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Title: Adaptive Mixture of Low-Rank Factorizations for Compact Neural Modeling

Paper content:
Modern deep neural networks have a large amount of weights, which make them difficult to deploy on computation constrained devices such as mobile phones.
One common approach to reduce the model size and computational cost is to use low-rank factorization to approximate a weight matrix.
However, performing standard low-rank factorization with a small rank can hurt the model expressiveness and significantly decrease the performance.
In this work, we propose to use a mixture of multiple low-rank factorizations to model a large weight matrix, and the mixture coefficients are computed dynamically depending on its input.
We demonstrate the effectiveness of the proposed approach on both language modeling and image classification tasks.
Experiments show that our method not only improves the computation efficiency but also maintains (sometimes outperforms) its accuracy compared with the full-rank counterparts.
Modern neural networks usually contain millions of parameters BID4 BID8 , and they are difficult to be deployed on mobile devices with limited computation resources.
To solve this problem, model compression techniques are proposed in recent years.
Low-rank factorization is a popular way of reducing the matrix size.
It has been extensively explored in the literature BID5 BID6 BID3 BID10 .
Mathematically, a large weight matrix W ∈ R m×n is factorized to two small rank-d matrices U ∈ R m×d , V ∈ R n×d with W = U V T .
Since both U and V are dense, no sparsity support is required from specialized hardware.
It naturally fits the general-purpose, off-the-shelf CPUs and GPUs.To significantly reduce the model size and computation, the rank d in the low-rank factorization needs to be small.
However, a small rank can limit the expressiveness of the model BID9 and lead to worse performance.
To understand the limitations, given a n-dim feature vector h, we observe that DISPLAYFORM0 , is a linear projection from a high-dimensional space (n dims) to a low-dimensional space (d dims).
This can lead to a significant loss of information.
The conflict between the rank d and the model expressiveness prevents us from obtaining a both compact and accurate model.To address the dilemma, we propose to increase the expressiveness by learning an adaptive, inputdependent factorization, rather than performing a fixed factorization of a weight matrix.
To do so, we use a mixture of multiple low-rank factorizations.
The mixing weights are computed based on the input.
This creates an adaptive linear projection from a high-dimensional space to a low-dimensional space.
Compared to the conventional low-rank factorization, the proposed approach can significantly improve its performance while only introducing a small additional cost.
DISPLAYFORM1 where z can be treated as the middle layer.
Techniques like pooling can be applied to compute π to make it efficient.

assistant: text: A simple modification to low-rank factorization that improves performances (in both image and language tasks) while still being compact.