By serialized i mean that the values for an input come in discrete intervals of time and that size of the vector is also not known before hand. Con
Simple neural network as a structure doesn't have invariance across time scale deformation that's why it is impractical to apply it to recognize time series. To recognize time series usually a generic communication model is used (HMM). NN could be used together with HMM to classify individual frames of speech. In such HMM-ANN configuration audio is split on frames, frame slices are passed into ANN in order to calculate phoneme probabilities and then the whole probability sequence is analyzed for a best match using dynamic search with HMM.
HMM-ANN system usually requires initialization from more robust HMM-GMM system thus there are no standalone HMM-ANN implementation, usually they are part of a whole speech recognition toolkit. Among popular toolkits Kaldi has implementation for HMM-ANN and even for HMM-DNN (deep neural networks).
There are also neural networks which are designed to classify time series - recurrent neural networks, they can be successfully used to classify speech. The example can be created with any toolkit supporting RNN, for example Keras. If you want to start with recurrent neural networks, try long-short term memory networks (LSTM), their architecture enables more stable training. Keras setup for speech recognition is discussed in Building Speech Dataset for LSTM binary classification