  We present a deep neural network (DNN) acoustic model that includes
parametrised and differentiable pooling operators. Unsupervised acoustic model
adaptation is cast as the problem of updating the decision boundaries
implemented by each pooling operator. In particular, we experiment with two
types of pooling parametrisations: learned $L_p$-norm pooling and weighted
Gaussian pooling, in which the weights of both operators are treated as
speaker-dependent. We perform investigations using three different large
vocabulary speech recognition corpora: AMI meetings, TED talks and Switchboard
conversational telephone speech. We demonstrate that differentiable pooling
operators provide a robust and relatively low-dimensional way to adapt acoustic
models, with relative word error rates reductions ranging from 5--20% with
respect to unadapted systems, which themselves are better than the baseline
fully-connected DNN-based acoustic models. We also investigate how the proposed
techniques work under various adaptation conditions including the quality of
adaptation data and complementarity to other feature- and model-space
adaptation methods, as well as providing an analysis of the characteristics of
each of the proposed approaches.
