This paper proposes an algorithm called Forward Composition Propagation (FCP) to explain the predictions of feed-forward neural networks operating on structured pattern recognition problems. In the proposed FCP algorithm, each neuron is described by a composition vector indicating the role of each problem feature in that neuron. Composition vectors are initialized using a given input instance and subsequently propagated through the whole network until we reach the output layer. It is worth mentioning that the algorithm is executed once the network's training network is done. The sign of each composition value indicates whether the corresponding feature excites or inhibits the neuron, while the absolute value quantifies such an impact. Aiming to validate the FCP algorithm's correctness, we develop a case study concerning bias detection in a state-of-the-art problem in which the ground truth is known. The simulation results show that the composition values closely align with the expected behavior of protected features.

Forecasting windmill time series is often the basis of other processes such as anomaly detection, health monitoring, or maintenance scheduling. The amount of data generated on windmill farms makes online learning the most viable strategy to follow. Such settings require retraining the model each time a new batch of data is available. However, update the model with the new information is often very expensive to perform using traditional Recurrent Neural Networks (RNNs). In this paper, we use Long Short-term Cognitive Networks (LSTCNs) to forecast windmill time series in online settings. These recently introduced neural systems consist of chained Short-term Cognitive Network blocks, each processing a temporal data chunk. The learning algorithm of these blocks is based on a very fast, deterministic learning rule that makes LSTCNs suitable for online learning tasks. The numerical simulations using a case study with four windmills showed that our approach reported the lowest forecasting errors with respect to a simple RNN, a Long Short-term Memory, a Gated Recurrent Unit, and a Hidden Markov Model. What is perhaps more important is that the LSTCN approach is significantly faster than these state-of-the-art models.

In this paper, we present a recurrent neural system named Long Short-term Cognitive Networks (LSTCNs) as a generalisation of the Short-term Cognitive Network (STCN) model. Such a generalisation is motivated by the difficulty of forecasting very long time series in an efficient, greener fashion. The LSTCN model can be defined as a collection of STCN blocks, each processing a specific time patch of the (multivariate) time series being modelled. In this neural ensemble, each block passes information to the subsequent one in the form of a weight matrix referred to as the prior knowledge matrix. As a second contribution, we propose a deterministic learning algorithm to compute the learnable weights while preserving the prior knowledge resulting from previous learning processes. As a third contribution, we introduce a feature influence score as a proxy to explain the forecasting process in multivariate time series. The simulations using three case studies show that our neural system reports small forecasting errors while being up to thousands of times faster than state-of-the-art recurrent models.