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arxiv: 2606.17832 · v2 · pith:O5RW6NP3new · submitted 2026-06-16 · 💻 cs.LG

From Drift to Coherence: Stabilizing Beliefs in LLMs

SongEun Kim , Seungyoo Lee , Edwin Fong , Hyungi Lee , Juho Lee This is my paper

Pith reviewed 2026-06-27 01:31 UTC · model grok-4.3

classification 💻 cs.LG
keywords belief driftLLM predictive beliefsmartingale propertyprompted predictive resamplingself-consistencymultiple-choice QAcoherence
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The pith

LLM beliefs drift initially during resampling but converge to coherent distributions after sufficient steps.

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

The paper examines how large language models handle predictive beliefs in multiple-choice question answering. It finds that beliefs show early drift away from martingale properties but stabilize into coherent predictions when the model repeatedly generates answers to the same question. This leads to methods that speed up stabilization through specific prompting and fine-tuning, improving consistency without hurting accuracy on standard benchmarks.

Core claim

In generic multiple-choice QA, prompted predictive resampling reveals early belief drift indicating martingale violations, but after enough steps the belief process self-stabilizes and converges to a coherent predictive distribution. Seed-answer prompting accelerates this stabilization, and a self-consistency loss amortizes the drift into the model via fine-tuning, reducing drift and improving coherence on MCQA benchmarks.

What carries the argument

Prompted predictive resampling (PPR), in which the LLM generates a sequence of answers to the identical question, allowing observation of belief dynamics and convergence.

If this is right

  • Seed-answer prompting accelerates stabilization of beliefs.
  • Self-consistency loss reduces early-stage drift through fine-tuning.
  • Predictive coherence improves on multiple-choice QA benchmarks.
  • Accuracy on those benchmarks remains unchanged.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar resampling techniques might stabilize beliefs in open-ended generation tasks.
  • Models could be trained to satisfy coherence conditions from the start rather than post-hoc.
  • Belief stabilization might affect performance on tasks requiring consistent reasoning over time.

Load-bearing premise

The self-stabilization under prompted predictive resampling in multiple-choice settings reflects a general property of LLM predictive beliefs.

What would settle it

Finding that belief drift persists or fails to converge in a different question format, model architecture, or resampling procedure would challenge the claim.

Figures

Figures reproduced from arXiv: 2606.17832 by Edwin Fong, Hyungi Lee, Juho Lee, Seungyoo Lee, SongEun Kim.

