SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Rylan Schaeffer
rschaef@cs.stanford.edu
Brando Miranda
brando9@cs.stanford.edu
Sanmi Koyejo
sanmi@cs.stanford.edu
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.
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:
1. Sharpness, transitioning seemingly instantaneously from not present to present
(A) Mod. arithmetic
(B) IPA transliterate
(C) Word unscramble
(D) Persian QA
(E) TruthfulQA
Figure 1: Emergent abilities of large language models. Model families display sharp and unpredictable increases in performance at specific tasks as scale increases. Source: Fig. 2 from [38].
(F) Grounded mappings
Model scale (training FLOPs)
(G) Multi-task NLU
(H) Word in context
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:
$$
\text {M u l t i p l e C h o i c e G r a d e} \stackrel {{\text {d e f}}} {{=}} \left\{ \begin{array}{l l} 1 & \text {i f h i g h e s t p r o b a b i l i t y m a s s o n c o r r e c t o p t i o n} \\ 0 & \text {o t h e r w i s e} \end{array} \right.
$$
$$
\text {E x a c t S t r i n g M a t c h} \stackrel {{\text {d e f}}} {{=}} \left\{ \begin{array}{l l} 1 & \text {i f o u t p u t s t r i n g e x a c t l y m a t c h e s t a r g e t s t r i n g} \\ 0 & \text {o t h e r w i s e} \end{array} \right.
$$
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:
Figure 2: Emergent abilities of large language models are created by the researcher's chosen metrics, not unpredictable changes in model behavior with scale. (A) Suppose the per-token cross-entropy loss decreases monotonically with model scale, e.g.,  $\mathcal{L}_{CE}$  scales as a power law. (B) The per-token probability of selecting the correct token asymptotes towards 1. (C) If the researcher scores models' outputs using a nonlinear metric such as Accuracy (which requires a sequence of tokens to all be correct), the metric choice nonlinearly scales performance, causing performance to change sharply and unpredictably in a manner that qualitatively matches published emergent abilities (inset). (D) If the researcher instead scores models' outputs using a discontinuous metric such as Multiple Choice Grade (akin to a step function), the metric choice discontinuously scales performance, again causing performance to change sharply and unpredictably. (E) Changing from a nonlinear metric to a linear metric such as Token Edit Distance, scaling shows smooth, continuous and predictable improvements, ablating the emergent ability. (F) Changing from a discontinuous metric to a continuous metric such as Brier Score again reveals smooth, continuous and predictable improvements in task performance. Consequently, the observation of "emergent abilities" can be explained by the researcher's choice of metrics, and does not require fundamental changes in model family behavior on specific tasks with scale.
1. We make, test and confirm three predictions based on our alternative hypotheses using the InstructGPT [27] / GPT-3 [4] model family.
2. 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.
3. 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  $c > 0$ ,  $\alpha < 0$  (Fig. 2A):
$$
\mathcal {L} _ {C E} (N) = \left(\frac {N}{c}\right) ^ {\alpha}
$$
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  $\hat{p}_N$  denote the  $N$ -parameter model's predicted probability distribution. The per-token cross entropy as a function of number of parameters  $N$  is:
$$
\mathcal {L} _ {C E} (N) \stackrel {\text {d e f}} {=} - \sum_ {v \in V} p (v) \log \hat {p} _ {N} (v)
$$
In practice,  $p$  is unknown, so we substitute a one-hot distribution of the observed token  $v^{*}$ :
$$
\mathcal {L} _ {C E} (N) = - \log \hat {p} _ {N} (v ^ {*})
$$
A model with  $N$  parameters then has a per-token probability of selecting the correct token (Fig. 2B):
$$
p (\text {s i n g l e t o k e n c o r r e c t}) = \exp \left(- \mathcal {L} _ {C E} (N)\right) = \exp \left(- (N / c) ^ {\alpha}\right)
$$
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<sup>1</sup>, the probability of scoring 1 is:
$$
\operatorname {A c c u r a c y} (N) \approx p _ {N} (\text {s i n g l e t o k e n c o r r e c t}) ^ {\text {n u m . o f t o k e n s}} = \exp \left(- (N / c) ^ {\alpha}\right) ^ {L}
$$
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)?
$$
\text {T o k e n E d i t D i s t a n c e} (N) \approx L \left(1 - p _ {N} (\text {s i n g l e t o k e n c o r r e c t})\right) = L \left(1 - \exp \left(- (N / c) ^ {\alpha}\right)\right)
$$
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<sup>3</sup> displays emergent abilities at integer arithmetic tasks [9, 33, 38] (Fig. 1A). We chose these tasks as they were prominently presented
<sup>1</sup>While the independence assumption is not true, the approximation yields results qualitatively matching the observed emergence claims.
