Title: Are Emergent Abilities of Large Language Models a Mirage?
Venue: NeurIPS 2023
Accepted: yes
Keywords: large language models

foundation models

natural language processing

language modeling

emergent abilities
Abstract: Recent work claims that large language models display \textit{emergent abilities}, abilities not present in smaller-scale models that are present in larger-scale models.
What makes emergent abilities intriguing is two-fold: their \textit{sharpness}, transitioning seemingly instantaneously from not present to present, and their \textit{unpredictability}, appearing at seemingly unforeseeable model scales.
Here, we present an alternative explanation for emergent abilities: that for a particular task and model family, when analyzing fixed model outputs, emergent abilities appear due the researcher’s choice of metric rather than due to fundamental changes in model behavior with scale. Specifically, nonlinear or discontinuous metrics produce apparent emergent abilities, whereas linear or continuous metrics produce smooth, continuous, predictable changes in model performance.
We present our alternative explanation in a simple mathematical model, then test it in three complementary ways: we (1) make, test and confirm three predictions on the effect of metric choice using the InstructGPT/GPT-3 family on tasks with claimed emergent abilities, (2) make, test and confirm two predictions about metric choices in a meta-analysis of emergent abilities on BIG-Bench; and (3) show how to choose metrics to produce never-before-seen seemingly emergent abilities in multiple vision tasks across diverse deep networks.
Via all three analyses, we provide evidence that alleged emergent abilities evaporate with different metrics or with better statistics, and may not be a fundamental property of scaling AI models.

Are Emergent Abilities of Large Language Models a Mirage?

Abstract

Recent work claims that large language models display emergent abilities : abilities not present in smaller-scale models that are present in larger-scale models. What makes emergent abilities intriguing is two-fold: their sharpness , transitioning seemingly instantaneously from not present to present, and their unpredictability , appearing at seemingly unforeseeable model scales. Here, we present an alternative explanation for emergent abilities: for a particular task and model family, when analyzing fixed model outputs, emergent abilities appear due to the researcher's choice of metric rather than due to fundamental changes in models with scale. Specifically, nonlinear or discontinuous metrics produce seemingly emergent abilities, whereas linear or continuous metrics produce smooth, continuous, predictable changes in model performance. We present our alternative explanation in a simple mathematical model, then test it in three complementary ways: we (1) make, test and confirm three predictions on the effect of metric choice using the InstructGPT/GPT-3 family on tasks with claimed emergent abilities; (2) make, test and confirm two predictions about metric choices in a meta-analysis of emergent abilities on the Beyond the Imitation Game Benchmark (BIG-Bench); and (3) show how to choose metrics to produce never-before-seen seemingly emergent abilities in multiple vision tasks across diverse deep network architectures. Via all three analyses, we provide evidence that emergent abilities disappear with different metrics or with better statistics, and may not be a fundamental property of scaling AI models.

1 Introduction

Emergent properties of complex systems have long been studied across disciplines, from physics to biology to mathematics. The idea of emergence was popularized by Nobel Prize-winning physicist P.W. Anderson's 'More Is Different" [1], which argues that as the complexity of a system increases, new properties may materialize that cannot be predicted even from a precise quantitative understanding of the system's microscopic details. Recently, the idea of emergence gained significant attention in machine learning due to observations that large language models (LLMs) such as GPT [4], PaLM [7] and LaMDA [35] exhibit so-called 'emergent abilities" [38, 9, 33, 4] (Fig. 1).

The term 'emergent abilities of LLMs" was recently and crisply defined as 'abilities that are not present in smaller-scale models but are present in large-scale models; thus they cannot be predicted by simply extrapolating the performance improvements on smaller-scale models" [38]. Such emergent abilities were first discovered in the GPT-3 family [4]. Subsequent work emphasized the discovery, writing that '[although model] performance is predictable at a general level, performance on a specific task can sometimes emerge quite unpredictably and abruptly at scale" [9]. These quotations collectively identify the two defining properties of emergent abilities in LLMs:

Sharpness , transitioning seemingly instantaneously from not present to present

LaMDA

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(A) Mod. arithmetic

(B)IPA transliterate

(C) Word unscramble

(D) Persian QA

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2. Unpredictability , transitioning at seemingly unforeseeable model scales

These emergent abilities have garnered significant interest, raising questions such as: What controls which abilities will emerge? What controls when abilities will emerge? How can we make desirable abilities emerge faster, and ensure undesirable abilities never emerge? These questions are especially pertinent to AI safety and alignment, as emergent abilities forewarn that larger models might one day, without warning, acquire undesired mastery over dangerous capabilities [34, 12, 19, 20].

