---
kind: concept
slug: emergent-abilities
title: Emergent abilities
summary: >-
  How to tell whether a capability or prompting technique appears only above some model size, and why small-model tests and scaling curves can miss it. Covers the scale and training-time axes, metric and baseline choices, and nine cards: two surveys, prompting, label, sampling, distillation, training-suite and analogy studies, and a framing report.
tags: [scaling, evaluation, prompting]
papers: ["2108.07258", "2201.11903", "2206.07682", "2212.09196", "2301.12726", "2303.03846", "2304.01373", "2503.05788", "2601.07239"]
related: [chain-of-thought-prompting, in-context-learning, instruction-tuning, knowledge-distillation, language-model-pretraining, llm-evaluation, zero-shot-learning, large-reasoning-models, neural-scaling-laws, weight-quantization, decoding-strategies, self-consistency]
status: draft
updated_at: 2026-11-01
---

## Overview

An ability is emergent when it is absent in smaller models and present in
larger ones, so it cannot be read off the curve of smaller models [arxiv:2206.07682 §2].
On a plot of score against scale, the score sits near chance up to a critical
size and then rises well above chance [arxiv:2206.07682 §2]. For anyone who
picks a model size or a technique, the question is whether a capability will
appear at the size they can afford.

Every "emergent" label depends on three choices: the scale axis, the metric and
the baseline it is compared against [arxiv:2206.07682 §2, app. A.1]. The
variants below are these choices, and each can move the verdict.

The field has no shared definition of emergence. A 2025 survey lists the
competing meanings and argues that an abrupt curve alone does not establish
emergence [arxiv:2503.05788 §1, §2].

This page rests on nine cards. Two surveys carry most of the claims: the
2022 survey [arxiv:2206.07682] and the 2025 survey [arxiv:2503.05788], which
also reviews the evidence on metrics, compression, prediction and mechanisms.
A distillation study reports smooth scaling for its small models
[arxiv:2301.12726 §4.2]. The chain-of-thought paper gives the most
detailed per-size results for one prompting technique [arxiv:2201.11903]. A
study of in-context learning with flipped and unrelated labels reports that
the override of priors appears with scale in the families it tests
[arxiv:2303.03846 §3] [§4]. A sampling study argues that greedy evaluation hides
capability; its emergence-related results are per model rather than a size
sweep, and several of its tables are simulated [arxiv:2601.07239 §2]
[tab. reasoning-brittleness]. A
training suite adds a view over training time [arxiv:2304.01373]. The
foundation-model report frames the topic and has no experiments
[arxiv:2108.07258 §1.1]. A zero-shot analogy study reports one large model's
results against human samples, with a preliminary check on a second model for
one task, and records no sweep over sizes [arxiv:2212.09196 §2] [§2.4]. The
survey's thresholds are compiled from other papers'
results and from the authors' own labelling of BIG-Bench tasks
[arxiv:2206.07682 app. A.3, tab. 1]. Those other papers have no cards on
wikillm, so their content is not used here.

## Variants

These are ways to test for emergence, not algorithms.

### Few-shot emergence on a task

A task is emergent under few-shot prompting when the model is at random up to
some scale and then clearly above random [arxiv:2206.07682 §3]. Examples from
the survey: 3-digit addition moves above chance at about 2·10^22 training FLOPs
(13B parameters, GPT-3) [arxiv:2206.07682 §3] [fig. 2A]. TruthfulQA stays at
chance for GPT-3 and only rises for the 280B Gopher model [arxiv:2206.07682 §3]
[fig. 2E]. WiC is at chance for models up to about 5·10^23 FLOPs and above
chance for PaLM 540B [arxiv:2206.07682 §3] [fig. 2H]. The paper does not set a
numeric threshold for "at random" or "well above". It labelled these by hand,
with two co-authors agreeing jointly [arxiv:2206.07682 app. A.3].

