Title: THE CURIOUS CASE OF NEURAL TEXT DeGENERATION

Abstract: Despite considerable advances in neural language modeling, it remains an open question what the best decoding strategy is for text generation from a language model (e.g. to generate a story). The counter-intuitive empirical observation is that even though the use of likelihood as training objective leads to high quality models for a broad range of language understanding tasks, maximization-based decoding methods such as beam search lead to degeneration -output text that is bland, incoherent, or gets stuck in repetitive loops.
To address this we propose Nucleus Sampling, a simple but effective method to draw considerably higher quality text out of neural language models than previous decoding strategies. Our approach avoids text degeneration by truncating the unreliable tail of the probability distribution, sampling from the dynamic nucleus of tokens containing the vast majority of the probability mass. To properly examine current maximization-based and stochastic decoding methods, we compare generations from each of these methods to the distribution of human text along several axes such as likelihood, diversity, and repetition. Our results show that (1) maximization is an inappropriate decoding objective for openended text generation, (2) the probability distributions of the best current language models have an unreliable tail which needs to be truncated during generation and (3) Nucleus Sampling is currently the best available decoding strategy for generating long-form text that is both high-quality -as measured by human evaluation -and as diverse as human-written text.
Context: In a shocking finding, scientist discovered a herd of unicorns living in a remote, previously unexplored valley, in the Andes Mountains. Even more surprising to the researchers was the fact that the unicorns spoke perfect English.

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Figure 1 : Even with substantial human context and the powerful GPT-2 Large language model, Beam Search (size 32) leads to degenerate repetition (highlighted in blue) while pure sampling leads to incoherent gibberish (highlighted in red). When b ≥ 64, both GPT-2 Large and XL (774M and 1542M parameters, respectively) prefer to stop generating immediately after the given context.

1. INTRODUCTION:

On February 14th 2019, OpenAI surprised the scientific community with an impressively highquality article about Ovid's Unicorn, written by GPT-2. 1 Notably, the top-quality generations ob-tained from the model rely on randomness in the decoding method, in particular through top-k sampling that samples the next word from the top k most probable choices (Fan et al., 2018; Holtzman et al., 2018; Radford et al., 2019) , instead of aiming to decode text that maximizes likelihood.

In fact, decoding strategies that optimize for output with high probability, such as beam search, lead to text that is incredibly degenerate, even when using state-of-the-art models such as GPT-2 Large, as shown in Figure 1 . This may seem counter-intuitive, as one would expect that good models would assign higher probability to more human-like, grammatical text. Indeed, language models do generally assign high scores to well-formed text, yet the highest scores for longer texts are often generic, repetitive, and awkward. Figure 2 exposes how different the distribution of probabilities assigned to beam search decoded text and naturally occurring text really are.

Perhaps equally surprising is the right side of Figure 1 , which shows that pure sampling -sampling directly from the probabilities predicted by the model -results in text that is incoherent and almost unrelated to the context. Why is text produced by pure sampling so degenerate? In this work we show that the "unreliable tail" is to blame. This unreliable tail is composed of tens of thousands of candidate tokens with relatively low probability that are over-represented in the aggregate.

To overcome these issues we introduce Nucleus Sampling ( §3.1). The key intuition of Nucleus Sampling is that the vast majority of probability mass at each time step is concentrated in the nucleus, a small subset of the vocabulary that tends to range between one and a thousand candidates. Instead of relying on a fixed top-k, or using a temperature parameter to control the shape of the distribution without sufficiently suppressing the unreliable tail, we propose sampling from the top-p portion of the probability mass, expanding and contracting the candidate pool dynamically.

In order to compare current methods to Nucleus Sampling, we compare various distributional properties of generated text to the reference distribution, such as the likelihood of veering into repetition and the perplexity of generated text. 

