Since such time-shifted networks are only copies, however, the position dependence is removed by weight sharing. In this example, this is done by averaging the gradients from each time-shifted copy before performing the weight update. In speech, time-shift invariant training was shown to learn weight matrices that are independent of precise positioning of the input. The weight matrices could also be shown to detect important acoustic-phonetic features that are known to be important for human speech perception, such as formant transitions, bursts, etc. TDNNs could also be combined or grown by way of pre-training. The precise architecture of TDNNs (time-delays, number of layers) is mostly determined by the designer depending on the classification problem and the most useful context sizes. The delays or context windows are chosen specific to each application. Work has also been done to create adaptable time-delay TDNNs where this manual tuning is eliminated. TDNN-based phoneme recognizers compared favourably in early comparisons with HMM-based phone models. Modern deep TDNN architectures include many more hidden layers and sub-sample or pool connections over broader contexts at higher layers. They achieve up to 50% word error reduction over GMM-based acoustic models. While the different layers of TDNNs are intended to learn features of increasing context width, they do model local contexts. When longer-distance relationships and pattern sequences have to be processed, learning states and state-sequences is important and TDNNs can be combined with other modelling techniques. TDNNs used to solve problems in speech recognition that were introduced in 1987 and initially focused on shift-invariant phoneme recognition. Speech lends itself nicely to TDNNs as spoken sounds are rarely of uniform length and precise segmentation is difficult or impossible. By scanning a sound over past and future, the TDNN is able to construct a model for the key elements of that sound in a time-shift invariant manner. This is particularly useful as sounds are smeared out through reverberation. Large phonetic TDNNs can be constructed modularly through pre-training and combining smaller networks. Large vocabulary speech recognition requires recognizing sequences of phonemes that make up words subject to the constraints of a large pronunciation vocabulary. Integration of TDNNs into large vocabulary speech recognizers is possible by introducing state transitions and search between phonemes that make up a word. The resulting Multi-State Time-Delay Neural Network (MS-TDNN) can be trained discriminative from the word level, thereby optimizing the entire arrangement toward word recognition instead of phoneme classification.