Predicting Emergent Capabilities by Finetuning
Authors: Charlie Victor Snell
Eric Wallace
Dan Klein
Sergey Levine
Venue: COLM (2024)
Keywords: Capability Prediction, Scaling Laws, Emergence
TL;DR: We demonstrate that it is possible to predict emergent capabilities in GPT-N+1 by fine-tuning GPT-N.

Abstract: A fundamental open challenge in modern LLM scaling is the lack of understanding around emergent capabilities. In particular, language model pretraining loss is known to be highly predictable as a function of compute. However, downstream capabilities are far less predictable---sometimes even exhibiting emergent jumps---which makes it challenging to anticipate the capabilities of future models. In this work, we first pose the task of emergence prediction: given access to current LLMs that have random few-shot accuracy on a task, can we predict whether future models (GPT-N+1) will have non-trivial accuracy on that task? We then discover a simple insight for this problem: directly finetuning LLMs on a given task can shift the point in scaling at which emergence occurs towards less capable models. To operationalize this insight, we can finetune LLMs with varying amounts of data and fit a parametric function that predicts when emergence will occur (i.e., ``emergence laws''). To validate this approach, we use four standard NLP benchmarks where large-scale open-source LLMs already demonstrate emergence (MMLU, GSM8K, CommonsenseQA, and CoLA). Using only small-scale LLMs, we find that, in some cases, we are able to accurately predict whether models trained with up to 4x more compute have emerged.

Published as a conference paper at COLM 2024
Predicting Emergent Capabilities by Finetuning
Charlie Snell Eric Wallace
Dan Klein
Sergey Levine
University of California, Berkeley
Abstract
A fundamental open challenge in modern LLM scaling is the lack of un- derstanding around emergent capabilities. In particular, language model pretraining loss is known to be highly predictable However, downstream capabilities are far less predictable-sometiee even exhibiting emergent jumps-which makes it challenging to anticipate the capabilities of future models. In this work, we first pose the task of emergence prediction: given access to current LLMs that have random few- shot accuracy on task, can we predict whether future models (GPT-N+1) will have non-trivial accuracy on that task? We then discover a simple insight for this problem: directly finetuning LLMs on a given task can shift the point in scaling at which emergence occurs towards less capable models. To operationalize this insight, we can finetune LLMs with varying amounts of data and fit a parametric function that predicts when emergence will occur (i.e., "emergence laws"). To validate this approach, NLP benchmarks where large-scale open-source LLMs already demonstrate emergence (MMLU, GSM8K, CommonsenseQA. and CoLÁ). Using only small-scale LLMs, we find that, in some cases, we are able to accurately predict whether models trained with up to 4x more compute have emerged.
function of compute.
use four standard
1 Introduction
The pretraining loss for language models has been shown to follow a simple predictable power law as function of compute, model parameters, and data (Kaplan al.) 2020 Hoffmann et al.) 2022). This finding has enabled a precise empirical science to develop around the scaling behavior of LMs (Muennighoff et al.) 2023 Aghajanyan et al.) 2023
Krajewski et al. 2024), which has in turn led to much of the rapid improvement of language model capabilities in recent years (OpenAT et al. 2024 Team et al. 2023). On the other hand, the specific downstream capabilities corresponding to given pretraining loss are generally much less predictable, posing significant challenges for 1) model developers who may want to make specific model or architectural decisions on the basis of future LM capabilities: 2) policymakers who will need time to assess, plan for, and prepare for potentially dangerous future LM capabilities like deception, bio-risk, malicious software agents (Shevlane et al., 2023 Bengio et al. 2023); and 3) the ability for stakeholders to make reliable business, financial, and investment decisions on the basis of future LLM capabilities.
Of particular concern and interest is the phenomenon of emergent capabilities in large language models Wei al. (2022a). On certain downstream tasks, models may exhibit "emergence" wherein only beyond a certain, seemingly arbitrary, threshold in LM scaling (e.g. the point of emergence) do models spontaneously improve beyond random-chance, In cases where existing models have already crossed the point of emergence on given task, demonstrating smooth performance improvements (the post-emergence regime), it possi- ble to make highly accurate predictions about the performance of future models [Caballero et al. 2013 Gadre et al.] 2224 OpenAl et al. 2024 Owen| 2024). However, on tasks which all existing models demonstrate random-chance performance (the pre-emergence regime), making any kind of prediction at all about future model capabilities remains an important unsolved challenge in LM scaling. In this case, there is no known method for predicting
Corresponding author(s): csnell22@berkeley.edu
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Figure 1: On the left, we compare LLMs that are few-shot prompted or finetuned on GSM8K. Our key finding is that fineluning effectively shifls the point of emergence from stronger to weaker models. Moreover, by varying the amount of finetuning data, the emergence point is shifted accordingly. We can leverage this predict when few-shot emergence will happen by fitting parametric functions on the emergence points from finetuning and taking the limit (right figure).
at what point, if any, models will demonstrate emergence, let alone how performance will scale thereafter. To this end, we pose the problem of emergence prediction. Concretely, can accurately predict the point in scaling at which emergence will occur on given task, while only having access to pre-emergence model checkpoints?
We demonstrate an extremely simple yet highly effective solution to this problem; namely that it is possible to predict fewshot emergent capabilities in future LMs (e.g. GPT-N+1) by finetuning today's s weaker LMs (e.g. GPT-N). For example, in Figure[]left we see that finetuning models for GSMSK, rather than prompting them, systematically shifts the point of emergence on this task from stronger to weaker LMs. Moreover, by varying the amount of finetuning data, the emergence point is shifted accordingly. Motivated by this finding, we develop an emergence law; parametric function that models how the point of emergence shifts function of the size of the finetuning dataset. Using this emergence law, we can then extrapolate a prediction the point in scaling at which emergence will occur in the few-shot setting (Figure (FigureTright) right).
To validate our approach, we use four standard NLP benchmarks MMMU, GSM8K, Com- monsenseQA, and CoLA-whers large-scale open-source LMs have already demonstrated emergence. By fitting an emergence law using only small-scale, pre-emergence LLMs, we find that will occur with more capable LLMs, but also in some cases, we can do so using models trained with only 1/4th the FLOPS needed achieve emergence.
not only able to accurately predict the point in scaling at which emergence
2 Background
Emergence in Large Language Models. Emergence Wei et al. (002aa) refers to the phe- nomenon which past certain point in LM scaling models suddenly improve beyond random-chance performance on a given task. As a result, despite the fact that pretraining loss can be reliably predicted as a function of model scale, the downstream capabilities corresponding to particular loss cannot. In our work, we define the x-axis for emergence ("model scale") to be the pretraining loss, rather than the number of model parameters or the FLOPS used in pretraining Wei et al. (2022a). In line with recent works (Du et al. 2024 Gadre et al. 2024 Huang et al. 2024 Xia et al. 2023), we find that the pretraining loss is highly predictive of downstream capabilities, and thus makes for more natural and precise independent variable when studying emergence.
Emergence is a Mirage? A recent work by Schaeffer et al. (2023 claimed that the phe- nomenon of emergence observed by Wei et al. (2022a) is not due to sudden fundamental changes in the model, but rather due to the researcher's 's choice of metric. Namely, they argue that emergence is typically observed when using discontinuous metrics of accuracy, such as
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exact-match, and that using a continuous metric, such the model's correct answer proba- bility, will instead yield smooth and predictable improvements in performance. However, in many practical policy-relevant and realistic settings, the metric of primary interest may be fundamentally discontinuous. Additionally, in some cases finding metrics that yield smooth scaling behavior may be challenging (Barak) (203).. In particular, in Figure [10 we show that when using a continuous probability-based evaluation metric on two canonical language model benchmarks, namely MMLU (Hendrycks et al., 2021) and CAmmonsenseQA [Talmor et al. 2019), we still observe emergence. Theretore, additional tools are needed in order to resolve the practical challenges induced by the phenomenon of emergence.
Practical challenges with emergence. The phenomenon of emergent capabilities intro- duces significant challenges for safety preparedness, frontier model development, and business decision making with regards to language models. In particular, it is possible that future language models may demonstrate dangerous emergent capabiliiiis, such planning, deception, bio-risk, or the ability to generate malicious software (Anwar et al. 2024 Hendrycks al. 2023). Without any ability to predict when and if these capabilities will emerge, we are only left to speculate, which is highly sub-optimal given the potentially high stakes. Furthermore, model developers may need make architecture and dataset decisions on the basis of downstream capabilities which may only emerge with scale, mak- ing it challenging to do so. As a result, the inability to reason about and predict emergent capabilities in advance presents significant unsolved challenge in language model scaling,
3 Scaling Laws for Emergence Prediction
We now introduce the problem of emergence prediction, and then we describe our specific approach for predicting emergence.
3.1 Emergence Prediction
We define emergence prediction as the problem of identifying the point in scaling at which emergence will occur using only checkpoints from models that are pre-emergence (i.e., have near-random or trivial performance scale" to be the pretraining loss of a given model. We therefore aim to predict the point in the pretraining loss at which emergence will occur.
task of interest). In our case, define "model
Making an exact pointwise prediction may not always be reasonable, and indeed due to noise in both the model checkpoints and the prediction method, we may have considerable uncertainty about the exact point of emergence. To this end, we not only aim to predict single maximum likelihood point-wise estimate for when emergence will occur, but also calibrated probability distribution over all possible points at which it may occur.
3.2 Finetuning shifts the point of emergence
Our specific approach emergence prediction builds off of the observation that on tasks which exhibit emergence, finetuning models for a specific task can effectively shift the point of emergence from strong to weak models. In particular, we see that in Figure and Figure that finetuning models on MMLU, GSM8K, and Commonsensee significantly shifts the point at which emergence would typically occur in the few-shot setting towards less capable models. Furthermore, by varying the size of the finetuning dataset, the magnitude of this shift is adjusted accordingly.
To determine the extent to which a similar shift in emergence can be achieved by merely tuning the few-shot prompt, in Appendix(A.1 A.1 we conduct experiments with continuous prefix tuning (Li & Liang 2021 and with varying the number of shots in the prompt. We find that neither of these strategies are able to produce a meaningful shift in the point of emergence. On the other hand, in Appendix A.1 we find that low-rank finetuning (e.g. LoRA) (Hu et al. 2021) shifts the point of emergence to nearly the same degree as that of full parameter finetuning, suggesting that modifying model parameters may be critical for
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VILL Pinstuning on Subacts of Oasa
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Figure 2: On both MMLU and CommonsenseQA, we observe clear trend in which finetun- ing effectively shifts the point of emergence from stronger weaker models. Moreover, the size of the finetuning dataset controls the magnitude of this shift.
inducing an emergence shift. However, we leave further exploration of this phenomenon to future work.
Taken together, these results indicate that finetuning language models for specific tasks can unlock capabilities that are not inherently present in the base model itself, and thus, in a sense, weaker models can be made to simulate the capabilities of stronger models. We can then use this insight to precisely predict the exact point in scaling at which these capable models will demonstrate emergence, by extrapolating how the emergence point shifts we vary the amount of finetuning data.
3.3 Fitting Emergence Laws
To predict when emergence will occur, we can model how the point of emergence shifts function of the amount of finetuning data and then take the limit as the amount of finetuning data approaches the number of examples used in the few-shot setting. In particular, we develop an emergence lav: a simple scaling-law inspired parametric function from which we can precisely extrapolate the point in scaling at which emergence will occur in the few-shot setting. In this section, we will first describe our procedure for collecting the data to fit our emergence law, and then we will describe the specific functional form that we use.
Collecting datapoints for emergence modeling. Our emergence law takes as input two variables: the pretraining loss corresponding to a particular model and the amount of data used for finetuning it. then outputs a prediction of the performance of the finetuned task of interest. The parameters of our emergence law fit to number of empirical examples of this form obtained by finetuning different models on varying amounts of data. In order accurately model the emergence, we will therefore need sufficiently granular set of models of varying capability levels that were pretrained on the same data, and 2) a wide range of finetuning data amounts.
model
To satisfy 1), we can avoid the need to fully pretrain multiple models from scratch by instead utilizing number of evenly spaced intermediate checkpoints from single pretraining run. Similar to recent work (Du et al., 2024 Gadre et al. 2024), we find that downstream performance is highly correlated with pretraining loss, and thus using multiple intermediate checkpoints from the same training run is just effective using separate pretraining runs of varying scale.
To obtain wide range of finetuning data amounts, we take random subsets of the full finetuning dataset for a given task. Since we ultimately want to predict emergence by ex- trapolating model into the low-data limit, it is important that we focus our experiments on smaller data amounts for which we can still observe emergence with weaker models. In our case this is often on the order of few hundred finetuning examples.
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Figure 3: We plot the maximum likelihood predictions from emergence law each task. On each plot we include a subset of the finetuning datapoints used for fitting the emergence law (see Appendix A.5 for all the datapoints). The grey line represents our extrapolated prediction and the multi-color lines correspond to the fit produced by the emergence law for the various data levels. We see that across all tasks we are able to successfully predict the point of emergence within 0.1 nats and in many cases much less than that.
Modeling the point of emergence. After finetuning number of different language models on varying data amounts, we can then fit an emergence law to the results. The emergence law should effectively model how the point of emergence shifts vary the amount of finetuning data. We find that this shift is well modeled by a power-law in the logarithm of the amount of finetuning data:
E(D) k log(D)*
Where D is the number of finetuning examples. We also experimented with using power- law in data amount (e.g. without the logarithm) but found this to generally produce worse extrapolations (see Appendix A.4). To then model the actual emergence in the downstream performance, we use ReLU, where the elbow of the ReLU parameterized by E(D):
Perf(L, A max(E(D)- L, B
Here L is pretraining loss (in nats). While prior work Gadre et al. (2024) has found down- stream performance to be well modeled by an exponential in pretraining loss, we use ReLU in this work because our primary focus is on modeling the point at which emergence occurs, rather than accurately extrapolating performance after emergence. The ReLU elbow, in this case, provides clear denotation of the precise point at which emergence begins.
In addition to the results from our finetuning runs, we may also optionally want to include the fhw-shot results from our pre-emergence models when fitting the emergence law. While these few-shot results should all have near-random performance, they will still be somewhat informative for telling the model that emergence hasn't happened yet.
To effectively enable this, we add an optional additional parameter which effectively models the upwards shift in the base of the ReLU that when finetuning in Figure