### Emergence of an augmented prompt or finetune

A technique is emergent when it gives no gain, or hurts, relative to the plain
baseline until the model is large enough [arxiv:2206.07682 §4]. The survey's
examples:

- Chain-of-thought prompting beats standard prompting only from about 10^23
  FLOPs (~100B parameters) [arxiv:2206.07682 §4] [fig. 3A]. The chain-of-thought
  paper reports the same scale range in its own runs. PaLM 540B with eight
  exemplars reaches 56.9% on GSM8K against 17.9% for standard prompting, and
  LaMDA 137B goes from 6.5% to 14.3% (mean of five seeds), both author-reported
  [arxiv:2201.11903 app. B]. Most models below about 10B parameters do not
  benefit [arxiv:2201.11903 app. A]. See
  [chain-of-thought prompting](/concepts/chain-of-thought-prompting).
- Instruction finetuning (FLAN) hurts at 7·10^21 FLOPs and below (8B) and helps
  from about 10^23 FLOPs [arxiv:2206.07682 §4] [fig. 3B].
- Scratchpad helps 8-digit addition from about 9·10^19 FLOPs (40M parameters)
  [arxiv:2206.07682 §4] [fig. 3C].
- P(True) calibration beats standard calibration only at the largest model
  tested, about 3·10^23 FLOPs (52B) [arxiv:2206.07682 §4] [fig. 3D].
- Distilling chain-of-thought maths solutions from a large teacher into T5 and
  FlanT5 students (250M to 11B parameters) gives a log-linear curve, not a flat
  one, in the authors' description [arxiv:2301.12726 §4.2] [fig. 2]. The same
  students score 0.0 on BIG-Bench Hard chain of thought at 11B and 3B, and 0.3
  and 0.1 at 760M and 250M [arxiv:2301.12726 tab. 1]. Here the technique is
  training, not prompting. See [Specializing Smaller Language Models towards
  Multi-Step Reasoning](/papers/2301.12726) and [knowledge distillation](/concepts/knowledge-distillation).

### Emergence of overriding a prior: flipped or unrelated labels

Another test asks whether a model learns the input-label mapping from the
prompt, or only recalls the task it already knows. Flipping the exemplar labels
of a binary task, or replacing the label words with meaningless ones such as
"Foo" and "Bar", separates the two. The paper reports that large models follow
the flipped exemplars and still learn the unrelated-label mapping, while small
models keep their prior behaviour [arxiv:2303.03846 §3] [§4].

- With flipped labels, text-davinci-002 falls from 90.3% at 0% flipped to 22.5%
  at 100% flipped [arxiv:2303.03846 §3]. Small models stay near their prior
  accuracy, and large ones drop well below chance [arxiv:2303.03846 §3]
  [fig. 2]. The paper reports the override as emerging with scale.
- For PaLM, accuracy at 100% flipped goes as low as 31%. Flan-PaLM does not
  fall below chance [arxiv:2303.03846 §5] [fig. 7].
- With unrelated targets, Flan-PaLM-8B scores 9.6 points above PaLM-8B
  [arxiv:2303.03846 §5] [fig. 6].
- In a linear-classification task with N=16, the largest Codex model is about
  19 points above chance, against about 9 for the smaller Codex models
  [arxiv:2303.03846 §6] [fig. 8]. The paper finds code-davinci-002 working up to
  N=64, and finds no scale effect for PaLM in that range [arxiv:2303.03846 app. C.4].

The card has caveats on this variant. Each dataset uses 100 evaluation
examples, with no confidence intervals or repeated runs [arxiv:2303.03846 §2.3].
The sizes of InstructGPT and Codex are not public, and the scale claim for
those families assumes they grow in size [arxiv:2303.03846 §2.2]. The paper
also says that davinci behaves like a small model in the unrelated-label
setting, so the threshold depends on family and task [arxiv:2303.03846 §3]
[app. C.1] [app. C.2]. At 50% flipped, binary labels are at chance, so that
point gives no information [arxiv:2303.03846 §3].

