Introduction

• 作者提出 Autoregressive KD with Adaptive Teaching Modes (ATKD)，通过对难易样本采用不同的学习策略来解决 larger teachers might dramatically
  result in a poorer student, especially when the model capability gap is large 的问题，可以作为一种通用的学习策略提升不同的已有 KD 算法的精度
  

Method

Rethinking Knowledge Distillation for Autoregressive LMs

• Reformulation of ${\mathcal{L}}_{\mathbf{KL}}$. KL 散度可以被分解为 ground truth 类别上的 binary KL loss $\mathrm{KL}({\mathrm{p}}_{\mathrm{b}}^t||{\mathrm{q}}_{\mathrm{b}}^t)$ 和非 ground truth 类别上的 KL loss $\mathrm{KL}({\hat{\mathrm{p}}}^{\mathrm{t}}||{\hat{\mathrm{q}}}^{\mathrm{t}})$，前者可以帮助 student 学习 target 相关的信息，被称为 target-oriented knowledge distillation (TKD)，后者可以帮助 student 学习 non-target 中蕴含的知识，被称为 diversity-oriented knowledge distillation (DKD)；此外，这两部分的蒸馏损失被加上了一个权值 $p_{\backslash g_t}^t$，该项反映了 teacher 的 uncertainty，被称为 uncertainty coefficient (UNC)
  $$\begin{array}{rl}{\mathcal{L}}_{\mathrm{KL}}& =\sum _{t=1}^T(p_{g_t}^t\log (\frac{p_{g_t}^t}{q_{g_t}^t})+\sum _{j=1,j\ne g_t}^C{p}_j^t\log (\frac{p_j^t}{q_j^t}))\\ & =\sum _{t=1}^T(p_{g_t}^t\log (\frac{p_{g_t}^t}{q_{g_t}^t})\\ & +p_{\backslash g_t}^t\sum _{j=1,j\ne g_t}^C{\hat{p}}_j^t\left(\log (\frac{{\hat{p}}_j^t}{{\hat{q}}_j^t})+\log (\frac{p_{\backslash g_t}^t}{q_{\backslash g_t}^t})\right)\\ & =\sum _{t=1}^T(p_{g_t}^t\log (\frac{p_{g_t}^t}{q_{g_t}^t})+p_{\setminus g_t}^t\log (\frac{p_{\setminus g_t}^t}{q_{\setminus g_t}^t})\\ & +p_{\setminus g_t}^t\sum _{j=1,j\ne g_t}^C{\hat{p}}_j^t\log (\frac{{\hat{p}}_j^t}{{\hat{q}}_j^t})\\ & =\sum _{t=1}^T\left(\mathrm{KL}({\mathrm{p}}_{\mathrm{b}}^t||{\mathrm{q}}_{\mathrm{b}}^t)+p_{\backslash g_t}^t\mathrm{KL}({\hat{\mathrm{p}}}^{\mathrm{t}}||{\hat{\mathrm{q}}}^{\mathrm{t}})\right)\end{array}$$其中，$T$ 为序列长度，$p,q$ 分别为 teacher 和 student 的概率分布，$gt$ 为 teacher 预测的 ground-truth 类别，$p_{g_t}^t=\frac{\exp (z_{g_t}^t)}{{\sum }_{j=1}^C\exp (z_j^t)},p_{\setminus g_t}^t=\frac{{\sum }_{k=1,k\ne g_t}^C\exp (z_k^t)}{{\sum }_{j=1}^C\exp (z_j^t)},{\hat{p}}_i^t=\frac{\exp (z_i^t)}{{\sum }_{j=1,j\ne g_t}^C\exp (z_j^t)}$，$p_i^t=p_{\setminus g_t}^t\cdot {\hat{p}}_i^t$，${\mathrm{p}}_{\mathrm{b}}^t=[p_{g_t}^t,p_{\setminus g_t}^t]$
• Empirical Analyses. (1) UNC measures the learning difficulties of tokens, where the hard-to-learn ones are more important for KD. 根据 $p_{\backslash g_t}^t$ 的大小可以把 tokens 分为难样本 (top-50% uncertainty) 和简单样本，实验发现难样本对 student 的学习更重要，尤其是 student 和 teacher 差距比较大的时候，这可能是因为难样本能让 student 学到丰富的类间信息，同时避免过拟合
  (2) DKD contributes more (than TKD) but is greatly suppressed, especially for the larger teachers. 作者对 TKD 和 DKD 做了解耦，去除了权重 $p_{\backslash g_t}^t$ 来考察它们各自的作用，作者发现 DKD 显著优于 TKD，但在 KL loss 中，由于 $p_{\backslash g_t}^t$ 的存在，DKD 的权值被降低了，并且这一现象在更大规模的模型中尤为显著，这也是作者认为的导致 larger teachers might dramatically result in a poorer student 的原因(3) TKD plays different roles in tokens with different learning difficulties. TKD 在简单样本上可能会导致 student 过拟合，从而影响泛化性；在难样本上能降低难样本的学习难度，从而提升 student 精度
  

Improving Knowledge Distillation with Adaptive Teaching Modes

• Autoregressive KD with Adaptive Teaching Modes (ATKD). 基于上述观察很容易想到，不同的 tokens 根据其难易程度，应该有不同的学习策略；简单样本仅使用 DKD，难样本 (top-50% uncertainty) 使用 DKD + TKD
  $$\begin{array}{rl}& {\mathcal{L}}_{\mathrm{KL}}^e=-\sum _{t\in {\mathcal{D}}_e}\mathrm{KL}({\hat{\mathbf{p}}}^{\mathbf{t}}||{\hat{\mathbf{q}}}^{\mathbf{t}}),\\ & {\mathcal{L}}_{\mathrm{KL}}^h=-\sum _{t\in {\mathcal{D}}_h}\mathrm{KL}({\mathbf{p}}_{\mathbf{b}}^{\mathbf{t}}||{\mathbf{q}}_{\mathbf{b}}^{\mathbf{t}})+\mathrm{KL}({\hat{\mathbf{p}}}^{\mathbf{t}}||{\hat{\mathbf{q}}}^{\mathbf{t}})\end{array}$$最终的损失函数为简单样本和难样本上损失的加权和$${\mathcal{L}}_{\mathrm{KL}}^{all}=\lambda \ast {\mathcal{L}}_{\mathrm{KL}}^e+(1-\lambda )\ast {\mathcal{L}}_{\mathrm{KL}}^h$$其中，$\lambda =0.2$

Experiments

• Compared Results. ${\mathcal{S}}_{\text{NLG}}$ 为语言生成任务，由 GPT-4 打分；${\mathcal{S}}_{\text{NLU}}$ 为语言理解任务，为 benchmark 得分
  
• Ablation Study. (1) Impact of ratio $k$. $k$ 用于确定 top-$k$ uncertainty 的 tokens 为难样本；(2) Impact of coefficient $\lambda$. 用于确定难易样本损失的权重
  

References

• Zhong, Qihuang, et al. “Revisiting knowledge distillation for autoregressive language models.” arXiv preprint arXiv:2402.11890 (2024).