Inverse Scaling Can Become U-Shaped
Authors: Jason Wei
Najoung Kim
Yi Tay
Quoc V Le
Venue: EMNLP 2023 Main (2023)
Keywords: inverse scaling
scaling
language models
evaluation
TL;DR: The broad observation of U-shaped scaling shows the difficulty of extrapolating inverse scaling trends as model scale continues to increase. 1-shot and 1-shot CoT prompting appear to be effective mitigation strategies for adverse scaling trends.

Abstract: Scaling up language models has been empirically shown to improve performance on a wide range of downstream tasks. However, if we were to observe worse performance as a function of scale ("inverse scaling") on certain tasks, this would indicate that scaling can also encourage behaviors that are misaligned with human preferences. The Inverse Scaling Prize (McKenzie et al. 2023) identified eleven such inverse scaling tasks, evaluated on models of up to 280B parameters and up to 500 zettaFLOPs of training compute. This paper takes a closer look at these inverse scaling tasks. In this paper, we evaluate models of up to 540B parameters, trained on five times more compute than those evaluated in the Inverse Scaling Prize. With this increased range of model sizes and compute, only four out of the eleven tasks remain inverse scaling. Six tasks exhibit "U-shaped scaling", where performance decreases up to a certain size, and then increases again up to the largest model evaluated (the one remaining task displays positive scaling). In addition, 1-shot examples and chain-of-thought can help mitigate undesirable scaling patterns even further. U-shaped scaling suggests that the inverse scaling trend observed in McKenzie et al. (2023) may not continue to hold for larger models, which we attribute to the presence of distractor tasks that only sufficiently large models can avoid.

Inverse Scaling Can Become U-Shaped
Jason Wei
Najoung Kim*
Yi Tay
Quoc V. Le
Google "OpeAA j jasonwel@openai. com, najoungégoogle.com
*eka Al
Abstract
Inverse Scaling Prize Tasks
100
PaLM
Gopher
Scaling up language models has been empir- ically shown to improve performance on wide range of downstream tasks. However, we were to observe worse performance as function of scale (inverse scaling) tain tasks, this would indicate that scaling can also encourage behaviors that are misaligned with human preferences. The Inverse Scaling Prize (McKenzie et al., 2023) identified eleven such inverse scaling tasks, evaluated on mod- els of up to 280B parameters and up to 500 zettaFLOPs of training compute. In this pa- per, evaluate models of up 540B param- eters, trained on five times more compute than those evaluated in the Inverse Scaling Prize. With this increased range of model sizes and compute, only four out of the eleven tasks remain inverse scaling.
Accuracy (10 task average in
Anthooiic
Chinchilla
Random
50
0.1
10
100 IK
10K
ZeutaFLPs for pre-training
Figure I: Across ten tasks from the Inverse Scal- ing Prize (McKenzie et al., 2022a), PaLM (Chowdh- ery et al., 2022) average exhibits U-shaped seal- ing, which means that performance first decreases and then increases again as the model gets larger. Model scale can be viewed through the axis of either com- pute (zettaLLOPs for pretraining) or model size (# of parameters) see Appendix E, Figure for the model size plot. The y-axis denotes the average accuracy of ten tasks that use accuracy as the metric, excluding Prompt Injection that uses loss the metric.
tasks exhibit U- shaped scaling, where performance decreases up to certain size, and then increases again up the largest model evaluated (the one re- maining task displays positive scaling). In ad- dition, 1-shot examples and chain-of of-thhught help mitigate undesirable scaling patterns even further. U-shaped scaling suggests that the inverse scaling trend observed McKen- zic et al. (2023) may not continue to hold for larger models, which we attribute to the pres- ence of distractor tasks that only sufficiently large models can avoid.
such tasks can help reveal flaws in the models' train- ing data objectives (McKenzie et al., 2022a). The Inverse Scaling Prize was created to identify such tasks for which larger LMs show increasingly undesirable behavior (McKenzie et al., 2023). Sub- missions were scored based on range of criteria including inverse scaling strength, task importance, novelty/surprisingness, task coverage, reproducibil- ity, and inverse scaling generality across different models. Eleven tasks were awarded Third Prizes, the datasets for which have been publicly released. The scaling curves for these eleven tasks (see Fig- ure and also Appendix C, Figure 6) were shown on range of LMs with scales spanning several or- ders of magnitude in parameters, including Gopher 122M-80BB; Rae et al., 2021), Chinchilla (400M- 70B; Hoffmann et al., 2022), and an Anthropic
1 Introduction
Scaling up language models (LMs) has been shown improve model performance for wide range of downstream tasks and and has been claimed unlock emergent abilities (Kaplan et al., 2020; Brown et al., 2020; Srivastava et al., 2022: Wei et al., 2022a, L..). However, are there any tasks for which performance gets worse as models scale? Tasks that exhibit this property have been referred to as inverse scaling tasks (Lin et al., 2022), and
"qqua contribution. work done while at Google.