### Sampling budget: a lever that is not a size axis

A sampling study argues that a single greedy completion can understate a
model's capability, and that the spread across samples is worth measuring
[arxiv:2601.07239 §2]. It compares greedy decoding (temperature 0) with
temperature 0.7 and top-p 0.9 sampling, and with majority vote over k samples
[arxiv:2601.07239 §3] [§4]. Its gains are per model, with weights held fixed,
and the card records no size sweep for them [arxiv:2601.07239 §4].

- On BESSTIE, greedy accuracy for many model and task pairs lies between 40%
  and 65%. Best-of-16 typically adds 10 to 20 points, and best-of-64 adds
  2 to 5 more [arxiv:2601.07239 §4]. These are author-reported. The paper does
  not state a tie rule for even k [arxiv:2601.07239 §4].
- On InstruSum, the style gain saturates near k=8, reaching about 10 to 13
  points for LLaMA-3, Gemma-2 and Mixtral-8x22B [arxiv:2601.07239 §4].

Two parts of this card are not measured results. The chain-of-thought table is
captioned "simulated", and the safety table is captioned "our simulations"
[arxiv:2601.07239 tab. reasoning-brittleness] [tab. safety-concealed-risk]. The
card says not to present them as measured results. The sampling gains compare
decoders at fixed sizes, so they show how a verdict can change with the decoding
protocol, not whether a size threshold exists.

### Scale axis: compute, parameters, data or training time

The main x-axis is training FLOPs. Parameter-count versions of the plots are in
the appendix [arxiv:2206.07682 §2] [app. D]. Dataset size is not used, because
many model families train every size on the same number of tokens
[arxiv:2206.07682 §2]. WikiText103 perplexity is offered as an alternative axis
[arxiv:2206.07682 §5.3] [fig. 4].

The two main axes agree only when compute grows with parameters, as in dense
model families. Chinchilla has about a quarter of Gopher's parameters at similar
compute, and sparse mixture-of-experts models break the link
[arxiv:2206.07682 §2]. The perplexity axis tracks FLOPs only for Gopher and
Chinchilla, and is confounded across families by training data
[arxiv:2206.07682 §5.3].

A third axis is the training step. Pythia keeps 154 checkpoints per model and
a fixed data order, so the data seen by each checkpoint can be recovered
[arxiv:2304.01373 §2.4] [§2.7]. Its term-frequency study reports that a
correlation between answer accuracy and how often the relevant facts appear in
the training data shows up only after about step 65,000 (about 45% of training),
for models of 2.8B parameters and up [arxiv:2304.01373 §1] [§3.3] [fig. 4]. A
jump found this way is only located to the gap between saved checkpoints.

Compression is a further axis. The 2025 survey reports LLaMA models from 7B to
65B keeping most in-context learning, chain-of-thought and instruction-following
ability at 4 bits, and falling near random at 2 bits [arxiv:2503.05788 §3.4].
In a study of about 40 methods, a 70B model at 2 bits kept about 90% of its MMLU
accuracy, while models below 10B lost 25% or more [arxiv:2503.05788 §3.4]. The
collapse points differ by method: unstructured pruning near 55 to 65% sparsity,
quantization below 3 bits [arxiv:2503.05788 §3.4].

Pre-training loss is a candidate predictor, not a size axis. The survey reports
one two-stage loss-based prediction with relative error of 5% at 7B and 10% at
13B [arxiv:2503.05788 §3.7]. The same survey says the loss-threshold account is
not causal, and that a common confounder is plausible [arxiv:2503.05788 §3.3].

### Metric: discrete score or smooth loss

Exact match, accuracy and similar scores can sit at chance while the loss on
the target keeps improving. For the six BIG-Bench tasks that the paper calls
emergent for LaMDA, the cross-entropy loss improved even where the score was
at random, at up to about 10^22 FLOPs [arxiv:2206.07682 app. A.1]. For
generative tasks the loss shows an elbow at the point where the score jumps
[arxiv:2206.07682 app. A.1] [fig. 5].

