Forking Paths in Neural Text Generation

Ari Holtzman; Eric Bigelow; Hidenori Tanaka; Tomer Ullman

REVIEW 3 major objections 5 minor 4 cited by

Forking Paths in Neural Text Generation

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A single token swapped for a probable alternative can redirect an LLM's entire subsequent generation, and static uncertainty estimates miss this.

desk verdict A genuinely new method and a plausible hypothesis, but the headline prevalence numbers are undercut by an unvalidated extractor that demonstrably over-splits surface variants; the qualitative existence claim holds. read the letter →

arxiv 2412.07961 v1 pith:67SOKW7I submitted 2024-12-10 cs.CL cs.AIcs.LG

Eric Bigelow , Ari Holtzman , Hidenori Tanaka , Tomer Ullman This is my paper · ORCID

classification cs.CLcs.AIcs.LG

keywords forkingtokensuncertaintyestimationlargelanguagemodelschangepointdetectionsurvivalanalysistextgeneration

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper sets out to show that uncertainty in large language models is not just a property of the final answer: it lives at individual tokens along the way. The authors propose the Forking Tokens Hypothesis, namely that replacing one token with a probable alternative can change the distribution of everything that follows. They test it by re-sampling many completions from every likely alternate token in GPT-3.5 outputs across seven tasks, extracting final answers with a second LLM, and using change point detection and survival analysis to find where outcome distributions break. They report forking tokens in content words, spaces, and punctuation, and find that a majority of analyzed sequences have a low probability of surviving to the end without a major outcome shift. If correct, the result means existing token-level or final-token confidence scores can be systematically misleading, and safety evaluations that sample one response per prompt can miss large parts of the model's actual behavior.

What carries the argument

The machinery is Forking Paths Analysis, built on the Forking Tokens Hypothesis. For a greedily decoded base path $x^*$, the pipeline records the top probable alternate tokens at each index $t$, re-samples fresh completions conditioned on each alternate token, and maps every completion to a categorical outcome $R$ using a second LLM. These outcomes are aggregated into probability-weighted histograms $o_{t,w}$, and the marginal distribution $o_t$ becomes a multivariate time series. A one-dimensional 'semantic drift' series $y_t = d(o_0, o_t)$ with an $L^2$ distance feeds a Bayesian change point detection model that flags indexes where the outcome distribution shifts abruptly; a separate discrete-time survival analysis computes, for each token, a hazard $h(t) = \sum_w p(x_t=w \mid x_{<t}) \mathbb{1}[d(o_{t,w}, o_{t,w^*})>\epsilon]$ and the cumulative survival $S(t)$, so a 'forking token' is an index or alternate value where a small probable substitution changes the downstream answer distribution.

What would settle it

Take the HotpotQA example in Figure 23 and re-run Forking Paths Analysis with an extractor that merges surface variants of the same person ('Natalia Lafourcade', 'Nati', 'Natalia y La Forquetina') into one semantic outcome. If the change point probability and survival hazards at the separating tokens drop below significance, the apparent fork is an extraction artifact. A broader check: if merging such variants across all HotpotQA sequences moves the majority of end-of-sequence survival rates above 0.2, the headline claim of widespread low survival would not survive its own measurement assumptions.

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Extended reading notes

Core claim

The paper's central claim is empirical support for the Forking Tokens Hypothesis: in LLM text generation there exist token positions where exchanging the sampled token for a probable alternate significantly changes the distribution of eventual outcomes. The authors demonstrate this by building per-token outcome distributions from re-sampled completions and analyzing them with Bayesian change point detection and survival analysis. They find forking tokens across all seven tasks, including seemingly innocuous tokens such as spaces, parentheses, and the word 'that' versus 'who'. In many sequences the outcome distribution is stable for most of the text and then collapses to a different answer at a single forking token, often a hallucinated reasoning step. Their survival analysis shows that for a large fraction of GPT-3.5 sequences the cumulative probability of reaching the end of the base path without hitting a fork is below 0.2, even with a generous distance threshold, so the paper concludes that static final-token confidence estimates can be unstable and misleading.

