Can Local Representation Alignment RNNs Solve Temporal Tasks?

Recurrent Neural Networks (RNNs) are commonly used for real-time processing, streaming data, and cases where the amount of training samples is limited. Backpropagation Through Time (BPTT) is the predominant algorithm for training RNNs; however, it is frequently criticized for being prone to exploding and vanishing gradients and being biologically implausible. In this paper, we present and evaluate a target propagation-based method for RNNs, which uses local updates and seeks to reduce the said instabilities. Having stable RNN models increases their practical use in a wide range of fields such as natural language processing, time-series forecasting, anomaly detection, control systems, and robotics. The proposed solution uses local representation alignment (LRA). We thoroughly analyze the performance of this method, experiment with normalization and different local error functions, and invalidate certain assumptions about the behavior of this type of learning. Namely, we demonstrate that despite the decomposition of the network into sub-graphs, the model still suffers from vanishing gradients. We also show that gradient clipping as proposed in LRA has little to no effect on network performance. This results in an LRA RNN model that is very difficult to train due to vanishing gradients. We address this by introducing gradient regularization in the direction of the update and demonstrate that this modification promotes gradient flow and meaningfully impacts convergence. We compare and discuss the performance of the algorithm, and we show that the regularized LRA RNN considerably outperforms the unregularized version on three landmark tasks: temporal order, 3-bit temporal order, and random permutation.

On the biological plausibility of orthogonal initialisation for solving gradient instability in deep neural networks

Initialising the synaptic weights of artificial neural networks (ANNs) with orthogonal matrices is known to alleviate vanishing and exploding gradient problems. A major objection against such initialisation schemes is that they are deemed biologically implausible as they mandate factorization techniques that are difficult to attribute to a neurobiological process. This paper presents two initialisation schemes that allow a network to naturally evolve its weights to form orthogonal matrices, provides theoretical analysis that pre-training orthogonalisation always converges, and empirically confirms that the proposed schemes outperform randomly initialised recurrent and feedforward networks.