Partial-credit metrics (BLEU, ROUGE, BLEURT) still show the jump on the three
generative tasks the authors re-plotted, so the smoothness of the metric does
not remove emergence on its own [arxiv:2206.07682 app. A.2] [fig. 7]. On
multiple-choice tasks, the average log-probability of correct and incorrect
answers both rise with scale, because larger models give less extreme
probabilities [arxiv:2206.07682 app. A.1] [fig. 6].

A threshold on a score is another way to label a jump. The 2025 survey reports
a meta-analysis that calls a metric-task pair emergent when a spread-to-gap
score exceeds 100, and says that 20 to 100 may still mark a discontinuous jump.
The "median difference" in that score is not defined precisely in the text
[arxiv:2503.05788 §3.1].

### Mechanistic evidence

The 2025 survey's test asks three things: whether a low-dimensional internal
structure tracks the ability, whether changing that structure changes the
behaviour, and whether the structure screens off the individual weights
[arxiv:2503.05788 §2]. It reports that few abilities pass this test in the cited
work [arxiv:2503.05788 §2]. One example is a set of symbolic abstraction heads,
which a linear decoder reads with above 98% accuracy on disjoint token sets
[arxiv:2503.05788 §3.6]. That result comes from one study.

## When to use which

| Situation | Use | Why |
|---|---|---|
| Deciding whether a small-model ablation of a prompting technique is informative | Run the baseline and the technique at more than one size, and don't read the sign from one small model | The survey places the chain-of-thought gain at about 100B and FLAN's instruction finetuning hurt at 8B [arxiv:2206.07682 §4]; the chain-of-thought paper finds most models below about 10B do not benefit [arxiv:2201.11903 app. A] |
| Forecasting whether a capability will appear at a larger size | Don't extrapolate from a smaller model's curve through the jump | The survey's definition is that emergent abilities cannot be predicted this way [arxiv:2206.07682 §2] |
| Exact-match or final-answer-only scoring on small models | Also log the log-likelihood of the target answer | Loss improves before the score moves [arxiv:2206.07682 app. A.1]; the survey notes that loss curves do not predict where the jump happens [arxiv:2206.07682 §5.1] |
| Multiple-choice scoring | Compare the log-probabilities of correct and incorrect options, not the correct option's average alone | Both rise with scale [arxiv:2206.07682 app. A.1] [fig. 6] |
| Comparing families or choosing the x-axis for a plot | Plot against training FLOPs, and check parameters separately for sparse or differently sized models | Compute and parameters diverge for Chinchilla vs Gopher and for sparse models [arxiv:2206.07682 §2] |
| Asking when during training a behaviour appears | Use saved checkpoints from a suite with a fixed data order, and locate the step, not only the size | Pythia's checkpoints and data-loader tools let the data seen at each step be recovered [arxiv:2304.01373 §2.4] [§2.7]; its term-frequency jump appears after about step 65,000 [§3.3] |
| Reporting a jump seen in one run at one size | Repeat with another seed, or report the spread across seeds | Pythia trains each size once per dataset and gives no seed-variance measure; it puts 25 seeds at about 10 million USD [arxiv:2304.01373 app. F.2]. The chain-of-thought paper averages only LaMDA over five orders [arxiv:2201.11903 §3.1] |
| Citing a zero-shot capability of one large model as evidence of emergence | Look for a comparison across sizes before calling it emergent; a single-model result shows the capability at one size only | The survey's definition needs a size curve [arxiv:2206.07682 §2]; the analogy study evaluates one model variant on its main tasks [arxiv:2212.09196 §2] [§4.2] |