Human:

...which grant increased life span and three years warranty. The Antec HCG series consists of five models with capacities spanning from 400W to 900W. Here we should note that we have already tested the HCG-620 in a previous review and were quite satisfied With its performance. In today's review we will rigorously test the Antec HCG-520, which as its model number implies, has 520W capacity and contrary to Antec's strong beliefs in multi-rail PSUs is equipped... The latter reveals that text generated by maximization or top-k sampling is too probable, indicating a lack of diversity and divergence in vocabulary usage from the human distribution.

On the other hand, pure sampling produces text that is significantly less likely than the gold, corresponding to lower generation quality.

Vocabulary usage and Self-BLEU (Zhu et al., 2018) 

2. BACKGROUND:



2.1. TEXT GENERATION DECODING STRATEGIES:

A number of recent works have alluded to the disadvantages of generation by maximization, which tend to generate output with high grammaticality but low diversity (Kulikov et al., 2019; Holtzman et al., 2018; Fan et al., 2018) . Generative Adversarial Networks (GANs) have been a prominent research direction (Yu et al., 2017; Xu et al., 2018) , but recent work has shown that when quality and diversity are considered jointly, GAN-generated text fails to outperform generations from language models (Caccia et al., 2018; Tevet et al., 2019; Semeniuta et al., 2018) . Work on neural dialog systems have proposed methods for diverse beam search, using a task-specific diversity scoring function or constraining beam hypotheses to be sufficiently different (Li et al., 2016a; Vijayakumar et al., 2018; Kulikov et al., 2019; Pal et al., 2006) . While such utility functions encourage desirable properties in generations, they do not remove the need to choose an appropriate decoding strategy, and we believe that Nucleus Sampling will have complementary advantages in such approaches. Finally, Welleck et al. (2020) begin to address the problem of neural text degeneration through an "unlikelihood loss", which decreases training loss on repeated tokens and thus implicitly reduces gradients on frequent tokens as well. Our focus is on exposing neural text degeneration and providing a decoding solution that can be used with arbitrary models, but future work will likely combine training-time and inference-time solutions.

2.2. OPEN-ENDED VS DIRECTED GENERATION:

Many text generation tasks are defined through (input, output) pairs, such that the output is a constrained transformation of the input. Example applications include machine translation (Bahdanau et al., 2015) , data-to-text generation (Wiseman et al., 2017) , and summarization (Nallapati et al., 2016) . We refer to these tasks as directed generation. Typically encoder-decoder architectures are used, often with an attention mechanism (Bahdanau et al., 2015; Luong et al., 2015) or using attention-based architectures such as the Transformer (Vaswani et al., 2017) . Generation is usually performed using beam search; since output is tightly scoped by the input, repetition and genericness are not as problematic. Still, similar issues have been reported when using large beam sizes (Koehn & Knowles, 2017 ) and more recently with exact inference (Stahlberg & Byrne, 2019) , a counter-intuitive observation since more comprehensive search helps maximize probability.

Open-ended generation, which includes conditional story generation and contextual text continuation (as in Figure 1 ), has recently become a promising research direction due to significant advances in neural language models (Clark et al., 2018; Holtzman et al., 2018; Fan et al., 2018; Peng et al., 2018; Radford et al., 2019) . While the input context restricts the space of acceptable output generations, there is a considerable degree of freedom in what can plausibly come next, unlike in directed generation settings. Our work addresses the challenges faced by neural text generation with this increased level of freedom, but we note that some tasks, such as goal-oriented dialog, may fall somewhere in between open-ended and directed generation.

3. LANGUAGE MODEL DECODING:

Given an input text passage as context, the task of open-ended generation is to generate text that forms a coherent continuation from the given context. More formally, given a sequence of m tokens x 1 . . . x m as context, the task is to generate the next n continuation tokens to obtain the completed sequence x 1 . . . x m+n . We assume that models compute P (x 1:m+n ) using the common left-to-right decomposition of the text probability,

EQUATION

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

Maximization-based decoding:

The most commonly used decoding objective, in particular for directed generation, is maximization-based decoding. Assuming that the model assigns higher probability to higher quality text, these decoding strategies search for the continuation with the highest Poor nutrition has led to a rise in the number of stranded humpback whales on the West Australian coast, veterinary researchers have said. Carly Holyoake, from Murdoch University, at the Australian Veterinary Association's annual conference in Perth on Wednesday, said an unprecedented number of mostly young whales had become stranded on the coast since 2008.