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Authropic
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Figure 2: Scaling curves for the eleven Inverse Scaling Prize tasks. Prompt Injection (Injection) uses loss as the evaluation metric and is not included in the average. The only model that has been added in this paper is PaLM (Chowdhery et al., 2022). Results from other models are taken from McKenzie et al. (2022b).
Pretrain zettaFFLOPs
internal model (13M-52B).
Model family
# params
In this paper, we take a closer look at the scaling behaviors for these eleven tasks. First, we evaluate PaL.M models of up to 540B parameters (Chowdh- ery et al., 2022), trained on about five times more compute than the models evaluated in the Inverse Scaling Prize submissions (see Table 1). Under this setup, we find that six out of the eleven tasks ex- hibit what we call U-shaped scaling: performance first decreases, and then increases again for larger models. With one task demonstrating positive seal- ing (monotonically increasing performance) with PaLM, this brings the number of inverse scaling tasks down to four with the additional scale pro- vided in our experiments. This finding of U-shaped scaling consistent with prior observations of U- shaped scaling on BIG-Bench tasks such as Truth- fulQA (Lin et al., 2022), Persian Idioms, and Iden- tify Math Theorems (Srivastava et al., 2022, see
Anthropic
52B
124
GPT-3
175B
315
OPT
175B
315
Gopher
280B
546
Chinchilla
70B
563
Pal.M (this paper)
540B
2,527
Table 1: Scale of the largest model in each model fam- ily in the Inverse Scaling Prize compared to this paper.
Appendix B, Figure 5). The implication of U- shaped scaling that inverse scaling curves may not extrapolate to larger scales, since performance could either keep decreasing (true inverse scaling), or start increasing (U-shaped scaling).
The second part of this paper explores whether
'Sce McKenzie ct al. (2023) for a more comprehensive review of prior ohscrvations of inverse scaling.

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different prompting strategies can help mitigate inverse scaling. Specifically, we test 1-shot demon- strations and chain-of-thought (CoT) prompting (Wei et al., 2022b) a form of prompt engineering that encourages the model to decompose the task into intermediate steps. We find that simply provid- ing 1-shot examples as part of the prompt changes all four tasks that remained inverse scaling in our evaluation to U-shaped or flat scaling. With CoT prompting, four out of the nine classification tasks that are U-shaped under I-shot changes to positive scaling, and one of the tasks reaches near-perfect accuracy across all model sizes tested. Even when the scaling pattern does not change to positive, task performance generally improves with CoT in 8B+ models. These results show that (even minimal) demonstrations are critically effective for avoiding distractor tasks, and point towards promising future directions for developing prompting techniques for mitigating undesirable scaling patterns.
Potential explanation. A natural question about the U-shaped scaling results is, why does perfor- mance decrease and then increase again? One spec- ulative hypothesis is the following. Each Inverse Scaling Prize task can be decomposed into two tasks: (1) the true task and (2) a distractor task where performing the distractor task well hurts per- formance on the true task. Small models cannot perform either task, and performs around chance. Medium-sized models can perform the distractor task, which results in worse performance compared to smaller models. Large models are able to ignore the distractor task and perform the true task, which then leads back to increased performance and po- tentially solving the task. We describe potential distractor tasks for each of the inverse scaling tasks in Appendix D, Table 3. Note that while it could be possible measure model performance on the distractor task only, this would be an imperfect ab- lation since the distractor task and true task could not only have a competing but also a joint effect on performance. We leave further exploration of why U-shaped scaling occurs to future work.
2 U-shaped scaling
Setup. We evaluate PaLM models all eleven Inverse Scaling Prize tasks. We use 8B, 62B, and 540B PaLM models from the original paper and also include 1B model trained on 40B tokens, which is 0.2 zettaFL.PP of compute. The param- eter count of PaLM 540B is about twice as large as the parameter count of the largest model evaluated in the Inverse Scaling Prize (Gopher 280B), and the amount of compute used is about five times as much-2.5K zettal-LOPs versus 560 zettaFFLOPs of Chinchilla 70B. We follow the exact experimen- tal setup from McKenzie et al. (2023), with the same prompts and scoring protocol, where all an- swer choices are scored and the option with the highest probability is chosen as the prediction. Results. The results for PaLM on the eleven tasks are shown in Figure 2, with the cross-task aver- age highlighted in the first figure. We also plot results for other LMs reported in McKenzie et al. (2022b) for comparison. In summary, only four out of eleven tasks remain inverse scaling once the PaLM 540B model is included. Six out of cleven tasks change from inverse scaling to U-shaped, and one task (Repetitive Algebra) shows positive scaling with PaI.M. This broad observation of U- shaped scaling demonstrates the difficulty of ex- trapolating inverse scaling curves to larger models.
3 Mitigation for inverse scaling
We next explore possible mitigation strategies for inverse scaling. In Section 2, we hypothesized the primary cause of inverse scaling to be distractor tasks that mislead the models towards different lution from the true task. Then, in-context demon- strations of a problem/solution pair could discour- age the models from solving the distractor task, since the answer according to the true task diverges from the answer according to the distractor task. If such demonstrations are accompanied by explicit rationales, this could guide the models towards identifying the true task even more strongly. To this end, we explore whether 1 1-shot demonstrations and 1-shot demonstrations with chain-of-thought reasoning improve undesirable scaling patterns.
3.1 1-shot demonstrations make all inverse scaling tasks U-shaped flat
To gauge the effect of demonstrations, we re- evaluate the PaLM models on all tasks with 1-shot prompts, using the 1-shot dataset from the official Inverse Scaling Prize data release. This official 1- shot dataset is created by pairing each example in the dataset with a randomly sampled, different ex- ample. These examples are then simply prepended to the default prompts (see Appendix C, Figure 6).
"This IB model was not used in the Pal .M paper (Chowd- hery et al., 2022) hut it followed the same training protocol.