| Expecting a threshold from a published table to hold for your model | Treat thresholds as properties of those models and data | Emergence depends on data quality and architecture. PaLM 62B is above random on 14 BIG-Bench tasks where LaMDA 137B and GPT-3 175B are at chance [arxiv:2206.07682 §5.2] [app. F] |
| Safety-relevant behaviour such as bias, toxicity or memorisation | Measure at your target scale; don't assume lower scale is safer | The survey cites work where these risks grow with scale [arxiv:2206.07682 §5.4] |
| Fine-tuning on a narrow task where broad behaviour matters | Evaluate broad behaviours such as honesty and misalignment after tuning, not only the target task | Insecure-code fine-tuning gave a broad misalignment rate of about 20% in GPT-4o and about 50% in GPT-4.1 [arxiv:2503.05788 §7] [tab. 2]. The survey reports that 1% misaligned data in an instruction mix cut honesty by more than 20%, while MMLU, GSM8K, HumanEval and GPQA did not change [arxiv:2503.05788 §7] |
| Compressing a model to fit a memory budget | Measure the abilities you need at each bit width or sparsity you would deploy | Collapse points differ by method, and 2-bit weights fell near random for LLaMA [arxiv:2503.05788 §3.4] |
| Judging whether a reasoning model shows a new ability | Read the reported gain as a model-to-model comparison, not as a size threshold | The survey reports o1 at 83.3% on AIME 2024 against 13.4% for GPT-4o, and o3 at 88% on ARC-AGI against 13.33% for o1 [arxiv:2503.05788 §5]. These compare models, not sizes |
| Checking whether a few-shot gain comes from prior knowledge or from the prompt's mapping | Flip a share of the labels, or replace them with unrelated words, and run at several sizes | Large models follow flipped exemplars and learn unrelated mappings, small ones keep their priors [arxiv:2303.03846 §3] [§4]. Results are on 100 examples per dataset with no intervals [§2.3] |
| Choosing an instruction-tuned model for prompts that rely on the label mapping | Test both the tuned and base models on the flipped or unrelated-label setting | Instruction tuning raises learning from exemplars, and it also strengthens priors more [arxiv:2303.03846 §5]. The Flan-PaLM-8B gain is 9.6 points [§5] |
| Reporting one greedy score for a model whose outputs vary | Also sample k outputs and report the best-of-k gain beside the greedy score, with the sampling settings | The sampling study finds best-of-16 adds 10 to 20 points on BESSTIE for many pairs, author-reported [arxiv:2601.07239 §4]. Gains depend on the decoder, so state it |
| Predicting a capability from pre-training loss instead of size | Check the reported error on a held-out size, and treat the link as correlational | One study reports 5% relative error at 7B and 10% at 13B [arxiv:2503.05788 §3.7]; the survey says the loss-threshold story is not causal [§3.3] |
| A small model must do step-by-step solving on one narrow task, and losing general reasoning is acceptable | Distil chain-of-thought solutions from a larger teacher into a small student, and select checkpoints on held-out tasks | The 11B student reaches 27.1% on GSM8K against 16.1% before specialization (author-reported), but BIG-Bench Hard chain-of-thought accuracy falls to 0.0 [arxiv:2301.12726 tab. 1] |
| The small model must keep general reasoning | Don't rely on the narrow distillation recipe; test the general benchmark at your size | Every specialized model in [arxiv:2301.12726 tab. 1] scores 0.0 or near it on BIG-Bench Hard chain of thought |

