In supervised machine learning, the choice of loss function implicitly assumes a particular noise distribution over the data. For example, the frequently used mean squared error (MSE) loss assumes a Gaussian noise distribution. The choice of loss function during training and testing affects the performance of artificial neural networks (ANNs). It is known that MSE may yield substandard performance in the presence of outliers. The Cauchy loss function (CLF) assumes a Cauchy noise distribution, and is therefore potentially better suited for data with outliers. This papers aims to determine the extent of robustness and generalisability of the CLF as compared to MSE. CLF and MSE are assessed on a few handcrafted regression problems, and a real-world regression problem with artificially simulated outliers, in the context of ANN training. CLF yielded results that were either comparable to or better than the results yielded by MSE, with a few notable exceptions.
Neural networks have been criticised for their inability to perform continual learning due to catastrophic forgetting and rapid unlearning of a past concept when a new concept is introduced. Catastrophic forgetting can be alleviated by specifically designed models and training techniques. This paper outlines a novel Spline Additive Model (SAM). SAM exhibits intrinsic memory retention with sufficient expressive power for many practical tasks, but is not a universal function approximator. SAM is extended with the Kolmogorov-Arnold representation theorem to a novel universal function approximator, called the Kolmogorov-Arnold Spline Additive Model -KASAM. The memory retention, expressive power and limitations of SAM and KASAM are illustrated analytically and empirically. SAM exhibited robust but imperfect memory retention, with small regions of overlapping interference in sequential learning tasks. KASAM exhibited greater susceptibility to catastrophic forgetting. KASAM in combination with pseudo-rehearsal training techniques exhibited superior performance in regression tasks and memory retention.
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