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Patfern Matching Suppression
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Providing I-shot demonstrations changes the four inverse scaling tasks PaLM U-shaped or flat scaling. The performance of the largest model benefits from 1-shot prompting in all cases.
We find that all four tasks that continued be in- verse scaling after including the 540B model shift to U-shaped or flat scaling when prompted with I-shot demonstrations. Specifically, Pattern Match- ing Suppression, Into the Unknown, and Prompt Injection change to U-shaped scaling, and Redefine changes to flat scaling (see Figure 3). Furthermore, the performance of the largest model benefits from I I-shot prompting in all four tasks. These results show that even a single example of a problem/solu- tion pair effectively encourages the models towards solving the true task, especially for larger models.
evaluate model performance. This requires one ad- ditional modification to the prompt to facilitate the postprocessing of the model generations. Specif- ically, the model is prompted to output the final answer following the expression "So the answer is" Other than these changes, the instructions and the structure of the prompts are kept as close pos- sible the 1-shot prompts used in Section 3.1. We construct CoT prompts for inverse scaling tasks, excluding Prompt Injection that is evaluated on loss instead of classification accuracy. See Appendix C, Figure 7 for examples of CoT prompts.
The tasks that were already U-shaped with modified prompts remain U-shaped. See Ap- pendix A, Table 2 for full results on all tasks.
We show results for six tasks in Figure 4: three classification tasks that were inverse scaling in PaLM (Into the Unknown, Pattern Matching Sup- pression, and Redefine) and all other U-shaped tasks where the 540B model performed worse only similarly to the 1B model even after 1-shot (Negation QA, Modus Tollens, and Memo Trap). Overall, CoT substantially improves performance on these tasks with the exception of Redefine where there is a small gain only in the 540B model (~-6% points over 1-shot). The scaling curves change to positive for Into the Unknown, Pattern Match- ing Suppression, Redefine, and Negation QA, al- though for Redefine this is byproduct of smaller models underperforming their 1-shot counterparts, For Memo Trap, we observe an inverted- inverted-U-shapee U-shaped curve where the performance drops slightly with the largest model; nevertheless, there are consistent performance gains via CoT in 8B+ models.* 4 For Modus Tollens, CoT-prompted models achieved almost perfect accuracy regardless of size (i.e., flat scaling but saturated performance). See Ap- pendix A. Table for full results.
3.2 Chain-of-thought helps U-shaped scaling become positive scaling
While our 1-shot results are promising in that even a single demonstration helps shift the inverse scal- ing trend to U-shaped flat scaling, for most tasks, the performance of the largest model (540B) still fell behind was not substantially better than the smallest model (IB). This pattern held true for six out of the ten U-shaped or flat tasks with 1-shot. We explore whether chain-offthoughi (CoT) prompting can help in such scenarios, based on recent work showing that CoT can greatly improve performance for multi-step reasoning tasks (Wei et al., 2022b; Kojima et al., 2022: Suzgun et al., 2022, i.a.)
For the experiments in this section, we follow the protocol of Wei et al. (2022b) and follow-up work that includes intermediate reasoning steps in the in-context demonstrations. We continue to use single example as in Section 3.1, but now the demonstrations are paired with step-by-step ratio- nales. Because CoT prompting also requires the models to generate intermediate steps, we use free- form generation followed by exact string match to
? All prompts are available at: https://githh: com/ jasonwe iesonwei2e/inv--aoa
"The occasional performance drop in is likely due to the limited capacity of smaller models to perform CoT reasoning.

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Into the Unknown
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Figure 4: Chain-of-thought (CoT) prompting generally improves performance in 8B+ models, and changes many U-shaped tasks into positive flat scaling. To control for the effect of the choice of demonstration examples, we compare CoT against 1 1-shot experiments that use the same fixed demonstration example as our CoT prompts (minus rationale), rather than comparing directly against results from Section 3.1 evaluated on the official dataset that uses randomly sampled demonstration for each example (also Appendix A).
4 Conclusions
the effectiveness this approach is limited for the inverse scaling tasks. This leaves open an inter- esting area of future research of developing novel solutions for inverse scaling that do not require explicit demonstrations.
This paper has two simple takeaways. First, in- verse scaling can turn into U-shaped scaling when evaluated on models of sufficiently large scale, as demonstrated on six out of eleven Inverse Scaling Prize tasks. The prevalence U-shaped scaling we identified in this paper shows that inverse scal- ing curves do not necessarily extrapolate to larger models. Second, demonstrations and rationales are effective for mitigating undesirable scaling patterns. All inverse scaling tasks change to U-shaped or flat scaling when single demonstration provided as part of the prompt. With additional intermediate reasoning steps, many of the U-shaped tasks fur- ther shift to positive scaling, as well as substantial performance gains throughout.
Limitations
The prevalence of U-shaped scaling does not mean that the Inverse Scaling Prize tasks are solved. Even when U-shaped scaling is observed, ten the case that the performance of the largest model is still close to or worse than the perfor- mance of the smallest model (e.g., Resisting Cor- rection, Modus Tollens). For several tasks, the absolute performance of the models are poor, with the best model performing near chance (e.g.. Nega- tion QA) or much worse (Pattern Matching Sup- pression). While we discuss several mitigation strategies to guard against undesirable scaling be- havior in the paper, these observations demonstrate the inherently challenging nature of the task, high- lighting opportunity for future research towards improving absolute performance these tasks. Furthermore, the mitigation strategies explored in this paper require manual construction of demon- strations. While this is relatively low-effort, only requiring one demonstration per task, the example
of-
Taken together, a combination of scaling and prompting techniques appears to be viable method for mitigating inverse scaling. However, the prompting approaches we explored has limita- tions in that they require manual construction of demonstrations and reasoning steps tailored to in- dividual tasks. The 0-shot CoT approach proposed by Kojima et al. (2022) is one method that does not require manual prompt construction, but as we show in the additional experiment in Appendix F,