2 Resolution is defined as "The smallest interval measurable by a scientific instrument; the resolving power."
<sup>3</sup>As of 2023-03-15, 4 models with 350M, 1.3B, 6.7B, 175B parameters are available via the OpenAI API.
Mathematical Model
2-Integer 2-Digit Multiplication
2-Integer 4-Digit Addition
Figure 3: Claimed emergent abilities evaporate upon changing the metric. Top: When performance is measured by a nonlinear metric (e.g., Accuracy), the InstructGPT/GPT-3 [4, 27] family's performance appears sharp and unpredictable on longer target lengths. Bottom: When performance is instead measured by a linear metric (e.g., Token Edit Distance), the family exhibits smooth, predictable performance improvements.
2-Integer 4-Digit Addition
Figure 4: Claimed emergent abilities evaporate upon using better statistics. Based on the predictable effect Accuracy has on performance, measuring performance requires high resolution. Generating additional test data increases the resolution and reveals that even on Accuracy, the InstructGPT/GPT-3 family's [4, 27] performance is above chance and improves in a smooth, continuous, predictable manner that qualitatively matches the mathematical model.
[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:
1. 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.
2. 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.
3. 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.
1. 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.
2. 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  $y_{i} \in \mathbb{R}$  denote model performance at model scales  $x_{i} \in \mathbb{R}$ , sorted such that  $x_{i} < x_{i + 1}$ , the emergence score is:
$$
\text {E m e r g e n c e S c o r e} \left(\left\{\left(x _ {n}, y _ {n}\right) \right\} _ {n = 1} ^ {N}\right) \quad \stackrel {{\text {d e f}}} {{=}} \quad \frac {\operatorname {s i g n} (\arg \max  _ {i} y _ {i} - \arg \min  _ {i} y _ {i}) (\max  _ {i} y _ {i} - \min  _ {i} y _ {i})}{\sqrt {\operatorname {M e d i a n} \left(\left\{\left(y _ {i} - y _ {i - 1}\right) ^ {2} \right\} _ {i}\right)}}
$$
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.
% of Metrics with  $>1$  Model-Task Pair Exhibiting Emergent Abilities
Metrics of Model-Task Pairs Exhibiting Emergent Abilities
Figure 5: Emergent abilities appear only for specific metrics, not task-model families. (A) Possible emergent abilities appear with at most 5 out of 39 BIG-Bench metrics. (B) Hand-annotated data by [37] reveal emergent abilities appear only under 4 preferred metrics.  $(\mathrm{C}) > 92\%$  of emergent abilities appear under one of two metrics: Multiple Choice Grade and Exact String Match.
Because emergence score only suggests emergence, we also analyzed hand-annotated task-metric model 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.
Figure 6: Changing the metric when evaluating task-model family pairs causes emergent abilities to disappear. Top: The LaMDA model family displays emergent abilities when measured under the discontinuous Multiple Choice Grade. Bottom: The LaMDA model family's emergent abilities disappear when measured under a continuous BIG-Bench metric: Brier Score.
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  $c$ :
$$
\operatorname {R e c o n s t r u c t i o n} _ {c} \left(\left\{x _ {n} \right\} _ {n = 1} ^ {N}\right) \stackrel {\text {d e f}} {=} \frac {1}{N} \sum_ {n} \mathbb {I} \left[ \left| \left| x _ {n} - \hat {x} _ {n} \right| \right| ^ {2} <   c \right], \tag {1}
$$
where  $\mathbb{I}(\cdot)$  denotes an indicator variable and  $\hat{x}_n$  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  $L \in [1,5]$ , 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).