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and Figure 1 We believe that this shift is likely due to the model learning trivial features from the fine-tuning data, such as the base-rate of the correct answer Our final model is:
Perf(L, D, is finetuned) A max (E(D) 0) + B A li finetuned
In total our emergence law has 5 parameters A, B, k, a, C- and an optional 6th parameter A. To obtain an maximum likelihood estimate for the point of emergence, we fit these parameters to our data, and then we take the limit under E(D) as D approaches the number of examples in our fewshot prompt. We can also obtain a probability distribution for the point of emergence by running MCMC on the posterior of the emergence law parameters.
To learn the parameters, we use mean squared error and weight the loss for each datapoint in an inverse proportion to the size of the finetuning dataset. Intuitively this ensures that the optimizer focuses on fitting the emergence more accurately in the low data limit, since this is where ultimately want to extrapolate.
Predicting Emergence
We now empirically validate the efficacy of our emergence law, on standard NLP bench- marks where large-scale open-source LLMs already demonstrate emergence. In this setting, we fit an emergence law using smaller-scale LLMs, which have random chance performance on the task, and then check the accuracy of our predictions against the true point of emer- gence observed with larger models. We are particularly interested in understanding exactly how far in advance, in terms of pretraining FLOPS, our emergence law can successfully predict the point of emergence.
Models and tasks. Since fitting our emergence law requires access number of in- termediate model checkpoints, we use the OpenLLaMA V1 models Geng & Liu (023),, for which we have checkpoints for models of three different sizes: 3B, 7B, and 13B. We also include an additional experiment with Open-LLaMA V2 in Appendix A.2 We use 4 standard NLP benchmarks MMLU U (Hendrycks al. 2021), GSMSK (Cobbe et al. 2021), CommonsenseQA (Talmor et al., 2019) (CSQA), and COLA (Wang et al. 2018 for which we observe emergence the tew-shot setting with our most capable model checkpoints. On each of these tasks, we find that all 3B model checkpoints have yet to emerge, whereas the 7B and 13B models demonstrate emergence by the end of training. We therefore only fine-tune the 3B model checkpoints for fitting our emergence law, and then make use of the 7B and 13B checkpoints for validating the accuracy of our predictions. We include additional details in Appendix A.6
Fitting the emergence law. We fit the emergence law parameters with the L-BFGS opti- mizer, following the procedure in Hoffmann al. (2022). We obtain distribution for the point of emergence by taking 100k posterior samples using the No-U-Turn Sampler (Hoff) man et al. 2014). The ground truth point of emergence is determined by fitting a ReLU to the full set of tew-shot results of all model checkpoints. We consider prediction successful the predicted emergence point of our maximum likelihood estimate falls within 0.1 nats of the true emergence point. Additional details are in Appendix A.7
Can we successfully predict emergence? In Figure we plot the maximum likelihood fit for our emergence law on all four tasks. We see that on all tasks our emergence law our predictions of when emergence will happen are overall very accurate and fall well within 0.1 nats of the true emergence point 2 In Figure 4 we additionally plot the cumulative distribution function (CDF) of our MCMC posterior estimate for the emergence point. We
For example, on GSMSK simply always guessing the most common answer in the training set achieves 2.6% accuracy the test-set.
WW note that on GSM8K three of the 3B model checkpoints that we used for fitting the emergence law are technically considered post-emergence by the ground truth. However, these points have trivial fewshot performance the task 3%, and therefore without access to the more capable models they