There has been an unprecedented number of calves caught in the nets of whaling stations that operate in WA. Pilot whales continue to migrate to feeding grounds to feed their calves. They are now vulnerable due to the decline of wild populations; they are restricted to one breeding site each year. Image copyright Yoon Bo Kim But, with sharp decline in wild populations the size of the Petrels are shrinking and dwindling population means there will only be room for a few new fowl.

Pumping Station #3 shut down due to construction damage Find more at: www.abc.net.au/environment/species-worry/ in-the-top-10-killer-whale-catastrophes-in-history.html "In the top 10 killer whale catastrophes in history: 1) 1986: Up to 12 orcas struck by lightning; many drowned and many more badly injured.

Last week's intense storms and a series of powerful cyclones have been officially blamed for the deaths of at least nine large fin whales near Whitsundays -the largest loss of any species globally. The fin whales: packed in the belly of one killer whale thrashing madly in fear as another tries to bring it to safety. When the colossal animal breached the waters of Whitsundays, he'd been seen tagged for a decade.

The Australian Food Safety Authority has warned Australia's beaches may be revitalised this year because healthy seabirds and seals have been on the move. More than 50,000 seabirds, sea mammals and seahorses have been swept into the sea by the Holden CS118 and Adelaide Airport CS300 from 2013. A major white-bat and umidauda migration across Australia is under way in Australia for the first time, with numbers reaching an estimated 50,000.

The number of stranded whales has increased by more than 50 per cent in the past year, with the number of stranded whales on the West Australian coast increasing by more than 50 per cent in the past year. The number of whales stranded on the West Australian coast has increased by more than 50 per cent in the past year, with the number of stranded whales on the West Australian coast increasing by more than 50 per cent in the past year.

Sampling, t=0.9

WebText WebText Beam Search, b=16 Pure Sampling Top-k, k=640

Top-k, k=40, t=0.7

The whale's fate was confirmed late last week when the animal was found by fishermen off the coast of Bundaberg. Experts believe the whale was struck by a fishing vessel off the coast of Bundaberg, and died after being sucked into the ocean. The whale's fate was confirmed late last week when the animal was found by fishermen off the coast of Bundaberg.

Nucleus, p=0.95 likelihood. Since finding the optimum argmax sequence from recurrent neural language models or Transformers is not tractable (Chen et al., 2018) , common practice is to use beam search (Li et al., 2016b; Shen et al., 2017; Wiseman et al., 2017) . However, several recent studies on open-ended generation have reported that maximization-based decoding does not lead to high quality text (Fan et al., 2018; Holtzman et al., 2018) .

3.1. NUCLEUS SAMPLING:

We propose a new stochastic decoding method: Nucleus Sampling. The key idea is to use the shape of the probability distribution to determine the set of tokens to be sampled from. Given a distribution P (x|x 1:i-1 ), we define its top-p vocabulary V (p) ⊂ V as the smallest set such that Figure 4 : The probability of a repeated phrase increases with each repetition, creating a positive feedback loop. We found this effect to hold for the vast majority of phrases we tested, regardless of phrase length or if the phrases were sampled randomly rather than taken from human text.

EQUATION

Figure 5 : The probability mass assigned to partial human sentences. Flat distributions lead to many moderately probable tokens, while peaked distributions concentrate most probability mass into just a few tokens. The presence of flat distributions makes the use of a small k in top-k sampling problematic, while the presence of peaked distributions makes large k's problematic.