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still has to be tailored to individual tasks. We ex- pect future work develop more generalizable mit-
lan R. McKenzie, Alexander Lyzhov, Michael Pieler, Alicia Parrish, Aaron Mueller, Ameya Prabhu, Euan McLean, Aaron Kirtland, Alexis Ross, Alisa Liu, Andrew Gritsevskiy, Daniel Wurgaft, Derik Kauff- man, Gabriel Recchia, Jiacheng Liu, Joe Cavanagh, Max Weiss, Sicong Huang, The Floating Droid, Tom Tseng, Tomasz Korbak, Xudong Shen, Yuhui Zhang, Zhengping Zhou, Najoung Kim, Samuel R. Bow- man, and Ethan Perez. 2023. Inverse scaling: When bigger isn't 't better. arXiv:2306.0443
igation strategies, possibly inspired by the causes of inverse scaling identified in McKenzie et al. (2023).
Acknowledgements
We thank Denny Zhou, Ed Chi, Le Hou, Ethan Perez, Ian McKenzie, and the anonymous EMNLP reviewers for their feedback on the paper. We thank Ethan Perez and lan McKenzie again for their help with sharing the Round data. Finally, we really appreciate the spirit and organization of the Inverse Scaling Prize-we we thank the organizers for this!
Jack W. Rac, Sebastian Borgeaud, Trevor Cai, Katie Millican, Jordan Hoffmann, Francis Song. John Aslanides, Sarah Henderson, Roman Ring. et al. 2021. Scaling language models: Meth- ods, analysis & insights from training Gopher. arXiv:2112.11446.
Aarohi Srivastava, Abhinav Rastogi, Abhishek Rao, Abu Awal Md Shoeb, Abubakar Abid, Adam Fisch, Adam R. Brown, et al. 2022. Beyond the imitation game: Quantifying and extrapolating the capabilities of language models. 2rXiv:2206.04615
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Jason Wei, Xuezhi Wang. Dale Schuurmans, Maarten Bosma, Brian Ichter, Fei Xia, F'd Chi, Quoc Le, and Denny Zhou, 2022b. Chain-of-thought prompting elicits reasoning in large language models. NeurIPS.
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A
Full results
The full results for all eleven Inverse Scaling Prize tasks reported this paper are shown in Table 2. We used the exact dataset and protocol from McKenzie et al. (2023) for the main experiments (Section 2). and used the officially released 1-shot dataset for the 1-shot experiments (Section 3.1). These ex- periments are marked 1-shot (official). We addi- tionally ran 1-shot experiments where we fixed the 1-shot demonstration to be the same as the CoT demonstration, except for the step-by-step rationale, marked I-shot (controlled). This is be- cause the official 1-shot dataset used a randomly sampled example from the dataset as the 1-shot demonstration example, which varied across each example in the test set. Since our CoT experiments
Takeshi Kojima, Shixiang Shane Gu, Machel Reid, Yu- taka Matsuo, and Yusuke Iwasawa. 2022. Large lan- guage models are zero-shot reasoners. NeurIPS.
Stephanie Lin, Jacob Hilton, and Owain Evans. 2022, TruthfulQA: Measuring how models mimic human falsehoods. In Proceedings of the 60th Annual Meet- ing of the Association for Computational Linguistics (Volume 1: Long Papers), pages 3214-3252, Dublin, Treland. Association for Computational Linguisties.
Ian McKenzie, Alexander Lyzhov, Alicia Parrish, Ameya Prabhu, Aaron Mueller, Najoung Kim, Sam Bowman, and Ethan Perez. 2022a. The Inverse Scal- ing Prize.
Tan McKenzie, Alexander Lyzhov, Alicia Parrish, Ameya Prabhu, Aaron Mueller, Najoung Kim, Sam Bowman, and Ethan Perez 2022b. Inverse scaling prize: Second round winners. Lesswrong.
"The official 0- and 1-shot datasets are from https://gi https://ggttuu.ooot www.essessaaainn/rrrieeee htnn/dtaa-eeeeaee

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(Section 3.2) use single manually written demon- stration for every test example, the CoT results are more directly comparable to the controlled 1 I-shot experiments where the demonstrations are fixed.
the difference from the official 1-shot prompts high- lighted in blue.
D Distractor tasks
A possible hypothesis for why U-shaped scaling emerges is as follows. U-shaped scaling tasks con- sist of true task and distractor task. Medium- sized models are good enough perform the dis- tractor tasks, which hurts performance compared to smaller models that cannot perform the distractor task nor the true task. Larger models can ignore the distractor task and perform the true task, which leads to increased performance again. We show speculative decomposition of tasks into the true task and a distractor task in Table 3.
B Prior examples of U-shaped scaling
See Figure 5 for examples of U-shaped scaling reported in the literature.
E
Model scale: parameters, data, and compute
As shown in Table 4, we computed training FLOPs following the protocol of Brown et al. (2020). See also Figure 8 for the average performance of differ- ent LMs on the Inverse Scaling Prize tasks, viewed through the axis of compute and model size.
F 0-shot CoT experiments
We additionally investigate whether 0-shot CoT approach proposed by Kojima et al. (2022) is effec- tive against inverse scaling, given that this approach does not require task-specifi prompt construction. Following their method, we first append the origi- nal prompt with "Let's think step by step". Then, we extract the rationale generated by the model, and append the rationale after "Let's think step by step". Then, we append "So the answer is" at the end, and prompt the model for the final answer. We run the O-shot CoT experiments for 8B+ models only, given that 1B models generally show limited ability perform CoT reasoning (this trend was also evident in our main CoT experiment). The results are shown in Table The results are highly mixed but rarely beneficial-onfe two tasks clearly benefit from 0-shot CoT compared to the default setup (Pattern Matching Suppression, Modus Tol- lens). Two tasks only show substantial gains for the 8B model (Hindsight Neglect, Repetitive Al- gebra). The rest either remains similar (Negation QA. Into the Unknown) or show lower performance (Memo Trap, Redefine, Sig Figs. Resisting Correc- tion). In tasks where 0-shot CoT leads to lower performance, we often observed that the models failed to produce any reasoning chain at all at the
17
12"
(c)
Figure 5: Three examples of U-shaped scaling be- havior from BIG-Bench (Srivastava et al., 2022). a: identify math theorems. b: persian id- ioms. truthful_qa. The above are screen- shots from https://github. BBm/googe/BII-benchh ttre//aaiibiigeeen/nnnnnnrrrr.. taskk///
Prompts
Figure 6 shows the original prompts of the tasks
from the Inverse Scaling Prize. Figure 7 shows examples of the CoT prompts we constructed, with

