Our ASR approaches have always used neural networks, Idiap researchers having pioneered the hybrid approach to ASR based on posterior probabilities. The work currently continues in high-profile EU-funded projects such as SUMMA and MALORCA, and in high-profile toolkits such as Kaldi. Our work exploits leading-edge in HMM-DNN, including end-to-end acoustic modeling methods and KL-HMM-DNN approaches, including cross-lingual multi-level adaptive networks as well as improvements of diverse acoustic model adaptation techniques which are able to represent the differences between languages using far fewer parameters than would be necessary to represent a whole language in isolation. This in turn allows adaptation to under-resourced languages. Further, cross-lingual failure analysis will facilitate training by identifying training data most likely to benefit multilinguality. In SARAL, Idiap will leverage its current work on multilingual ASR along four research topics.