Improved Photometric Classification of Supernovae using Deep Learning

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We present improved photometric supernovae classification using deep recurrent neural networks. The main improvements over previous work are (i) the introduction of a time gate in the recurrent cell that uses the observational time as an input; (ii) greatly increased data augmentation including time translation, addition of Gaussian noise and early truncation of the lightcurve. For post Supernovae Photometric Classification Challenge (SPCC) data, using a training fraction of $5.2\%$ (1103 supernovae) of a representational dataset, we obtain a type Ia vs. non type Ia classification accuracy of $93.2 \pm 0.1\%$, a Receiver Operating Characteristic curve AUC of $0.980 \pm 0.002$ and a SPCC figure-of-merit of $F_1=0.57 \pm 0.01$. Using a representational dataset of $50\%$ ($10660$ supernovae), we obtain a classification accuracy of $96.6 \pm 0.1\%$, an AUC of $0.995 \pm 0.001$ and $F_1=0.76 \pm 0.01$. We found the non-representational training set of the SPCC resulted in a large degradation in performance due to a lack of faint supernovae, but this can be migrated by the introduction of only a small number ($\sim 100$) of faint training samples. We also outline ways in which this could be achieved using unsupervised domain adaptation.

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Learning to store information over extended time intervals by recurrent backpropagation takes a very long time, mostly because of insufficient, decaying error backflow. We briefly review Hochreiter's (1991) analysis of this problem, then address it by introducing a novel, efficient, gradient-based method called long short-term memory (LSTM). Truncating the gradient where this does not do harm, LSTM can learn to bridge minimal time lags in excess of 1000 discrete-time steps by enforcing constant error flow through constant error carousels within special units. Multiplicative gate units learn to open and close access to the constant error flow. LSTM is local in space and time; its computational complexity per time step and weight is O(1). Our experiments with artificial data involve local, distributed, real-valued, and noisy pattern representations. In comparisons with real-time recurrent learning, back propagation through time, recurrent cascade correlation, Elman nets, and neural sequence chunking, LSTM leads to many more successful runs, and learns much faster. LSTM also solves complex, artificial long-time-lag tasks that have never been solved by previous recurrent network algorithms.
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