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Redefine
Meroo trap
Sig figs
Repetitive algebra
View number as text, Do not perform computation. Q: What digit
[..] Write quote that ends the "heevy" Absence makes the heart grow
Input
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significant digits.
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[..] Question: Devid the option to play game where David has 94 percent chance losing and a percent chance of earning dollors, David plays the game ends up earning 5 dollars. Did David make the right decision?
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and planned to make fish tacos. Even though he got of the ingredients for tacos, eventually decided make grilled fish instead. ... Why did ha decide to make griled fish instead??
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2. John doesn't have a dog. Conclusion: Therefore, John doeen't have pet.
Input: dercy, she left Elizabett to walk herself.
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Question: conclusion correct?
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Figure 6: Prompts for eleven inverse scaling tasks from McKenzie et (2022a). [...] marks where few-shot exemplars placed. Few-shot exemplars relevant in the following scenarios: (1) when they part of the original task (e.g., Hindsight Neglect), and (2) in our I-shot/CoT experiments in Section 3.
first reasoning extraction step (e.g., sequence of newlines and nothing else following "Let's think step by step"), which led instabilities in the final answer stage. Overall, this shows that 0-shot CoT is not a reliable solution for inverse scaling tasks, and further research needed.

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step
Aenon croboarms. gottin company.
Let's think step by step. First, the symbol has been repeated times. repeated pattorn 2 being predictable
Ampor:: step by steas, food lla ersiaaanta tarta. this for cemmatioon closs nat help unclenatand why carcaded his Parta trip,
So the answer 1s
hand gatting en plan for suarmou which anslanation for him carnollli lina the Mii..
So the enswer is".
Figure 7: Example 1-shot CoT demonstrations for the three classification tasks that are inverse scaling in PaLM. The demonstrations contain CoT reasoning and the expression "So the answer is" immediately before the final answer. These demonstrations are prepended the default prompt containing the actual problem that the model has to solve (Figure 6). The blue highlights denote the difference between the I-shot CoT prompts and the simple 1-shot prompts used Section 3.1.
Inverse Scaling Prize Tasks
Inverse Scaling Prize Tasks
100
PaL.
Gopher
100
Pal.M
Gopher
Accuracy (10 task average in %))
Accuracy (10 average %6)
Amhropic
Chinchilla
Anthropic
Chinchilla
Rankon
Random
75
75
50
50
25
0.1
10
100 IK
10K
10M 100M IB
10B
100B
IT
ZettaFLOPs for pre-training
model parameters
Figure 8: Across ten tasks from the Inverse Scaling Prize (McKenzie et al., 2022a), PaLM (Chowdhery et al., 2022) on average exhibits U-shaped scaling, which means that performance first decreases and then increases again as the model gets larger. Model scale can be viewed through the axis of either compute (zettaLOPPs for pretraining: left) or model size (# of parameters: right). The y-axis denotes the average accuracy of ten tasks that use accuracy as the metric, excluding Prompt Injection that uses loss as the metric. All results are obtained using the exact prompts and evaluation format specified by Inverse Scaling Prize.

---

.M model size
Task
Prompting
IB
8B
62B
S40B
Scaling
Negation QA
Default
43.7
46.3
29.0
40.0
U-shaped
1-shot (official)
51.7
56.0
34.7
52.7
U-shaped
I I-shot (controlled)
53.7
54.7
32.7
61.7
U-shaped
1-shot CoT
53.7
52.7
69.3
89.0
Positive
O-shot CoT
50.0
33.7
35.3
Memo trap
Default
54.6
33.5
31.0
40.2
U-shaped
I I-shot (official)
55.9
38.3
44.1
57.8
U-shaped
1 1-shot (controlled)
55.1
53.1
69.7
65.9
Other
I I-shot CoT
4.5
77.1
90.4
82.5
Other
0-shot CoT
1.1
0.1
0.3
Pattern matching suppression
Default
4.8
0.0
0.0
0.1
Inverse
1 I-shot (official)
2.7
1.4
7.1
24.4
U-shaped
1-shot (controlled)
2.8
0.0
0.2
0.2
Inverse
1 1-shot CoT
1.8
87.1
42.0
52.2
Other
0-shot CoT
20.7
20.9
13.2
Into the unknown
Default
50.4
49.6
36.0
36.7
Inverse
1-shot (official)
49.3
50.8
24.3
47.9
U-shaped
1 1-shot (controlled)
52.2
50.8
28.4
47.5
U-shaped
1-shot CoT
47.4
54.6
60.4
83.4
Positive
0-shot CoT
45.0
38.4
39.0
Modus tollens
Default
100.0
0.0
57.7
76.0
U-shaped
1-shot (official)
100.0
0.0
12.6
50.5
U-shaped
1-shot (controlled)
100.0
0.0
12.5
78.4
U-shaped
1-shot CoT
99.6
99.4
99.8
99.9
Flat (saturated)
0-shot CoT
46.3
67.6
95.4
Redefine
Default
71.5
64.7
56.7
44.1
Inverse
1-shot (official)
64.8
68.2
67.1
69.1
Flat
1-shot (controlled)
69.3
65.2
64.6
65.3
Flat
1-shot CoT
47.8
62.5
64.8
71.4
Positive
0-shot CoT
25.6
28.9
17.0
Sig figs
Default
40.8
37.8
26.8
59.9
U-shaped
1-shot (official)
41.2
37.7
34.5
74.2
U-shaped
1-shot (controlled)
40.2
34.3
31.1
72.8
U-shaped
1-shot CoT
31.6
37.2
14.2
43.1
U-shaped
0-shot CoT
11.8
5.5
27.7
Hindsight Neglect
Default
46.7
20.0
44.8
88.3
U-shaped
1-shot (official)
53.0
21.3
62.5
84.1
U-shaped
1-shot (controlled)
54.0
14.0
61.3
86.7
U-shaped
1-shot CoT
54.9
56.5
90.8
97.1
Positive
0-shot CoT
41.6
49.2
84.8
Resisting correction
Default
92.6
72.8
76.7
82.7
U-shaped
1 I-shot (official)
95.2
90.9
96.6
98.4
U-shaped
1-shot (controlled)
96.1
88.8
96.7
98.3
U-shaped
1 1-shot CoT
0.8
87.4
99.3
98.4
Other
O-shot CoT
7.8
14.4
19.2
Repetitive algebra!
Default
22.0
39.9
90.6
Positive
1-shot (official)
24.4
89.6
Positive
1-shot (controlled)
79.3
Positive
1-shot CoT
46.0
64.5
Positive
0-shot CoT
63.5
68.2
Prompt injection' (loss)
Default
0.3
1.8
2.2
1.7
Inverse
1-shot (official)
0.1
0.8
1.2
0.4
U-shaped
1-shot (controlled)
0.1
0.6
0.4
0.2
U-shaped
Table 2: Exact results for all Inverse Scaling Prize tasks used in this paper (eleven tasks including both Rounds and 2). The tasks marked with contain few-shot demonstrations as a part the default prompt. Our 1-shot demonstration of the full (few-shots, question) pair, following the official experiments for these tasks Inverse Scaling Prize data release.