Let p = x∈V (p) P (x|x 1:i-1 ). The original distribution is re-scaled to a new distribution, from which the next word is sampled:

EQUATION

In practice this means selecting the highest probability tokens whose cumulative probability mass exceeds the pre-chosen threshold p. The size of the sampling set will adjust dynamically based on the shape of the probability distribution at each time step. For high values of p, this is a small subset of vocabulary that takes up vast majority of the probability mass -the nucleus.

3.2. TOP-k SAMPLING:

Top-k sampling has recently become a popular alternative sampling procedure (Fan et al., 2018; Holtzman et al., 2018; Radford et al., 2019) . Nucleus Sampling and top-k both sample from truncated Neural LM distributions, differing only in the strategy of where to truncate. Choosing where to truncate can be interpreted as determining the generative model's trustworthy prediction zone.

At each time step, the top k possible next tokens are sampled from according to their relative probabilities. Formally, given a distribution P (x|x 1:i-1 ), we define its top-k vocabulary V (k) ⊂ V as the set of size k which maximizes x∈V (k) P (x|x 1:i-1 ). Let p = x∈V (k) P (x|x 1:i-1 ). The distribution is then re-scaled as in equation 3, and sampling is performed based on that distribution. Note that the scaling factor p can vary wildly at each time-step, in contrast to Nucleus Sampling.

Difficulty in choosing a suitable value of k While top-k sampling leads to considerably higher quality text than either beam search or sampling from the full distribution, the use of a constant k is sub-optimal across varying contexts. As illustrated on the left of Figure 5 , in some contexts the head of the next word distribution can be flat across tens or hundreds of reasonable options (e.g. nouns or verbs in generic contexts), while in other contexts most of the probability mass is concentrated in one or a small number of tokens, as on the right of the figure. Therefore if k is small, in some contexts there is a risk of generating bland or generic text, while if k is large the top-k vocabulary will include inappropriate candidates which will have their probability of being sampled increased by the renormalization. Under Nucleus Sampling, the number of candidates considered rises and falls dynamically, corresponding to the changes in the model's confidence region over the vocabulary which top-k sampling fails to capture for any one choice of k.

3.3. SAMPLING WITH TEMPERATURE:

Another common approach to sampling-based generation is to shape a probability distribution through temperature (Ackley et al., 1985) . Temperature sampling has been applied widely to text generation (Ficler & Goldberg, 2017; Fan et al., 2018; Caccia et al., 2018) . Given the logits u 1:|V | and temperature t, the softmax is re-estimated as

EQUATION

)

Setting t ∈ [0, 1) skews the distribution towards high probability events, which implicitly lowers the mass in the tail distribution. Low temperature sampling has also been used to partially alleviate the issues of top-k sampling discussed above, by shaping the distribution before top-k sampling (Radford et al., 2018; Fan et al., 2018) . However, recent analysis has shown that, while lowering the temperature improves generation quality, it comes at the cost of decreasing diversity (Caccia et al., 2018; Hashimoto et al., 2019) .

4. LIKELIHOOD EVALUATION:

4.1 EXPERIMENTAL SETUP While many neural network architectures have been proposed for language modeling, including LSTMs (Sundermeyer et al., 2012) and convolutional networks (Dauphin et al., 2017) , the Transformer architecture (Vaswani et al., 2017) has been the most successful in the extremely large-scale training setups in recent literature (Radford et al., 2018; 2019) . In this study we use the Generatively Pre-trained Transformer, version 2 (GPT2; Radford et al., 2019) , which was trained on WebText, a 40GB collection of text scraped from the web. 3 We perform experiments using the Large model (762M parameters). Our analysis is based on generating 5,000 text passages, which end upon reaching an end-of-document token or a maximum length of 200 tokens. Texts are generated conditionally, conditioned on the initial paragraph (restricted to 1-40 tokens) of documents in the held-out portion of WebText, except where otherwise mentioned.