In this paper, we call into question the claim that LLMs possess emergent abilities, by which we specifically mean sharp and unpredictable changes in model outputs as a function of model scale on specific tasks. Our doubt stems from the observation that emergent abilities seem to appear only under metrics that nonlinearly or discontinuously scale any model's per-token error rate. For instance, as we later show, > 92% of emergent abilities on BIG-Bench tasks [33] (hand-annotated by [37]) appear under either of these two metrics:

This raises the possibility of an alternative explanation for the origin of LLMs' emergent abilities: sharp and unpredictable changes might be induced by the researcher's choice of measurement, even though the model family's per-token error rate changes smoothly, continuously and predictably with increasing scale. Specifically, our alternative posits that emergent abilities are a mirage caused primarily by the researcher choosing a metric that nonlinearly or discontinuously deforms per-token error rates, and secondarily by possessing too few test data to accurately estimate the performance of smaller models, thereby causing smaller models to appear wholly unable to perform the task.

To communicate our alternative explanation, we present it as a simple mathematical model and demonstrate how it quantitatively reproduces the evidence offered in support of emergent abilities of LLMs. We then test our alternative explanation in three complementary ways:

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We make, test and confirm three predictions based on our alternative hypotheses using the InstructGPT [27] / GPT-3 [4] model family.

We meta-analyze published benchmarks [33, 38] to reveal that emergent abilities only appear for specific metrics, not for model families on particular tasks, and that changing the metric causes the emergence phenomenon to disappear.

We induce never-before-seen, seemingly emergent abilities in multiple architectures across various vision tasks by intentionally changing the metrics used for evaluation.

2 Alternative Explanation for Emergent Abilities

How might smooth, continuous, predictable changes in model family performance appear sharp and unpredictable? The answer is that the researcher's choice of a nonlinear or discontinuous metric can distort the model family's performance to appear sharp and unpredictable.

To expound, suppose that within a model family, the test loss falls smoothly, continuously, and predictably with the number of model parameters. One reason to believe this is the phenomenon known as neural scaling laws: empirical observations that deep networks exhibit power law scaling in the test loss as a function of training dataset size, number of parameters or compute [15, 32, 13, 18,

10, 14, 17, 39, 16, 8, 29]. For concreteness, suppose we have a model family of different numbers of parameters N > 0 and assume that each model's per-token cross entropy falls as a power law with the number of parameters N for constants c > 0 , α < 0 (Fig. 2A):

To be clear, we do not require this particular functional form to hold; rather, we use it for illustrative purposes. Let V denote the set of possible tokens, p denote the true but unknown probability distribution, and ˆ p N denote the N -parameter model's predicted probability distribution. The pertoken cross entropy as a function of number of parameters N is:

In practice, p is unknown, so we substitute a one-hot distribution of the observed token v ∗ :

A model with N parameters then has a per-token probability of selecting the correct token (Fig. 2B):

Suppose the researcher then chooses a metric that requires selecting L tokens correctly. For example, our task might be L -digit integer addition, and a model's output is scored 1 if all L output digits exactly match all target digits with no additions, deletions or substitutions, 0 otherwise. If the probability each token is correct is independent 1 , the probability of scoring 1 is:

This choice of metric nonlinearly scales performance with increasing token sequence length. When plotting performance on a linear-log plot, one sees a sharp, unpredictable emergent ability on longer sequences (Fig. 2C) that closely matches claimed emergent abilities (inset). What happens if the researcher switches from a nonlinear metric like Accuracy, under which the per-token error rate scales geometrically in target length (App. A.3), to an approximately linear metric like Token Edit Distance, under which the per-token error rate scales quasi-linearly in target length (App. A.2)?

The linear metric reveals smooth, continuous, predictable changes in model performance (Fig. 2E). Similarly, if the researcher uses a discontinuous metric like Multiple Choice Grade, the researcher can find emergent abilities (Fig. 2D), but switching to a continuous metric like Brier Score removes such abilities (Fig. 2F). In summary, sharp and unpredictable changes with increasing scale can be fully explained by three interpretable factors: (1) the researcher choosing a metric that nonlinearly or discontinuously scales the per-token error rate, (2) having insufficient resolution to estimate model performance in the smaller parameter regime, with resolution 2 set by 1 / test dataset size, and (3) insufficiently sampling the larger parameter regime.

3 Analyzing InstructGPT/GPT-3's Emergent Arithmetic Abilities

Previous papers prominently claimed the GPT [4, 27] family 3 displays emergent abilities at integer arithmetic tasks [9, 33, 38] (Fig. 1A). We chose these tasks as they were prominently presented

2-Integer 2-Digit Multiplication

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[4, 9, 33, 38], and we focused on the GPT family due to it being publicly queryable. As explained mathematically and visually in Sec. 2, our alternative explanation makes three predictions:

Changing the metric from a nonlinear or discontinuous metric (Fig. 2CD) to a linear or continuous metric (Fig. 2 EF) should reveal smooth, continuous, predictable performance improvement with model scale.

For nonlinear metrics, increasing the resolution of measured model performance by increasing the test dataset size should reveal smooth, continuous, predictable model improvements commensurate with the predictable nonlinear effect of the chosen metric .

Regardless of metric, increasing the target string length should predictably affect the model's performance as a function of the length-1 target performance: approximately geometrically for accuracy and approximately quasilinearly for token edit distance.