---

Distractor task
True task
Negation QA
Answer the question without negation
Answer the negated question
Hindsight Neglect
Understand outcome of bet
Analyze expected value of bet
Resisting Correction
Produce most likely completion given prefix
Repeat the input exactly
Redefine
Use common definition of symbols
Use redefined definition symbols according to the instruction
Repetitive Algebra
Select answer that matches the answer of the most recent few-shot example
Perform arithmetic computation
Memo Trap
Repeat famous quote verbatim
Produce different ending to famous quote according the instruction
Prompt Injection
Follow the most recent injected instruction
Ignore the injected instruction following the initial instruction ignore it
Into the Unknown
Select answer similar to information given prompt
Select answer that helps solve the given reasoning problem. considering the information in prompt
Pattern Matching
Sup-
Produce most likely completion the pattern
Produce unlikely completion of the pattern according to instruction
pression
Sig Figs
Round based the number of decimal places
Round based the number of significant figures
Modus Tollens
Produce most likely answer (and replicate common human errors)
Perform valid logical reasoning
Table 3: A speculative decomposition of inverse scaling tasks into distractor and true tasks.

---

params (B)
tokens (B)
zettaF-LOss
GPT-3
0.35
300
0.64
1.3
6.7
300
12
175
315
Anthropic
0.013
400
0.03
0.042
400
0.1
0.197
400
0.5
0.805
30
Gopher
0.044
300
0.08
0.117
300
0.2
0.417
300
0.8
1.4
300
2.5
7.1
300
12.8
280
325
546
Chinchilla
0.4
314
0.8
1
314
1.9
7
199
8.4
70
1,340
563
PaLM
1
40
0.24
8
780
37
62
780
290
540
780
2,530
Table 4: Computation of training FLOPs for GPT-3, Anthropic, Gopher, and Chinchilla, and PaL.M.


