Most deep neural networks (DNNs) consist fundamentally of convolutional
and/or fully connected layers, wherein the linear transform can be cast as the
product between a filter matrix and a data matrix obtained by arranging feature
tensors into columns. The lately proposed deformable butterfly (DeBut)
decomposes the filter matrix into generalized, butterflylike factors, thus
achieving network compression orthogonal to the traditional ways of pruning or
low-rank decomposition. This work reveals an intimate link between DeBut and a
systematic hierarchy of depthwise and pointwise convolutions, which explains
the empirically good performance of DeBut layers. By developing an automated
DeBut chain generator, we show for the first time the viability of homogenizing
a DNN into all DeBut layers, thus achieving an extreme sparsity and
compression. Various examples and hardware benchmarks verify the advantages of
All-DeBut networks. In particular, we show it is possible to compress a
PointNet to < 5% parameters with < 5% accuracy drop, a record not achievable by
other compression schemes.

通过将滤波矩阵分解为类似于蝴蝶的因子，DeBut 图层可以实现与传统剪枝或低秩分解不同的网络压缩，通过开发自动化的 DeBut 链生成器，首次实现了将 DNN 全面均匀化为所有的 DeBut 图层，从而实现极度稀疏化和压缩，并通过各种例子和硬件基准测试验证了 All-DeBut 网络的优势，特别地，我们展示了将一个 PointNet 压缩到小于 5% 的参数并且准确率下降小于 5％的可能性，这是其他压缩方案所无法实现的。

轻盈飞行：一种全可变形蝴蝶网络

Lite it fly: An All-Deformable-Butterfly Network

Non-negative matrix factorization models based on a hierarchical
Gamma-Poisson structure capture user and item behavior effectively in extremely
sparse data sets, making them the ideal choice for collaborative filtering
applications. Hierarchical Poisson factorization (HPF) in particular has proved
successful for scalable recommendation systems with extreme sparsity. HPF,
however, suffers from a tight coupling of sparsity model (absence of a rating)
and response model (the value of the rating), which limits the expressiveness
of the latter. Here, we introduce hierarchical compound Poisson factorization
(HCPF) that has the favorable Gamma-Poisson structure and scalability of HPF to
high-dimensional extremely sparse matrices. More importantly, HCPF decouples
the sparsity model from the response model, allowing us to choose the most
suitable distribution for the response. HCPF can capture binary, non-negative
discrete, non-negative continuous, and zero-inflated continuous responses. We
compare HCPF with HPF on nine discrete and three continuous data sets and
conclude that HCPF captures the relationship between sparsity and response
better than HPF.

介绍了一种新的基于双重泊松分层 Gamma 结构的非负矩阵分解模型，可以更好地处理极端稀疏数据的推荐系统， 分离了因素之间的稀疏性和用户行为的响应，可以为响应变量选择最合适的分布类型。