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Figure We plot the cumulative distribution function of our estimated posterior distribution over the point of emergence each task. The stars correspond to few-shot performance on the task and represent the true emergence curve. The point at which the slope of the CDF peaks represents the mode of the distribution. We see that across all tasks that the distribution spikes near the true point of emergence and is followed by a long tail.
see general trend in which the distribution spikes near the true emergence point, followed by somewhat long tail: our emergence law is generally confident about when emergence will occur but has some uncertainty about the possibility of emergence occurring much later.
How far in advance can we predict emergence? Now that we've demonstrated that can reliably predict when emergence will occur using our pre-emergence 3B model checkpoints, we would like to better understand exactly how far in advance, in terms of pretraining FLOPS, we successfully make such predictions. To do this can hold out additional 3B checkpoints when fitting our emergence law. In Figure 5 we plot our emergence predictions against the number of pretraining FLOPS required for training the most capable model used for emergence prediction. We find that the degree to which we can predict emergence in advance somewhat task dependent. In particular, on GSM8K and MMLU we are able to reliably make predictions well in advance of the emergence point. On CommonsenseQA and CoLA, on the other hand, we find that our ability make predictions in advance is much more limited. In particular, if we compare the minimum FLOPS from which we can make a successful emergence prediction against the FLOPS required for training the first post-emergence checkpoint, we obtain estimate for how many FLOPS in advance our emergence law can make predictions. We find that on MMLU and GSM8K we successfully predict emergence up to 4.3x and 3.9x FLOPS in advance respectively. However, on CommonsenseQAA and CoLA we are only able predict by factor of 1.9x and 2.3x in advance respectively.
would generally be considered pre-emergence. Additionally, in Figure 5 we find that even in the absence of these three checkpoints, we still able make successful predictions.
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Figure 5: On each task we hold out model checkpoints to understand how far in advance, in terms of pretraining FLOPS, we can successfully predict emergence 5 The y-axis of each blue error-bar represents the maximum number of pretraining FLOPS used for fitting the emergence law. Each blue circle represents the median of the emergence prediction posterior, and the error bar represents the range of the 5th 95th percentile predictions. If the maximum likelihood estimate for an emergence is further than 0.1 nats from the true emergence point, we consider the prediction unsuccessful and denote it by a red-cross on the plo 0 "LMs we have access to" refers the set of pre-emergence model checkpoints which we use for fitting our emergence law. "LMs we don't have access to" refers to our held-out 7B and 13B OpenLLaMA V1 checkpoints. We see that on MMLU we are able to make reasonable predictions about the point of emergence using models trained with 10 FLOPS, but not with fewer than 1022 FLOPS. The first post emergence model on MMLU was trained with ~ 5 x 10 FLOPS, hence we are able to predict 4-5x the FLOPS in advance on this task. For GSM8K, we can do the same calculation, and we see that in this case we are also able to predict emergence with up to 4x the FLOPS in advance. However, on CoLA and CommonsenseeA (CSQA) we are only able to predict emergence 2x the FLOPS in advance.
5 Limitations and Future Directions
We found that our specific approach to emergence prediction (e-g. emergence law) is able to accurately predict the point of emergence with up to 4x the FLOPS in advance, which repre- sents meaningful progress on the challenging unsolved problem of emergence prediction. However, our prediction ability falls far short of the 1000x demonstrated in OpenAl et al. (2024) for predicting post-emergence downstream capabilities. Such advance predictions may be necessary in some high-stakes settings; therefore further progress on the problem of emergence prediction is needed. Below we outline the limitations of our approach and potential future directions for improving emergence prediction.
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Better data subset selection may improve predictions. In this work, we did not specifi- cally optimize our experimental setup for maximizing the degree to which we can make predictions in advance. In particular, in Figure 5 we use the same data subsets for making predictions at all FLOPS levels. By training on more data subsets specifically chosen to be closer to the limit at which emergence with finetuning is observable, we may have been able to further improve our predictions at earlier FLOPS levels. Additionally, all of the finetuning datasets we used have no more than 10K examples in total, which we found to generally be sufficient for our experiments. However, it is possible that using larger finetuning datasets (e.g. on the order of 100K or more examples) may enable even larger shifts in the emergence point, allowing for even further advance capability prediction. We believe that these limitations in our data subset selection procedure may be the reason why on some tasks we were able to predict 4x the FLOPs in advance and on others only 2x. Though we leave further exploration of this to future work.
What methods can shift the point of emergence? In Section 3.2 we showed that targeted finetuning can systematically shift the point of emergence towards less capable models. We also experimented with alternative methods of shifting the point of emergence, finding that modifying model parameters seems to be critical for effectively shifting the point of emergence. However, our understanding of this phenomenon is limited, and future work should aim to better understand the limitations of and mechanisms by which the point of emergence can be shifted.
Predictions may not transfer in some settings. All of our experiments are conducted using series of transformer model checkpoints that were pretrained on the same corpus and that only meaningfully differ in the amount of data used for pretraining and their parameter counts. LMs with sufficiently different architectural choices (e.g. state-space models) (Tay) et al. 2022 Arora et al. 2023 Gu & Dao 2023 or trained on a different pretraining corpa may exhibit different downstream capabilities even at the same level of pretraining loss. Our emergence laws may therefore not successfully transfer to extrapolating predictions in these settings.
Task-specific finetuning is limited. Prior work Gudibande al. (2023) has shown that models finetuning models broadly on many tasks at once, often fails to sigmificanlly improve the model's capabilities. In our work, we instead focus on finetuning models for specific tasks. However, it is possible that for certain more complex capabilities of interest, models may be required to compose many different skills together. In these settings, finetuning may be less effective tool for enabling emergence prediction.
Related Work
Emergence in LLMs. A number of works Wei et al. (2022a) Suzgun al. (2022): ; Ganguli al. (2022) have observed the phenomenon of emergence in language models, wherein certain downstream capabilities suddenly appear beyond a certain model scale. However, more recent works Schaeffer et al. ) Xia et al. (2023); Hu et al. (2024) have suggested that the phenomenon of emergence may vanish when using continuous metrics, in place of discontinuous ones. The generality of this claim has since been challenged by Du et al. (2024), which shows that in some cases emergence can even occur in the presence of continuous metrics. Several works have aimed to provide explanations for why emergence occurs, attributing the phenomenon to in-context learning (Lu et al. 2024), emergent multiple-choice circuts (Lieberum et al., 2023), or the composition of multiple skills (Arora & Goyal 2023
Du
Hu et al.] 2024). Our work Is most closely related to concurrent work from Blakeney et al. (2024). which demonstrates that by up-sampling domain-specific datasets at the end of
"Our emergence prediction is in terms of loss but the quantity of interest is FLOPS. Therefore, plot pretraining loss the x-axis and pretraining FL.PP on the y-axis, since there is not standard 1-to-1 mapping between loss and FLOPS.
We do this because in some cases the failed predictions would be well off the plot and we would like to the keep the axis bounds constrained for presentation clarity.

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pretraining, downstream LM performance can be made much more predictable at low FLOP budgets, even with emergent downstream tasks. In contrast to [lakeney et al. (2024), our work instead focuses on predicting the precise point in scaling at which emergence will occur, rather than the degree of scaling thereafter.
Neural scaling laws. A number of works have studied the scaling behavior of language model pretraining loss Kaplan et al. (2020); Hoffmann et al. (2022) Aghajanyyn et al. (2023); Muennighoff et al. (2024); Henighan et al. (2020); Krajewski et al. (2024). Most related to our work are Hernandez model finetuning scales as a function of model size and linetuning data amount. However, these works critically differ from ours, in that they study performance on settings which are already smoothly improving with scale.
al. (202T) and Isik et al. (2024), which study how language
Scaling laws for downstream metrics. In addition to understanding the scaling behavior of upstream metrics, number of works have proposed methods for modeling the scaling of downstream metrics (Caballero et al., 2023 Gadre et al.) 2024: Isik et al. 2024 Owen 2024; Ruan et al., 2024 Hu et al., 2024). These works assume that the downstream metric of
interest is already showing some signs of smooth improvement as function of model scale (i.e. post-emergence). Our work instead focuses on predicting the point in scaling which capabilities will begin to emerge, given access to only pre-emergence checkpoints.
Conclusion
In this work we introduced the problem of emergence prediction; namely, identifying the point in pretraining at which performance on a given task demonstrates emergence using only pre-emergence model checkpoints. We then proposed one such approach to making emergence predictions: we fit a scaling-law inspired parametric function (e.g. an emergence- law) from which we extrapolate an emergence prediction. We finally demonstrated the predictive power of our emergence law using a set of four standard LM benchmarks: MMLU, GSMSK, CommonsenseQA, and CoLA. Using only pre-emergence checkpoints we are able to effectively predict the point of emergence using only 1/4th the FLOPS needed to reach the point of emergence on two of our four tasks. We believe that our findings represent meaningful progress towards better understanding and reasoning about emergent capabilities in large language models.
Acknowledgements
We thank Jason Wei, Kevin Liu, Jonathan Uesato, and Young Geng for discussion and feedback on earlier drafts of our paper. Charlie Snell is supported by the OpenAl Super- alignment Fellowship. This research was supported with Cloud TPUs from Google's TPU Research Cloud (TRC).
References
Rishabh Agarwal, Avi Singh, Lei M. Zhang, Bernd Bohnet, Luis Rosias, Stephanie Chan, Biao Zhang, Ankesh Anand, Zaheer Abbas, Azade Jova,John D. Co-Reyes, Eric Chu, Feryal Behbahani, Aleksandra Faust, and Hugo Larochelle. Many-shot in-context learning, 2024.
URL httpttttt///xiiii httg/abs/2404.11 11018
Armen Aghajanyan, Lili Yu, Alexis Conneau, Wei-Ning Hsu, Karen Hambardzumyan, Susan Zhang, Stephen Roller, Naman Goyal, Omer Levy, and Luke Zettlemoyer. Scaling laws for generative mixed-modas language models, 2023.
Usman Anwar, Abulhair Saparov, Javier Rando, Daniel Paleka, Miles Turpin, Peter Hase, Ekdeep Singh Lubana, Erik Jenner, Stephen Casper, Oliver Sourbut, Benjamin L. Edel- man, Zhaowei Zhang, Mario Günther, Anton Korinek, Jose Hernandez-Orallo,, Lewis Hammond, Eric Bigelow, Alexander Pan, Lauro Langosco, Tomasz Korbak, Heidi Zhang,
10

