作者：gongel

1.PPL

PPL是用在自然语言处理领域（NLP）中，衡量语言模型好坏的指标。它主要是根据每个词来估计一句话出现的概率，并用句子长度作normalize，公式为

由公式可知，perplexity越小，模型越好。从公式最后一部分，感觉更像是描述GPT这种生成模型。

还有一种说法是：

2.Language Model

• autoregressive (AR) language model

GPT：

• autoencoding (AE)language model

BERT(denoising auto-encoding)：

where mt = 1 indicates xt is masked.

3.Reference

• 求通俗解释NLP里的perplexity是什么？
• 语言模型评价指标Perplexity
• [2011EMNLP]Domain Adaptation via Pseudo In-Domain Data Selection

一.Language model decoding

given a sequence of m tokens as context, the task is to generate the next n continuation tokens to obtain the completed sequence . We assume that models compute using the common left-to-right decomposition of the text probability,

which is used to generate the generation token-by-token using a particular decoding strategy

二.Decoding Strategies

1.Maximization-based decoding

解码器的输出层后面通常会跟一个softmax函数来将输出概率归一化。如果词表比较大的话，softmax的计算复杂度会比较高(分母需要计算整个词表大小的维度)

• Greedy decoding

每次选最高概率的一项作为输出，直到遇到结束符号，将这些输出的概率相乘，得到该sequence的概率。

缺点：每次选择都是最大的，但是整体的概率不一定是最大的，有可能错过最优的结果

• Beam-search decoding

考虑到`Beam Size=2`，第一步选择概率最大的两个A和B，第二步选择AB和BB（橙色大箭头）。然后以选择的AB和BB继续向上传播，又出现了四种情况ABA/ABB/BBA/BBB，依然是选择综合概率最大的两个ABB/BBB。以此类推，直至句子结束。

缺点：

• • 由于beam search的概率是一個连续相乘的結果，越早遇到结束符号，所得到的概率会越大，所以更倾向于生成短文本。解决办法是对输出概率取log，然后相加求最大概率。
  • beam size过大会导致计算复杂度过高，时间复杂度为O(N*b*V)，N为序列长度，b为beam size，v为词表大小
  • 语言模型通常为格式良好的文本分配高分，但较长文本的最高分往往是通用的、重复的和尴尬的。beam search的输出，与人讲话的概率分布，很不一样。

2.Stochastic Decoding

• Sampling with temperature

• Top-k Sampling

从词表选择topk个词，使得概率之和最大，即

缺点：k的取值难以界定。k太小，会生成比较bland和generic的结果，即缺乏diversity；k太大，会退化成随机sampling(pure sampling)，会陷入语义表达错误，即sample from tail distribution

• Top-p Sampling(nucleus sampling)

丛词表选择p个概率之和大于给定阈值的词，即

采样集的大小将根据每个时间步长的概率分布动态调整。对于高的阈值来说，这一个小部分的词汇，就占据了绝大多数的概率—-核。

三.Implementation

def top_k_top_p_filtering(logits, top_k=0, top_p=0.0, filter_value=-float('Inf')):
    """ Filter a distribution of logits using top-k and/or nucleus (top-p) filtering
        Args:
            logits: logits distribution shape (vocabulary size)
            top_k >0: keep only top k tokens with highest probability (top-k filtering).
            top_p >0.0: keep the top tokens with cumulative probability >= top_p (nucleus filtering).
                Nucleus filtering is described in Holtzman et al. (http://arxiv.org/abs/1904.09751)
    """
    assert logits.dim() == 1  # batch size 1 for now - could be updated for more but the code would be less clear
    top_k = min(top_k, logits.size(-1))  # Safety check
    if top_k > 0:
        # Remove all tokens with a probability less than the last token of the top-k
        indices_to_remove = logits < torch.topk(logits, top_k)[0][..., -1, None]
        logits[indices_to_remove] = filter_value

    if top_p > 0.0:
        sorted_logits, sorted_indices = torch.sort(logits, descending=True)
        cumulative_probs = torch.cumsum(F.softmax(sorted_logits, dim=-1), dim=-1)

        # Remove tokens with cumulative probability above the threshold
        sorted_indices_to_remove = cumulative_probs > top_p
        # Shift the indices to the right to keep also the first token above the threshold
        sorted_indices_to_remove[..., 1:] = sorted_indices_to_remove[..., :-1].clone()
        sorted_indices_to_remove[..., 0] = 0

        indices_to_remove = sorted_indices[sorted_indices_to_remove]
        logits[indices_to_remove] = filter_value
    return logits

# Here is how to use this function for top-p sampling
temperature = 1.0
top_k = 0
top_p = 0.9

# Get logits with a forward pass in our model (input is pre-defined)
logits = model(input)

# Keep only the last token predictions of the first batch item (batch size 1), apply a temperature coefficient and filter
logits = logits[0, -1, :] / temperature
filtered_logits = top_k_top_p_filtering(logits, top_k=top_k, top_p=top_p)

# Sample from the filtered distribution
probabilities = F.softmax(filtered_logits, dim=-1)
next_token = torch.multinomial(probabilities, 1)

四.Reference

• [ICLR2020]The Curious Case of Neural Text Degeneration
• 文本生成中的decoding strategy整理
• 十分钟读懂Beam Search 2：一些改进
• Beam search之後，讓文本生成更加靈動的解碼方法
• [李宏毅]Gated RNN & Sequence Generation
• thomwolf/top-k-top-p.py
• huggingface

paper