To test these predictions, we collected outputs from the InstructGPT/GPT-3 family on two tasks: 2-shot multiplication between two 2-digit integers and 2-shot addition between two 4-digit integers.

Prediction: Emergent Abilities Disappear With Different Metrics On both arithmetic tasks, the GPT family displays emergent abilities if the target has 4 or 5 digits and if the metric is Accuracy (Fig. 3, top) [4, 9, 38]. However, if one changes from nonlinear Accuracy to linear Token Edit Distance while keeping the models' outputs fixed , the family's performance smoothly, continuously and predictably improves with increasing scale (Fig. 3, bottom). This confirms our first prediction and supports our alternative explanation that the observation of emergent abilities can be explained by the researcher's choice of metric, not changes in the model family's outputs . We also observe that under Token Edit Distance, increasing the length of the target string from 1 to 5 predictably decreases the family's performance in an approximately quasilinear manner, confirming the first half of our third prediction.

Prediction: Emergent Abilities Disappear With Better Statistics We next tested our second prediction: that even on nonlinear metrics such as accuracy, smaller models do not have zero accuracy, but rather have non-zero above-chance accuracy commensurate with choosing to use accuracy as the metric . In order to accurately measure models' accuracy, we increased the resolution by generating additional test data, and found that on both arithmetic tasks, all models in the InstructGPT/GPT-3 family achieve above-chance accuracy (Fig. 4). This confirms our second prediction. We also observe that as the target string length increases, the accuracy falls approximately geometrically with the length of the target string, confirming the second half of our third prediction. These results additionally demonstrate that the researcher's choice of metric has the effect that one should predict accuracy to have, i.e., geometric decay with the target length.

4 Meta-Analysis of Claimed Emergent Abilities

Analyzing the GPT family is possible because the models are publicly queryable. However, at the time of this analysis, other model families claimed to exhibit emergent abilities are not publicly queryable, nor are their generated outputs publicly available, meaning we are limited to analyzing the published results themselves [9, 38, 37]. Our alternative explanation makes two predictions.

At the 'population level" of Task-Metric-Model Family triplets, emergent abilities should appear predominantly on specific metrics , not task-model family pairs, and specifically with nonlinear and/or discontinuous metrics.

On individual Task-Metric-Model Family triplets that display an emergent ability, changing the metric to a linear and/or continuous metric should remove the emergent ability.

To test these predictions, we used claimed emergent abilities on BIG-Bench [33, 38] due to the benchmark being pertinent and publicly available.

Prediction: Emergent Abilities Should Appear with Metrics, not Task-Model Families If emergent abilities are real, one should expect task-model family pairs to show emergence for all reasonable metrics. However, if our alternative explanation is correct, we should expect emergent abilities to appear only under certain metrics. To test this, we analyzed on which metrics emergent abilities appear. To determine whether a task-metric-model family triplet exhibits a possible emergent ability, we used a metric from previous work [33]. Letting y i ∈ R denote model performance at model scales x i ∈ R , sorted such that x i < x i +1 , the emergence score is:

We found that most metrics used in BIG-Bench have zero task-model family pairs that exhibit emergent abilities: of the 39 preferred metrics in BIG-Bench, at most 5 display emergence (Fig. 5A). Many of the 5 are nonlinear and/or discontinuous, e.g., Exact String Match, Multiple Choice Grade, ROUGE-L-Sum (App. A.4). Notably, because BIG-Bench often scores models on tasks using multiple metrics, the lack of emergent abilities under other metrics suggests that emergent abilities do not appear when model outputs are scored using other metrics.

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Metric

%ofMetricswith>1 Model-TaskPair

MetricsofModel-TaskPairs

ExhibitingEmergentAbilities

ExhibitingEmergentAbilities

16.42% (11)

10.26% (4)

exact_str_match

Emergent

2.99% (2)

bleu

NotEmergent

normalized_aggregate_score

4.48%(3)

multiple_choice_grade

89.74% (35)

76.12% (51)

Because emergence score only suggests emergence, we also analyzed hand-annotated task-metricmodel family triplets [37], which revealed emergent abilities appear with 4 / 39 metrics (Fig. 5B), and 2 metrics account for > 92% of claimed emergent abilities (Fig. 5C): Multiple Choice Grade and Exact String Match. Multiple Choice Grade is discontinuous, and Exact String Match is nonlinear.

Prediction: Changing Metric Removes Emergent Abilities To test our second prediction, we focused on the LaMDA family [35] because its outputs are available through BIG-Bench. We identified tasks on which LaMDA displays emergent abilities with Multiple Choice Grade, then asked whether LaMDA still displays emergent abilities on the same tasks with a different BIG-Bench metric: Brier Score [3]. Brier Score is a strictly proper scoring rule for predictions of mutually exclusive outcomes; for a binary outcome, the Brier Score simplifies to the squared error between 1 and the model's probability mass on the outcome. LaMDA's emergent abilities on the discontinuous Multiple Choice Grade disappeared when we changed the metric to the continuous Brier Score (Fig. 6). These results support our alternative explanation that emergent abilities are induced by the chosen metric.