---

Published as a conference paper at COLM 2024
Ruiqi Zhong, Seán Ô hEigeartaigh, Gabriel Recchia, Giulio Corsi, Alan Chan, Markus Anderljung, Lilian Edwards, Yoshua Bengio, Danqi Chen, Samuel Albanie, Tegan Maharaj, Jakob Foerster, Florian Tramer, He He, Atoosa Kasirzadeh, Yejin Choi, and David Krueger. Foundational challenges in assuring alignment and safety of large language models, 2024. URL https: htop::://arxxv. org/ wttpxxiww.rrggbb//40/200
09932
Sanjeev Arora and Anirudh Goyal. A theory for emergence of complex skills in language models, 2023. /tlLL/ttee//aaxx.orr////aa///
15936
Simran Arora, Sabri Eyuboglu, Aman Timalsina, Isys Johnson, Michael Poli, James Zou, Atri Rudra, and Christopher Ré. Zoology: Measuring and improving recall efficient language models. arxiv preprint ar axXt::2312.0492, 2023.
Boaz Barak. or both?, 2023.
Emergent abilities and grokking Fundamental, mirage,
URL http:://winooosooteeeerr httpeeorrr..rg//233///3/
org/2023/12/2/
-nwp::ttt-bbblltiiie-a-a--rooeee -tre::ann-uuuummmmmam-nnnaraeee bbttthh 08-07-2024.
Accessed:
Yoshua Bengio, Geoffrey Hinton, Andrew Yao, Dawn Song, Pieter Abbeel, Yuval Noah Harari, Ya-Qin Zhang, Lan Xue, Shai Shalev-Shwartz, Gillian Hadfield, al. Managing ai risks in an era of rapid progress. ar arviv preprint ar arXiv:2310.17688, 2023.
Cody Blakeney, Mansheej Paul, Brett W. Larsen, Sean Owen, and Jonathan Frankle. Does your data spark joy? performance gains from domain upsampling at the end of training, 2024. URL htttpts::://// h/ap:::///rrxxvv org/ abs/2406..222..0// 03476
James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake VanderPlas, Skye Wanderman-Mine and Qiao Zhang. JAX: composable transformations of Python+NumPy programs, 2018. URL
http://github. http:/hiwbb..ooggggg///////
Ethan Caballero, Kshitij Gupta, Trina Rish, and David Krueger. Broken neural scaling laws, 2023.
Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reichiro Nakano, et al. Training verifiers to solve math word problems. aro preprint Xffo:2110.14168, 2021.
Together Computer. Redpajama-data: An open source recipe to reproduce llama training dataset, 2023.
Zhengxiao Du, Aohan Zeng, Yuxiao Dong, and lie Tang. Understanding emergent abilities of language models from the loss perspective, 2024. URL https://arxxii... http:://aaxxvv.oggabbba wwtpiii..rrr/ab/////////
15796
Samir Yitzhak Gadre, Georgios Smyrnis, Vaishaal Shankar, Suchin Gururangan, Mitchell Wortsman, Rulin Shao, Jean Mercat, Alex Fang, Jeffrey Li, Sedrick Keh, Rui Xin, Mar- ianna Nezhurina, Igor Vasiljevic, Jenia Jitsev, Alexandros G. Dimakis, Gabriel Ilharco, Shuran Song, Thomas Kollar, Yair Carmon, Achal Dave, Reinhard Heckel, Niklas Muen- nighoff, and Ludwig Schmidt, Language models scale reliably with over-training and on downstream tasks, 2024.
Deep Ganguli, Danny Hernandez, Liane Lovitt, Amanda Askell, Yuntao Bai, Anna Chen, Tom Conerly, Nova Dassarma, Dawn Drain, Nelson Elhage, Sheer El Showk, Stanislav Fort, Zac Hatfield-Dodds, Tom Henighan, Scott Johnston, Andy Jones, Nicholas Joseph, Jackson Kernian, Shauna Kravec, Ben Mann, Neel Nanda, Kamal Ndousse, Catherine Olsson, Daniela Amodei, Tom Brown, Jared Kaplan, Sam McCandlish, Christopher Olah, Dario Amodei, and Jack Clark. Predictability and surprise in large generative models. In 2022 ACM Conference on Fairness, Accountability, and Transparency, FAccT '22. ACM, June 2022. doi: 00.1155/33311463333229 URL http:/ /dxx doi org/10. 1145//311115 3533229
11

---

Published as a conference paper at COLM 2024
Xinyang Geng and Hao Liu. Openllama: An open reproduction of Ilama, May 2023. URL https://gittubb com/ cww/openlmmeeeecoommmmcc hta.rllooerearrcoopp....__ 11ama
Young Geng. Scalax: scaling utilities for jax, 2024. URL cowp:tuuu..cooooounngggg..n geng/ scalax
Albert Gu and Tri Dao. Mamba: Linear-time sequence modeling with selective state spaces. arv preprint ar arXto:2312.0075,, 2023.
Arnav Gudibande, Eric Wallace, Charlie Snell, Xinyang Geng, Hao Liu, Pieter Abbeel, Sergey Levine, and Dawn Song. The false promise of imitating proprietary llms, arxio preprint ar Xix::3355.1571,, 2023.
Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Jacob Steinhardt. Measuring massive multitask language understanding, 2021.
Dan Hendrycks, Mantas Mazeika, and Thomas Woodside. An overview of catastrophic ai risks, 2023.
12001.
Tom Henighan, Jared Kaplan, Mor Katz, Mark Chen, Christopher Hesse, Jacob Jackson, Heewoo Jun, Tom B Brown, Prafulla Dhariwal, Scott Gray, et al. Scaling laws for autore- gressive generative modeling. Xiv preprint ar arXiv:2010.14701 2020.
Danny Hernandez, Jared Kaplan, Tom Henighan, and Sam McCandlish. Scaling laws for transfer. arxiv preprint xrX1::2102.01293, 2021.
Matthew D Hoffman, Andrew Gelman, et al. The no-u-turn sampler: adaptively setting path lengths in hamiltonian monte carlo. Mach. Learn. Res., 15(1):1593-1623, 2014.
Jordan Hoffmann, Sebastian Borgeaud, Arthur Mensch, Elena Buchatskaya, Trevor Cai, Eliza Rutherford, Diego de Las Casas, Lisa Anne Hendricks, Johannes Welbl, Aidan Clark, Tom Hennigan, Eric Noland, Katie Millican, George van den Driessche, Bogdan Damoc, Aurelia Guy, Simon Osindero, Karen Simonyan, Erich Elsen, Jack W. Rae, Oriol Vinyals, and Laurent Sifre. Training compute-optimal large language models, 2022.
Edward Hu, Yelong Shen, Phillip Wallis, Zeyuan All, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen. Lora: Low-rank adaptation of large language models. arxie preprint ar Xiv::2066009683 2021.
Shengding Hu, Xin Liu, Xu Han, Xinrong Zhang, Chaoqun He, Weilin Zhao, Yankai Lin, Ning Ding, Zebin Ou, Guoyang Zeng, Zhiyuan Liu, and Maosong Sun. Predicting emergent abilities with infinite resolution evaluation, 2024. URL htttt:://///////// org/ ob322310.03262
Yuzhen Huang, Jinghan Zhang, Zifei Shan, and Junxian He. Compression represents intelligence linearly, 2024. URL httpt://axxxix......./ org/ httg//bb/2404... 09t5//9344499937777
Berivan Isik, Natalia Ponomareva, Hussein Hazimeh, Dimitris Paparas, Sergei Vassilvitskii, and Sanmi Koyejo. Scaling laws for downstream task performance of large language models. arXiv preprint ar 4rXin:2402.04177, 2024.
Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B. Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models, 2020.
Jakub Krajewski, Jan Ludziejewski, Kamil Adamczewski, Maciej Pióro, Michal Krutul, Szymon Antoniak, Kamil Ciebiera, Krystian Król, Tomasz Odrzygóćdž, Piotr Sankowski, Marek Cygan, and Sebastian Jaszczur. Scaling laws for fine-grained mixture of experts, 2024.
12

