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Possibilities frontiers for the similar tasks experiment. 

Possibilities frontiers for the similar tasks experiment. 

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Catastrophic forgetting is a problem faced by many machine learning models and algorithms. When trained on one task, then trained on a second task, many machine learning models "forget'' how to perform the first task. This is widely believed to be a serious problem for neural networks. Here, we investigate the extent to which the catastrophic forge...

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... not improved for 100 epochs. After running all 25 randomly configured experiments for all 8 conditions, we make a possibilities frontier curve showing the minimum amount of test error on the new task obtaining for each amount of test error on the old task. Specifically, these plots are made by drawing a curve that traces out the lower left frontier of the cloud of points of all (old task test error, new task test error) pairs encountered by all 25 models during the course of training on the new task, with one point generated after each pass through the training set. Note that these test set errors are computed after training on only a subset of the training data, because we do not train on the validation set. It is possible to improve further by also training on the validation set, but we do not do so here because we only care about the relative performance of the different methods, not necessarily obtaining state of the art results. (Usually possibilities frontier curves are used in sce- narios where higher values are better, and the curves trace out the higher edge of a convex hull of scatterplot. Here, we are plotting error rates, so the lower values are better and the curves trace out the lower edge of a convex hull of a scatterplot. We used error rather than accuracy so that log scale plots would com- press regions of bad performance and expand regions of good performance, in order to highlight the differences between the best-performing methods. Note that the log scaling sometimes makes the convex regions apear non-convex) Many naturally occurring tasks are highly similar to each other in terms of the underlying structure that must be understood, but have the input presented in a different format. For example, consider learning to understand Italian after already learning to understand Spanish. Both tasks share the deeper underlying structure of being a natural language understanding problem, and fur- thermore, Italian and Spanish have similar grammar. However, the specific words in each language are different. A person learning Italian thus benefits from having a pre-existing representation of the general struc- ture of the language. The challenge is to learn to map the new words into these structures (e.g., to attach the Italian word “sei” to the pre-existing concept of the second person conjugation of the verb “to be”) without damaging the ability to understand Spanish. The ability to understand Spanish could diminish if the learning algorithm inadvertently modifies the more abstract definition of language in general (i.e., if neurons that were used for verb conjugation before now get re-purposed for plurality agreement) rather than exploiting the pre-existing definition, or if the learning algorithm removes the associations between individual Spanish words and these pre-existing concepts (e.g., if the net retains the concept of there being a second person conjugation of the verb “to be” but forgets that the Spanish word “eres” corresponds to it). To test this kind of learning problem, we designed a simple pair of tasks, where the tasks are the same, but with different ways of formatting the input. Specifically, we used MNIST classification, but with a different permutation of the pixels for the old task and the new task. Both tasks thus benefit from having concepts like penstroke detectors, or the concept of penstrokes being combined to form digits. However, the meaning of any individual pixel is different. The net must learn to associate new collections of pixels to penstrokes, without significantly disrupting the old higher level concepts, or erasing the old connections between pixels and penstrokes. The classification performance results are presented in Fig. 1. Using dropout improved the two-task validation set performance for all models on this task pair. We show the effect of dropout on the optimal model size in Fig. 2. While the nets were able to basically succeed at this task, we don’t believe that they did so by mapping different sets of pixels into pre-existing concepts. We visualized the first layer weights of the best net (in terms of combined validation set error) and their apparent semantics do not noticeably change between when training on the old task concludes and training on the new task begins. This suggests that the higher layers of the net changed to be able to ac- comodate a relatively arbitrary projection of the input, rather than remaining the same while the lower layers adapted to the new input format. We next considered what happens when the two tasks are not exactly the same, but semantically similar, and using the same input format. To test this case, we used sentiment analysis of