Published Emergent Abilities with Metric=Multiple Choice Grade

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5 Inducing Emergent Abilities in Networks on Vision Tasks

To demonstrate how emergent abilities can be induced by the researcher's choice of metric, we show how to produce emergent abilities in deep networks of various architectures: fully connected, convolutional, self-attentional. We focus on vision tasks because abrupt transitions in vision models' capabilities have not been observed to the best of our knowledge; this is one reason why emergence in large language models is considered so interesting. For the convolutional example, see App. B.

Emergent Reconstruction of CIFAR100 Natural Images by Nonlinear Autoencoders We first induce an emergent ability to reconstruct images in shallow (i.e., single hidden layer) nonlinear autoencoders trained on CIFAR100 natural images [21]. To emphasize that the sharpness of the metric is responsible for emergent abilities, and to show that sharpness extends to metrics beyond Accuracy, we intentionally define a discontinuous metric that measures a network's ability to reconstruct a dataset as the average number of test data with squared reconstruction error below cutoff c :

where I ( · ) denotes an indicator variable and ˆ x n is the autoencoder's reconstruction of x n . The autoencoder family displays smoothly decreasing squared reconstruction error as the number of bottleneck units increases (Fig. 7B). Under our newly defined Reconstruction c metric and for particular choices of c , the autoencoder family exhibits a sharp and seemingly unpredictable image reconstruction ability (Fig. 7C) that qualitatively matches published emergent abilities (Fig. 7A).

Emergent Classification of Omniglot Characters by Autoregressive Transformers We next induce emergent abilities in Transformers [36] trained to autoregressively classify Omniglot handwritten characters [22], in a setup inspired by recent work [6]: Omniglot images are embedded by convolutional layers, then sequences of embedded image-image class label pairs are fed into decoder-only transformers. We measure image classification performance on sequences of length L ∈ [1 , 5] , again via subset accuracy : 1 if all L images are classified correctly (Fig. 8B), 0 otherwise. Causal transformers display a seemingly emergent ability to correctly classify Omniglot handwritten characters (Fig. 8C) that qualitatively matches published emergent abilities (Fig. 8A).

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6 Limitations

This paper has several limitations. First, nothing in this paper should be interpreted as claiming that large language models cannot display emergent abilities; rather, our message is that some previously claimed emergent abilities appear to be mirages induced by researcher analyses. Second, our experiments and analyses are limited because some LLMs with claimed emergent abilities (e.g., PaLM 1, Gopher, Chinchilla) are private and not queryable at the time of our analysis. Lastly, the best metric(s) arguably depends on human preferences, which may exhibit qualitatively different behavior; we are unaware of studies quantifying whether human judgment is thresholded in an 'emergent" way.

7 Related Work

Srivastava et al. [33] observed that while accuracy at a particular task can empirically appear sharp and unpredictable, cross-entropy does not appear so; the authors then discussed whether emergent abilities may be partially attributed to the metric. Our paper converts their discussion into precise predictions, then quantitatively tests the predictions to reveal metric choice is possibly responsible for some claimed emergent abilities; well-known and widely-used metrics (including metrics used by [33]) capture graded improvements; emergent abilities do not appear only on tasks involving multiple steps, such as the discontinuous Multiple Choice Grade; metric choice can be used to induce emergent abilities in a novel domain (vision) in diverse architectures and tasks.

Alternative explanations exist for the origin of emergent abilities. Caballero et al. [5] explain emergence by assuming a piece-wise power law functional form; under this view, emergent abilities are real, caused by a 'break" (or possibly multiple breaks) in the governing power law. In contrast, our work suggests that emergent abilities can be induced by the researcher under a single power law. Both

explanations could be true: some emergent abilities might genuinely be abruptly appearing, whereas some emergent abilities might be attributable to the metric. Michaud et al. [28] posits that language modeling data might be comprised of discrete subtasks ('quanta') that networks learn; if larger networks have greater capacity, and are thus more capable of learning more of these quanta, then if some downstream task requires a network to learn some combination of quanta, larger networks are more likely to have all the requisite capabilities and thus are capable of performing this downstream task. We think that this is a very interesting hypothesis. Whether language modeling data can or should be understood from this quantization perspective, and whether these quanta indeed are the origin of emergent abilities, are really exciting questions that we think merit more study.

8 Discussion

Our paper presents an alternative explanation for the claimed emergent abilities of large language models. For a fixed task and a fixed model family, the researcher can choose a metric to create an emergent ability or choose a metric to ablate an emergent ability. Ergo, emergent abilities may be creations of the researcher's choices, not a fundamental property of the model family on the specific task.