---

Published as a conference paper at COLM 2024
Raymond Li, Loubna Ben Allal, Yangtian Zi, Niklas Muennighoff, Denis Kocetkov, Cheng- hao Mou, Marc Marone, Christopher Akiki, Jia Li, Jenny Chim, Qian Liu, Evgenii Zheltonozhskii, Terry Yue Zhuo, Thomas Wang, Olivier Dehaene, Mishig Davaadorj, Joel Lamy-Poirier, João Monteiro, Oleh Shliazhko, Nicolas Gontier, Nicholas Meade, Armel Zebaze, Ming-Ho Yee, Logesh Kumar Umapathi, Jian Zhu, Benjamin Lipkin, Muh- tasham Oblokulov, Zhiruo Wang, Rudra Murthy, Jason Stillerman, Siva Sankalp Patel, Dmitry Abulkhanov, Marco Zocca, Manan Dey, Zhihan Zhang, Nour Fahmy,, Urvashí Bhattacharyya, Wenhao Yu, Swayam Singh, Sasha Luccioni, Paulo Villegas, Maxim Ku- nakov, Fedor Zhdanov, Manuel Romero, Tony Lee, Nadav Timor, Jennifer Ding, Claire Schlesinger, Hailey Schoelkopf, Jan Ebert, Tri Dao, Mayank Mishra, Alex Gu, Jennifer Robinson, Carolyn Jane Anderson, Brendan Dolan-Gavitt, Danish Contractor, Siva Reddy, Daniel Fried, Dzmitry Bahdanau, Yacine Jernite, Carlos Muñoz Ferrandis, Sean Hughes, Thomas Wolf, Arjun Guha, Leandro von Werra, and Harm de Vries, Starcoder: may the source be with you! 2023.
Xiang Lisa Li and Percy Liang. Prefix-tuning: Optimizing continuous prompts for generation. aivivv preprint arXit:2101.00199 2021.
Tom Lieberum, Matthew Rahtz, János Kramár, Neel Nanda, Geoffrey Irving, Rohin Shah, and Vladimir Mikulik. Does circuit analysis interpretability scale? evidence from multiple choice capabilities in chinchilla, 2023. URL
Sheng Lu, Irina Bigoulaeva, Rachneet Sachdeva, Harish Tayyar Madabushi, and Iryna Gurevych. Are emergent abilities in large language models just in-context learning?, 2024. URt org/ abs /209 01809
Niklas Muennighoff, Alexander M. Rush, Boaz Barak, Teven Le Scao, Aleksandra Piktus, Nouamane Tazi, Sampo Pyysalo, Thomas Wolf, and Colin Raffel. Scaling data-constrained language models, 2023.
Niklas Muennighoff, Alexander Rush, Boaz Barak, Teven Le Scao, Nouamane Tazi, Aleksan- dra Piktus, Sampo Pyysalo, Thomas Wolf, and Colin A Raffel. Scaling data-constrained language models. Advances in Neural Information Processing Systems, 36, 2024.
OpenAI, Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Floren- cia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, Red Avila, Igor Babuschkin, Suchir Balaji, Valerie Balcom, Paul Baltescu, Haiming Bao, Mohammad Bavarian, Jeff Belgum, Irwan Bello, Jake Berdine, Gabriel Bernadett-Shapiro, Christopher Berner, Lenny Bogdonoff, Oleg Boiko, Madelaine Boyd, Anna-Luisa Brak- man, Greg Brockman, Tim Brooks, Miles Brundage, Kevin Button, Trevor Cai, Rosie Campbell, Andrew Cann, Brittany Carey, Chelsea Carlson, Rory Carmichael, Brooke Chan, Che Chang, et al. GPT-4 technical report, 2024.
David Owen. How predictable is language model benchmark performance?, 2024. URL http:://aaxii..orra//////////// 04757
Guilherme Penedo, Quentin Malartic, Daniel Hesslow, Ruxandra Cojocaru, Alessandro Cappelli, Hamza Alobeidli, Baptiste Pannier, Ebtesam Almazrouei, and Julien Launay. The RefinedWeb dataset for Falcon LLM: outperforming curated corpora with web data, and web data only. Xio preprint ar XXxx:2306.01116 2023. htLphttts://arra org/ /ba/ 2306.01116
Du Phan, Neeraj Pradhan, and Martin Jankowiak. Composable effects for flexible and accelerated probabilistic programming in numpyro. arXiv preprint arXio:1912.11554, 2019.
Yangjun Ruan, Chris J. Maddison, and Tatsunori Hashimoto. Observational laws and the predictability of language model performance, 2024. htRpssss:///axx org/ abs/2405. 10938
Rylan Schaeffer, Brando Miranda, and Sanmi Koyejo. Are emergent abilities of large language models mirage?, 2023.
13

