# Time-aware Large Kernel Convolutions

ICML, pp. 6172-6183, 2020.

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Abstract:

To date, most state-of-the-art sequence modelling architectures use attention to build generative models for language based tasks. Some of these models use all the available sequence tokens to generate an attention distribution which results in time complexity of $O(n^2)$. Alternatively, they utilize depthwise convolutions with softmax ...More

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Introduction

- Sequence modelling has seen some great breakthroughs through recent years with the introduction of the use of neural networks.
- All modern approaches of sequence encoding rely on the use of attention to “filter” the excessive information given at a current time-step.
- The transformer network (Vaswani et al, 2017) assigns attention weights for a given time-step to all available context token representations, while the newly proposed dynamic convolution (Wu et al, 2019) only computes an attention over a fixed context window.
- The more recent approach of dynamic convolution (Wu et al, 2019) successfully reduced the time complexity to O(k·n) where k is the kernel size specified for each layer

Highlights

- Sequence modelling has seen some great breakthroughs through recent years with the introduction of the use of neural networks
- We introduce a novel type of adaptive convolution, Time-aware Large Kernel (TaLK) convolutions, that learns the kernel size of a summation kernel for each time-step instead of learning the kernel weights as in a typical convolution operation
- We introduce a novel adaptive convolution based on summation kernel for sequence encoding
- The key of the proposed method is an adaptive time-aware large kernel convolution operation which has kernel sizes that vary over time as a learned function of the individual time steps; that is, we propose to learn the offsets of the summation kernel above for each time-step
- Machine Translation On the machine translation task, we report results on three mainstream benchmark datasets: WMT English to German (En-De), WMT English to French (En-Fr) and IWSLT German to English (De-En)
- We presented Time-aware Large Kernel Convolutions, a novel adaptive convolution method based on summation kernel for sequence representation and encoding

Methods

- Self-Attention DynamicConv (k = 3) DynamicConv (k = 31) TaLK Convolution n = 10 iter/sec Mem.
- ↓. 898 3.1x n = 10, 000 iter/sec Mem.
- ↓ OOM 45 29 Param Test.
- Grave et al (2017) Dauphin et al (2017) Merity et al (2018) Rae et al (2018) Baevski & Auli (2019).
- TaLK Convolution (Ours) 240M 20.3

Results

**Results on Language Modeling**

The authors evaluated the method on the task of language modeling.- The authors use less number of parameters than the best comparison method.
- Table 2 shows that the method is able to achieve comparable results to current state-of-the-art methods.
- The authors' method was able to match the state-of-the-art score on WMT EnFr, a benchmark dataset that is considered indicative for the effectiveness of a method due to the large number of training examples (36M) it contains.
- The authors' method was able to outperform all other methods setting a new state-of-the-art result

Conclusion

- The authors presented Time-aware Large Kernel Convolutions, a novel adaptive convolution method based on summation kernel for sequence representation and encoding.
- It learns to predict the kernel boundaries for each time-step of the sequence.
- The authors will explore this novel convolution mechanism in the area of computer vision

Summary

## Introduction:

Sequence modelling has seen some great breakthroughs through recent years with the introduction of the use of neural networks.- All modern approaches of sequence encoding rely on the use of attention to “filter” the excessive information given at a current time-step.
- The transformer network (Vaswani et al, 2017) assigns attention weights for a given time-step to all available context token representations, while the newly proposed dynamic convolution (Wu et al, 2019) only computes an attention over a fixed context window.
- The more recent approach of dynamic convolution (Wu et al, 2019) successfully reduced the time complexity to O(k·n) where k is the kernel size specified for each layer
## Objectives:

The goal of this paper is to reduce the encoding time complexity for sequence modeling to O(n).## Methods:

Self-Attention DynamicConv (k = 3) DynamicConv (k = 31) TaLK Convolution n = 10 iter/sec Mem.- ↓. 898 3.1x n = 10, 000 iter/sec Mem.
- ↓ OOM 45 29 Param Test.
- Grave et al (2017) Dauphin et al (2017) Merity et al (2018) Rae et al (2018) Baevski & Auli (2019).
- TaLK Convolution (Ours) 240M 20.3
## Results:

**Results on Language Modeling**

The authors evaluated the method on the task of language modeling.- The authors use less number of parameters than the best comparison method.
- Table 2 shows that the method is able to achieve comparable results to current state-of-the-art methods.
- The authors' method was able to match the state-of-the-art score on WMT EnFr, a benchmark dataset that is considered indicative for the effectiveness of a method due to the large number of training examples (36M) it contains.
- The authors' method was able to outperform all other methods setting a new state-of-the-art result
## Conclusion:

The authors presented Time-aware Large Kernel Convolutions, a novel adaptive convolution method based on summation kernel for sequence representation and encoding.- It learns to predict the kernel boundaries for each time-step of the sequence.
- The authors will explore this novel convolution mechanism in the area of computer vision

- Table1: Maximum path lengths, per-layer complexity and minimum number of sequential operations for different layer types. n is the sequence length, d is the representation dimension and k is the kernel size of convolutions
- Table2: Machine translation accuracy in terms of BLEU for WMT En-De and WMT En-Fr on newstest2014
- Table3: Machine translation accuracy in terms of BLEU on IWSLT De-En
- Table4: Throughput and memory consumption decrease measured for different sequence lengths (n) on a batch of size 10 with each token being represented with d = 1024 and H = 16. Throughput is calculated across 100K iterations of a single input encoding execution for each method. Memory decrease is computed as how many times less memory we need to encoding the input embedding compared to Self-Attention. Larger numbers indicate better performance
- Table5: Test perplexity on WikiText-103. We used adaptive inputs similar to <a class="ref-link" id="cBaevski_2019_a" href="#rBaevski_2019_a">Baevski & Auli (2019</a>) and show that our method yields better perplexity than self-attention using adaptive intputs
- Table6: Ablation on IWSLT De-En validation set. (+) indicates that a result includes all preceding features

Related work

- In this section, we provide a brief review over various related sequence modeling methods, and related methods that enlarge the receptive filed of a convolution operation.

2.1. Sequence Modeling

Sequence modeling is an important task in machine learning. An effective system should be able to comprehend and generate sequences similar to real data. Traditional approaches typically rely on the use of various kinds of recurrent neural networks such as long-short term memory networks (Hochreiter & Schmidhuber, 1997; Sutskever et al, 2014; Li et al, 2016; 2018) and gated recurrent unit networks (Cho et al, 2014; Nabil et al, 2016). These recurrent approaches are auto-regressive, which slows the process down for long sequences since they linearly depend on their own previous output tokens. Recent work is focused on exploring convolutional neural networks (CNN) methods (Kalchbrenner et al, 2016; Gehring et al, 2017; Wu et al, 2019) or self-attention methods (Vaswani et al, 2017; Dai et al, 2019; Kitaev et al, 2020) which both facilitate the parallilazation of the encoding process. In addition, since they are not auto-regressive, they allow the encoding process to capture stronger global and local dependencies.

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