Reviews:
[{"review_id": "5MPfIp19Yo", "reviewer": "Reviewer_bS6X", "summary": "", "questions": "Question A: Regarding the prompts shown in Figure 5, I am curious about the potential impact of the target label order on the models' performance. Zhao et al. [1] have discussed tendencies like a recency bias (models favoring the last target label) and a \"common token\" bias (frequently occurring answers from the pre-training data). Have you verified whether the labels are evenly distributed in the prompts for each task, ensuring that the correct answer is not disproportionately positioned as the first or second option?\n\nZhao et al. \"Calibrate Before Use: Improving Few-shot Performance of Language Models.\" In Proceedings of the 38th International Conference on Machine Learning (ICML'21). https://proceedings.mlr.press/v139/zhao21c.html\n\n", "limitations": "", "rating": 4, "confidence": 3, "soundness": 4, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks so much for your review!\n\n> However, it would have been interesting if this study had incorporated more non-proprietary models that could be easily reproduced for further investigation.\n\nWe agree that it would be ideal to extend this study to non-proprietary models (although PaLM, while not completely open-source, has become accessible via the PaLM/Google Cloud API https://developers.generativeai.google/). Nevertheless, we point out that the largest non-proprietary models (in terms of # parameters) are BLOOM and OPT (~176B), which both fall in the range of model sizes already evaluated in the original inverse scaling paper (https://arxiv.org/abs/2306.09479), and therefore would not have been helpful in addressing the core research question of our paper (i.e., “Do models that are even larger than the largest models evaluated in the inverse scaling paper continue to show inverse scaling trends?”). In the future, we would love to extend our analysis to open-source models should larger models become available. \n\n> Have you verified whether the labels are evenly distributed in the prompts for each task, ensuring that the correct answer is not disproportionately positioned as the first or second option?\n\nWe believe with the exception of Modus Tollens, the labels are evenly distributed. We also note that the tasks shown in Figure 5 are directly taken from the original inverse scaling paper (https://arxiv.org/abs/2306.09479) to maintain comparability with the previously reported results, and more justifications about the task/dataset design can be found in their respective descriptions in the said paper.\n\n> I have two minor remarks regarding the presentation:\n\nThank you for the stylistic suggestions! We will try to incorporate them in the camera-ready version if the paper is accepted.", "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": "This study challenges the inverse scaling law, which indicated that an increase in pre-training compute leads to a decrease in performance. The authors demonstrate that certain models defy this scaling law, rendering it unsuitable for reliable extrapolation as an indicator of future model performance. Furthermore, the authors illustrate that adequately large language models are able to identify the \"true task\" from a single in-context example, while also presenting possibilities for future research on imitation strategies that eliminate the need for task-specific tuning or example selection.", "reasons_to_reject": "There are no particular grounds for rejection. However, it would have been interesting if this study had incorporated more non-proprietary models that could be easily reproduced for further investigation.", "questions_to_authors": "Question A: Regarding the prompts shown in Figure 5, I am curious about the potential impact of the target label order on the models' performance. Zhao et al. [1] have discussed tendencies like a recency bias (models favoring the last target label) and a \"common token\" bias (frequently occurring answers from the pre-training data). Have you verified whether the labels are evenly distributed in the prompts for each task, ensuring that the correct answer is not disproportionately positioned as the first or second option?\n\nZhao et al. \"Calibrate Before Use: Improving Few-shot Performance of Language Models.\" In Proceedings of the 38th International Conference on Machine Learning (ICML'21). https://proceedings.mlr.press/v139/zhao21c.html\n\n", "paper_topic_and_main_contributions": "This paper delves into the phenomenon of inverse scaling in language models and brings attention to how larger pre-trained models can counter the trends observed by McKenzie et al. The presence of U-shaped curves suggests that relying on inverse scaling laws to predict a model's performance during training may not be accurate, as the performance could decrease, stabilize, or even improve.\n\nMoreover, the study explores different prompting strategies, such as 1-shot in-context learning and chain-of-thought reasoning, aiming to tackle challenging tasks effectively with sufficiently large language models. The experimental results provide supporting evidence that the effect of inverse scaling can be mitigated when models are guided through demonstrations, enabling them to steer clear of \"distractor tasks\" that are concealed within each task in the Inverse Scaling Prize benchmark.", "excitement": 4, "reproducibility": 2, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {"Typos_Grammar_Style_and_Presentation_Improvements": "I have two minor remarks regarding the presentation:\n\nFigure 1: I understand that the purpose of this figure is to compare the trends of PaLM with previous models. However, I find the marker and line size to be slightly too large, making it difficult to discern the general trends of all the models.\n\nTable 1: While I recognize that space constraints might have influenced its placement on the first page, I personally find that featuring something like the \"average\" subplot from Figure 1 would be more captivating for engaging a new reader."}}, {"review_id": "9X8q4rmz91", "reviewer": "Reviewer_95LF", "summary": "", "questions": "- A. It would be interesting to see the effect of instruction tuning on the models' ability to follow the *true* task. Were there any experiments on this?\n- B. It would be interesting to see if zero-shot CoT [Kojima 2022] can help the model overcome the distractor tasks through step-by-step reasoning. This may help isolate the effect of (1) task guidance/position and (2) step-by-step reasoning / introspection elicited by few-shot CoT. Zero-shot CoT has the potential to be a generalizable mitigation strategy discussed in the limitations. Were there any experiments on this?\n- C. Can you explain the prompt engineering efforts that went into constructing the CoT prompts, if any? The level of effort needed to achieve the performance gains shown in the paper is somewhat important to understand the applicability of the mitigation strategy. Also, details/findings from the prompt engineering process may provide helpful insights for readers. This is not discussed in Appendix C.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 4, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks so much for your review! \n\n> The results are not reproducible due to the use of PaLM, a proprietary model.\n\nPaLM, while not completely open-source, is now accessible via the PaLM/Google Cloud API (https://developers.generativeai.google/). \n\n> Side note: it would be interesting to see results on GPT-4.\n\nWe agree, and there are some partial results in the GPT-4 technical report, where GPT-4 seems to do quite well. However, it is unclear what the significance of the results from GPT-4 is in the context of scaling, since we do not know the model size or compute used to train GPT-4.\n\n> Qualitative analysis on the success/failure cases is not considered. This would help support the proposed hypothesis that there are true tasks and distractor tasks, and possibly give more insights into how larger models or proposed techniques overcome inverse scaling.\n\nThis is a great idea and we will try to add qualitative analysis to the camera-ready, if the paper were to be accepted.\n\n> It would be interesting to see the effect of instruction tuning on the models' ability to follow the true task. Were there any experiments on this?\n\nWe do not currently have experimental results on the effects of instruction tuning, but we could evaluate the Flan-PaLM series to measure this effect.\n\n> It would be interesting to see if zero-shot CoT [Kojima 2022] can help the model overcome the distractor tasks through step-by-step reasoning. This may help isolate the effect of (1) task guidance/position and (2) step-by-step reasoning / introspection elicited by few-shot CoT. Zero-shot CoT has the potential to be a generalizable mitigation strategy discussed in the limitations. Were there any experiments on this?