Information encoding by deep neural networks: what can we learn?

The recent advent of deep learning techniques in speech tech-nology and in particular in automatic speech recognition hasyielded substantial performance improvements. This suggeststhat deep neural networks (DNNs) are able to capture structurein speech data that older methods for acoustic modeling, suchas Gaussian Mixture Models and shallow neural networks failto uncover. In image recognition it is possible to link repre-sentations on the first couple of layers in DNNs to structuralproperties of images, and to representations on early layers inthe visual cortex. This raises the question whether it is possi-ble to accomplish a similar feat with representations on DNNlayers when processing speech input. In this paper we presentthree different experiments in which we attempt to untanglehow DNNs encode speech signals, and to relate these repre-sentations to phonetic knowledge, with the aim to advance con-ventional phonetic concepts and to choose the topology of aDNNs more efficiently. Two experiments investigate represen-tations formed by auto-encoders. A third experiment investi-gates representations on convolutional layers that treat speechspectrograms as if they were images. The results lay the basisfor future experiments with recursive networks

DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling

This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to solve the problem of least squares multidimensional scaling for generating maps that approximately preserve geodesic distances. By training with only a few landmarks, we show a significantly improved local and nonlocal generalization of the isometric mapping as compared to analogous non-parametric counterparts. Importantly, the combination of a deep-learning framework with a multidimensional scaling objective enables a numerical analysis of network architectures to aid in understanding their representation power. This provides a geometric perspective to the generalizability of deep learning.Comment: 10 pages, 11 Figure

Geometry of Deep Learning for Magnetic Resonance Fingerprinting

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy storage and computation requirements of a dictionary-matching (DM) step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. In this paper we study a deep learning approach to address these shortcomings. Coupled with a dimensionality reduction first layer, the proposed MRF-Net is able to reconstruct quantitative maps by saving more than 60 times in memory and computations required for a DM baseline. Fine-grid manifold enumeration i.e. the MRF dictionary is only used for training the network and not during image reconstruction. We show that the MRF-Net provides a piece-wise affine approximation to the Bloch response manifold projection and that rather than memorizing the dictionary, the network efficiently clusters this manifold and learns a set of hierarchical matched-filters for affine regression of the NMR characteristics in each segment