Load-bearing premise

The results assume the second model used to extract final answers treats surface variants as the same answer whenever they are semantically the same answer; if it does not, many detected 'forks' and low survival rates could be artifacts of word choice rather than real changes in meaning.

Editorial extensions

If this is right

Static final-token confidence, such as a near-100% logit at the last token, can hide a sequence that was close to a different answer for most of its length.
Evaluators should treat low survival rates as a warning that a single sampled completion is not a stable measurement of model knowledge.
Safety and alignment checks that sample one or a few responses can miss paths reachable by probable token substitutions, including hallucinated or harmful completions.
Token logit probability is not a reliable flag for forking: punctuation and space tokens can carry as much outcome-changing weight as content words.
The analysis works without fine-tuning or model weights, so it can be applied to black-box APIs and to any task where final answers or semantic embeddings can be extracted.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If forking tokens generalize across models, the per-token hazard profile could be used as a model diagnostic: where in a prompt a model commits to an answer, and how sharply.
A natural extension is to use semantic embeddings instead of categorical extraction, which would let the same machinery measure forking in open-ended creative text rather than only tasks with extractable answers.
The survival rate $S(T)$ could be turned into a calibration-style metric: of two models with equal accuracy, the one with higher survival rate is more stable under token-level perturbations.
Forking positions may be a target for adversarial token edits: an attacker who can identify probable alternate tokens at high-hazard positions can steer the model's outcome with minimal surface changes.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The core idea here is good: the per-token counterfactual re-sampling pipeline and the outcome-distribution time series are genuinely new relative to static uncertainty estimation work like Kadavath, Tian, and Xiong. The concrete examples are compelling—Robin Tunney versus Mia Sara, 2021 versus 2024, the parenthesis token in GSM8k—and they make a real case that forking tokens exist. The paper is also clearly written and admirably honest about its own limitations, including the extractor issue in App. E.

The soft spot is the quantitative extent claim. Survival rates in Sec. 4.2 come from Eq. (3), where a fork is declared when d(ot,w, ot,w*) > epsilon, and that distance is computed over histograms of extracted outcomes. The extractor is a second LLM with Python cleansing, never validated against human judgment. App. E, Fig. 23 shows the same person returned as 'Natalia Lafourcade', 'Nati', 'Nati Lafourcade', and 'Natalia y La Forquetina'—four bins for one answer. If that over-splitting is at all common, L2 distances inflate, hazards rise, and S(T) is biased downward. So the 'majority of sequences have S(T) < 0.2' headline is not yet supported. The post hoc tuning of the change-point detector (noise injection, alpha, epsilon chosen to match qualitative judgment) and the absence of released code or data make those numbers even harder to check.

That said, the existence of forking tokens does not rest on the extractor. The case studies show real semantic flips at individual tokens, and even if the true prevalence is lower than reported, the phenomenon is real and the method is a useful tool. The correlation analysis in App. C.2 (token logits do not predict change points) is a nice sanity check.

This paper deserves a serious referee. The referee should press for extractor validation or a similarity-based distance that does not treat surface variants as distinct outcomes, for sensitivity analysis on epsilon and binning, and for released code and data. As it stands, the qualitative contribution is solid, but the headline quantitative claims should be treated with caution.

Referee Report

3 major / 5 minor

Summary. The paper introduces the Forking Tokens Hypothesis: that in LLM text generation a single token substitution at certain positions can dramatically change the final outcome. To test this, the authors develop Forking Paths Analysis, a three-stage black-box pipeline: (1) decode a greedy base path and record the top alternate token probabilities; (2) at each token position, resample S=30 completions conditioned on each plausible alternate token; (3) extract a categorical outcome from each completion using a second LLM (Gemini Flash). The resulting per-token outcome distributions ot and ot,w are analyzed with Bayesian change point detection (BEAST) on a univariate drift series, and with a discrete-time survival analysis on per-token hazards. Experiments on 7 tasks across 4 domains with GPT-3.5 report both individual qualitative examples of forking tokens (e.g., HotpotQA-8076 flipping from Robin Tunney to Mia Sara) and aggregate quantitative results: change-point fractions per task and low terminal survival rates S(T), with mean S(T) below 0.2 for a majority of sequences at typical thresholds. The paper concludes that static final-token uncertainty estimates miss substantial dynamical uncertainty and that LLMs are often one token away from a very different answer.