## Implementation sketch

The survey has no algorithm of its own. The closest thing is its procedure for
labelling a task's scaling curve, which it applied by hand to 210 BIG-Bench
tasks [arxiv:2206.07682 app. A.3]. A rewrite for your own evaluation runs, with
a log-likelihood column added:

```text
# Order one model family by training compute (or parameters) [arxiv:2206.07682 §2]
models = sorted(family, key=train_flops)

# Record the task score and the target log-likelihood at each size
# (the second is the metric check in [arxiv:2206.07682 app. A.1])
for m in models:
    score[m] = accuracy_or_exact_match(m, task)
    ll[m]    = mean_log_prob_of_target(m, task)

# Label the curve; "near random" and "well above" are judged, not set
if all(score[m] is near chance r for m in models):
    label = "flat"
elif score rises steadily with scale:
    label = "smoothly increasing"
elif score is near r below some size s*, and well above r beyond s*:
    label = "emergent at s*"
else:
    label = "other"

# If ll keeps rising while score is flat, the jump may be
# partly a metric effect, not a change in the model
```

Where variants differ:

- **Augmented prompts:** run the same loop with the technique on and off at each
  size, and label the gap rather than the score [arxiv:2206.07682 §4].
- **Partial credit:** replace the score with a graded metric such as BLEU or
  ROUGE, and keep the exact-match score next to it [arxiv:2206.07682 app. A.2].
- **Training time:** if checkpoints are saved, run the loop over steps as well
  as sizes, with the same data order at every step [arxiv:2304.01373 §2.4].
- **Compression:** run the loop over bit widths or sparsity levels in place of
  sizes, since collapse points differ by method [arxiv:2503.05788 §3.4].
- **Prior check:** replace the score with the flipped-label or unrelated-label
  score at each size, and label the curve on that score [arxiv:2303.03846 §3]
  [§4].
- **Sampling:** at each size, add a best-of-k column next to the greedy score,
  with the decoder and k stated [arxiv:2601.07239 §4].

## Contradictions

Within the survey, the same model is given different sizes or FLOPs in different
tables and sections. The paper does not reconcile them. Both sides are listed:

- **Scratchpad model.** The 8-digit addition emergence point is 40M parameters
  at 8.9·10^19 FLOPs in the text and table 1 [arxiv:2206.07682 §4] [tab. 1].
  Table 2 lists a LaMDA model at 8.90E+19 FLOPs with 57M parameters
  [arxiv:2206.07682 tab. 2].
- **Anthropic 52B model.** Table 1 gives 2.6E+23 FLOPs for the P(True) model.
  Table 2 gives 2.65E+22 for the same 52B model, a value below the 12B model's
  6.12E+22. The card reads the table 2 value as likely a typo; this is an
  inference, not stated in the paper [arxiv:2206.07682 tab. 1] [tab. 2].
- **LaMDA size.** 68B in the text and table 1 [arxiv:2206.07682 §3] [tab. 1];
  69B in table 2 [arxiv:2206.07682 tab. 2]. The appendix gives 27B for the
  same family in one place and table 2 gives 29B [arxiv:2206.07682 app. A.1]
  [tab. 2].
- **Gopher 280B and Chinchilla 70B.** Table 1 gives 5.0E+23 FLOPs for both
  [arxiv:2206.07682 tab. 1]. Table 2 gives 5.46E+23 and 5.63E+23
  [arxiv:2206.07682 tab. 2].
- **PaLM 540B compute.** 2.5·10^24 FLOPs in the text and table 1
  [arxiv:2206.07682 §3] [tab. 1]; 3·10^24 in the discussion section
  [arxiv:2206.07682 §5].
- **Chain-of-thought scale.** The survey places the chain-of-thought gain at
  about 10^23 FLOPs (~100B) [arxiv:2206.07682 §4] [fig. 3A], and lists chain of
  thought on math word problems as emergent at LaMDA 68B, 1.3·10^23 FLOPs
  [arxiv:2206.07682 tab. 1]. The chain-of-thought paper states its gains at
  about 100B parameters [arxiv:2201.11903 §3.2] and gives LaMDA 137B results
  [arxiv:2201.11903 app. B]. Its card does not transcribe a 68B number, so the
  two cannot be checked against each other from wikillm's sources. The 10B
  figure for "most models do not benefit" comes from the chain-of-thought
  paper's appendix, and no source here reports the 10B to 100B range.

