[Note] wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations

• https://arxiv.org/abs/2006.11477
• Self-supervised speech representation
• contrastive loss: masked continous speech input -> quantized target
• quantized module: gumbel softmax(latent representation codebooks)
• wav2vec2.0 Large with 10min data:  5.2/8.6 LS-clean test
• Fairseq
• Well explained: https://neurosys.com/wav2vec-2-0-framework

Feature Encoder(CNN)

將 raw audio \( \mathcal{X} \) encode 成 latent speech representation $z_1, \cdots, z_T$

Contextualized representation(Transformers)

• 將 $z_1, \cdots, z_T$  Mask 過後，經過 Transformers 產生 contextualized representation (看過前後)
• Note: use relitive positional embeddings

Quantization module

• wav2vec2.0 將目標表示為有限的 representation，比起學習還原連續的 output 有更好的效果
• 要怎麼離散化？ 如何將 $z$ 表示成離散的表示法？
• 給定 $G$ codebooks 每本 codebook 裡面有 $V$ 個向量($e \in \mathbb{R}^{V \times d / G}$)
• 每個 $z$ 會從每本 codebook 中選擇一個向量，並連接起來 $R^{d}$
• 最後經過一層 Linear 轉換為  $q \in \mathbb{R}^f$
• 怎麼訓練？
• 使用 Gumbel softmax：可微分
• $z$ 被 mapping 到 $l \in \mathbb{R}^{G \times V}$
• $p_{g,v}$: prob of codebook $g$ entry $v$
• $$p_{g,v} = \frac{\exp(l_{g,v} + n_v)/\tau}{ \sum ^V _{k=1} \exp(l_{g,k} + n_k) / \tau }$$
• $\tau$: temperature, $n$: noise

Training

Masking

• Mask 掉一部分的 feature encoder output $Z$，（置換成學來的 mask 向量）
• 以機率 $p$ 從所有 time step 選擇，並 mask 掉其後面的 $M$ 個 token

Objective

$$ \mathcal{L} = \mathcal{L}_m + \alpha \mathcal{L}_d$$

Contrastive loss

$$ \mathcal{L}_m =  -\log \frac{ \exp( sim (c_t, q_t) / \kappa) }{ \sum _ {\tilde{q} \sim Q_t} \exp (sim (c_t , q_t )/ \kappa) } $$

• $sim(a, b) = a^\top b / ||a|| ||b||$: cosine similarity
• $Q_t$: 1 positive q_t 和 $K$ 個 negative sample。從同個 utterance 中其他被 masked 掉的 time step 選

Diversity Loss

• 簡單來說就是讓 codebook 中的每個 entries 都可以被選到。Maximize entropy
• 可以得到更好的 quantized codebook
• 如果沒有這個限制，會讓模型壞掉
• i.e. 所有 representation 都選同個 entry，contrastive loss 最低

$$\mathcal{L}_d =  \frac{1}{GV} \sum _{g=1} ^G - H(\bar{p}_g)  =  \frac{1}{GV} \sum ^G _ {g=1} \sum _{v=1} ^V \bar{p}_{g,v} \log \bar{p}_{g,v} $$

Fine-tuning

此論文中用 pretrain 好的 wav2vec2 ，加上一層 Linear，訓練 CTC loss。

Experiments

• Pretrained dataset:
• LS-960
• LV-60K

Pretraining

• Fairseq
• p = 0.065, M=10. 49% of all time steps to be masked

Base model:

• 12 Transformer layers
• 768 model dim
• 8 head
• 3072 inner dim
• Batches: cropping 250k audio sample
• batched less than 1.4m samples per GPU
• 64 V100 GPU  for 1.6 days
• Adam optimizer:
• lr:  $5 \times 10^{-4}$
• Base: 400k updates
• G= 2, V=320: 102.4k codewords
• d/G = 128
• K = 100
• choose the training checkpoint with lowest $\mathcal{L}_m$ on the valid set

Results

Low-Resource

• The LARGE model pre-trained on LV-60k and fine-tuned on only 10 minutes of labeled data achieves
  a word error rate of 5.2/8.6 on the Librispeech clean/other test sets.
• Joint learning discrete units and contetulaized representation clearly improves over previous work

High-Resource

Ablation study

wav2vec2 最大的不同是，將 contrastive loss 的目標設為 quantized codewords

• Baseline
• Continuous input: retain more information
• Quantized target: more robust training
• Continuous target
• overfit to background

Tools:

• Fairseq
• Huggingface
• Espnet2