Our work has several implications. Firstly, a task and a metric are distinct and meaningful choices when constructing a benchmark. Secondly, when choosing metric(s), if the goal is to accurately predict scaling behavior, then one should consider the interplay between cross-entropy, transformations, and resolution-limited evaluations so that one isn't surprised. As a corollary, continuous/linear metrics are probably better for accurate scaling forecasts, but if discontinuous/nonlinear metrics are preferred, then one may need a lot of data for sufficient resolution to accurately measure performance. The key is thinking through the consequences of one's choices! Thirdly, when making claims about capabilities of large models, including proper controls is critical. In this particular setting, emergent abilities claims are possibly infected by a failure to control for multiple comparisons. In BIG-Bench alone, there are ≥ 220 tasks, ∼ 40 metrics per task, ∼ 10 model families, for a total of ∼ 10 6 taskmetric-model family triplets, meaning the probability that no task-metric-model family triplet exhibits an emergent ability by random chance might be small. Fourthly, scientific progress can be hampered when models and their outputs are not made available for independent scientific investigation.

9 Contributions

RS conceived of the research direction collected data, ran experiments, and analyzed results. SK supervised and guided the project. BM also provided guidance. All authors helped write the manuscript.

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A Approximate Behavior of Metrics on Sequential Data

How do different metrics behave when used to measure autoregressive model outputs? Precisely answering this question is tricky and possibly analytically unsolvable, so we provide an approximate answer here.

Notationally, we consider N test data of length L (here, length is measured in tokens) with targets denoted t n def =( t n 1 , t n 2 , ...t nL ) , the autoregressive model has a true-but-unknown per-token error probability of ϵ ∈ [0 , 1] and the model outputs prediction ˆ t n def =(ˆ t n 1 , ˆ t n 2 , ... ˆ t nL ) . This assumes that the model's per-token error probability is constant, which is empirically false, but modeling the complex dependencies of errors is beyond our scope.

A.1 Per-Token Error Probability is Resolution-Limited

Note that because we have N test data, each of length L , our resolution for viewing the per-token error probability ϵ is limited by 1 /NL . Here, resolution refers to 'the smallest interval measurable by a scientific instrument; the resolving power." To explain what resolution means via an example, suppose one wants to measure a coin's probability of yielding heads. After a single coin flip, only two outcomes are possible (H, T), so the resolution-limited probability of heads is either 0 or 1 . After two coin flips, four outcomes are possible (HH, HT, TH, TT), so the resolution-limited probability of heads is now one of 0 , 0 . 5 , 1 . After F coin flips, we can only resolve the coin's probability of yielding heads up to 1 /F . Consequently, we introduce a resolution-limited notation:

A.2 Token Edit Distance

We first consider an adaptation of the Levenshtein (string edit) distance for models that function on tokens rather than characters, an adaptation we term the token edit distance . The token edit distance between two token sequences t n , ˆ t n is defined as the integer number of additions, deletions or substitutions necessary to transform t n into ˆ t n (or vice versa).

Token Edit Distance ( t n , ˆ t n ) def = Num Substitutions + Num. Additions + Num. Deletions (3)

̸

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The expected token edit distance is therefore:

The resolution-limited expected token edit distance is therefore:

From this, we see that the expected token edit distance scales approximately linearly with the resolution-limited per-token probability. The real rate is slightly higher than linear because additions

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and deletions contribute an additional non-negative cost, but modeling this requires a model of how likely the model is to overproduce or underproduce tokens, which is something we do not currently possess.

A.3 Accuracy

As with the Token Edit Distance (App. A.2), we ignore how likely the language model is to overproduce or underproduce tokens because we do not have a good model of this process. Continuing along,

Taking an approximation that would make most mathematicians cry:

(17)

This reveals that accuracy approximately falls geometrically with target token length. The resolutionlimited expected accuracy is therefore:

From this we can see that choosing a nonlinear metric like Accuracy is affected significantly more than a linear metric by limited resolution because Accuracy forces one to distinguish quantities that decay rapidly.

A.4 ROUGE-L-Sum

Another BIG-Bench metric [33] is ROUGE-L-Sum [25], a metric based on the longest common subsequence (LCS) between two sequences. Section 3.2 of [25] gives the exact definition, but the key property is that ROUGE-L-Sum measures the 'union" LCS, which means 'stitching" together LCSs across the candidate and multiple references. As explained in the original paper [25]: if the candidate sequence is c = w 1 w 2 w 3 w 4 w 5 , and if there are two reference sequences r 1 = w 1 w 2 w 6 w 7 w 8 and r 2 = w 1 w 3 w 8 w 9 w 5 , then LCS ( r 1 , c ) = w 1 w 2 and LCS ( r 2 , c ) = w 1 w 3 w 5 , then the union LCS of c, r 1 , r 2 is w 1 w 2 w 3 w 5 , with length 4. Intuitively, this disproportionately benefits models with smaller error rates because their mistakes can be 'stitched" across multiple references; this is confirmed in Monte Carlo simulation (Fig. 9).

