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Various neural network architectures have been proposed in the literature to model 2D correlations in the input signal, including convolutional layers, frequency LSTMs and 2D LSTMs such as time-frequency LSTMs, grid LSTMs and ReNet LSTMs. It has been argued that frequency LSTMs can model translational variations similar to CNNs, and 2D LSTMs can model even more variations [1], but no proper comparison has been done for speech tasks. While convolutional layers have been a popular technique in speech tasks, this paper compares convolutional and LSTM architectures to model time-frequency patterns as the first layer in an LDNN [2] architecture. This comparison is particularly interesting when the convolutional layer degrades performance, such as in noisy conditions or when the learned filterbank is not constant-Q [3]. We find that grid-LDNNs offer the best performance of all techniques, and provide between a 1–4% relative improvement over an LDNN and CLDNN on 3 different large vocabulary Voice Search tasks.