Abstract: Seen from an evolutionary perspective, cancer is a complex system subject to high mutation rates and strong selection pressures. Mutations, the substrate of selection, are caused by many different mutational processes. A multitude of such mutational processes, or "signatures", has been identified and associated with biochemical mechanisms of DNA lesions and repair. The mutational spectrum of any given tumor can be decomposed into these signatures in order to classify tumors into subtypes, determine exposure times to certain mutagens or characterize individual mutation origins. However, state-of-the-art methods to quantify the contributions of different mutational processes to a tumor sample fail to detect certain mutational signatures, only work well for a relatively high number of mutations and do not provide error estimates of signature contributions. Here, I will describe SigNet, a novel approach to signature decomposition based on an artificial neural network. By leveraging the correlations between signatures present in real data, this approach outperforms existing methods, particularly for samples with small to intermediate numbers of mutations. We applied SigNet to elucidate the effects of hypoxia on the tumor mutational footprint and discovered both known and novel correlations of mutational signatures with hypoxia, including a strong association of hypoxia with a decrease in the activity of DNA repair processes. These and other results demonstrate the potential of a mutational process decomposition that can be applied to DNA sequencing datasets of limited size.