Short-term Memory of Deep RNN

The extension of deep learning towards temporal data processing is gaining an increasing research interest. In this paper we investigate the properties of state dynamics developed in successive levels of deep recurrent neural networks (RNNs) in terms of short-term memory abilities. Our results reveal interesting insights that shed light on the nature of layering as a factor of RNN design. Noticeably, higher layers in a hierarchically organized RNN architecture results to be inherently biased towards longer memory spans even prior to training of the recurrent connections. Moreover, in the context of Reservoir Computing framework, our analysis also points out the benefit of a layered recurrent organization as an efficient approach to improve the memory skills of reservoir models.Comment: This is a pre-print (pre-review) version of the paper accepted for presentation at the 26th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN), Bruges (Belgium), 25-27 April 201

Emergent mechanisms for long timescales depend on training curriculum and affect performance in memory tasks

Recurrent neural networks (RNNs) in the brain and in silico excel at solving tasks with intricate temporal dependencies. Long timescales required for solving such tasks can arise from properties of individual neurons (single-neuron timescale, $\tau$, e.g., membrane time constant in biological neurons) or recurrent interactions among them (network-mediated timescale). However, the contribution of each mechanism for optimally solving memory-dependent tasks remains poorly understood. Here, we train RNNs to solve $N$-parity and $N$-delayed match-to-sample tasks with increasing memory requirements controlled by $N$ by simultaneously optimizing recurrent weights and $\tau$s. We find that for both tasks RNNs develop longer timescales with increasing $N$, but depending on the learning objective, they use different mechanisms. Two distinct curricula define learning objectives: sequential learning of a single-$N$ (single-head) or simultaneous learning of multiple $N$s (multi-head). Single-head networks increase their $\tau$ with $N$ and are able to solve tasks for large $N$, but they suffer from catastrophic forgetting. However, multi-head networks, which are explicitly required to hold multiple concurrent memories, keep $\tau$ constant and develop longer timescales through recurrent connectivity. Moreover, we show that the multi-head curriculum increases training speed and network stability to ablations and perturbations, and allows RNNs to generalize better to tasks beyond their training regime. This curriculum also significantly improves training GRUs and LSTMs for large-$N$ tasks. Our results suggest that adapting timescales to task requirements via recurrent interactions allows learning more complex objectives and improves the RNN's performance

Incremental Training of a Recurrent Neural Network Exploiting a Multi-Scale Dynamic Memory

The effectiveness of recurrent neural networks can be largely influenced by their ability to store into their dynamical memory information extracted from input sequences at different frequencies and timescales. Such a feature can be introduced into a neural architecture by an appropriate modularization of the dynamic memory. In this paper we propose a novel incrementally trained recurrent architecture targeting explicitly multi-scale learning. First, we show how to extend the architecture of a simple RNN by separating its hidden state into different modules, each subsampling the network hidden activations at different frequencies. Then, we discuss a training algorithm where new modules are iteratively added to the model to learn progressively longer dependencies. Each new module works at a slower frequency than the previous ones and it is initialized to encode the subsampled sequence of hidden activations. Experimental results on synthetic and real-world datasets on speech recognition and handwritten characters show that the modular architecture and the incremental training algorithm improve the ability of recurrent neural networks to capture long-term dependencies.Comment: accepted @ ECML 2020. arXiv admin note: substantial text overlap with arXiv:2001.1177

An extension of transformer neural networks in the context of multivariate stochastic processes

Increasingly, artificial neural networks are explored to learn relationships among temporal sequence data for purposes of classification, prediction, and anomaly detection with the hope of exceeding the performance of more traditional machine learning algorithms. While the underlying Long Short-Term Memory or Gated Recurrent Unit networks are still the preferred choices by many researchers, such recurrent networks are sub-optimal to learn relationships within and across longer sequences. Transformer neural networks, originally designed to improve the performance of natural language processing tasks, pose an interesting alternative as their attention mechanisms are more capable of capturing context and meaning within longer sequences. Such features present opportunities to apply transformer networks also to temporal sequence data of financial asset prices. This thesis introduces an extension of the original transformer neural network which is capable of multivariate time series representation learning in a supervised learning context and attempts to train temporal sequences of financial asset prices. The prediction accuracy of the transformer extension exceeds two of the most popular recurrent neural networks used for temporal sequence data prediction. The experiments are conducted in the context of a trading algorithm that showcases the practical potential and its implications. As the model is not input data specific, opportunities to transfer enhancements to other domains exist

Deep Learning algorithms for solving high dimensional nonlinear Backward Stochastic Differential Equations

We study deep learning-based schemes for solving high dimensional nonlinear backward stochastic differential equations (BSDEs). First we show how to improve the performances of the proposed scheme in [W. E and J. Han and A. Jentzen, Commun. Math. Stat., 5 (2017), pp.349-380] regarding computational time by using a single neural network architecture instead of the stacked deep neural networks. Furthermore, those schemes can be stuck in poor local minima or diverges, especially for a complex solution structure and longer terminal time. To solve this problem, we investigate to reformulate the problem by including local losses and exploit the Long Short Term Memory (LSTM) networks which are a type of recurrent neural networks (RNN). Finally, in order to study numerical convergence and thus illustrate the improved performances with the proposed methods, we provide numerical results for several 100-dimensional nonlinear BSDEs including nonlinear pricing problems in finance.Comment: 21 pages, 5 figures, 16 table