A.5 BLEU

Yet another BIG-Bench metric [33] is BLEU [30], a metric based on shared n-grams between the generated string and reference strings. BLEU is also a discontinuous and nonlinear metric for several

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reasons. For an explanation of its discontinuity, consider bleu.compute(predictions=["hello there general"], references=[["hello there general"]]). At first glance, this might seem like it should also result in a BLEU score of 1.0 since the prediction matches the reference. However, the issue here is the absence of longer n-grams. For the unigrams, bigrams, and trigrams, the precision is 1.0 since they match perfectly. However, for the 4-grams, there are none in both the candidate and the reference. This results in a precision of 0 for the 4-grams because the BLEU score takes the geometric mean of the n-gram precisions, meaning any 0 in the set will make the entire product 0. Hence, despite the match in unigrams, bigrams, and trigrams, the absence of 4-grams results in a BLEU score of 0.0. This behavior of BLEU has been a point of criticism, as short sentences or those with fewer n-grams than the maximum considered (often 4) can yield scores that are counter-intuitive. This is confirmed in Monte Carlo simulations (Fig. 10)

B Inducing Emergent Abilities in Networks on Vision Tasks

B.1 Emergent Classification of MNIST Handwritten Digits by Convolutional Networks

We begin by inducing an emergent classification ability in a LeNet convolutional neural network family [24], trained on the MNIST handwritten digits dataset [23]. This family displays smoothly increasing test accuracy as the number of parameters increases (Fig. 11B). To emulate the accuracy metric used by emergence papers [9, 38, 33], we use subset accuracy : 1 if the network classifies K out of K (independent) test data correctly, 0 otherwise. Under this definition of accuracy, the model family displays an 'emergent" ability to correctly classify sets of MNIST digits as K increases from 1 to 5 , especially when combined with sparse sampling of model sizes (Fig. 11C). This convolutional

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family's emergent classification ability qualitatively matches published emergent abilities, e.g., at the BIG-Bench Grounded Mappings task [38] (Fig. 11A).

C Relationship Between Emergent Abilities and Grokking

Emergent abilities [4, 9, 33, 38] are sometimes compared with grokking [31, 26, 2, 11], a phenomenon whereby a single model will, over the course of learning, achieve high training accuracy and only much later achieve high test accuracy. There are several differences between grokking and emergent abilities:

Grokking is primarily studied within a single model, whereas emergent abilities are studied within a model family (i.e., multiple models).

Grokking occurs with increasing gradient steps, whereas emergent abilities occur with increasing model scale, typically measured in parameters or effective parameters (although more recently compute).

Grokking explicitly studies a discrepancy between the model's train and test behavior, whereas emergent abilities (to the best of our knowledge) do not present separate train & test curves.

Grokking is primarily studied on toy 'algorithmic" tasks in small networks, whereas emergent abilities are often studied on benchmark NLP tasks in large language models.

