF LINKS Abstract Abstract Abstract 1 Introduction 1 Introduction 1 Introduction 2 Related Work 2 Related Work 2 Related Work 3 Problem Formulation 3 Problem Formulation 3 Problem Formulation 4 Measuring Catastrophic Forgetting 4 Measuring Catastrophic Forgetting 4 Measuring Catastrophic Forgetting 5 Experimental Setup 5 Experimental Setup 5 Experimental Setup 6 Results 6 Results 6 Results 7 Discussion 7 Discussion 7 Discussion 8 Conclusion 8 Conclusion 8 Conclusion 9 Future Work and References 9 Future Work and References 9 Future Work and References 4 Measuring Catastrophic Forgetting 4 Measuring Catastrophic Forgetting In this section, we examine the various ways which people have proposed to measure catastrophic forgetting. The most prominent of these is retention. Retention-based metrics directly measure the drop in performance on a set of previously-learned tasks after learning a new task. Retention has its roots in psychology (e.g., Barnes and Underwood (1959)), and McCloskey and Cohen (1989) used this as a measure of catastrophic forgetting. The simplest way of measuring the retention of a learning system is to train it on one task until it has mastered that task, then train it on a second task until it has mastered that second task, and then, finally, report the new performance on the first task. McCloskey and Cohen (1989) used it in a two-task setting, but more complicated formulations exist for situations where there are more than two tasks (e.g., see Kemker et al. (2018)). An alternative to retention that likewise appears in psychological literature and the machine learning literature is relearning. Relearning was the first formal metric used to quantify forgetting in the psychology community (Ebbinghaus, 1913), and was first used to measure catastrophic forgetting in Hetherington and Seidenberg (1989). The simplest way of measuring relearning is to train a learning system on a first task to mastery, then train it on a second task to mastery, then train it on the first task to mastery again, and then, finally, report how much quicker the learning system mastered the first task the second time around versus the first time. While in some problems relearning is of lesser import than retention, in others it is much more significant. A simple example of such a problem is one where forgetting is made inevitable due to resource limitations, and the rapid reacquisition of knowledge is paramount. A third measure for catastrophic forgetting, activation overlap, was introduced in French (1991). In that work, French argued that catastrophic forgetting was a direct consequence of the overlap of the distributed representations of ANNs. He then postulated that catastrophic forgetting could be measured by quantifying the degree of this overlap exhibited by the ANN. The original formulation of the activation overlap of an ANN given a pair of samples looks at the activation of the hidden units in the ANN and measures the element-wise minimum of this between the samples. To bring this idea in line with contemporary thinking (e.g., Kornblith et al. (2019)) and modern network design, we propose instead using the dot product of these activations between the samples. Mathematically, we can thus write the activation overlap of a network with hidden units h0, h1, ..., hn with respect to two samples a and b as Authors:

Dylan R. Ashley
Sina Ghiassian
Richard S. Sutton Authors: Dylan R. Ashley
Sina Ghiassian
Richard S. Sutton Dylan R. Ashley Dylan R. Ashley Sina Ghiassian Sina Ghiassian Richard S. Sutton Richard S. Sutton This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv available on arxiv

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Measuring Catastrophic Forgetting in AI

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