4.2. PERPLEXITY:

Our first evaluation is to compute the perplexity of generated text using various decoding strategies, according to the model that is being generated from. We compare these perplexities against that of the gold text (Figure 6 ). Importantly, we argue that the optimal generation strategy should produce text which has a perplexity close to that of the gold text: Even though the model has the ability to generate text that has lower perplexity (higher probability), such text tends to have low diversity and get stuck in repetition loops, as shown in §5 and illustrated in Figure 4 .

We see that perplexity of text obtained from pure sampling is worse than the perplexity of the gold. This indicates that the model is confusing itself: sampling too many unlikely tokens and creating context that makes it difficult to recover the human distribution of text, as in Figure 1 

4.3. NATURAL LANGUAGE DOES NOT MAXIMIZE PROBABILITY:

One might wonder if the issue with maximization is a search error, i.e., there are higher quality sentences to which the model assigns higher probability than to the decoded ones, beam search has just failed to find them. Yet Figures 2 & 6 show that the per-token probability of natural text is, on average, much lower than text generated by beam search. Natural language rarely remains in a high probability zone for multiple consecutive time steps, instead veering into lower-probability but more informative tokens. Nor does natural language tend to fall into repetition loops, even though the model tends to assign high probability to this, as seen in Figure 4 .

Why is human-written text not the most probable text? We conjecture that this is an intrinsic property of human language. Language models that assign probabilities one word at a time without a global model of the text will have trouble capturing this effect. Grice's Maxims of Communication (Grice, 1975) show that people optimize against stating the obvious. Thus, making every word as predictable as possible will be disfavored. This makes solving the problem simply by training larger models or improving neural architectures using standard per-word learning objectives unlikely: such models are forced to favor the lowest common denominator, rather than informative language.

5. DISTRIBUTIONAL STATISTICAL EVALUATION:



5.1. ZIPF DISTRIBUTION ANALYSIS:

In order to compare generations to the reference text, we begin by analyzing their use of vocabulary. Zipf's law suggests that there is an exponential relationship between the rank of a word and its frequency in text. The Zipfian coefficient s can be used to compare the distribution in a given text 0. 1 0. 5 0. 9 0. 99 0. 99 9 0. 99 99 p

Nucleus:

Figure 6 : Perplexities of generations from various decoding methods. Note that beam search has unnaturally low perplexities. A similar effect is seen using a temperature of 0.7 with top-k as in both Radford et al. (2019) and Fan et al. (2018) . Sampling, Top-k, and Nucleus can all be calibrated to human perplexities, but the first two face coherency issues when their parameters are set this high. . 9 p = 0 . 9 5 p = 0 . 9 7 5 p = 0 . 9 8 7 5 p = 0 . 9 9 3 7 5 p = 0 . 9 9 6 8 7 5 p = 0 . 9 9 8 4 3 7 5 p = 0 . 9 9 9 2 1 8 7 5 p = 0 . 9 9 9 6 0 9 3 7 5 p = 0 . 9 9 9 8 0 4 6 8 7 5 p = 0 . 9 9 9 9 0 2 3 4 3 7 5 p = 0 . 9 9 9 9 5 1 1 7 1 8 7 5

Self-BLEU of Generations Over 5000 Documents:

Self-BLEU4

Self-BLEU5

Figure 8 : Self-BLEU calculated on the unconditional generations produced by stochastic decoding methods; lower Self-BLEU scores imply higher diversity. Horizontal blue and orange lines represent human self-BLEU scores. Note how common values of t ∈ [0.5, 1] and k ∈ [1, 100] result in high self-similarity, whereas "normal" values of p ∈ [0.9, 1) closely match the human distribution of text.

to a theoretically perfect exponential curve, where s = 1 (Piantadosi, 2014). Figure 7 shows the vocabulary distributions along with estimated Zipf coefficients for selected parameters of different decoding methods. As expected, pure sampling is the closest to the human distribution, followed by Nucleus Sampling. The visualization of the distribution shows that pure sampling slightly overestimates the use of rare words, likely one reason why pure sampling also has higher perplexity than human text. Furthermore, lower temperature sampling avoids sampling these rare words from the tail, which is why it has been used in some recent work (Fan et al., 2018; Radford et al., 2019) .