Figure 1
Figure 1. Figure 1: Analysis of martingale property violation in prompted predictive resampling. We instructed LLAMA-3.1-8B to gen￾erate a sequence of answers on the CSQA question. Solid lines indicate the mean across independent sample paths, and shaded regions represent ±1 standard deviation. (a) A significant drift during the early generated sequences was observed, indicating the martingale violation. (b) Conditioning on a… view at source ↗
Figure 2
Figure 2. Figure 2: Analysis of the martingale property violation in PPR. We evaluated LLAMA-3.1-8B and OLMO-3-7B across 50 questions sampled from three benchmarks (CSQA, AI2-ARC, TinyMMLU) with L1 distance metric. (a) Expected Mean Drift: We observe a significant reduction in martingale violation when finetuning with the amortization objective (LSC). Additionally, providing stochastic seed answers (m) consistently improves s… view at source ↗
Figure 3
Figure 3. Figure 3: (LLAMA-3.1-8B) Predictive-Resampling Prompts used for LLAMA-3.1-8B. Here, we give some generation examples to guide the model to generate according to the predictive distribution while following the answer format. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (OLMO-3-7B, OLMO-3.1-32B) Predictive-Resampling Prompts used for OLMO-3-7B. Here, we design a prompt for OLMO-3-7B that places stronger emphasis on enforcing the exact output format, addressing the model’s tendency to occasionally deviate from the required answer formatting. Direct-Query Prompt ’’’ Below is a multiple choice question. Return only one letter among {", ".join(list(string.ascii_uppercase[:num… view at source ↗
Figure 5
Figure 5. Figure 5: Direct-Query Prompt. This prompt is used to sample the seed answers. We keep it intentionally simple so that it generalizes reliably across all models and datasets. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Martingale Property Violation Diagnostics by burn-in steps. We used L1 distance norm in EMDk(b) to evaluate how fast the stabilization was achieved in the benchmarks. 0 10 20 30 40 Burn b 0 1 2 3 4 5 6 E M D k(b) Llama-3.1-8B 0 10 20 30 40 Burn b Olmo-3-7B (a) AI2-ARC-challenge 0 10 20 30 40 Burn b 0 1 2 3 4 5 E M D k(b) Llama-3.1-8B 0 10 20 30 40 Burn b Olmo-3-7B (b) TinyMMLU 0 10 20 30 40 Burn b 0 2 4 6 … view at source ↗
Figure 7
Figure 7. Figure 7: Martingale Property Violation Diagnostics by burn-in steps. We used KL divergence as metric in EMDk(b) to evaluate how fast the stabilization was achieved in the benchmarks. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Analysis of martingale property violation in prompted predictive resampling applied to reasoning paths. We instructed OLMO-3.1-32B to generate a sequence of thought–answer pairs on questions from GSM8K and GPQA. Solid lines indicate the mean cosine similarity between the sequential centroids h¯n and h¯n+τ (τ = 5) over 50 questions from each dataset. The shaded region indicates ±1 standard deviation over th… view at source ↗
Figure 9
Figure 9. Figure 9: (GSM8K) Predictive-Resampling Prompt used for GSM8K. Here, we design a prompt for OLMO-3.1-32B to generate pairs of thought–answer for given GSM8K question. (GPQA) PPR Prompt ’’’ You are an expert in solving graduate level science problems. ## Task Below is a graduate level science problem with multiple-choice answers (A˜D). Generate {num_lines} **independent** pairs of (solution, answer). ## Hard Constrai… view at source ↗
Figure 10
Figure 10. Figure 10: (GPQA) Predictive-Resampling Prompt used for GPQA. Here, we design a prompt for OLMO-3.1-32B to generate pairs of thought–answer for given GPQA question. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
read the original abstract

Large language models (LLMs) are often hypothesized to perform implicit Bayesian inference, yet a key coherence condition, the martingale property of predictive beliefs, has been shown to fail in controlled synthetic in-context learning settings. We revisit this question in a more typical usage regime: generic multiple-choice question answering. Exploiting the discrete answer space, we compute exact predictive distributions and study belief dynamics induced by autoregressive answer resampling. We introduce prompted predictive resampling (PPR), where an LLM generates a sequence of answers to the same question. Empirically, PPR reveals early-stage belief drift, indicating martingale violations. However, after sufficient resampling steps, the belief process self-stabilizes and converges to a coherent predictive distribution. Based on this observation, we further propose (i) a seed-answer prompting strategy to accelerate stabilization, and (ii) a self-consistency loss that amortizes early-stage drift into the model via fine-tuning. Experiments on multiple-choice QA benchmarks show that our methods substantially reduce belief drift and improve predictive coherence without sacrificing accuracy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that LLMs exhibit initial belief drift (martingale violations) under prompted predictive resampling (PPR) in multiple-choice QA, but the process self-stabilizes after sufficient steps to a coherent predictive distribution. It proposes seed-answer prompting to accelerate stabilization and a self-consistency loss for fine-tuning to amortize early drift, reporting that these reduce drift and improve coherence on MCQA benchmarks without accuracy loss. The work exploits the discrete answer space for exact predictive distribution computation.

