Memory-Non-Linearity Trade-Off in Distance-Based Delay Networks

The performance of echo state networks (ESNs) in temporal pattern learning tasks depends both on their memory capacity (MC) and their non-linear processing. It has been shown that linear memory capacity is maximized when ESN neurons have linear activation, and that a trade-off between non-linearity and linear memory capacity is required for temporal pattern learning tasks. The more recent distance-based delay networks (DDNs) have shown improved memory capacity over ESNs in several benchmark temporal pattern learning tasks. However, it has not thus far been studied whether this increased memory capacity comes at the cost of reduced non-linear processing. In this paper, we advance the hypothesis that DDNs in fact achieve a better trade-off between linear MC and non-linearity than ESNs, by showing that DDNs can have strong non-linearity with large memory spans. We tested this hypothesis using the NARMA-30 task and the bitwise delayed XOR task, two commonly used reservoir benchmark tasks that require a high degree of both non-linearity and memory.