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REVIEW 3 major objections 4 minor 89 references

This paper claims that hallucination in larger language models is driven by a decoding-time risk that grows with scale and is invisible to the model itself.

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Hallucination in LLMs is driven by an oracle-invisible “decoding risk” term that grows with scale and causally compounds errors within a response.

T0 review reviewed 2026-08-02 challenge →

load-bearing objection Reliability anti-scaling is a real empirical package worth taking seriously, but the causal and 'invisible' claims run ahead of the evidence. the 3 major comments →

arxiv 2607.18292 v3 pith:E43A3EKY submitted 2026-06-30 cs.LG cs.AIcs.CL

Reliability Scales Inversely: Hallucinations Snowball Faster in Bigger Language Models

Kushal Chakrabarti This is my paper
classification cs.LG cs.AIcs.CL
keywords hallucinationlarge language modelsinverse scalingdecoding riskuncertaintyreliabilityautoregressive decodingoracle disagreement
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

The paper's central claim is that long-form hallucination in language models is not primarily a knowledge gap but a decoding-time risk: the spread between the model's token probabilities and a stronger oracle's. This risk grows with model scale even as the model's start-of-response knowledge improves, and once a fabrication is committed the risk persists long after the model's felt uncertainty relaxes, making the next fabrication likelier. The paper proves an exact identity splitting model–oracle disagreement into a bias term (which includes the model's own entropy) and a risk term (which does not), and demonstrates by intervention that shrinking the risk at fixed bias removes 35–74% of web-verified hallucinations across three model families. If correct, reliability is a distinct scaling axis that worsens with parameters and is structurally invisible to standard self-monitoring detectors.

Core claim

The paper's central discovery is that the per-position disagreement δ = log p_M − log p_O between a model and a stronger oracle has a second moment that splits exactly into bias² = KL(p_M∥p_O)² and decoding risk Var[δ]. The model's own uncertainty H(p_M) enters only the bias term, so the risk term has no model-readable component. Empirically, the risk term takes a growing share of the squared error as models scale (31% to 49% from 1.7B to 14B), persists 23× longer than felt uncertainty after a fabrication onset, and causally drives subsequent fabrications: a mean-preserving contraction of the variance at fixed KL removes 35–74% of web-verified hallucinations across six model×family rungs. Th

What carries the argument

The central object is the disagreement variable δ = log p_M − log p_O between the model and a stronger oracle, together with the exact identity E[δ²] = KL(p_M∥p_O)² + Var[δ], which splits squared error into bias² and decoding risk. The identity does interpretative work before statistical work: the model's self-readable entropy H(p_M) appears only inside the bias term, so the risk term is structurally inaccessible from the model's own probabilities. The causal test is a mean-preserving variance contraction qλ ∝ p_M exp(−λ(δ−μ)² + νδ), which lowers Var[δ] while holding E[δ] fixed (bias drift kept ~11 orders of magnitude below the bias), isolating the decoding-risk channel from the mean-gap cha

Load-bearing premise

The load-bearing premise is that a stronger same-family (or cross-family) model serves as a truthful oracle, so every 'knowledge gap,' 'risk,' and 'degradation' is measured as disagreement with that oracle; if the oracle is confidently wrong or miscalibrated in a way that correlates with scale, the mechanism is disagreement with a fallible model rather than error against truth.

What would settle it

Use a benchmark with ground-truth labels (e.g., arithmetic word problems or code execution) and construct two oracles: one known to be highly accurate and one deliberately poisoned or miscalibrated with scale. If the risk term Var[δ] and the intervention's effect are largely unchanged when measured against the poisoned oracle, then the paper's mechanism is a property of divergence from any referent rather than of hallucination; if the effect tracks only the accurate oracle, the truth-referent is essential.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Scaling a model family improves the start-of-response knowledge gap up to 7× but increases within-response knowledge degradation up to 39×, so capability and reliability are distinct scaling axes.
  • Risk's share of squared model–oracle error grows from 31% to 49% between 1.7B and 14B, and the disagreement tail grows heavier (excess kurtosis 8.9→33.0), meaning larger models agree with the oracle more often but diverge more when they do.
  • A committed fabrication raises the probability of the next fabrication by a factor that grows with scale (1.08× to 1.71× on a topic-controlled sample), and a confident-but-precarious regime (low entropy, high risk) increasingly occupies the bridge between consecutive fabrications, up to +69% at 14B.
  • Contracting decoding risk at fixed mean gap reduces rest-of-response web-verified hallucinations by 35–74% across six model×family rungs, with every bootstrap CI excluding zero; confounds like length, claim count, and diversity move insignificantly.
  • Semantic entropy, a detector that reads only the model's probabilities, fires 28–34% less on the inter-claim bridge than at onset despite the bridge carrying ~4× as many fabrications, consistent with the claim that pM-only detectors are blind to the dominant failure mode.

