In the wake of the success of convolutional neural networks in image classification, object recognition, speech recognition, etc., the demand for deploying these compute-intensive ML models on embedded and mobile systems with tight power and energy constraints at low cost, as well as for boosting throughput in data centers, is growing rapidly. This has sparked a surge of research into specialized hardware accelerators. Their performance is typically limited by I O bandwidth, power consumption is dominated by I O transfers to off-chip memory, and on-chip memories occupy a large part of the silicon area. We introduce and evaluate a novel, hardware-friendly and lossless compression scheme for the feature maps present within convolutional neural networks. Its hardware implementation fits into 2.8 kGE and 1.7 kGE of silicon area for the compressor and decompressor, respectively. We show that an average compression ratio of 5.1x for AlexNet, 4x for VGG-16, 2.4x for ResNet-34 and 2.2x for MobileNetV2 can be achieved---a gain of 45--70 over existing methods. Our approach also works effectively for various number formats, has a low frame-to-frame variance on the compression ratio, and achieves compression factors for gradient map compression during training that are even better than for inference.
Oher compression methods are focusing on minimizing the model size and are very complex (silicon area) to implement in hardware. One such method, deep compression @cite_48 , combines pruning, trained clustering-based quantization, and Huffman coding. Most of these steps cannot be applied to the intermediate feature maps, which change for every inference as opposed to the weights which are static and can be optimized off-line. Furthermore, applying Huffman coding---while being optimal in terms of compression rate and given a specification of input symbols and their statistics---implies storing a very large dictionary: encoding a 16 ,bit word requires a table with @math k entries, but effectively multiple values would have to be encoded jointly in order to exploit their joint distribution (e.g. the smoothness), immediately increasing the dictionary size to @math G even for just two values. Similar issues arise when using Lempel-Ziv-Welch (LZW) coding @cite_38 @cite_42 as present in e.g. the ZIP compression scheme, where the dictionary is encoded in the compressed data stream. This makes it unsuitable for a lightweight and energy-efficient VLSI implementation @cite_0 @cite_10 .
@cite_38 @cite_48 @cite_42 @cite_0 @cite_10
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Spanners, emulators, and approximate distance oracles can be viewed as lossy compression schemes that represent an unweighted graph metric in small space, say O(n1+Δ) bits. There is an inherent tradeoff between the sparsity parameter Δ and the stretch function f of the compression scheme, but the qualitative nature of this tradeoff has remained a persistent open problem. It has been known for some time that when Δ ≥ 1 3 there are schemes with constant additive stretch (distance d is stretched to at most f(d) = d + O(1)), and recent results of Abboud and Bodwin show that when Δ In this paper we show that the lower bound of Abboud and Bodwin is just the first step in a hierarchy of lower bounds that characterize the asymptotic behavior of the optimal stretch function f for sparsity parameter Δ ∈ (0,1 3). Specifically, for any integer k ≥ 2, any compression scheme with size [EQUATION] has a sublinear additive stretch function f: f(d) = d + Ω(d1−1 k). This lower bound matches Thorup and Zwick's (2006) construction of sublinear additive emulators. It also shows that Elkin and Peleg's (1 + ϵ, β)-spanners have an essentially optimal tradeoff between Δ, ϵ, and β, and that the sublinear additive spanners of Pettie (2009) and Chechik (2013) are not too far from optimal. To complement these lower bounds we present a new construction of (1 + ϵ, O(k ϵ)k−1)-spanners with size [EQUATION], where hk Our lower bound technique exhibits several interesting degrees of freedom in the framework of Abboud and Bodwin. By carefully exploiting these freedoms, we are able to obtain lower bounds for several related combinatorial objects. We get lower bounds on the size of (β, ϵ)-hopsets, matching Elkin and Neiman's construction (2016), and lower bounds on shortcutting sets for digraphs that preserve the transitive closure. Our lower bound simplifies Hesse's (2003) refutation of Thorup's conjecture (1992), which stated that adding a linear number of shortcuts suffices to reduce the diameter to polylogarithmic. Finally, we show matching upper and lower bounds for graph compression schemes that work for graph metrics with girth at least 2γ + 1. One consequence is that 's (2010) additive O(γ)-spanners with size [EQUATION] cannot be improved in the exponent. In this paper, we propose a new two-stage hardware architecture that combines the features of both parallel dictionary LZW (PDLZW) and an approximated adaptive Huffman (AH) algorithms. In this architecture, an ordered list instead of the tree-based structure is used in the AH algorithm for speeding up the compression data rate. The resulting architecture shows that it not only outperforms the AH algorithm at the cost of only one-fourth the hardware resource but it is also competitive to the performance of LZW algorithm (compress). In addition, both compression and decompression rates of the proposed architecture are greater than those of the AH algorithm even in the case realized by software Variants of Huffman codes where words are taken as the source symbols are currently the most attractive choices to compress natural language text databases. In particular, Tagged Huffman Code by offers fast direct searching on the compressed text and random access capabilities, in exchange for producing around 11 larger compressed files. This work describes End-Tagged Dense Code and (s, c)-Dense Code, two new semistatic statistical methods for compressing natural language texts. These techniques permit simpler and faster encoding and obtain better compression ratios than Tagged Huffman Code, while maintaining its fast direct search and random access capabilities. We show that Dense Codes improve Tagged Huffman Code compression ratio by about 10 , reaching only 0.6 overhead over the optimal Huffman compression ratio. Being simpler, Dense Codes are generated 45 to 60 faster than Huffman codes. This makes Dense Codes a very attractive alternative to Huffman code variants for various reasons: they are simpler to program, faster to build, of almost optimal size, and as fast and easy to search as the best Huffman variants, which are not so close to the optimal size. Deep compression refers to removing the redundancy of parameters and feature maps for deep learning models. Low-rank approximation and pruning for sparse structures play a vital role in many compression works. However, weight filters tend to be both low-rank and sparse. Neglecting either part of these structure information in previous methods results in iteratively retraining, compromising accuracy, and low compression rates. Here we propose a unified framework integrating the low-rank and sparse decomposition of weight matrices with the feature map reconstructions. Our model includes methods like pruning connections as special cases, and is optimized by a fast SVD-free algorithm. It has been theoretically proven that, with a small sample, due to its generalizability, our model can well reconstruct the feature maps on both training and test data, which results in less compromising accuracy prior to the subsequent retraining. With such a warm start to retrain, the compression method always possesses several merits: (a) higher compression rates, (b) little loss of accuracy, and (c) fewer rounds to compress deep models. The experimental results on several popular models such as AlexNet, VGG-16, and GoogLeNet show that our model can significantly reduce the parameters for both convolutional and fully-connected layers. As a result, our model reduces the size of VGG-16 by 15&#xd7;, better than other recent compression methods that use a single strategy.