---

Published as a conference paper at COLM 2024
Toby Shevlane, Sebastian Farquhar, Ben Garfinkel, Mary Phuong, Jess Whittlestone, Jade Leung, Daniel Kokotajlo, Nahema Marchal, Markus Anderljung, Noam Kolt, et al. Model evaluation for extreme risks. arviv preprint ar (tti::305.1532222 2023.
Mirac Suzgun, Nathan Scales, Nathanael Schärli, Sebastian Gehrmann, Yi Tay, Hyung Won Chung, Aakanksha Chowdhery, Quoc V. Le, Ed H. Chi, Denny Zhou, and Jason Wei. Challenging big-bench tasks and whether chain-of-thouge can solve them, 2022. URL
httts://arxiv..rrg absgg/bss/20 2ttp://221...99920
Alon Talmor, Jonathan Herzig, Nicholas Lourie, and Jonathan Berant. Commonsensega: A
question answering challenge targeting commonsense knowledge, 2019.
Yi Tay, Mostafa Dehghani, Samira Abnar, Hyung Won Chung, William Fedus, Jinfeng Rao, Sharan Narang, Vinh Q Tran, Dani Yogatama, and Donald Metzler. Scaling laws vs model architectures: How does inductive bias influence scaling? arv preprint ar Xit:2207.10551. 2022.
Gemini Team, Rohan Anil, Sebastian Borgeaud, Yonghui Wu, Jean-Baptiste Alayrac, Ji- ahui Yu, Radu Soricut, Johan Schalkwyk, Andrew M. Dai, Anja Hauth, Katie Millican, David Silver, Slav Petrov, Melvin Johnson, Ioannis Antonoglou, Julian Schrittwieser, et al. Gemini: A family of highly capable multimodal models, 2023.
Hugo Touvron, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timothée Lacroix, Baptiste Rozière, Naman Goyal, Eric Hambro, Faisal Azhar, et al. Llama: Open and efficient foundation language models. arXiv preprint ar arXiv:2302.13971, 2023.
Alex Wang, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel Bow- man. GLUE: A multi-task benchmark and analysis platform for natural language understanding. In Proceedings of the 2018 EMNLP Workshop BlackboxNLP: Analyzing and Interpreting Neural Networks for NLP, pp. 353-355, Brussels, Belgium, November 2018. Association for Computational Linguistics. doi: 10.18653/v1/WS /1/.//1111111..66. URL https://aclanthologg. org /11//W18-4466
Jason Wei, Yi Tay, Rishi Bommasani, Colin Raffel, Barret Zoph, Sebastian Borgeaud, Dani Yo- gatama, Maarten Bosma, Denny Zhou, Donald Metzler, Ed H. Chi, Tatsunori Hashimoto, Oriol Vinyals, Percy Liang, Jeff Dean, and William Fedus. Emergent abilities of large language models, 2022a.
Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoe V Le, Denny Zhou, et al. Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems, 35:24824-248377 2022b.
Mengzhou Xia, Mikel Artetxe, Chunting Zhou, Xi Victoria Lin, Ramakanth Pasunuru, Danqi Chen, Luke Zettlemoyer, and Ves Stoyanov. Training trajectories of language models across scales, 2023. URL htt.acppp//rrrrrooor//////22//// 09803
Eric Zelikman, Yuhuai Wu, Jesse Mu, and Noah Goodman. Star: Bootstrapping reasoning with reasoning. Advances in Neural Information Processing Systems, 35:15476-15488, 2022.
A
Appendix
A.1
Alternative Methods for Shifting the Point of Emergence
We are interested in understanding other methods that can shift the point of emergence. We therefore conduct additional experiments on MMLU with 1) varying the number shots in the prompt, 2) performing continuous prefix tuning Li & Liang (2021), and 3) using low-rank finetuning with LoRA. We see in Figure 6 that both prefix tuning and using few-shots in the few-shot prompt have little effect shifting the point of emergence. On the other hand, in Figure 7 we see that low-rank finetuning shifts the point of emergence to a comparable degree to that of full finetuning, even in the rank-1 setting.
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Together these results suggest that updating the model's parameters may be necessary for shifting the point of emergence. Though further exploration of this phenomenon is needed. In particular, it is possible that using hundreds or thousands of shots in the prompt may enable more of a shift than what we observed (Agarwal et al. 2024).
For the prefix tuning baseline we use prefix length of 8, parameterized by 2-layer MLP with input and hidden-dim 512. We train with learning rate of 3e-4 and keep all other hyprpaaraeeters the same as our full finetuning experiments. We found attempts to increase the capacity of the prefix tuning (e.g. using longer prefix or dropping the MLP and directly tuning the embeddings) to make training more unstable and generally yield worse performance.
For LoRA we use the same finetuning hyper-parameters full fine-tuning, including the learning rate. To ensure that the LoRA updates are of similar magnitude to full finetuning with the same learning rate, we set the LoRA hyper-parameter be equal to the model's hidden dimension. We found this setup to yield the best results with minimal changes between our full finetuning and LoRA setup.
MKLW Full Finetuning Versus Prefix Turning
MMLU 5-shot Versus O-shot Tuning
Pul Rietunng
55-
Freéx Tining
Promotil
S-hho
45
Accurazy
35-
30-
2.4
2.3
22
23
2.2
2.0
3.0
2.7
2.4
23
22
23.
2.0
1.0
2.5
Pretrsining Loss
Pretraining Loss
Figure 6: One the left we compare full fine-tuning against continuous prefix tuning on MMLU. We find that prefix tuning provides effectively no shift to the point of emergence, despite improving the performance of post-emergence models. On the right we compare 0-shot verses 5-shot prompting on MMLU. We see that using fewer shots has no meaningful effect on the point of emergence. Together these results suggest that the ability for prompt tuning to shift the point of emergence is very limited.
Figure 7: Comparing LoRA finetuning, with rank 2, 4, and 64 against full finetuning on MMLU. We see that LoRA finetuning even with rank 1 shifts the point of emergence to comparable degree to that of full finetuning.
A.2 Using Emergence Prediction Cheaply Make Modeling Decisions
One use case for emergence prediction is to enable model developers to cheaply make modeling decisions on the basis of a model's downstream capabilities. Without emergence prediction, making such decisions may be extremely costly, requiring model developers to train large models before seeing any signal. As we found in Section our emergence law can enable us to up to 4x less compute when running such experiments.
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MMLU Accuracy Eval
CSQA Accuracy vs Eval Loss
OpenLLaMA V1
OpenLL V1
OpenLL
40.0
Random
Random
MMU Accuray (90)
37.5
CSQA CSQA Accuracy (86)
40
35.0
35
32.5
30.0
25
27.5
25.0
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.7
2.6
2.5
2.4
2.3
2.2
2.1
C4 Eval
C4 Eval Loss
Figure 8: Comparing the point of emergence for few-shot prompted OpenLLaMA V1 and V2 models as function C4 validation loss. We see that on both MMLU and Commonsense@A,, the point of emergence differs between the two model series, with V2 emerging earlier than V1 in both cases, suggesting that the pretraining copus used for training the V2 models is likely of higher quality than that used for the V1 models.
Determining data quality with emergence prediction. As a proof of concept of how emergence prediction can be to make modeling decisions, we use emergence prediction to help us determine which two different pretraining corpa downstream tasks, using only pre-emergence models. To do this, extend our experiments with the LaeLLaMM V1 models in Section by also conducting emergence prediction on the LaMA V2 models (Geng & Liu 2023) on MMLU, which different corpus from the V1 models. Since, the two model series (V1 and V2) were trained on different corpa, should expect them to have different emergence points as a function of loss. We might therefore expect the corpus which shows emergence earlier in pre-training to be the superior dataset for the task hand. In this way, we can use emergence prediction to help us more cheaply make decisions about pretraining data.
higher quality for
pretrained on
Comparing V1 and V2 corpa. Specifically, the V1 models were trained on the RedPa- jama (Computer) 2023) dataset, whereas the V2 models were trained on custom mixture of the Falcon Relined-web (Penedo et al. 2023) dataset, the StarCoder (Li et al. 2023) dataset, and the RedPajama [Computer (203) dataset. The V2 models also used a different tokenizer, which was trained on its corresponding pretraining dataset. Most other hyperparameters between the two series of models remain the same.
Since the two model series were pre-trained on different corpa, their respective pretraining losses are not strictly comparable, making the point of emergence in terms of these different x-axes largely uninformative for deciding which dataset is better. In order to enable an informative comparison between the point of emergence for models trained on different corpa, we use loss on standardized held out corpus as the x-axis. Specifically, we use loss on the C4 validation set. In Figure g we plot fewshot performance as function validation loss for the V1 and V2 models on MMLU and CSQA. We see that indeed the point of emergence differs between the two model series. On both benchmarks the V2 data seems to be superior, in that emergence occurs earlier, enabling greater performance earlier in pretraining.
Prediction results. We now use our emergence law methodology to predict the point of emergence for both model series using only pre-emergence checkpoints. Similar, to the V1 series, the 3B checkpoints in the V2 series are all pre-emergence. Therefore, just as we did in Section hold out the larger models and only use finetune our 3B model checkpoints for fitting our emergence law. For both model series we use the same finetuning datasubsets for fitting the emergence law (see Appendix A.6). We see in Figure that indeed our emergence
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MMLU Predicting Emergence
MMLU Cumuietive
62.5
Fansnci Pesteraace
Prodicted Emergence
Tue Orergence Pont
Erne gance
10.0
Drispone Prssciin
Fou shot marforancee
OpeniLaMA V.
OpeniLaHi V3
OpeRiLLMA 92
OpeniLLMÁ V2
20.2
12.5
38.5
21.4
26
500
27 24
23
Evai Loss
C4 Evall Loss
Figure 9: Comparing emergence predictions for OpenLLaMA V1 verses V2 on MMLU function of C4 validation loss. We plot the maximum likelihood predictions on the left and the CDFs the right. Our emergence law predicts that the V2 models will emerge before the V1 models, suggesting that the V2 data may be of higher quality. This result provides proof of concept demonstration for the utility of emergence prediction for enabling model developers to more cheaply make decisions on the basis of downstream capabilities.
Sentin Giraler
Figure 10: On standard 5-shot MMLU and 6-shot Commonsense (CSQA) evaluation, we observe emergence using both the standard correct answer accuracy evaluation and continuous LMM bog-probability metric.
law predicts that OpenLLaMA V2 will emerge before OpenLLaMA V1, informing us that the V2 pretraining data may be of higher quality.
This experiment demonstrates the utility of emergence prediction for enabling model devel- opers to more cheaply make modeling decisions on the basis of downstream performance. According to Section we can potentially save up to 4x the pretraining compute by using emergence laws to more cheaply make decisions. While our emergence law does not nec- essarily tell us how performance will scale after the point of emergence, simply knowing that emergence will occur earlier may be sufficient signal for making decisions in many settings. Future work should also build on our findings enable ad- ditional post-emergence predictions (e.g. the rate of improvement post-emergence) from pre-emergence model checkpoints.
A.3 Emergence with Continuous Metrics
In Figure 10 present two LM tasks (MMLU and CommonsenseQA) in which observe emergence with both continuous and discontinuous metrics.
A.4 Comparing Emergence Law Functional Forms
In Table we compare the prediction accuracy of several different emergence law functional forms. We that power-law in the log of the data makes better predictions than power- law without the log. Additionally, we see that removing the optional few-shot term has little effect on prediction quality, and therefore consider this term to be optional.
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Funchional Form
GSMSKK
MMEU
CSQJ
CoLA
Log power law
0.022 10.004, 0.170]
0.041
[0.011, 0.055]
0.003 [0.001, 0.045]
0.064 [0.030, 0.121
Power law
[0.004, 0.149]
0.046
[0.002, 0.113]
0.127 (0.102, 0.165]
0.127 [0.094, 0.179]
No few shot
0.030 [0.004, 0.141]
0.060 [0.059, 0.061]
0.004 (0.001, 0.073]
0.064 [0.030, 0.120]
Table 1: Comparing the prediction error between different emergence law functional forms. "log power law" is the full emergence law, including the optional few-shot term, presented in Section 3.3 The "power law" law differs from "log power law" in that models the shift in the emergence point using power law in the data rather than in the log of the data. Finally, "no few shot" represents removing the extra few-shot term from the "log power law" emergence law. We present the absolute error between the maximum likelihood predicted point of emergence and the ground truth. In brackets we include the 5th and 95th percentile of prediction errors produced by our MCMC posterior sampling. We see that removing the log generally results in much worse predictions, suggesting that a power-law in the log of the data more natural model. We also that the additional few-shot term has relatively little effect on our prediction quality, and therefore it should be considered optional.
GSNIK Emernrrce Preditionn
CSQA Emergenre Fredictio
Nottked Encoppice
10
35.
910
106
Retmaannn Lost
Emergance dE
CoLA Emerggence Prodiction
Fretaed
0.00
The Coapence
Tra Energance hoir
5.50
36
23
2.5 244 2. 10.0
Figure 11: We plot the maximum likelihood predictions from our emergence law on each task. These plots include results from every finetuning run used for fitting the emergence law. The grey line represents our extrapolated prediction and the multi-color lines correspond to the fit produced by the emergence law for the various data levels. We see that across all tasks we are able to successfully predict the point of emergence within 0.1 nats and in many cases much less than that.
A.5 Full Emergence Prediction Plots
In Figure 11 we plot all of the data for our maximum likelihood emergence predictions from Section
A.6 Additional Experiment Details
To select the set of finetuning data subsets used for fitting our emergence law, first conduct a logarithmic sweep over various data amounts and then collect additional subsets nearer to the limit at which emergence is visible with our 3B checkpoints. To account for
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noise in the data sub-sampling process, we finetune two different sampled subsets for each data subset level.
For each task perform full parameter finetuning using the AdamW optimizer. We use 0.05 dropout, 0.01 weight decay, Adam L = 0.9, f2 = 0.95, and learning rate schedule with linear warmup followed by constant learning rate. On all experiments, we hold our 10% of our training data for validation. For each task we perform a small sweep over learning rate, batch size, and the number of learning-rate warm-up steps, selecting the best setting that produces the best validation loss. We perform early stopping according to validation loss on all tasks except on CoLA, which we describe in more detail below. For all of our experiments, except those in Appendix A.2 we use the OpenLLaMA VI (Geng & Liu 2023
models that were pretrained on 1T tokens from the Red-pajama dataset [Computer 2023).
In Appendix [.2] we also use the OpenLLaMM, V2 models which were pretrained on different corpus, also for 1T tokens. Below we include more details on our experiments for each task.
MMLU. For predicting emergence on MMLU we use 6 intermediate 3B model checkpoints pretrained for 42B, 210B, 419B, 629B, and 1T tokens. We train on the MMLU test set and then evaluate on the validation set. In addition to the full data, we train each checkpoint on two
1 3 different randomly sampled dataset subsets of each fraction: 2, 8 I5. To and 3 We use learning rate 5e-6, batch size 256, and 24 learning-rate warmup steps. We use the standard 5-shot LM evaluation harness (Touvron al. 2023) prompt for our few-shot results. We use these same settings for our experiments with OpeALLaMA V2 in Appendix A.2
For predicting emergence on GSM8K we use 8 intermediate 3B model check- points pretrained for 21B, 31B, 42B, 210B, 419B, 629B, and 1T tokens. We train and test on the standard splits. On this task our models are trained to output a chain-of-thought followed by an answer. In addition the full data, we train each checkpoint on two different randomly
GSM8K.
1 sampled dataset subsets of each fraction: 1, 1 8 T6 32, and & We use learning rate of 1e-5, batch size of 32, and no learning-ran warmup steps. For our prompted evaluation, we use the 6-shot chain-of-thouu tottuughttthhtthtth prompt from Zelikman et al. (0022).
CommonsenseQA. For predicting emergence on Commonsense@AA A we use 9 intermediate 3B model checkpoints pretrained for 10B, 21B, 31B, 42B, 210B, 419B, 629B, and 1T tokens. We train on the standard train set and evaluate on the validation set. In addition to the full data, we train each checkpoint
two different randomly sampled dataset subsets of each
3 3 and 3 We use a learning rate of 5e-6, a batch size of 64, and 4/ 8' 16 32 64 32, 96 learning-rate warmup steps. For our prompted evaluation we use the 7-shot prompt from Wei et al. (2022b) with the chain of thought examples stripped from the prompt, just showing the final answer.
fraction: 1 1
16
CoLA. For predicting emergence on CoLA we use 9 intermediate 3B model checkpoints pretrained for 10B, 21B,31 31B, 42B, 210B, 419B, 629B, and 1T tokens. We train on the standard train set and evaluate on the validation set. In addition to the full data, we train each checkpoint on two different randomly sampled dataset subsets of each fraction: 3, / I B To 32, 64, 128 64, 128, and 256 We use a learning rate of 5e-6, batch size of 256, and 48 learning-ratt warmup steps. For our prompted evaluation we use the standard 5-shot prompt in the LM evaluation harness (Touvron et al., 2023). On CoLA we deviate slightly from our realy stopping procedure. We find that for some of the smaller data subsets, downstream validation performance continues to improve after overfitting. In these cases we perform early stopping according to the downstream MCC evaluation on the validation set rather than the validation loss.
1
3 3
3
All finetuning experiments were done on TPU-V3 pods using JAX (Bradbury et al. 2018 and Scalax (Geng 2024) for distributed training.
19

