However, these models suffer from quadratic computational cost in the input sequence lengthn to compute pairwise attention in each layer.

Adaptive parameterization is a means of increasing this flexibility and thereby increasing the model's capacity to learn non-linear patterns. We focus on the feed-forward layer, f(x):= φ(W x+b),for some activation functionφ: R 7 R. Define the pre-activation layer as a = A(x):= Wx+band denote byg(a):= φ(a)/athe activation effect ofφgivena, where divisioniselement-wise.

The use of neural networks trained on individual claims data has become increasingly popular in the actuarial reserving literature. We consider how to best input historical payment data in neural network models. Additionally, case estimates are also available in the format of a time series, and we extend our analysis to assessing their predictive power. In this paper, we compare a feed-forward neural network trained on summarised transactions to a recurrent neural network equipped to analyse a claim's entire payment history and/or case estimate development history. We draw conclusions from training and comparing the performance of the models on multiple, comparable highly complex datasets simulated from SPLICE (Avanzi, Taylor and Wang, 2023). We find evidence that case estimates will improve predictions significantly, but that equipping the neural network with memory only leads to meagre improvements. Although the case estimation process and quality will vary significantly between insurers, we provide a standardised methodology for assessing their value.