Encouraged by the success of deep convolutional neural networks on a variety of visual tasks, much theoretical and experimental work has been aimed at understanding and interpreting how vision networks operate. At the same time, deep neural networks have also achieved impressive performance in audio processing applications, both as sub-components of larger systems and as complete end-to-end systems by themselves. Despite their empirical successes, comparatively little is understood about how these audio models accomplish these tasks.In this work, we employ a recently developed statistical mechanical theory that connects geometric properties of network representations and the separability of classes to probe how information is untangled within neural networks trained to recognize speech. We observe that speaker-specific nuisance variations are discarded by the network's hierarchy, whereas task-relevant properties such as words and phonemes are untangled in later layers. Higher level concepts such as parts-of-speech and context dependence also emerge in the later layers of the network. Finally, we find that the deep representations carry out significant temporal untangling by efficiently extracting task-relevant features at each time step of the computation. Taken together, these findings shed light on how deep auditory models process their time dependent input signals to carry out invariant speech recognition, and show how different concepts emerge through the layers of the network.

The paper is overall well written, and the experimental design is fundamentally well thought out and rasonable - I cannot say if it is entirely novel or if similar looking graphs could have been achieved with different or similar techniques. The results look intuitively correct and confirm ones expectations. I find some parts of the experimental setup confusing: the CNN *model* has been trained on WSJ and Spoken Wikipedia, and is not performing an ASR task, but a closed-set word recognition task (in addition to the speaker ID task). Why was Spoken Wikipedia used in addition to WSJ? Would it not have been possible to use Librispeech or another well-known corpus? The entire paper would be much "cleaner" if both types of systems ("CNN" word recognition "DS2" ASR) would have been trained and evaluated on the same type of data.

The authors propose to borrow some recently developed statistical mechanical theory, and apply it to neural networks in the context of speech recognition, to study hidden representations. As noted by the reviewers, findings are already known - the novelty lies more into the application of the theory to ASR. The idea could be possibly extended to other applications in future work.

Encouraged by the success of deep convolutional neural networks on a variety of visual tasks, much theoretical and experimental work has been aimed at understanding and interpreting how vision networks operate. At the same time, deep neural networks have also achieved impressive performance in audio processing applications, both as sub-components of larger systems and as complete end-to-end systems by themselves. Despite their empirical successes, comparatively little is understood about how these audio models accomplish these tasks.In this work, we employ a recently developed statistical mechanical theory that connects geometric properties of network representations and the separability of classes to probe how information is untangled within neural networks trained to recognize speech. We observe that speaker-specific nuisance variations are discarded by the network's hierarchy, whereas task-relevant properties such as words and phonemes are untangled in later layers. Higher level concepts such as parts-of-speech and context dependence also emerge in the later layers of the network.

Encouraged by the success of deep convolutional neural networks on a variety of visual tasks, much theoretical and experimental work has been aimed at understanding and interpreting how vision networks operate. At the same time, deep neural networks have also achieved impressive performance in audio processing applications, both as sub-components of larger systems and as complete end-to-end systems by themselves. Despite their empirical successes, comparatively little is understood about how these audio models accomplish these tasks.In this work, we employ a recently developed statistical mechanical theory that connects geometric properties of network representations and the separability of classes to probe how information is untangled within neural networks trained to recognize speech. We observe that speaker-specific nuisance variations are discarded by the network's hierarchy, whereas task-relevant properties such as words and phonemes are untangled in later layers. Higher level concepts such as parts-of-speech and context dependence also emerge in the later layers of the network.