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Title: Tensorized Embedding Layers for Efficient Model Compression

Paper content:
The embedding layers transforming input words into real vectors are the key components of deep neural networks used in natural language processing.
However, when the vocabulary is large, the corresponding weight matrices can be enormous, which precludes their deployment in a limited resource setting.
We introduce a novel way of parametrizing embedding layers based on the Tensor Train (TT) decomposition, which allows compressing the model significantly at the cost of a negligible drop or even a slight gain in performance.
We evaluate our method on a wide range of benchmarks in natural language processing and analyze the trade-off between performance and compression ratios for a wide range of architectures, from MLPs to LSTMs and Transformers.
Deep neural networks (DNNs) typically used in natural language processing (NLP) employ large embeddings layers, which map the input words into continuous representations and usually have the form of lookup tables.
Despite such simplicity and, arguably because of it, the resulting models are cumbersome, which may cause problems in training and deploying them in a limited resource setting.
Thus, the compression of large neural networks and the development of novel lightweight architectures have become essential problems in NLP research.
One way to reduce the number of parameters in the trained model is to imply a specific structure on its weight matrices (e.g., assume that they are low-rank or can be well approximated by low-rank tensor networks).
Such approaches are successful at compressing the pre-trained models, but they do not facilitate the training itself.
Furthermore, they usually require an additional fine-tuning stage to recover the performance of the original model.
In this paper, we introduce a new, parameter efficient embedding layer, termed TT-embedding, which can be plugged in into any model and trained end-to-end.
The benefits of our compressed TT-layer are twofold.
Firstly, instead of storing huge embedding matrix, we store a sequence of much smaller 2-dimensional and 3-dimensional tensors, necessary for reconstructing the required embeddings, which allows compressing the model significantly at the cost of a negligible performance drop.
Secondly, the overall number of parameters can be relatively small (and constant) during the whole training stage, which allows to use larger batches or train efficiently in a case of limited resources.
To validate the efficiency of the proposed approach, we have tested it on several popular NLP tasks.
In our experiments, we have observed that the standard embeddings can be replaced by TT-embeddings with the compression ratio of 1 − 3 orders without any significant drop (and sometimes even with a slight gain) of the metric of interest.
Specifically, we report the following compression ratios of the embedding layers: 441 on the IMDB dataset with 0.2% absolute increase in classification accuracy; 15 on the WMT 2014 En-De dataset with 0.3 drop in the BLEU score.
Additionally, we have also evaluated our algorithm on a task of binary classification based on a large number of categorical features.
More concretely, we applied TT-embedding to the click through rate (CTR) prediction problem, a crucial task in the field of digital advertising.
Neural networks, typically used for solving this problem, while being rather elementary, include a large number of embedding layers of significant size.
As a result, a majority of model parameters that represent these layers, may occupy hundreds of gigabytes of space.
We show that TT-embedding not only considerably reduces the number of parameters in such models, but also sometimes improves their accuracy.
We propose a novel embedding layer, the TT-embedding, for compressing huge lookup tables used for encoding categorical features of significant cardinality, such as the index of a token in natural language processing tasks.
The proposed approach, based on the TT-decomposition, experimentally proved to be effective, as it heavily decreases the number of training parameters at the cost of a small deterioration in performance.
In addition, our method can be easily integrated into any deep learning framework and trained via backpropagation, while capitalizing on reduced memory requirements and increased training batch size.
Our experimental results suggest several appealing directions for future work.
First of all, TTembeddings impose a concrete tensorial low-rank structure on the embedding matrix, which was shown to improve the generalization ability of the networks acting as a regularizer.
The properties and conditions of applicability of this regularizer are subject to more rigorous analysis.
Secondly, unlike standard embedding, we can introduce non-linearity into TT-cores to improve their expressive power (Khrulkov et al., 2019) .
Additionally, it is important to understand how the order of tokens in the vocabulary affects the properties of the networks with TT-embedding.
We hypothesize that there exists the optimal order of tokens which better exploits the particular structure of TT-embedding and leads to a boost in performance and/or compression ratio.
Finally, the idea of applying higher-order tensor decompositions to reduce the number of parameters in neural nets is complementary to more traditional methods such as pruning (Han et al., 2015) and quantization (Hubara et al., 2017; Xu et al., 2018) .
Thus, it would be interesting to make a thorough comparison of all these methods and investigate whether their combination may lead to even stronger compression.

assistant: text: Embedding layers are factorized with Tensor Train decomposition to reduce their memory footprint.