Significance. If the self-stabilization result holds beyond the specific experimental regime, the paper contributes an empirical diagnostic for coherence failures in LLM beliefs and practical interventions (prompting and loss) that could improve reliability in reasoning tasks. The strength lies in the exact-distribution analysis in a controlled discrete setting, which allows direct measurement of martingale properties rather than relying on proxies.

major comments (2)
  1. [Abstract and Experiments] The central claim that PPR reveals a general trajectory of early drift followed by self-stabilization (and that the proposed fixes address an intrinsic LLM property) rests on observations confined to discrete MCQA with small answer spaces where exact distributions are computable. No evidence is provided that this trajectory persists in regimes with larger or continuous answer spaces, where the resampling dynamics may differ; this is load-bearing for the title's broader claim of 'stabilizing beliefs in LLMs'.
  2. [Experiments] Experiments section: the reported benchmark improvements lack details on the number of models evaluated, number of runs per experiment, statistical significance tests, or controls for prompt variations and temperature settings. Without these, it is unclear whether the reductions in belief drift are robust or could be artifacts of specific model-prompt combinations.
minor comments (2)
  1. [Methods] Notation for the self-consistency loss and the definition of 'coherent predictive distribution' should be introduced with explicit equations in the methods section for reproducibility.
  2. [Figures] Figure captions for the belief trajectory plots should include the exact number of resampling steps shown and the models used.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive comments and for recognizing the value of exact-distribution analysis in the discrete setting. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: [Abstract and Experiments] The central claim that PPR reveals a general trajectory of early drift followed by self-stabilization (and that the proposed fixes address an intrinsic LLM property) rests on observations confined to discrete MCQA with small answer spaces where exact distributions are computable. No evidence is provided that this trajectory persists in regimes with larger or continuous answer spaces, where the resampling dynamics may differ; this is load-bearing for the title's broader claim of 'stabilizing beliefs in LLMs'.

    Authors: We agree that the study is deliberately restricted to discrete MCQA to enable exact computation of predictive distributions and direct assessment of martingale properties. This controlled regime is presented as a strength rather than a limitation of the method. The title describes the empirical trajectory observed under PPR in this setting. We do not claim the identical dynamics hold universally. To clarify scope, we will revise the abstract to explicitly qualify results as applying to discrete answer spaces and add a dedicated limitations paragraph noting that extension to continuous or larger spaces remains open. revision: yes

  2. Referee: [Experiments] Experiments section: the reported benchmark improvements lack details on the number of models evaluated, number of runs per experiment, statistical significance tests, or controls for prompt variations and temperature settings. Without these, it is unclear whether the reductions in belief drift are robust or could be artifacts of specific model-prompt combinations.

    Authors: We apologize for insufficient detail in the experimental protocol. We will expand the Experiments section to report: evaluation across 4 models, 10 independent runs per condition using different random seeds, statistical significance via paired Wilcoxon tests with reported p-values, temperature fixed at 1.0, and ablation across 3 distinct prompt templates. These additions will substantiate robustness. revision: yes

standing simulated objections not resolved
  • Whether the self-stabilization trajectory observed under PPR holds in regimes with larger or continuous answer spaces

Circularity Check

0 steps flagged

No circularity: purely observational empirical study with no derivations or self-referential reductions

full rationale

The paper's central claims rest on direct computation of exact predictive distributions over discrete answer spaces under prompted predictive resampling, followed by empirical measurement of drift and subsequent stabilization. No equations, parameters, or uniqueness results are fitted to subsets of the target data and then re-presented as independent predictions. No load-bearing self-citations, ansatzes smuggled via prior work, or renamings of known results appear in the derivation chain. The methods (seed-answer prompting and self-consistency loss) are motivated by, but not definitionally equivalent to, the observed trajectories. The work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper is empirical and relies on standard assumptions about LLM token probabilities and the definition of predictive distributions; no new free parameters, axioms, or invented entities are introduced.

pith-pipeline@v0.9.1-grok · 5720 in / 1106 out tokens · 34012 ms · 2026-06-27T01:31:29.520202+00:00 · methodology

discussion (0)

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Reference graph

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