We develop and present a novel deep convolutional neural network architecture, where heterogeneous pooling is used to provide constrained frequency-shift invariance in the speech spectrogram while minimizing speech-class confusion induced by such invariance. The design of the pooling layer is guided by domain knowledge about how speech classes would change when formant frequencies are modified. The convolution and heterogeneouspooling layers are followed by a fully connected multi-layer neural network to form a deep architecture interfaced to an HMM for continuous speech recognition.  During training, all layers of this entire deep net are regularized using a variant of the “dropout” technique. Experimental evaluation demonstrates the effectiveness of both heterogeneous pooling and dropout regularization. On the TIMIT phonetic recognition task, we have achieved an 18.7% phone error rate, lowest on this standard task reported in the literature with a single system and with no use of information about speaker identity. Preliminary experiments on large vocabulary speech recognition in a voice search task also show error rate reduction using heterogeneous pooling in the deep convolutional neural network.