Significance. The qualitative phenomenon documented here is genuinely interesting and, if the quantitative claims are correct, would be an important finding for uncertainty estimation and evaluation of LLMs: it would show that final-answer confidence can be misleading and that outcome uncertainty can collapse or shift abruptly at individual tokens. The method is novel, model-agnostic, black-box, and the interactive dashboard is a useful public artifact. The paper also demonstrates concrete, semantically meaningful forking examples (2021 vs 2024; Robin Tunney vs Mia Sara) that are not explained by simple low-probability sampling noise, and it shows a lack of correlation between token logit probability and change-point probability (App. C.2). However, the paper's load-bearing quantitative claims rest on an unvalidated second-LLM outcome extractor that the authors themselves show splits one semantic answer into several surface forms, and on a survival function that appears mis-specified as written. These issues must be resolved before the extent of the phenomenon can be accepted.

major comments (3)

[Sec. 4.2, Eq. (3)] The survival function is defined as S(t) = 1 - ∏_{t'=1}^{t} h(t'), where h(t) is the probability that a sampled alternate token is forking. This is not the standard discrete survival function, which is ∏_{t'=1}^{t} (1 - h(t')). For typical small hazard values, 1 - ∏ h(t') is close to 1 and does not decrease monotonically over a long sequence, yet the plotted S(t) curves in Fig. 7 (Bottom Left) decrease smoothly from 1 to below 0.3, which matches the standard survival definition. As written, the equation is therefore inconsistent with the paper's own plots and with the reported low S(T) values. Please correct Eq. (3) and re-derive the numerical results in Table 1 and Fig. 7 under the intended definition, and state clearly whether S(T) is a survival probability or a cumulative fork probability.
[Sec. 2.4 and App. E (Fig. 23)] The outcome extractor R maps each continuation to a categorical string, and every distance d(ot,w, ot,w*) in Eq. (3) is computed over these categories. The paper itself documents in App. E (Fig. 23) that the single entity 'Natalia Lafourcade' is returned as 'Natalia Lafourcade', 'Nati', 'Nati Lafourcade', and 'Natalia y La Forquetina' and counted as distinct outcomes. This over-splitting inflates distances, inflates the hazard h(t), and biases S(T) downward. The extractor is never validated against human judgment, and no error analysis is reported. Please provide a human-validation study of R on a random sample of extractions per task, and recompute the survival analysis after collapsing semantic equivalents (e.g., via a secondary aggregation step or a semantic-similarity threshold), reporting both the raw and collapsed estimates.
[Sec. 4.2, Table 1 and Fig. 7] The claim that a majority of sequences have S(T) < 0.2 is reported as a mean over 30 examples per task, with no confidence intervals, no per-task distribution, and no sensitivity analysis for the two most consequential free choices: the distance threshold epsilon (Table 1 uses epsilon = 0.6; Fig. 7 reports 'for all epsilon < 0.9' without error bars) and the alternate-token sampling rule (k <= 10, p >= 5%). Because S(T) is computed on the unvalidated extractor's bins, the quantitative headline may be an artifact of the binning and threshold choices. Please report the full distribution of S(T) per task (e.g., box plots), and include a robustness check with a coarser outcome space (multiple-choice letter only; numeric answers normalized as in the existing cleansing functions) to demonstrate that the conclusion is not driven by the chosen granularity.

minor comments (5)

