text: recently introduced a method for aggregating multiple decision trees into a strong predictor by interpreting a path taken by a sample down each tree as a binary vector and performing linear regression on top of these vectors stacked together. They provided experimental evidence that the method offers advantages over the usual approaches for combining decision trees (random forests and boosting). The method truly shines when the regression target is a large vector with correlated dimensions, such as a 2D face shape represented with the positions of several facial landmarks. However, we argue that their basic method is not applicable in many practical scenarios due to large memory requirements. This paper shows how this issue can be solved through the use of quantization and architectural changes of the predictor that maps decision tree-derived encodings to the desired output.
  @cite_30: Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems with limited hardware resources. To address this limitation, we introduce "deep compression", a three stage pipeline: pruning, trained quantization and Huffman coding, that work together to reduce the storage requirement of neural networks by 35x to 49x without affecting their accuracy. Our method first prunes the network by learning only the important connections. Next, we quantize the weights to enforce weight sharing, finally, we apply Huffman coding. After the first two steps we retrain the network to fine tune the remaining connections and the quantized centroids. Pruning, reduces the number of connections by 9x to 13x; Quantization then reduces the number of bits that represent each connection from 32 to 5. On the ImageNet dataset, our method reduced the storage required by AlexNet by 35x, from 240MB to 6.9MB, without loss of accuracy. Our method reduced the size of VGG-16 by 49x from 552MB to 11.3MB, again with no loss of accuracy. This allows fitting the model into on-chip SRAM cache rather than off-chip DRAM memory. Our compression method also facilitates the use of complex neural networks in mobile applications where application size and download bandwidth are constrained. Benchmarked on CPU, GPU and mobile GPU, compressed network has 3x to 4x layerwise speedup and 3x to 7x better energy efficiency.
  @cite_29: In this paper, we investigate the use of deep neural networks (DNNs) to generate a stacked bottleneck (SBN) feature representation for low-resource speech recognition. We examine different SBN extraction architectures, and incorporate low-rank matrix factorization in the final weight layer. Experiments on several low-resource languages demonstrate the effectiveness of the SBN configurations when compared to state-of-the-art hybrid DNN approaches.
  @cite_0: While Deep Neural Networks (DNNs) have achieved tremendous success for large vocabulary continuous speech recognition (LVCSR) tasks, training of these networks is slow. One reason is that DNNs are trained with a large number of training parameters (i.e., 10-50 million). Because networks are trained with a large number of output targets to achieve good performance, the majority of these parameters are in the final weight layer. In this paper, we propose a low-rank matrix factorization of the final weight layer. We apply this low-rank technique to DNNs for both acoustic modeling and language modeling. We show on three different LVCSR tasks ranging between 50-400 hrs, that a low-rank factorization reduces the number of parameters of the network by 30-50 . This results in roughly an equivalent reduction in training time, without a significant loss in final recognition accuracy, compared to a full-rank representation.
  @cite_19: This paper presents a highly efficient, very accurate regression approach for face alignment. Our approach has two novel components: a set of local binary features, and a locality principle for learning those features. The locality principle guides us to learn a set of highly discriminative local binary features for each facial landmark independently. The obtained local binary features are used to jointly learn a linear regression for the final output. Our approach achieves the state-of-the-art results when tested on the current most challenging benchmarks. Furthermore, because extracting and regressing local binary features is computationally very cheap, our system is much faster than previous methods. It achieves over 3, 000 fps on a desktop or 300 fps on a mobile phone for locating a few dozens of landmarks.
  @cite_27: 
  @cite_10: We present techniques for speeding up the test-time evaluation of large convolutional networks, designed for object recognition tasks. These models deliver impressive accuracy, but each image evaluation requires millions of floating point operations, making their deployment on smartphones and Internet-scale clusters problematic. The computation is dominated by the convolution operations in the lower layers of the model. We exploit the redundancy present within the convolutional filters to derive approximations that significantly reduce the required computation. Using large state-of-the-art models, we demonstrate speedups of convolutional layers on both CPU and GPU by a factor of 2 x, while keeping the accuracy within 1 of the original model.
summary: Our research is related to a large body of work in neural-network compression and speed improvement (e.g., @cite_0 @cite_29 @cite_27 @cite_10 @cite_30 ). Specifically, the work of @cite_0 and other similar approaches suggest to reduce the memory-related issues of machine learning models by introducing a low-dimensional "bottleneck" before the output, as we do in this paper. However, to the best of our knowledge, we are the first to investigate the use of these techniques in the context of decision-tree ensembles. We can say that our work is a blend of the interpretation introduced by @cite_19 and recent network compression techniques.