- **Smooth scaling of distilled chain of thought.** The survey places the
  chain-of-thought gain at about 10^23 FLOPs (~100B) for prompted models
  [arxiv:2206.07682 §4] [fig. 3A]. The distillation study says its specialized
  FlanT5 students scale log-linearly rather than flat [arxiv:2301.12726 §4.2]
  [fig. 2]. The two settings differ: one prompts models of different sizes, the
  other trains each student on teacher outputs. The sources do not reconcile
  them, and no reading is given here.

- **Prior use in few-shot prompting.** The flipped-label study cites earlier
  random-label work that reads small effects of label noise as a sign that
  models rely on priors [arxiv:2303.03846 §1] [§7.1]. The same study reports
  that large models follow flipped exemplars [arxiv:2303.03846 §3]. Both are
  cited here. The two studies use different tasks and label settings, and this
  page does not reconcile them.
- **Metric artifacts.** The 2025 survey reports that Schaeffer et al. argue
  jumps vanish under linear metrics, while Du et al. and Zhao et al. argue they
  survive [arxiv:2503.05788 §3.1]. Gu et al. report transitions under validation
  loss [arxiv:2503.05788 §3.1]. The 2022 survey says partial-credit metrics still
  show the jump on three generative tasks [arxiv:2206.07682 app. A.2]. This page
  does not pick a side. Check the metric and the seed count before choosing one.
- **Predictability.** The 2022 survey defines an emergent ability as one that a
  smaller model's curve does not predict [arxiv:2206.07682 §2]. The 2025 survey
  reports a loss-based two-stage prediction with 5% to 10% relative error
  [arxiv:2503.05788 §3.7]. The two predictors differ, since one uses scale and
  the other uses loss, so the sources do not settle whether jumps can be
  forecast.

For thresholds, use the values from the table you are comparing against, and
note which one.

## Papers

- [Emergent Abilities of Large Language Models](/papers/2206.07682): defines
  emergence on scaling curves, lists emergent few-shot tasks and augmented
  prompts from prior work, and re-analyses BIG-Bench with loss and partial-credit
  metrics.
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](/papers/2201.11903):
  shows chain-of-thought gains that appear only at about 100B parameters, with
  per-size results and the small-model cost. Results are author-reported.
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](/papers/2304.01373):
  a suite of models with checkpoints and a fixed data order, with a
  term-frequency study of when accuracy starts to track training frequency.
  Each case study is a single run per model.
- [On the Opportunities and Risks of Foundation Models](/papers/2108.07258):
  names emergence as one of two central themes of foundation models. It has no
  experiments, so use it for framing only.
- [Emergent Analogical Reasoning in Large Language Models](/papers/2212.09196):
  reports zero-shot analogy results for GPT-3 text-davinci-003 against
  undergraduate samples on four task families. One model variant, author-reported,
  with no size sweep.
- [Specializing Smaller Language Models towards Multi-Step Reasoning](/papers/2301.12726):
  distils GSM8K chain-of-thought solutions into T5 and FlanT5 students, reports
  log-linear scaling for them, and shows a large loss of general reasoning.
- [Emergent Abilities in Large Language Models: A Survey](/papers/2503.05788):
  reviews the competing definitions and the evidence on metrics, compression,
  prediction, mechanisms, reasoning models and misalignment. It reports no
  experiments of its own, so its numbers are quoted from cited studies.
- [Larger language models do in-context learning differently](/papers/2303.03846):
  flips or unrelates the labels of few-shot prompts and reports that large
  models override priors and learn unrelated mappings, with a Flan-PaLM
  comparison. Author-reported, 100 examples per dataset.
- [Stochastic CHAOS: Why Deterministic Inference Kills, and Distributional Variability Is the Heartbeat of Artifical Cognition](/papers/2601.07239):
  argues that greedy decoding hides capability and tail risk, and measures
  best-of-k gains. Several tables are simulated, and no code was found.