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Published as a conference paper at COLM 2024
A.7 Emergence Law Fitting
For obtaining our maximum-likelihodd fits we follow the procedure in Hoffmann et al. (2022) and use the L-BFGS optimizer, selecting the best fit from sweep over initial- izations. In particular, we first perform a brute-force grid-search over all the values in: .0. 4.0,, B E {0.0, 0.2, ..., ..0,,.,,,..1 1.0], k {0.0, 0.05, 0.1, 1.0), a e (1,0, 10.0), grid-search with the lowest loss and then run the L-BFGS optimizer initialized from each one. We then select the best fit final fit out of each of these. We fit the ReLU for the true emergence point using the same procedure.
(0.0,0.5, 1.0, ..., 10.0}. We select the 100K parameters from this
For posterior sampling, we use the No-U-Turn Sampler Hoffman et al. 2014 implemented in Numpyro (Phan et al. 2019). We use chains with 25k samples each and 15k warmup steps each, totaling 100k samples. We initialize each chain using the parameters maximum likelihood parameters found using the procedure described above. We find that without tun- ing the temperature of the energy function the sampler is extremely unstable, demonstrating wildly out-of-distribution posterior samples. To control this we sweep over temperature values 1e-3, le-4, le-5, 1e-6, 1e-7, 1e-8, le-9 and select the lowest such temperature for which the mode of the sampled distribution is centered around the maximum likelihood estimate.
20