5.2. SELF-BLEU:

We follow previous work and compute Self-BLEU (Zhu et al., 2018) as a metric of diversity. Self-BLEU is calculated by computing the BLEU score of each generated document using all other generations in the evaluation set as references. Due to the expense of computing such an operation, we sample 1000 generations, each of which is compared with all 4999 other generations as references. A lower Self-BLEU score implies higher diversity. Figure 8 shows that Self-BLEU results largely follow that of the Zipfian distribution analysis as a diversity measure. It is worth noting that very high values of k and t are needed to get close to the reference distribution, though these result in unnaturally high perplexity ( §4).

5.3. REPETITION:

One attribute of text quality that we can quantify is repetition. Figure 9 shows that Nucleus Sampling and top-k sampling have the least repetition for reasonable parameter ranges. Generations from temperature sampling have more repetition unless very high temperatures are used, which we have shown negatively affects coherence (as measured by high perplexity). Further, all stochastic methods face repetition issues when their tuning parameters are set too low, which tends to overtruncate, mimicking greedy search. Therefore we conclude that only Nucleus Sampling satisfies all the distributional criteria for desirable generations.

6 HUMAN EVALUATION 6.1 HUMAN UNIFIED WITH STATISTICAL EVALUATION (HUSE)

Statistical evaluations are unable to measure the coherence of generated text properly. While the metrics in previous sections gave us vital insights into the different decoding methods we compare, human evaluation is still required to get a full measure of the quality of the generated text. However, pure human evaluation does not take into account the diversity of the generated text; therefore we use HUSE (Hashimoto et al., 2019) to combine human and statistical evaluation. HUSE is computed by training a discriminator to distinguish between text drawn from the human and model distributions, based on only two features: The probability assigned by the language model, and human judgements of typicality of generations. Text that is close to the human distribution in terms of quality and diversity should perform well on both likelihood evaluation and human judgements.

As explored in the previous sections, the current best-performing decoding methods rely on truncation of the probability distribution, which yields a probability of 0 for the vast majority of potential tokens. Initial exploration of applying HUSE directly led to top-k and Nucleus Sampling receiving scores of nearly 0 due to truncation, despite humans favoring these methods. As a proxy, when generating the text used to compute HUSE, we interpolate (with mass 0.1) the original probability distribution with the top-k and Nucleus Sampling distribution, smoothing the truncated distribution.

For each decoding algorithm we annotate 200 generations for typicality, with each generation receiving 20 annotations from 20 different annotators. This results in a total of 4000 annotations per a decoding scheme. We use a KNN classifier to compute HUSE, as in the original paper, with k = 13 neighbors, which we found led to the higher accuracy in discrimination. The results in Table 1 shows that Nucleus Sampling obtains the highest HUSE score, with Top-k sampling performing second best.

6.2 QUALITATIVE ANALYSIS Figure 3 shows representative example generations. Unsurprisingly, beam search gets stuck in a repetition loop it cannot escape. Of the stochastic decoding schemes, the output of full sampling is clearly the hardest to understand, even inventing a new word "umidauda", apparently a species of bird. The generation produced by Nucleus Sampling isn't perfect -the model appears to confuse whales with birds, and begins writing about those instead. Yet, top-k sampling immediately veers off into an unrelated event. When top-k sampling is combined with a temperature of 0.7, as is commonly done (Radford et al., 2019; Fan et al., 2018) , the output devolves into repetition, exhibiting the classic issues of low-temperature decoding. More generations are available in Appendix B.