[Sec. 3, paragraph 2] The sentence 'For (1), we collect N=300 full text responses' refers to an undefined item (1); this is presumably the outcome distribution ot at t=0, but it should be stated explicitly.
[App. G] The prompt listings contain stray '→' characters and '⁄tildelow' placeholders that appear to be rendering artifacts; these should be cleaned before publication.
[Sec. 2.1] The text refers to 'logit probabilities' when it appears to mean next-token probabilities after the softmax; please use consistent terminology.
[Sec. 2.3] The semantic drift transformation yt = d(o0, ot) uses L2 distance on probability histograms; the choice of distance metric is a free parameter and the justification for L2 over other metrics (e.g., total variation or Jensen-Shannon) should be expanded.
[Reproducibility statement] The reproducibility statement says code and data 'will be made publicly available in the near future'; for a methods paper, a stable repository link or a specific commitment is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the forking-token results come from a nontrivial sampling and statistical pipeline, not from a definitional reuse of the hypothesis.

full rationale

The paper's central claim (the Forking Tokens Hypothesis) is tested by an explicitly operationalized pipeline: sample alternate tokens, extract outcome representations R, aggregate them into ot,w, compute distances d(ot,w, ot,w*) > epsilon, and then report change-point and survival statistics. The reported quantities (Bayes factors, S(T)) are genuine outputs of a nontrivial sampling experiment; they are not restatements of the input token logits or of the definition of a forking token. The choice of R, epsilon, and the distance metric are measurement decisions, and the paper's own Appendix E documents over-splitting of surface forms (e.g., 'Natalia Lafourcade' vs 'Nati' for the same entity). This is a real threat to construct validity and to the quantitative survival rates, but it is an instrumentation concern rather than a circular derivation: the extractor is not fitted to the hypothesis, no load-bearing self-citation is used, and the qualitative forking examples (HotpotQA-8076, GSM8k-59) provide independent content. The only self-citation (Bigelow et al., 2024) appears in a speculative Discussion passage and does not carry the argument. No step in the derivation chain reduces to its own inputs by construction.

Assumptions & free parameters 7 free parameters · 5 assumptions · 1 invented entities

The paper introduces no physical entities, but the 'forking token' construct is defined entirely by the measurement pipeline that also serves as its evidence. The most load-bearing free choices are the hazard threshold epsilon, the L2 metric selection, the noise injection used to suppress false positives, and the outcome bucketing; all of them directly shape the aggregate survival rates that motivate the 'single token away' headline. The axiomatic content is concentrated in the faithfulness of the second-LLM extractor and in the counterfactual interpretation of conditioned re-sampling.

free parameters (7)

hazard distance threshold epsilon = 0.6 (scanned up to 0.9)
Survival analysis counts a token as forking only if d(ot,w, ot,w*) > epsilon; the final survival rates S(T) in Fig. 7 and the 'majority below 0.2' claim are computed at epsilon = 0.6, and the rates are directly sensitive to this hand-chosen threshold.
Bayes factor threshold = 9
A sequence is declared to have at least one change point when p(m >= 1 | y) / p(m = 0 | y) > 9, a standard Kass-Raftery threshold; the .1 quantile of p(m | y) is treated as the 90%-confidence estimate of the number of change points.
alternate token sampling cutoff = k <= 10 tokens with p >= 5%
Only tokens with next-token probability at least 0.05 among the top 10 are re-sampled; hazards are sums over this restricted set, so the reported survival rates are conservative only if the cutoff excludes nothing important, which is itself an assumption.
sample counts S and N = S = 30 continuations per (t, w); N = 300 at t = 0
Outcome distributions are estimated from 30 continuations per alternate token; App. D shows change-point counts are stable with 10 to 20 samples, but the distance estimates used in hazards have no error bars.
noise injection and noise prior alpha = Gaussian noise with variance 0.03; alpha manually tuned
Noise is added to the drift series yt and the BEAST noise hyper-prior alpha is manually tuned specifically to reduce a documented high false-positive rate in change point detection (App. B); this is post-hoc calibration of the central detector.
distance metric d = L2 (L1 and KL divergence rejected)
L2 was chosen because it 'most reliably corresponded to qualitative judgments of change points' (App. B), so the detector's output is a function of a metric selected to match the authors' visual inspection of the same examples.
outcome bucketing = top 6 outcomes plus 'Other'
Extracted answers outside the top 6 most probable outcomes are lumped into a single 'Other' bin; distances computed on these buckets depend on the bucket count, and the bucket count is a free choice.