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors argue that purported emergent abilities of language models are mostly explained by the use of specific metrics, including non-linear or discontinuous scoring, and evaporate when linear or continuous scoring metrics are applied. The authors (1) present a toy model to explain emergence, (2) demonstrate that most abilities previously reported as emergent no longer appear emergent under an alternative metric, and then synthetically cause the appearance of emergence in an image reconstruction task.\n\nSTRENGTHS:\n- Simply and clearly addresses the enigmatic phenomenon of emergence\n\n- Formalizes and quantitatively tests the hypothesis of [1] that emergence is due in part to metric\n\n- Compelling toy model to illustrate how emergence can appear with non-linear metric (accuracy) but vanishes with linear metric (token edit distance)\n\n- Convincingly demonstrates that emergence is (at least often) a result of the metric\n\nWEAKNESSES:\n- As the authors point out in their related work, the idea that emergence appears due to the metric is not novel, and was proposed by [1], so the novelty of this paper lies in the quantitative evaluation of this hypothesis\n\n- There has been work on examining emergence and progress measures in similar contexts, e.g. grokking, which should be addressed in the related work [2–5]\n\n- There was no discussion of the relationship to alternative hypotheses. The authors mention in the related work multiple papers that suggest that abilities do, in fact, emerge with scale, but the authors should explain how their hypothesis relates\n\n- There was no discussion of the BLEU score metric, even though there are many tasks that have a very high score with this metric\n\n- Minor: a lot of the figures are small and therefore hard to read\n\n[1] Srivastava, Aarohi, et al. \"Beyond the imitation game: Quantifying and extrapolating the capabilities of language models.\" arXiv preprint arXiv:2206.04615 (2022).\n\n[2] Power, Alethea, et al. \"Grokking: Generalization beyond overfitting on small algorithmic datasets.\" arXiv preprint arXiv:2201.02177 (2022).\n\n[3] Liu, Ziming, Eric J. Michaud, and Max Tegmark. \"Omnigrok: Grokking beyond algorithmic data.\" arXiv preprint arXiv:2210.01117 (2022).\n\n[4] Nanda, Neel, et al. \"Progress measures for grokking via mechanistic interpretability.\" arXiv preprint arXiv:2301.05217 (2023).\n\n[5] Barak, Boaz, et al. \"Hidden progress in deep learning: Sgd learns parities near the computational limit.\" Advances in Neural Information Processing Systems 35 (2022): 21750-21764.\n\nQUESTIONS:\nSee weaknesses\n\nLIMITATIONS:\nThe authors adequately address the limitations.", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 4, "DATE": "2023-07-05"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper aims to debunk a possibly myth about the emergent properties of language models with regard to scale. The emergent behaviors are defined as abilities that are not demonstrated with smaller models, but emerge suddenly with an increase in the model capacity, and cannot be explained by smoothly extrapolating from the model capacity -- i.e., emergent abilities are sharp and unpredictable. The claim that the authors seek to validate is that emergent abilities are actually artifacts of the fact that the choice of evaluation metric, and that continuous metrics (instead of discrete) show smooth increases in performance with scale -- i.e., that \"emergent\" abilities are in fact smooth and predictable.\n\nSTRENGTHS:\nThis paper has many strengths:\n- First off, it is well-written. \n- The paper is timely -- large language models have only become moreso in the center of attention in the past year with abundant claims surrounding emergent abilities. \n- The claim that discrete metrics are a source of so-called \"emergence\" of new abilities is reasonable and makes intuitive sense. \n- The empirical evaluation is thorough, with evaluations of GPT-3/InstructGPT models, a meta-analysis using BigBench, and using discrete metrics to artificially induce \"emergent behavior\" in existing vision models.\n\nWEAKNESSES:\nI may have misunderstood parts of the argument, but I am not entirely convinced that emergent abilities might not be real, when it is clear that they are real with respect to discrete metrics (that often have practical interpretations). The paper seems to question the basic premise of emergent abilities, i.e., whether or not they are real. The authors cite the following definition early on -- emergent abilities are \"abilities that are not present in smaller-scale models but are present in large-scale models; thus they cannot be predicted by simply extrapolating the performance improvements on smaller-scale models,” which itself depends on an evaluation metric. Since the definition depends on an evaluation metric, why does changing the metric make emergent abilities a mirage? Shouldn't emergent abilities only hold, then, with respect to a metric? \n\nPer my understanding of this work, it seems to me that incorrect conclusions have been drawn in prior work by *only* considering discrete evaluation metrics, which is not the full picture -- pointing this out is the main contribution of this paper, and this is an important point to make. However, it still seems that these properties are real with respect to discrete metrics, and these discrete metrics are often desirable. Does this make the choice of metric bad, and emergence a mirage as a result? Or does this render prior analyses incomplete, since they do not consider metrics in which performance **does** smoothly change?\n\nQUESTIONS:\n- Why are smooth evaluation metrics necessarily desirable if they are sometimes a relaxation of the real objective, which may actually be discrete (e.g. the 0-1 loss)? \n- NOTE: please switch to the NeurIPS 2023 template, I noticed that you are using the 2022 version of the template.\n\nLIMITATIONS:\nThe authors address this.", "TITLE": "Official Review", "RECOMMENDATION": 8, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-06"}

comments: SUMMARY:
This paper shows that the widely-discussed phenomenon of "emergent abilities" in large language models is largely due to the choice of (discontinuous/nonlinear) metrics and underpowered analyses.

STRENGTHS:
- Well-written paper studying an important/commonly discussed phenomenon
- Comprehensive, well-designed, and convincing experiments + analysis

WEAKNESSES:
No major weaknesses - the paper was a pleasure to read!

QUESTIONS:
- l227: Not sure what is meant by "multiple controls" - is the implication that the community should have more aggregate / multi-metric benchmarks like BIG-Bench?
- comment: I found myself wanting to compare Fig 4 side-by-side with Fig 3 to understand the change from additional test data, but it was difficult to do so (especially with the diff y-axis scaling).

LIMITATIONS:
Yes
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 4
DATE: 2023-07-06

