We present a new technique for achieving source separation when given only a single channel recording. The main idea is based on exploiting the inherent time structure of sound sources by learning a priori sets of basis filters in time domain that encode the sources in a statistically efficient manner. We derive a learning algorithm using a maximum likelihood approach given the observed single channel data and sets of basis filters. This inference is possible due to the prior knowledge of the basis filters and the associated coefficient densities. A flexible model for density estimation allows accurate modeling of the observation and our experimental results exhibit a high level of separation performance for mixtures of two music signals as well as the separation of two voice signals.

Is there an initialization for deep networks that requires no learning? ExplainFix adopts two design principles: the "fixed filters" principle that all spatial filter weights of convolutional neural networks can be fixed at initialization and never learned, and the "nimbleness" principle that only few network parameters suffice. We contribute (a) visual model-based explanations, (b) speed and accuracy gains, and (c) novel tools for deep convolutional neural networks. ExplainFix gives key insights that spatially fixed networks should have a steered initialization, that spatial convolution layers tend to prioritize low frequencies, and that most network parameters are not necessary in spatially fixed models. ExplainFix models have up to 100x fewer spatial filter kernels than fully learned models and matching or improved accuracy. Our extensive empirical analysis confirms that ExplainFix guarantees nimbler models (train up to 17\% faster with channel pruning), matching or improved predictive performance (spanning 13 distinct baseline models, four architectures and two medical image datasets), improved robustness to larger learning rate, and robustness to varying model size. We are first to demonstrate that all spatial filters in state-of-the-art convolutional deep networks can be fixed at initialization, not learned.

It is well known that Convolutional Neural Networks (CNNs) have significant redundancy in their filter weights. Various methods have been proposed in the literature to compress trained CNNs. These include techniques like pruning weights, filter quantization and representing filters in terms of a basis functions. Our approach falls in this latter class of strategies, but is distinct in that that we show both compressed learning and representation can be achieved without significant modifications of popular CNN architectures. Specifically, any convolution layer of the CNN is easily replaced by two successive convolution layers: the first is a set of fixed filters (that represent the knowledge space of the entire layer and do not change), which is followed by a layer of one-dimensional filters (that represent the learned knowledge in this space). For the pre-trained networks, the fixed layer is just the truncated eigen-decompositions of the original filters. The 1D filters are initialized as the weights of linear combination, but are fine-tuned to recover any performance loss due to the truncation. For training networks from scratch, we use a set of random orthogonal fixed filters (that never change), and learn the 1D weight vector directly from the labeled data. Our method substantially reduces i) the number of learnable parameters during training, and ii) the number of multiplication operations and filter storage requirements during implementation. It does so without requiring any special operators in the convolution layer, and extends to all known popular CNN architectures. We apply our method to four well known network architectures trained with three different data sets. Results show a consistent reduction in i) the number of operations by up to a factor of 5, and ii) number of learnable parameters by up to a factor of 18, with less than 3% drop in performance on the CIFAR100 dataset.

We present a new technique for achieving source separation when given only a single channel recording. The main idea is based on exploiting the inherent time structure of sound sources by learning a priori sets of basis filters in time domain that encode the sources in a statistically efficient manner. We derive a learning algorithm using a maximum likelihood approach given the observed single channel data and sets of basis filters.

We present a new technique for achieving source separation when given only a single channel recording. The main idea is based on exploiting the inherent time structure of sound sources by learning a priori sets of basis filters in time domain that encode the sources in a statistically efficient manner. We derive a learning algorithm using a maximum likelihood approach given the observed single channel data and sets of basis filters.

We present a new technique for achieving source separation when given only a single channel recording. The main idea is based on exploiting the inherent time structure of sound sources by learning a priori sets of basis filters in time domain that encode the sources in a statistically efficient manner. We derive a learning algorithm using a maximum likelihood approach given the observed single channel data and sets of basis filters.