Long Expressive Memory for Sequence Modeling

We propose a novel method called Long Expressive Memory (LEM) for learning long-term sequential dependencies. LEM is gradient-based, it can efficiently process sequential tasks with very long-term dependencies, and it is sufficiently expressive to be able to learn complicated input-output maps. To derive LEM, we consider a system of multiscale ordinary differential equations, as well as a suitable time-discretization of this system. For LEM, we derive rigorous bounds to show the mitigation of the exploding and vanishing gradients problem, a well-known challenge for gradient-based recurrent sequential learning methods. We also prove that LEM can approximate a large class of dynamical systems to high accuracy. Our empirical results, ranging from image and time-series classification through dynamical systems prediction to speech recognition and language modeling, demonstrate that LEM outperforms state-of-the-art recurrent neural networks, gated recurrent units, and long short-term memory models.

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Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Time Series Classification EigenWorms LEM % Test Accuracy 92.3 # 1
Sequential Image Classification noise padded CIFAR-10 LEM % Test Accuracy 60.5 # 3
Sequential Image Classification Sequential MNIST LEM Unpermuted Accuracy 99.5% # 5
Permuted Accuracy 96.6% # 18


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