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper shows that the apparent suddenness with which capabilities of language models seem to emerge with scale may be an artifact of the metrics by which they are measured. Theoretically, emergence should be more gradual if the metric scales linearly with log loss on some test set. Three sources of empirical evidence are used to support this claim. First, the authors study the scaling of the GPT-3 family on arithmetic tasks and show directly that emergence is smoother when a linear metric is used. Second, they conduct a meta-analysis of BIG-Bench, and show that gradual emergence only occurs with non-linear metrics, and that the effect is reduced when switching to a linear metric. Third, they artificially induce sudden emergence by using non-linear metrics for autoencoders on CIFAR100 and for transformers on Omniglot.\n\nSTRENGTHS:\nThe basic point made by the paper is an important one that has not been fully appreciated by researchers. It is something that everyone studying scaling laws should understand and incorporate into their future work.\n\nWEAKNESSES:\nI think there are notable weaknesses in the empirical evidence given to support the basic point of the paper, and insufficient acknowledgement of the limitations of the evidence and other possibilities that could still give rise to sudden emergence.\n\nOn the empirical evidence:\n- The main direct evidence that previous claims of sudden emergence are an artifact of the metric comes from studying those previous claims directly, which is done in Section 3. However, the evidence here is somewhat inconclusive: for example for 2-digit multiplication with target str len 4 (which is presumably most 2-digit multiplications?) the jumps from 350M->1.3B->6.7B are gradual while there is a much bigger jump from 6.7B->175B. Moreover, this bigger jump is not predicted by the theoretical model. So it seems like there is still some relatively sudden emergence (even though it is reduced by using the right metric).\n- The BIG-Bench analysis is helpful, but again on logical_args it seems like there may still be an unpredictable jump. And on the other tasks, the emergence is not that sudden even with the original metric.\n- The induced emergence experiments are also helpful, but they show that sudden emergence can be induced by using a non-linear metric, not that it is always induced by a using a non-linear metric. So this evidence is more indirect.\n- Overall I think the paper would have come to more correct (and probably more nuanced) conclusions if it had studied all of the tasks from Figure 1, where sudden emergence had previously been claimed, in detail, instead of studying just one of these tasks combined with other, weaker sources of evidence.\n- Nevertheless, for an initial exploration of the topic, I think combining multiple source of evidence, even if somewhat weak, is helpful, and it is reasonable to defer a more careful analysis to future work.\n\nOn other theoretical possibilities:\n- There is no guarantee that because validation loss scales smoothly, cross-entropy loss on a specific sub-distribution must also scale smoothly. This depends on how the model allocates capacity to that sub-distribution. Therefore there is still an important theoretical possibility of sudden emergence, even with a linear metric. Indeed, this may explain why the data did not match the theoretical model in Section 3.\n- In some cases, it may not be possible to construct a linear metric. For example, for program synthesis, whether the program passes the unit tests cannot be easily converted to something like edit distance or log loss.\n- It is argued that log accuracy can be used in this case. But this is not necessarily feasible. For example, if current models pass unit tests with probability 1 in a trillion, it is not feasible to measure this accurately enough to perform any useful extrapolation. Therefore there may be sudden emergence for all practical purposes.\n\nOverall, I thought that the evidence was strong enough to support a conclusion that sudden emergence is partially explained by the choice of metric, and that researchers should prefer metrics that scale linearly with log loss when available. I also think that this conclusion is itself enough for the paper to be an important contribution. But I think the paper should take more care not to overstate its claims and acknowledge the limitations of the evidence and, space permitting, other theoretical possibilities. In particular, claims like \"metric choice is likely wholly responsible for emergent abilities\" (p. 9 line 204) are not justified and should be removed or reworded.\n\nI am recommending acceptance of this paper because of the importance of the contribution, but I think that some effort should be made to revise the paper prior to acceptance. However, I am confident in the ability of the authors to do this.\n\nSome presentation points:\n- I think it would be clearer to talk about \"sudden emergence\" and \"gradual emergence\" rather than \"emergence\" and \"no emergence\", since \"emergence\" can also be interpreted as \"appearing despite not being explicitly trained for\". However, I understand that the current terminology is taken from the existing literature and the paper cannot be blamed for this.\n- I suggest changing the title of the paper, because the current title can be misinterpreted as asking whether the _abilities_ are mirages, rather than whether the emergence (or sudden emergence as I prefer to put it) is a mirage. Any researcher who reads the abstract should not be misled, but unfortunately provocative titles that can easily be misinterpreted can be picked up on by the media and end up misleading the public. However, I acknowledge that choosing titles is hard and no title is perfect.\n\nMore minor points:\n- p. 4 line 78 - I am not familiar with this Delta notation (or I have a vague recollection of it). It is clear from the context so probably fine, but consider alternative notation/clarifying the definition.\n- p. 5 line 115 - Why choose this task from among all the tasks in Figure 1, and why 2-shot / 4-digit? (Would be even nicer to include results on other tasks/other numbers of digits, but absent that, it would be good to clarify how you chose, to make it clear it was not cherry-picked.)\n- Figure 3: Target str len 1: how do you get a 1-digit answer from multiplying two 2-digit numbers? I assume you are counting things like \"01 * 01\"? Maybe clarify.\n- Figure 3: I think it would be clearer to include titles at the top of each column saying \"Mathematical Model\", \"2-Integer 2-Digit Multiplication Task\", \"2-Integer 4-Digit Addition Task\", instead of putting this in the caption. That way people can easily see at a glance what each plot is showing, without having to dig into the caption.\n- Figure 4: Same comment.\n- Figure 5: It would be nicer to group the metrics based on their mathematical form. E.g. it is unclear what \"gender_bias_score\" is. This also might help spot if there are more examples with emergence that didn't have high emergence score.\n- Figure 5B is a bit redundant. Maybe just point out in figure 5A which of the 5 did not count as emergence. It's also a bit unclear why this didn't count despite the emergence score.\n- p. 9 line 209 - I don't think this work really contradicts broken neural scaling laws. Even if sudden emergence goes away when you change the metric, one might still be interested in forecasting the original metric.\n\nQUESTIONS:\nNo questions other than those given above\n\nLIMITATIONS:\nNo limitations other than those given above", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2023-07-24"}