\n\nThis is a great idea and we’d love to include results testing zero-shot CoT to Table 2. Thanks for the suggestion!\n\n> Can you explain the prompt engineering efforts that went into constructing the CoT prompts, if any? The level of effort needed to achieve the performance gains shown in the paper is somewhat important to understand the applicability of the mitigation strategy. Also, details/findings from the prompt engineering process may provide helpful insights for readers. This is not discussed in Appendix C.\n\nWe did not extensively prompt engineer the CoT prompts—for most prompts, one of the authors came up with one step-by-step formulation of the problem and that was sufficient. We can add this discussion to Appendix C. \n\n> There is limited discussion of related works.\n\nWe can add more discussion of related work using the additional page allowed in the camera-ready. If there is important related work that you’d like to suggest including, please feel free to share the references!", "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 paper identifies an interesting phenomena regarding the performance scaling and quirks of LLMs. The findings contradict the results of the inverse scaling challenge which has garnered much attention.\n- The paper brings attention to a plausible explanation for the U-shaped scaling curves and suggests effective ways to mitigate the unwanted performance degradations, i.e. inverse scaling.\n- The presentation is very clear.", "reasons_to_reject": "- A. The results are not reproducible due to the use of PaLM, a proprietary model. Though, arguably, the paper makes an important contribution by bringing forth these findings that would otherwise not be discoverable with current public models. GPT-4 is a possible avenue, but limited details on the model would hinder rigorous study. Side note: it would be interesting to see results on GPT-4.\n- B. Qualitative analysis on the success/failure cases is not considered. This would help support the proposed hypothesis that there are *true* tasks and *distractor* tasks, and possibly give more insights into how larger models or proposed techniques overcome inverse scaling. Such analysis would be very feasible considering the number of tasks (11).", "questions_to_authors": "- A. It would be interesting to see the effect of instruction tuning on the models' ability to follow the *true* task. Were there any experiments on this?\n- B. It would be interesting to see if zero-shot CoT [Kojima 2022] can help the model overcome the distractor tasks through step-by-step reasoning. This may help isolate the effect of (1) task guidance/position and (2) step-by-step reasoning / introspection elicited by few-shot CoT. Zero-shot CoT has the potential to be a generalizable mitigation strategy discussed in the limitations. Were there any experiments on this?\n- C. Can you explain the prompt engineering efforts that went into constructing the CoT prompts, if any? The level of effort needed to achieve the performance gains shown in the paper is somewhat important to understand the applicability of the mitigation strategy. Also, details/findings from the prompt engineering process may provide helpful insights for readers. This is not discussed in Appendix C.", "paper_topic_and_main_contributions": "The authors identify that many \"inverse scaling\" tasks actually exhibit U-shaped performance curves when we consider previously unexplored large model scales, i.e., PaLM 540B. The authors provide a plausible explanation for this, suggesting that medium-sized models are confused by distractor tasks, such as repetitive patterns, completing famous quotes, recent instructions, etc. Based on this intuition, the authors propose two ways to mitigate inverse scaling behavior by clarifying the distractor/true task, namely one-shot prompting and one-shot chain-of-thought prompting, which are shown to be quite effective.", "excitement": 4, "reproducibility": 2, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"Missing_References": "There is limited discussion of related works.", "Typos_Grammar_Style_and_Presentation_Improvements": "The writing is great."}, "extra_text": {}}, {"review_id": "oQa66Ag4q2", "reviewer": "Reviewer_Fce9", "summary": "", "questions": "1. As the potential explanation implies, when models are small, larger models are more likely to be confused by the distractors. Could you provide further discussion to explain this?\n2. What could be potential solutions to left-shift the bottom of U?\n", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks so much for your review!\n\n> The prompting method highly relies on manual construction.\n\nThis is true, and this is definitely a limitation of our proposed mitigation strategies. However, as we discuss in our response to Reviewer 95LF, the manual construction was not high-effort, and the method only requires a construction of just a single demonstration. We believe this is an interesting area for future improvement—zero-shot CoT, as Reviewer 95LF suggested, could be a potentially effective strategy, and pseudo-demonstrations (Lyu et al. 2023: https://arxiv.org/abs/2212.09865) could also be explored in the future.\n\n> Lack of direct support for the proposed explanation.\n\nWe agree that finding empirical support for the proposed explanation is important and we hope to explore this in more detail in future work. Qualitative analysis of the errors, which we plan to include in the next revision, could potentially provide insights.\n\n> As the potential explanation implies, when models are small, larger models are more likely to be confused by the distractors. Could you provide further discussion to explain this?\n\nWe are not sure we fully understood “when models are small, larger models are more likely to be confused by the distractors”, but assuming this is asking why larger models are more likely to be confused by distractors, our rationale is that sensitivity to the distractor task requires a degree of understanding that smaller models may lack. And because understanding and correctly solving the distractor task entails that the model answers will be incorrect in light of the true task (definition of a distractor task), larger models will perform more poorly than the smaller models. \n\n> What could be potential solutions to left-shift the bottom of U?\n\nAs can be seen from Figure 3, CoT prompting does left-shift the bottom of the U for some tasks (e.g., Into the Unknown: 62B -> 1B, Negation QA: 62B -> 8B). While CoT isn’t a universal solution, it would be a good starting point to build future solutions upon—e.g., meta-reasoning approach proposed in Yoran et al. (https://arxiv.org/abs/2304.13007).", "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. The finding of U-shape performance is highly worth noticing. \n2. And the authors provide a reasonable explanation for inverse scaling, which they further support with a mitigation strategy.\n3. The experiments are extensive and convincing, involving diverse inverse-scaling tasks and different models.\n", "reasons_to_reject": "1. The prompting method highly relies on manual construction.\n2. Lack of direct support for the proposed explanation.", "questions_to_authors": "1. As the potential explanation implies, when models are small, larger models are more likely to be confused by the distractors. Could you provide further discussion to explain this?\n2. What could be potential solutions to left-shift the bottom of U?\n", "paper_topic_and_main_contributions": "This paper studies the inverse scaling behavior of language models and finds that the declining performance increases again as the model continues to scale, (i.e., U-shaped scaling). The author hypothesizes that the cause of this phenomenon is the existence of distractors. Accordingly, the author proposes to mitigate the inverse scaling behavior by providing demonstrations or chain-of-thought. In all evaluated tasks, this simple approach turns the reverse scaling performances into a U-shape.", "excitement": 4, "reproducibility": 3, "ethical_concerns": "No", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper presents a U-shaped scaling curve that identifies the "inverse scaling" behavior may not hold when the model continues to scale. Authors hypothesizes that medium-sized models are confused by task distractors, e.g. repetitive patterns, famous quotes, etc. In addition, authors find that one-shot prompts/chain-of-thought can mitigate these distractors. The findings in this paper are very interesting and experiments are well-executed.
Decision: Accept-Main