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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.
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 open-ended 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 the best decoding strategy for generating long-form text that is both high-quality — as measured by human evaluation — and as diverse as human-written text.
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 obtained 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-2-117M, 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.
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 shortcomings 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 distribution, 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.
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) statistics reveal that high values of k are needed to make top-k sampling match human statistics.
Yet, generations based on high values of k are also found to have incredibly high variance in likelihood, hinting at qualitatively observable incoherency issues.
Nucleus Sampling can easily match reference perplexity through a proper value of p, without facing the resulting incoherence caused by setting k high enough to match distributional statistics.
Finally, we perform Human Unified with Statistical Evaluation (HUSE; Hashimoto et al., 2019) to jointly assess the overall quality and diversity of the decoding strategies, which cannot be captured using either human or automatics evaluation alone.
The HUSE evaluation demonstrates that Nucleus sampling is the best overall decoding strategy.
We include generated examples for qualitative analysis -see Figure 9 for a representative example, and further examples in the appendix.
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., 2018; 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., 2018; 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., 2018; 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.
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., dsfsadfd An unprecedented number of mostly young whales have become stranded on the West Australian coast since 2008.
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
Pure Sampling
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.
Figure 2: Example generations from 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.
All generations for all hyperparameters will be made publicly available, along with our codebase.
2016).
We refer to these tasks as directed generation.
Typically encoder-decoder architectures are used, often with an attention mechanisms (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) , a counter-intuitive observation since large beam sizes help 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.
Figure 3: 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.
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,
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 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) .
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
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:
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, it is a small subset of vocabulary that takes up most of the probability mass -the nucleus.
Figure 4: 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 problematic.
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 will be different 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 4 , 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 through the truncation.
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.
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
Setting t ∈ [0, 1) shapes the distribution to be more skewed 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 (Vaswani et al., 2017) has been the most successful in the extremely large-scale training setups in recent literature (Radford et al., 2018; .
In this study we use the Generative Pre-trained Transformer, version 2 (Radford et al., 2019) , which was trained on WebText, a 40GB collection of text scraped from the web.
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.
We consider a conditional generation setting, in which texts are conditioned on the initial paragraph (restricted to 1-40 tokens) of documents in the validation portion of WebText.
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 5 ).
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 be low-diverstiy and get stuck in repetition loops, as shown in §5 and illustrated in Figure 3 .
We see that perplexity of text obtained from pure sampling (sampling with t = 1) is actually worse than the perplexity of the gold.
This indicates that the model is actually confusing itself: sampling too many unlikely tokens and creating context that makes it difficult to recover the human distribution of text, as happens in Figure 1 .
Yet setting the temperature lower creates diversity repetition issues, as we shall see in §5.
Interestingly, even with the relatively fine-grained parameter sweep conducted, Nucleus Sampling gets closer perplexity in both the conditional and under conditional case, than any other method, as shown in Table 1 .
One might wonder if the issue with maximization search error is a, 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 Figure 5 shows 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 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 ?.
Sampling, Top-k, and Nucleus can all be calibrated to human perplexities, but we shall see the first two face coherency issues when their parameters are set this high.
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 3 .
Why is naturally existing human 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 context for the underlying document will have trouble capturing this effect.
Grice's Maxims of Communication (Grice, 1975) show that people optimize against stating the obvious.
Thus, it is natural that 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: models that are blindly predicting the future will be forced to predict the lowest common denominator, rather than information rich language.
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 to a theoretically perfect exponential curve, where s = 1 (Piantadosi, 2014).
Figure 6 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) .
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.
Thus a lower Self-BLEU score implies higher diversity.
Figure 7 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).
One attribute of text quality that we can quantify is repetition.
Figure 8 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
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, Self-BLEU of Generations Over 5000 Documents
Self-BLEU5
Figure 7: 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.
tokens.
Concretely, a phrase (sequence of words with minimum length 2) must repeat at least three times at the end of the generation to be considered a repetition.
Since all the methods described used different parameter ranges, we label points with the appropriate parameter value except for t and p.
Since values of k greater than 100 are rarely used in practice and values of p are usually in [0.9, 1), it becomes clear that Nucleus sampling is far closer to the human distribution in its usual parameter range.
Finally, temperatures lower than 0.9 severely effect repetition, making it problematic for use in long-form generation.
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.
The results in Table 1 shows that Nucleus Sampling obtains the highest HUSE score, with Top-k sampling performing next best.
6.2 QUALITATIVE ANALYSIS Figure 9 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 get get confused that it was talking about whales, and begins talking about birds instead.
Yet, Top-k Sampling immediately veers off into an unrelated event.
When top-k sampling is combine with a temperature of 0.7, as is commonly done (Radford et al., 2019; Fan et al., 2018) , the output devolves into repetition.
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 Samplingas 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.
We include another set of examples for further qualitative comparison.
What's the best way to read this one?
The blog post from the authors discusses the differences between how the marketing mix plays out in terms of visibility, trustworthiness, and engagement, among other things.
In my experience, this difference isn't necessarily obvious; it's hard to explain to a layperson, but in all honesty it's probably the most important point to consider when reviewing social media.
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Figure 9: More example generations from an initial tag line.
All generations for all hyperparameters will be made publicly available, along with our codebase.

assistant: text: Current language generation systems either aim for high likelihood and devolve into generic repetition or miscalibrate their stochasticity—we provide evidence of both and propose a solution: Nucleus Sampling.