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.
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