assumptions (5)

domain assumption The greedily decoded base path x* is a representative path for analyzing uncertainty at each position t.
Sec. 2.1: the analysis conditions on a single greedily decoded sequence and its prefixes; forking behavior off non-greedy paths is not sampled, so all conclusions are conditional on the greedy trajectory.
domain assumption Re-sampling continuations conditioned on the base prefix plus a forced token estimates the counterfactual outcome of that token choice.
Sec. 2.1, Eq. (1): ot,w is the probability-weighted expectation over continuations; this presumes the LLM's continuation distribution given the modified prefix is the right counterfactual object.
domain assumption The second LLM (Gemini Flash) extraction R is a faithful, noise-free mapping from text to semantic outcome.
Sec. 2.1 third stage and App. G; never validated against human labels; App. E (Fig. 23) documents surface-variant outcomes such as 'Nati' vs 'Natalia Lafourcade', showing the assumption fails in at least some cases.
domain assumption An abrupt change in the univariate drift series yt = d(o0, ot) with L2 distance corresponds to a meaningful semantic fork.
Sec. 2.3: the multivariate outcome distribution ot is collapsed to a univariate distance-from-initial series before applying BEAST; the link between statistical drift and semantic forking is assumed, not demonstrated.
standard math The next-token probabilities p(xt | x<t) returned by the API logits are correct and sufficient for probability weighting.
Sec. 2.1 and Eq. (2): all weighting uses next-token probabilities from black-box logits, treated as ground truth probabilities without verification.

invented entities (1)

Forking token independent evidence
purpose: A token index or token value where re-sampling a probable alternate leads to a dramatically different outcome distribution; the object of the paper's hypothesis test.
The paper provides operational handles outside the core claim: a re-sampling protocol that anyone can run, an interactive dashboard with all examples, and concrete falsifiable instances such as 'The current year is 2021 vs 2024' leading to Queen Elizabeth vs King Charles. However, its detection depends entirely on the unvalidated second-LLM outcome extractor, so the entity is only as reliable as that instrument.

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Cite this review

Pith. "Pith review of Forking Paths in Neural Text Generation." pith.science (2026). https://pith.science/paper/67SOKW7I

@misc{pith2026241207961,
  author       = {Pith},
  title        = {Pith review of: Forking Paths in Neural Text Generation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/67SOKW7I}},
  note         = {Machine review of arXiv:2412.07961}
}

read the original abstract

Estimating uncertainty in Large Language Models (LLMs) is important for properly evaluating LLMs, and ensuring safety for users. However, prior approaches to uncertainty estimation focus on the final answer in generated text, ignoring intermediate steps that might dramatically impact the outcome. We hypothesize that there exist key forking tokens, such that re-sampling the system at those specific tokens, but not others, leads to very different outcomes. To test this empirically, we develop a novel approach to representing uncertainty dynamics across individual tokens of text generation, and applying statistical models to test our hypothesis. Our approach is highly flexible: it can be applied to any dataset and any LLM, without fine tuning or accessing model weights. We use our method to analyze LLM responses on 7 different tasks across 4 domains, spanning a wide range of typical use cases. We find many examples of forking tokens, including surprising ones such as punctuation marks, suggesting that LLMs are often just a single token away from saying something very different.

Figures

Figures reproduced from arXiv: 2412.07961 by the authors.

**Figure 1.** Forking paths in text generation: can a single token alter the outcome? At each step of next-word text generation, an LLM has some probability of sampling a variety of possible next tokens. This raises the question: are there specific forking tokens, where choosing a certain token over other probable alternatives results in a distinct outcome? To test this hypothesis, we estimate uncertainty in text generation by sy… view at source ↗

**Figure 2.** (Top) Systematically sampling alternate paths in text generation. Our data collection proceeds in three stages. First, we decode a base path text completion x ∗ from an LLM given some prompt and record the most probable alternate tokens w at each step t. Next, we re-sample S completions x (s) >t by appending x ∗ <t to the original prompt, along with each alternate token xt = w. Finally, we extract outcome vector rep… view at source ↗

