Recurrent Neural Networks (RNN) can be difficult to deploy on resource constrained devices due to their size. As a result, there is a need for compression techniques that can significantly compress RNNs without negatively impacting task accuracy. This paper introduces a method to compress RNNs for resource constrained environments using Kronecker product (KP). KPs can compress RNN layers by 16-38x with minimal accuracy loss. We show that KP can beat the task accuracy achieved by other state-of-the-art compression techniques (pruning and low-rank matrix factorization) across 4 benchmarks spanning 3 different applications, while simultaneously improving inference run-time.

Recurrent Neural Networks (RNN) can be large and compute-intensive, making them hard to deploy on resource constrained devices. As a result, there is a need for compression technique that can significantly compress recurrent neural networks, without negatively impacting task accuracy. This paper introduces a method to compress RNNs for resource constrained environments using Kronecker products. We call the RNNs compressed using Kronecker products as Kronecker product Recurrent Neural Networks (KPRNNs). KPRNNs can compress the LSTM[22], GRU [9] and parameter optimized FastRNN [30] layers by 15 - 38x with minor loss in accuracy and can act as in-place replacement of most RNN cells in existing applications. By quantizing the Kronecker compressed networks to 8 bits, we further push the compression factor to 50x. We compare the accuracy and runtime of KPRNNs with other state-of-the-art compression techniques across 5 benchmarks spanning 3 different applications, showing its generality. Additionally, we show how to control the compression factors achieved by Kronecker products using a novel hybrid decomposition technique. We call the RNN cells compressed using Kronecker products with this control mechanism as hybrid Kronecker product RNNs (HKPRNN). Using HKPRNN, we compress RNN Cells in 2 benchmarks by 10x and 20x achieving better accuracy than other state-of-the-art compression techniques.

The purpose of this paper is to address the problem of learning dictionaries for multimodal datasets, i.e. datasets collected from multiple data sources. We present an algorithm called multimodal sparse Bayesian dictionary learning (MSBDL). The MSBDL algorithm is able to leverage information from all available data modalities through a joint sparsity constraint on each modality's sparse codes without restricting the coefficients themselves to be equal. Our framework offers a considerable amount of flexibility to practitioners and addresses many of the shortcomings of existing multimodal dictionary learning approaches. Unlike existing approaches, MSBDL allows the dictionaries for each data modality to have different cardinality. In addition, MSBDL can be used in numerous scenarios, from small datasets to extensive datasets with large dimensionality. MSBDL can also be used in supervised settings and allows for learning multimodal dictionaries concurrently with classifiers for each modality.

In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares (S-NNLS) problem. We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R- GSM) to model the sparsity enforcing prior distribution for the solution. The R-GSM prior encompasses a variety of heavy-tailed densities such as the rectified Laplacian and rectified Student- t distributions with a proper choice of the mixing density. We utilize the hierarchical representation induced by the R-GSM prior and develop an evidence maximization framework based on the Expectation-Maximization (EM) algorithm. Using the EM based method, we estimate the hyper-parameters and obtain a point estimate for the solution. We refer to the proposed method as rectified sparse Bayesian learning (R-SBL). We provide four R- SBL variants that offer a range of options for computational complexity and the quality of the E-step computation. These methods include the Markov chain Monte Carlo EM, linear minimum mean-square-error estimation, approximate message passing and a diagonal approximation. Using numerical experiments, we show that the proposed R-SBL method outperforms existing S-NNLS solvers in terms of both signal and support recovery performance, and is also very robust against the structure of the design matrix.

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the sparse codes. We show that the proposed framework encompasses a large class of S-NNLS algorithms and provide a computationally efficient inference procedure based on multiplicative update rules. Such update rules are convenient for solving large sets of S-NNLS problems simultaneously, which is required in contexts like sparse non-negative matrix factorization (S-NMF). We provide theoretical justification for the proposed approach by showing that the local minima of the objective function being optimized are sparse and the S-NNLS algorithms presented are guaranteed to converge to a set of stationary points of the objective function. We then extend our framework to S-NMF, showing that our framework leads to many well known S-NMF algorithms under specific choices of prior and providing a guarantee that a popular subclass of the proposed algorithms converges to a set of stationary points of the objective function. Finally, we study the performance of the proposed approaches on synthetic and real-world data.