two product categories of Amazon reviews (Blitzer et al., 2007) as the two tasks. The task is just to classify the text of a product review as positive or negative in sentiment. We used the same preprocessing as (Glorot et al., 2011b). The classification performance results are presented in Fig. 3. Using dropout improved the two-task validation set performance for all models on this task pair. We show the effect of dropout on the optimal model size in Fig. 6. We next considered what happens when the two tasks are semantically similar. To test this case, we used Amazon reviews as one task, and MNIST classification as another. In order to give both tasks the same output size, we used only two classes of the MNIST dataset. To give them the same validation set size, we randomly subsampled the remaining examples of the MNIST validation set (since the MNIST validation set was originally larger than the Amazon validation set, and we don’t want the estimate of the performance on the Amazon dataset to have higher variance than the MNIST one). The Amazon dataset as we preprocessed it earlier has 5,000 input features, while MNIST has only 784. To give the two tasks the same input size, we reduced the dimensionality of the Amazon data with PCA. Classification performance results are presented in Our experiments have shown that training with dropout is always beneficial, at least on the relatively small datasets we used in this paper. Dropout improved performance for all eight methods on all three task pairs. Dropout works the best in terms of performance on the new task, performance on the old task, and points along the tradeoff curve balancing these two extremes, for all three task pairs. Dropout’s resistance to forgetting may be explained in part by the large model sizes that can be trained with dropout. On the input-reformatted task pair and the similar task pair, dropout never decreased the size of the optimal model for any of the four activation functions we tried. However, dropout seems to have additional properties that can help prevent forgetting that we do not yet have an explanation for. On the dissimilar tasks experiment, dropout improved performance but reduced the size of the optimal model for most of the activation functions, and on the other task pairs, it occasionally had no effect on the optimal model size. The only recent previous work on catastrophic forget- ting(Srivastava et al., 2013) argued that the choice of activation function has a significant effect on the catastrophic forgetting properties of a net, and in particular that hard LWTA outperforms logistic sigmoid and rectified linear units in this respect when trained with stochastic gradient descent. In our more extensive experiments we found that the choice of activation function has a less consistent effect than the choice of training algorithm. When we performed experiments with different kinds of task pairs, we found that the ranking of the activation functions is very problem dependent. For example, logistic sigmoid is the worst under some conditions but the best under other conditions. This suggests that one should always cross-validate the choice of activation function, as long as it is computationally feasible. We also re- ject the idea that hard LWTA is particular resistant to catastrophic forgetting in general, or that it makes the standard SGD training algorithm more resistant to catastrophic forgetting. For example, when training with SGD on the input reformatting task pair, hard LWTA’s possibilities frontier is worse than all activation functions except sigmoid for most points along the curve. On the similar task pair, LWTA with SGD is the worst of all eight methods we considered, in terms of best performance on the new task, best performance on the old task, and in terms of attaining points close to the origin of the possibilities frontier plot. However, hard LWTA does perform the best in some cir- cumstances (it has the best performance on the new task for the dissimilar task pair ). This suggests that it is worth including hard LWTA as one of many activation functions in a hyperparameter search. LWTA is however never the leftmost point in any of our three task pairs, so it is probably only useful in sequential task settings where forgetting is an issue. When computational resources are too limited to experiment with multiple activation functions, we rec- ommend using the maxout activation function trained with dropout. This is the only method that appears on the lower-left frontier of the performance tradeoff plots for all three task pairs we considered. We would like to thank the developers of Theano (Bergstra et al., 2010; Bastien et al., 2012), Pylearn2 (Goodfellow et al., 2013a). We would also like to thank NSERC, Compute Canada, and Calcul Québec for providing computational resources. Ian Goodfellow is supported by the 2013 Google Fellowship in Deep Learning. Bastien, Frédéric, Lamblin, Pascal, Pascanu, Razvan, Bergstra, James, Goodfellow, Ian J., Bergeron, Arnaud, Bouchard, Nicolas, and Bengio, Yoshua. Theano: new features and speed improvements. Deep Learning and Unsupervised Feature Learning NIPS 2012 Workshop, 2012. Bergstra, James and Bengio, Yoshua. Random search for hyper-parameter optimization. ...

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