**Figure 3.** Uncertainty dynamics time series (Top) The outcome distribution ot is equivalent to a multivariate time series, where each possible outcome (e.g. King Charles or Queen Elizabeth) can be plotted as a separate line. To simplify our modeling, we convert ot into a univariate time series using a semantic drift transformation yt. Bayesian Change Point Detection model. (Bottom, Left) We use a Bayesian Change Point Detectio… view at source ↗

Figures from the paper (27 more)

**Figure 4.** Figure 4: The outcome distribution can collapse after a single step in chain-of-thought reasoning. (Left, Top) The outcome distribution ot and (Left, Bottom) change point probabilities p(τ = t|y) for a single question from HotpotQA and a greedily decoded base path x ∗ . (Right) …

**Figure 5.** Figure 5: Further examples of forking tokens Two examples of outcome distributions ot(x ∗ ) with forking tokens: a physics question from MMLU (Top; Correct Answer: B) and a mathematical reasoning question from GSM8k (Bottom; Answer: 21). In MMLU-12, we see a similar pattern to …

**Figure 6.** Figure 6: Change points occur closer to the beginning of sequences for some tasks, and near the middle of sequences for others Each point represents the fraction of question-answer examples in a task where our change point model predicts one or more change points approximately a…

**Figure 7.** Figure 7: Text generation has a low probability of surviving decoding without a major distribution shift (Top Left) The hazard function h(t) is the probability that ot,w will change significantly if a different token w is sampled, and (Bottom Left) S(t) measures the cumulative …

**Figure 8.** Figure 8: Plate diagram for change point model y is a univariate time series, m is an integer number of change points, τi ∈ {1 . . . |y|} is the time index when a change point occurs, θi includes model parameters such as abrupt change magnitude and polynomial trend model coeffic…

**Figure 9.** Figure 9: Comparing static uncertainty baselines to Forking Paths analysis (HotpotQA-8076; [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]

**Figure 10.** Figure 10: Comparing static uncertainty baselines to Forking Paths analysis (GSM8k-59; [PITH_FULL_IMAGE:figures/full_fig_p019_10.png]

**Figure 11.** Figure 11: Correlation between change point probability and token logit probability We find that token logit probability p(xt = w ∗ ) is not strongly predictive of the probability that a token is labeled a change point by our model p(τ = t | y). In fact we find a slight positive…

**Figure 12.** Figure 12: Correlation between change point model and survival analysis. We find no correlation between the number of change points estimated by our CPD model (the .1 quantile of p(m | y)) and the final survival rate S(T) of a sequence. Each point represents a single prompt and …

**Figure 13.** Figure 13: Correlation between number of change points estimated with our full dataset (S = 30) and estimated with smaller sample sizes S = N For each panel, we sub-sampled N completion texts for each token t and w, where N < 30. Given this smaller dataset and estimated outcome …

**Figure 14.** Figure 14: CoinFlip-1035 Outcome Distribution ot Other No 0 10 20 30 40 50 60 70 80 Token Index t Change Point Prob. p( = t | y) Question: A coin is heads up. Aalisha flips the coin over. Cleotha does not flip the coin over. Is the coin still heads up? Answer: Let's think step b…

**Figure 15.** Figure 15: CoinFlip-15426 23 [PITH_FULL_IMAGE:figures/full_fig_p023_15.png]

**Figure 16.** Figure 16: LastLetter-103 – Correct answer: aota Outcome Distribution ot Other eaaai easy eayi eayy eiya eiyy 0 50 100 150 200 250 Token Index t Change Point Prob. p( = t | y) Question: Take the last letter of each word in "Sue Cassandra Cody Cali" and concatenate them. Answer: …

**Figure 17.** Figure 17: LastLetter-220 – Correct answer: eayi 24 [PITH_FULL_IMAGE:figures/full_fig_p024_17.png]

**Figure 18.** Figure 18: AQuA-62 – Correct answer: A Outcome Distribution ot Other A B C E 0 25 50 75 100 125 150 175 Token Index t Change Point Prob. p( = t | y) Question: A cheerleading squad practices 1 hour a day from Monday through Thursday for a competition on Saturday. How many hours w…