7. CONCLUSION:

This paper provided a deep analysis into the properties of the most common decoding methods for open-ended language generation. We have shown that likelihood maximizing decoding causes repetition and overly generic language usage, while sampling methods without truncation risk sampling from the low-confidence tail of a model's predicted distribution. Further, we proposed Nucleus Sampling as a solution that captures the region of confidence of language models effectively. In future work, we wish to dynamically characterize this region of confidence and include a more semantic utility function to guide the decoding process.

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https://openai.com/blog/better-language-models/

Code and all generations are available at https://github.com/ari-holtzman/degen

Available at https://github.com/openai/gpt-2-output-dataset

Figures and Tables:

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Figure 2: The probability assigned to tokens generated by Beam Search and humans, given the same context. Note the increased variance that characterizes human text, in contrast with the endless repetition of text decoded by Beam Search.

An unprecedented number of mostly young whales have become stranded on the West Australian coast since 2008.

Figure 3: Example generations continuing an initial sentence. Maximization and top-k truncation methods lead to copious repetition (highlighted in blue), while sampling with and without temperature tends to lead to incoherence (highlighted in red). Nucleus Sampling largely avoids both issues.

Figure 7: A rank-frequency plot of the distributional differences between n-gram frequencies of human and machine text. Sampling and Nucleus Sampling are by far the closest to the human distribution, while Beam Search clearly follows a very different distribution than natural language.

Figure9: We visualize how often different decoding methods get "stuck" in loops within the first 200 tokens. A phrase (minimum length 2) is considered a repetition when it repeats at least three times at the end of the generation. We label points with their parameter values except for t and p which follow the x-axis. Values of k greater than 100 are rarely used in practice and values of p are usually in [0.9, 1); therefore Nucleus Sampling is far closer to the human distribution in its usual parameter range. Sampling with temperatures lower than 0.9 severely increase repetition. Finally, although beam search becomes less repetitive according to this metric as beam width increases, this is largely because average length gets shorter as b increases (see Appendix A).

Figure 10: The total number of trigrams produced by Beam Search with varying beam widths, with gold (human) data for comparison. Note how the average length of generations goes down linearly with beam width, while the number of distinct trigrams stays constant and extremely low in comparison to gold data.

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Figure 11: More example generations from an initial tag line. All generations available at https: //github.com/ari-holtzman/degen

Main results for comparing all decoding methods with selected parameters of each method. The numbers closest to human scores are in bold except for HUSE(Hashimoto et al., 2019), a combined human and statistical evaluation, where the highest (best) value is bolded. For Top-k and Nucleus Sampling, HUSE is computed with interpolation rather than truncation (see §6.1).

Table content: <table><tr><td>Method</td><td colspan="5">Perplexity Self-BLEU4 Zipf Coefficient Repetition % HUSE</td></tr><tr><td>Human</td><td>12.38</td><td>0.31</td><td>0.93</td><td>0.28</td><td>-</td></tr><tr><td>Greedy</td><td>1.50</td><td>0.50</td><td>1.00</td><td>73.66</td><td>-</td></tr><tr><td>Beam, b=16</td><td>1.48</td><td>0.44</td><td>0.94</td><td>28.94</td><td>-</td></tr><tr><td>Stochastic Beam, b=16</td><td>19.20</td><td>0.28</td><td>0.91</td><td>0.32</td><td>-</td></tr><tr><td>Pure Sampling</td><td>22.73</td><td>0.28</td><td>0.93</td><td>0.22</td><td>0.67</td></tr><tr><td>Sampling, t=0.9</td><td>10.25</td><td>0.35</td><td>0.96</td><td>0.66</td><td>0.79</td></tr><tr><td>Top-k=40</td><td>6.88</td><td>0.39</td><td>0.96</td><td>0.78</td><td>0.19</td></tr><tr><td>Top-k=640</td><td>13.82</td><td>0.32</td><td>0.96</td><td>0.28</td><td>0.94</td></tr><tr><td>Top-k=40, t=0.7</td><td>3.48</td><td>0.44</td><td>1.00</td><td>8.86</td><td>0.08</td></tr><tr><td>Nucleus p=0.95</td><td>13.13</td><td>0.32</td><td>0.95</td><td>0.36</td><td>0.97</td></tr></table>