Reviews:
[{"review_id": "5tgDeefNn6", "reviewer": "Reviewer_GYaM", "summary": "The paper presents a method to predict emergent capabilities in language models by finetuning on specific tasks. Using an \"emergence law\" to model shifts in performance based on finetuning data, the authors successfully predict task emergence on NLP benchmarks with high accuracy, often using significantly fewer computational resources. The study offers a valuable tool for anticipating future AI capabilities and outlines areas for further research to enhance prediction methods.", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We address one of the main concerns about the generalizability of our findings by running additional experiments on the extremely challenging GPQA and APPS benchmarks, using the LLaMA 2 models (7B/13B/70B).\n\nIn this setting we observe emergence with finetuned LLaMA 2 but random performance with few-shot. After additional finetuning experiments (on-going), we will fit an emergence law to the data and make a prediction about the point in scaling at which emergence would have occurred on these tasks with a hypothetical more capable LLaMA 2 model. See attached figures for [GPQA](https://imgur.com/a/nwa7FFi) and [APPS](https://imgur.com/a/2tqLHKm).\n\n> The paper falls...\n\nIn our work we propose a challenging new problem of emergence prediction and introduce an initial approach to solving it, which makes surprisingly good predictions. However, future work can improve our results further, by refining our methodology or using new approaches for prediction. We discuss this Section 5, but will include additional discussion.\n\n> The testing...\n\nWe focused on the OpenLLaMA-V1 series for the reasons outlined in Section 4, and we expect our findings to transfer to other models. To test this, we have experiments on LLaMA 2, as described above. We also will include additional experiments with OpenLLaMA-V2.\n\n> The task...\n\nIn the paper, we define the general task of emergence prediction and its importance (Section 2/3). We then outline one particular approach to solving this problem, which relies on the observation that finetuning shifts the point of emergence towards less capable models (Sections 3/4). These are two separate but related contributions. We will clarify this further.\n\n> The paper fails...\n\nAs discussed in 3.3, our goal with using a ReLU is to clearly model the point of emergence, rather than to accurately model performance after the point of emergence. In the latter case, alternative functional forms can be used ([1]). To model how the point of emergence shifts as a function of data, we use a power-law, which is commonly used in scaling laws ([2]).\n\nIn A.2, we include ablations of variants of our functional form, giving empirical support for our decisions.\n\n[1]: https://arxiv.org/pdf/2403.08540\n[2]: https://arxiv.org/pdf/2203.15556\n\n> The paper lacks...\n\nThanks for catching this! L is the pretraining loss and D the data amount. We will ensure this is clear in the final.\n\nThanks for the comments! Please let us know if you have any additional thoughts.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "- The phenomenon primarily investigated in the paper—namely, the observation that directly fine-tuning LLMs on a given task can shift the point in scaling at which emergence occurs towards less capable models—is intriguing and is supported by detailed experimental analysis.\n- Explored various methods for shifting the point of emergence and provided corresponding analyses.\n- Consideration of the impact of uncertainty is commendable, and the experimental results are highly reliable.", "reasons_to_reject": "- The paper falls short in providing a thorough explanation for its subpar performance on tasks such as CommonsenseQA and CoLA, failing to convincingly demonstrate the emergence law's robustness regarding these tasks.\n- The testing was limited to models within the Open-LLaMA V1 series, without indicating whether the emergence law is applicable to models of other architectures.\n- The task of emergence prediction and the phenomenon primarily studied by the authors, that directly fine-tuning LLMs on a given task can shift the point in scaling at which emergence occurs towards less capable models, do not have a direct relationship, considering that the former does not involve fine-tuning. The paper lacks an explanation of the connection between these two.\n- The paper fails to provide an explanation for why the emergence law curve takes a linear form.\n- The paper lacks clear elucidation regarding the meanings of variables in crucial formulas. For instance, in the formula Perf(L, D) = A ∗ max(L − E(D), 0) + B, the roles of L and D are not explicitly defined.", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "4SpiyrWmdf", "reviewer": "Reviewer_4TG4", "summary": "This paper proposes a model to predict when emergence will occur in LLMs. The idea is as follows. Pretraining loss scales predictably via an inverse power law with the amount of data, compute, or parameters. However, as training loss decreases, at a certain point there is a sharp uptick (popularly termed 'emergence') in performance on certain tasks. The argument of the paper is that rather than the training loss decreasing due to more parameters, compute, or large amounts of data, the decrease in training loss associated with e.g. larger models can be simulated by fine-tuning on the given dataset. The paper proposes a model to predict when the emergence 'elbow' will occur as a function of amount of finetuning data. The paper then takes a series of models and datasets, and fits parameters for their model. It is argued that their model fits the data very well.", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We will clarify/simplify Figure 5. While many of the reviewer’s questions are addressed in the paper, we will clarify these further with additional discussion in the final.\n\n> I may…\n\nAs outlined in Sections 1/2, we believe the utility is twofold:\n\n1) Predicting future capabilities in language models is important for safety preparedness.\n2) To make modeling decisions based on downstream capabilities, one will need to spend much compute to see non-trivial performance, making iterating expensive/slow. We can accelerate this with predictions.\n\n> As the…\n\nYes! In this work, we define the problem of emergence prediction and propose a particular approach, but there are many future directions (see Section 5).\n\n> In the…\n\nYes, data amount. We will clarify this.\n\n> The phrase…\n\nDetails about the prompts are in A.4; to answer: GSM8K=6-shot, MMLU=5-shot, CSQA=7-shot, CoLA=5-shot.\n\n> In Fig 3…\n\nFor the final we will include plots with/without all data for completeness/clarity.\n\n> The emergence…\n\nOn points corresponding to the larger data amounts, our fit may be imperfect. As explained in 3.3, we weigh the fit by the inverse data amount, to prioritize fitting in the low data limit. Our focus is on predicting the point of emergence in the limit, and our procedure is designed for this.\n\n> Related…\n\nWe do this throughout. The stars in Figure 3 correspond to all models (3/7/13B), but the finetuned circles correspond only to 3B. We will clarify this.\n\n> Similarly…\n\nFigure 5 demonstrates how early we can to predict. In practice, we care about how early in FLOPs. In general, there is not a 1-to-1 mapping between loss/FLOPs. We therefore denote the loss/FLOPs for the models with stars.\n\nThe “models we don’t have access to”, we do have access to (these are 7/13B models), we just don’t use them for fitting (only 3B). They are included for clarity.\n\nYes, the failed predictions would often be off the plot. The models corresponding to some X’s are off the plot. We constrained the plot bounds for clarity. We will clarify/simplify this.\n\nTo answer “Why is True Emergence only one line?”\n\nThere is a single point of emergence with the OpenLLaMA-V1 series. With a different series, emergence will change (see attached for [MMLU](https://imgur.com/a/P3tyuk4) and [CSQA](https://imgur.com/a/FWKYkla)). We discuss this in Section 2; this is also covered in concurrent work ([1](https://arxiv.org/pdf/2403.15796)).\n\nThank you for the comments! Let us know if there's anything else we can clarify.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "- The topic of how and when emergence occurs in models is important", "reasons_to_reject": "- I am not clear what the proposed model really tells us about how and when emergence occurs\n- I was unclear about some of the notation and claims (details below)", "questions_to_authors": "I may be missing something here, but I didn't understand how the model is useful. I can see that it is interesting to have a model of how and when emergence occurs. However, finetuning is used as a proxy for e.g. using more parameters, and the model a function of the amount of fine-tuning data (I think). So what does this tell us? Can it tell us how to predict emergence points as models grow in size or with the use of more training data? \n\nAs the emergence point depends on different facets, could the model be extended to depend on more than one variable?\n\nIn the first equation on p.5, the quantity D is used but not explained (I guess it is the amount of fine-tuning data). \n\nThe phrase 'taking the limit ... as D approaches the number of examples in our fewshot prompt' occurs on p6. It would be really helpful to write down what the sizes of D and the few-shot prompt are.\n\nIn Fig 3 there are so many prediction lines that it is not really clear whether the predicted emergence points are realistic. Might be better to have fewer at the low data fractions, say 4 in total.\n\nThe emergence points for GSM8K seem bad, looks to me like emergence happens at around 2.2 for all amounts of data. Emergence points also look early for MMLU. This is because the RELU puts baseline performance too low, should be around 4% accuracy for data fraction 1 for GSM8K, for example, rather than 2.\n\nRelated to my first question: the model is fitted using checkpoints from OpenLlama-3B. Then, the paper states that they \"then make us of the 7B and 13B checkpoints for validating the accuracy of their predictions\". I couldn't see where the paper did this though.\n\nSimilarly figure 5 was hard to interpret. I understand the LMs we don't have access to are those that are trained for longer. There aren't any predictions for these points though - why are they on the plots? Why is True Emergence only one line? It looks like this corresponds to the emergence loss values in Fig 3 for each dataset, but surely the emergence loss value is going to be different for different models. Why are the failed predictions all on the True Emergence line rather than being placed at their actual locations? (I guess the x value is too far off the plot?) Why do some of the failed predictions have no corresponding LM? I also don't see how to read from the plots the reported fact that 'on MMLU and GSM8K we are able to predict emergence with up to 4x the FLOPS in advance of the emergence point'. It would be good to give a bit more guidance on how to read this. I apologise if these questions are all very basic, but I feel like the plot could be explained better.\n\nMinor questions/typos:\n- Please number equations\n- Please make sure all your terms are defined.", "extra_scores": {}}, {"review_id": "u9SkxcSK9h", "reviewer": "Reviewer_8WHU", "summary": "This paper proposed a new approach by fine-tuning LLMs for making predictions of the so-called emergent abilities. They proposed using a parametric function to predict when emergence will occur, or \"emergence laws,\" and tested it on four NLP benchmarks where emergence has been observed. Results showed that with small-scale LLMs, they could predict emergence of models trained with more compute than the smaller models.", "questions": "", "limitations": "", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "There may be a misunderstanding about  the role of finetuning in our paper. The goal of emergence prediction is to make predictions about the point in pretraining at which emergence in the few-shot setting will occur. In Section 3.1 we clearly describe this setting:\n\n > We define emergence prediction as the problem of identifying the point in scaling at which emergence will occur using only checkpoints from models that are pre-emergence (i.e., have near-random or trivial performance on a task of interest). In our case, we define “model scale” to be the pretraining loss of a given model. We therefore aim to predict the point in the pretraining loss at which emergence will occur.\n\nThe specific approach to emergence prediction that we propose in the paper utilizes finetuning as a tool to make such predictions. The method is not, however, designed to make predictions about finetuning performance.\n\nWhile we do explain this throughout the paper --- in the abstract, introduction, and in Section 3 --- such confusion is understandable and we will make sure that this is extremely clear in the camera ready version of the paper.\n\n> The evaluation…\n\nThe tasks we selected were not selected due to their popularity and this has not impacted our analysis in any way; they could have been any tasks. As described in Section 4, we selected a diverse set of LM tasks on which larger, more capable models demonstrate emergence but not smaller, less capable models.\n\nTo further test the generalizability of our findings with other models/architectures, we have additional finetuning experiments on the extremely challenging GPQA and APPS Interview benchmarks, using the LLaMA 2 base models (7B/13B/70B).\n\nIn this setting we observe emergence with the finetuned LLaMA 2 models but random performance with all the few-shot models. With additional finetuning experiments (on-going), we will be able to fit an emergence law to the data and make a prediction about the point in scaling at which emergence would have occurred on these tasks with a hypothetical more capable model in the LLaMA 2 series. See attached figures for our current experiments with [GPQA](https://imgur.com/a/nwa7FFi) and [APPS](https://imgur.com/a/2tqLHKm).\n\nIn addition to the LLaMA 2 experiments, we plan to add additional experiments with OpenLLaMA V2.\n\n> Background…\n\nThanks! We will take this into account when preparing the camera ready.\n\nThank you for your comments! Let us know if we can further clarify anything.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "(1) An interesting extension to scaling law;", "reasons_to_reject": "(1) About the motivation. Generally, I think it is less interesting to see that this work has been done based on fine-tuning data. For LLMs, it is generally useful to predict model performance during the pre-training preriod (especially the beginning) but not the fine-tuning stage. It is very challenging to make accurate prediction on task performance given limited pretraining tokens. Specially, for LLMs, it would be very strange to fine-tune it according some specific task, because it is expected to generalize on donwstream tasks. \n\n(2) The evaluation sets. Currently, the examined tasks are widely studied or compared. It is not clear whether the approaches can generalize to more scenarios or tasks, especially difficult tasks. \n\n(3) Background and related work seem to be overlapping. I suggest you merge these two parts.", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "u4IwrFzgij", "reviewer": "Reviewer_Fqr2", "summary": "A central question for the field, given prior work, is whether we can predict emergent capabilities. This paper present a method that shows some success: if the emergent abilities are to be elicited via prompting models, then essentially the point of emergence can be shifted to the left via finetuning models, meaning emergence (when prompting) can be predicted using models of much less compute.\n\n1. The core idea is simple but deft. While it would be easy to dismiss the idea as quite straightforward, I see it as a a nice balance between simplicity (a good quality) and ingenuity (a good quality). \n2. The predictive accuracy of the method for \"emergence prediction\" seems reasonable. Of course, there is nothing too convincing this is the best method or so on, but that seems fine: given this work, other papers can refine the specifics on how to best do this going forward. \n3. The scale improvement of the method (i.e. how far can you shift left) seems reasonable. Similarly could be improved.", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank reviewer Fqr225 for their detailed and well thought out comments on our work! We are glad that they agree that the problem of emergence prediction is highly important, and that they think our method strikes a good balance between simplicity and ingenuity.\n\nWe answer the reviewer’s questions below:\n\n> You differentiate methods...\n\nYes, this is indeed a fascinating line of reasoning! From the experiments we've tried so far it seems that updating the model's parameters is critical for shifting the emergence point (e.g. prefix tuning does not effect the emergence point, neither does modifying the prompt).\n\nFor the camera ready, we will include some additional discussion about the potential for future work to investigate new methods which can more effectively shift the emergence point.\n\n> You identify two axes experimentally...\n\nYes this is a good suggestion. For the camera ready, we will include ablations where we hold out finetuning runs with larger / smaller amounts of data, so as to understand empirically how this influences the accuracy of our emergence predictions.\n\nPlease let us know if you have any additional comments or questions, as we believe that your feedback will help us improve the paper!", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "1. Good idea, which if it works more generically, would be a useful insight for solving a real problem of significant scientific and societal interest (i.e. \"can we predict, in advances, whether we will see emergent capabilities\")\n2. Results/experiments are generally interesting, reasonably executed, and provide some insight.\n3. Method seems like a fine starting point, though not especially remarkable.", "reasons_to_reject": "No major reasons to reject. I definitely don't think the paper is without flaws, but none feel so damning that I feel the need to proactively make the arguments against the paper.", "questions_to_authors": "1. You differentiate methods like prefix tuning from LoRA/full fine-tuning in terms of the successfulness of the left shift. Can you characterize some key properties that amount to this (e.g. is there some key property you need for this to work)? Since, if you could, this would then lead to a next question of how we search over methods with this property to identify the best method for maximizing the extent to which the emergence point gets left shited.\n2. You identify two axes experimentally: the amount the point shifts to the left and the predictive accuracy. Can you characterize the relationship between these, either empirically or theoretically in some toy model? (Basically thinking about interplay between final 2 paragraphs of page 7).", "extra_scores": {}}]

Author rebuttal:

Meta-review: The paper proposes a novel approach to predict emergent capabilities in language models by utilizing fine-tuning on specific tasks, thereby anticipating the emergence of performance improvements in models with fewer computational resources. This research addresses a significant challenge in AI and presents valuable insights, supported by extensive experimental analysis. While the methodology demonstrates promising predictive accuracy, particularly in shifting the point of emergence, the paper could benefit from clearer explanations of certain variables and further validation across diverse model architectures and tasks. The reviewers appreciated the innovative approach and potential impact but highlighted areas for clarification and further validation. Overall, the paper is marginally above the acceptance threshold, with reviewers recognizing its importance and suggesting constructive improvements for the final version. Therefore, I recommend acceptance, contingent upon addressing the noted concerns and enhancing clarity.
Decision: Accept