**Figure 19.** Figure 19: AQuA-160 – Correct answer: C 25 [PITH_FULL_IMAGE:figures/full_fig_p025_19.png]

**Figure 20.** Figure 20: GSM8k-1 – Correct answer: 70 Outcome Distribution ot Other 21.0 27.0 45.0 54.0 0 20 40 60 80 100 120 140 160 Token Index t Change Point Prob. p( = t | y) Question: Chase and Rider can ride their bikes thrice a day for 5 days; but on two other days, they ride twice the…

**Figure 21.** Figure 21: GSM8k-78 – Correct answer: 54 26 [PITH_FULL_IMAGE:figures/full_fig_p026_21.png]

**Figure 22.** Figure 22: HotpotQA-79442 – Correct answer: Peter Noone Outcome Distribution ot Other Natalia Lafourcade Natalia y La Forquetina Nati Nati Lafourcade Nati Lafourcade or Natalia 0 25 50 75 100 125 150 175 Token Index t Change Point Prob. p( = t | y) Question: The artist who relea…

**Figure 23.** Figure 23: HotpotQA-30010 – Correct answer: La Negra 27 [PITH_FULL_IMAGE:figures/full_fig_p027_23.png]

**Figure 24.** Figure 24: MMLU-3 – Correct answer: B Outcome Distribution ot Other A B C 0 20 40 60 80 100 Token Index t Change Point Prob. p( = t | y) Question: A national association brought suit in federal court against a city. The suit charged the city with violating several federal statut…

**Figure 25.** Figure 25: MMLU-58 – Correct answer: A 28 [PITH_FULL_IMAGE:figures/full_fig_p028_25.png]

**Figure 26.** Figure 26: MMLU-72 – Correct answer: A STORYCLOZE For StoryCloze, in some cases we observe change points, such as in [PITH_FULL_IMAGE:figures/full_fig_p029_26.png]

**Figure 27.** Figure 27: StoryCloze-1197 29 [PITH_FULL_IMAGE:figures/full_fig_p029_27.png]

**Figure 28.** Figure 28: StoryCloze-1482 AGGREGATED ANALYSIS FOR NUM. CHANGE POINTS 0 1 2 3+ Estimated # Change Points m 0.0 0.2 0.4 0.6 0.8 1.0 % of Examples with m C h a n g e P oints Multiple Choice Tasks AQuA MMLU 0 1 2 3+ 0.0 0.2 0.4 0.6 0.8 1.0 Free Response Tasks GSM8k HotpotQA LastLet…

**Figure 29.** Figure 29: Estimated number of change points m aggregated over each task We estimate the number of change points in each task by taking the .1 quantile of p(m|y) (rounded to the nearest integer) for each prompt and base path x ∗ . We then compute the fraction of all examples in …

**Figure 30.** Figure 30: Task-level estimates of CPD model results, varying threshold levels Here we show the results of Figs. 6, 29 while varying the thresholds we use for each. (Left) Varying the change point probability threshold for p(τ = t|m), and (Right) varying the quantile used to est…

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Forward citations

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Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages · cited by 4 Pith papers

[1]

Al Despertar

The first step is to find out who released the album "Al Despertar". A quick search on the internet reveals that the album was released by the Mexican singer-songwriter Natalia Lafourcade

work page
[2]

Nati Lafourcade

Now, we need to find out if Natalia Lafourcade has any other names or aliases that she is known by. Another search on the internet shows that she is sometimes referred to as "Nati Lafourcade" or simply "Natalia"

work page
[3]

Al Despertar

However, there is no mention of any other name or alias that she is known by in relation to the album "Al Despertar"

work page
[4]

Nati Lafourcade

Therefore, the answer to the question is that Natalia Lafourcade is sometimes known as "Nati Lafourcade" or "Natalia", but there is no specific name or alias that she is known by in relation to the album "Al Despertar". Figure 23: HotpotQA-30010 – Correct answer: La Negra 27 MMLU Sequences in the MMLU have the second most change points (Figs 24, 25, 26), ...

work page
[6]

Terry loves to swim but he never learned how to dive

The story must start with the sentence: "Terry loves to swim but he never learned how to dive."

work page
[7]

Terry hope to improve

The story must end with one of the following two sentences: - "Terry hope to improve." - "Terry has given up swimming."