Peer review (iclr2020):
In the domain of language models, the paper introduces a new heuristic sampling method called top-p sampling, or nucleus sampling (NS). It is a variant of top-k sampling where the smallest k is selected to ensure the combined likelihood is no less than p. The paper centers on claiming and showing that the generated samples are of higher quality and more diverse than common alternatives such as beam search, pure sampling, top-k sampling, and low-temperature sampling. While overall I think the proposed method is sound as an alternative to other heuristics such as beam search, I have reservations on the presentation and arguments made in the paper. Pros: 1. NS is sound as a heuristic sampling method. 2. The paper contains many interesting experimental observations and I speculate that some of them will find future uses. For example, the selection of parameter values (not just for NS, also for top-k) and the nontrivial perplexity of generated text. Cons: 1. The ultimate performance measure (open-ended generation) of “high quality” and “diversity” is very vague. It seems that the authors end up doing is to evaluate by high self-BLEU, HUSE, few repetitions, and perplexity. Furthermore, it is unclear why one _should_ train with cross-entropy (trying to match the distributions) and then rely on the sampling procedure to fulfill these desiderata (See also Min1 and Min2). 2. The comparison with beam search (BS) is not well motivated. BS is devised to find the maximal sentence and it is not stochastic. It seems out of place in the context of generating a “diverse” set of samples. 3. The arguments in the comparison with pure sampling is vague and sometimes misplaced. The key argument seems to hinge on the idea that the low likelihood tail is of “low confidence.” But this claim is problematic. If the estimate is wrong on the low probability tail, then so is the estimate on p(head) = 1-p(tail) by virtue of p being a probability measure. 4. The arguments in the comparison with top-k is vague and sometimes misplaced. The main argument against top-k is the “[d]ifficulty in choosing a suitable value of k” but the same can be said for choosing p. After all, top-k and top-p (NS) can be thought of as a variant of each other (by dynamically choosing k or p respectively). Moreover, in Figure 5, a selection for k value is suggested. I agree that this value might not _appear_ as intuitive as p, and maybe other works have chosen a smaller k than they should have, but similarly, people might intuitively choose too high a value for p (Figure 5). Possible mistakes/typos: 1. (2), “>=“ -> ?. 2. Figure 7, the human self-BLEU4 < human self-BLEU5 and that seems wrong, especially when all other bars show the opposite ordering. 3. In References, “Angela Fan, Mike Lewis, and Yann Dauphin. Hierarchical neural story generation. In ACL, 2018a” is duplicated. 4. In References, the citation of “Unifying human and statistical evaluation for natural language generation” is from NAACL 2019, not “2018.” 5. In References, the first names are shown as initials in “Sparse forward-backward using minimum divergence beams for fast training of conditional random fields.” Questions: 1. In Table 1, how is Human perplexity estimated? Minor issues: 1. Partly due to what the authors position NS to solve, i.e. open-ended generation, the core arguments is not as precise or rigorous as it could have been in my opinion. I feel that focusing on comparing NS to other heuristics as a heuristic might make the text appeal to a wider audience and the discussion more precise. 2. The distinction drawn between open-ended generation and directed generation is unpersuasive to me. In the context of language modeling, the former is to approximate a distribution (over an extended alphabet) whereas the latter is to approximate a conditional distribution (given the input). However, the most common formulation to solve the former is to decompose the distribution into a product of conditional distributions (1). 3. The caption in Figure 1 draws a misleading comparison. The “admirable” generation (presumably referring to the OpenAI blog post) was from the full GPT-2 model, not the initially released GPT-2-117M. Please point out my misunderstanding directly. I am open to acknowledging them and revising my assessment.