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[8]

Answer: Terry loves to swim but he never learned how to dive.He would watch his friends gracefully dive into the pool while he awkwardly jumped in

The last sentence must be exactly one of these sentences, not a rephrasing. Answer: Terry loves to swim but he never learned how to dive.He would watch his friends gracefully dive into the pool while he awkwardly jumped in. One day, his friends convinced him to try diving and he belly flopped, causing everyone to laugh. Embarrassed, Terry decided to give ...

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[10]

Holly asked her brother to put suntan lotion on her back

The story must start with the sentence: "Holly asked her brother to put suntan lotion on her back."

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Show all 14 references

[11]

Holly yelled at her brother to get back at him

The story must end with one of the following two sentences: - "Holly yelled at her brother to get back at him." - "Holly gave her brother money as compensation."
[12]

Answer: Holly asked her brother to put suntan lotion on her back.He reluctantly agreed, but as he was rubbing it in, he accidentally squirted some in her hair

The last sentence must be exactly one of these sentences, not a rephrasing. Answer: Holly asked her brother to put suntan lotion on her back.He reluctantly agreed, but as he was rubbing it in, he accidentally squirted some in her hair. Holly yelled at her brother to get back a...
[13]

The story must be exactly five sentences long
[14]

{ first sentence }

The story must start with the sentence: "{ first sentence } "
[15]

{ last sentence 1 }

The story must end with one of the following two sentences: - "{ last sentence 1 } " - "{ last sentence 2 } "
[16]

< last sentence 1 >

The last sentence must be exactly one of these sentences, not a rephrasing. Answer: { first sentence } OUTCOME REPRESENTATION PROMPTS The following prompts are used for extracting outcome representations R(·) from a second LLM. In our case, for cost efficiency the second LLM u...

2022

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

Al Despertar

The first step is to find out who released the album "Al Despertar". A quick search on the internet reveals that the album was released by the Mexican singer-songwriter Natalia Lafourcade

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[2] [2]

Nati Lafourcade

Now, we need to find out if Natalia Lafourcade has any other names or aliases that she is known by. Another search on the internet shows that she is sometimes referred to as "Nati Lafourcade" or simply "Natalia"

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[3] [3]

Al Despertar

However, there is no mention of any other name or alias that she is known by in relation to the album "Al Despertar"

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[4] [4]

Nati Lafourcade

Therefore, the answer to the question is that Natalia Lafourcade is sometimes known as "Nati Lafourcade" or "Natalia", but there is no specific name or alias that she is known by in relation to the album "Al Despertar". Figure 23: HotpotQA-30010 – Correct answer: La Negra 27 MMLU Sequences in the MMLU have the second most change points (Figs 24, 25, 26), ...

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[5] [6]

Terry loves to swim but he never learned how to dive

The story must start with the sentence: "Terry loves to swim but he never learned how to dive."

work page

[6] [7]

Terry hope to improve

The story must end with one of the following two sentences: - "Terry hope to improve." - "Terry has given up swimming."

work page

[7] [8]

Answer: Terry loves to swim but he never learned how to dive.He would watch his friends gracefully dive into the pool while he awkwardly jumped in

The last sentence must be exactly one of these sentences, not a rephrasing. Answer: Terry loves to swim but he never learned how to dive.He would watch his friends gracefully dive into the pool while he awkwardly jumped in. One day, his friends convinced him to try diving and he belly flopped, causing everyone to laugh. Embarrassed, Terry decided to give ...

work page

[8] [10]

Holly asked her brother to put suntan lotion on her back

The story must start with the sentence: "Holly asked her brother to put suntan lotion on her back."

work page