Where Pith is reading between the lines

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

  • The decomposition implies a quantitative ceiling on any pM-only hallucination detector: since the risk term has no model-readable component, the best such detector can do is catch the bias side plus whatever transient entropy signal appears at onset. Measuring detector recall on the 'precarious' regime (low entropy, high risk) would test this bound directly.
  • Because the mechanism is attributed to autoregressive decoding itself, it should transfer to any long-form generator for which a stronger oracle can be defined—code generation, summarization, multimodal captioning—where the same variance contraction may reduce fabrication; the paper's evidence is limited to English parametric text.
  • The label-free Markov-switching risk marker (AUROC 0.68–0.71 across scale) suggests a deployable online rule: when the model enters the high-risk, low-bias 'precarious' state, it could trigger verification or abstention before the next fabrication is committed, without needing an oracle at inference time beyond the model's own logits.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes that hallucination in long-form generation is driven by a decoding-time risk term that is invisible to the model's own uncertainty signals. The central object is the per-position disagreement δ = log p_M − log p_O between the model and a stronger oracle. Its second moment splits exactly into a bias term KL(p_M∥p_O)² and a decoding-risk term Var[δ] (Eq. 2). The paper argues that as models scale, this risk term grows as a share of the squared error, persists after a fabrication onset while entropy relaxes, forms a 'precarious' regime that bridges consecutive fabrications, is not readable by p_M-only detectors, and causally mediates downstream hallucinations. The claims are supported by scaling analyses on three model families and three benchmarks, onset-aligned trajectory analyses, a three-state Markov-switching regime model, and an in-silico variance-contraction intervention that removes 35–74% of web-verified hallucinations.

Significance. If the central claims hold, the paper would reframe hallucination from a knowledge-gap phenomenon to a self-conditioning decoding-risk phenomenon, with direct implications for detector design and for the interpretation of scaling laws. The paper has notable strengths: the identity in Eq. (2) is exact and correctly stated; bootstrap CIs are used throughout; the onset dynamics are rechecked against a cross-family oracle (Appendix D); the main intervention is explicitly labeled as an oracle-in-the-loop ceiling; and the experimental protocol is unusually transparent about seeds, trajectories, and verifier dependencies. The white-box risk marker (Appendix H) is a useful label-free contribution. However, the causal and interpretive claims depend on assumptions that are only partially defended: the oracle is treated as a truth proxy, and the headline causal estimate is based on a post hoc selected best arm.

major comments (3)
  1. [§4.3, Table F.2] The headline causal reduction (35–74%) is reported for the best arm selected post hoc over the causal grid K∈{0,1,2} × ρ∈{0.5,0.75}. The 95% bootstrap CIs for this selected arm are not adjusted for the selection, so they overstate significance. The dose-response paragraph in Appendix F partially mitigates this, but Table F.2 still reports only the best arm per rung. Please report all grid cells (or a pre-specified selection rule) and apply a multiple-comparison correction, or state explicitly that the CIs are conditional on the post hoc selection.
  2. [§2, Eqs. (1)–(3); Appendix D] The entire risk decomposition is relative to the oracle p_O, and the paper's 'knowledge degradation', 'risk', and 'fabrication' claims are measured as disagreement with that oracle. The cross-family oracle check in Appendix D shows the asymmetry is not a same-family artifact, but it does not establish that the oracle is calibrated with respect to factual truth. If the oracle's errors correlate with scale or topic, the mechanism becomes disagreement with a fallible referent rather than hallucination. The verifier labels provide some external grounding, but the paper's own Limitations concede verifier error. Please provide a direct calibration check of the oracle against verifier labels, or reframe the claims as risk-against-a-stronger-model and show separately that this risk predicts verifier-labeled hallucinations.
  3. [§4.3, Fig. 6] The intervention fires only at positions where the oracle-informed trigger detects a large divergence (Z=2 above the per-model mean). The manipulation check shows that the contraction changes variance and not the mean gap, but it does not isolate the variance reduction from the trigger mechanism itself. A control that applies the same contraction at non-trigger positions (or at random positions) is needed to rule out the possibility that the effect is driven by the oracle's detection signal rather than by the variance contraction. Without this control, the causal attribution to 'decoding risk' is not fully identified, even as an oracle-in-the-loop ceiling.
minor comments (4)
  1. [Abstract] The phrase 'bias² KL(pM ∥ pO)²' is redundant; the square of the KL divergence is already bias². Also, calling H(p_M) 'self-readable uncertainty' is confusing because H is entropy, not variance; the distinction is central to the paper and could be clarified at first use.
  2. [Table 2 vs §4.4] The table reports p<10^{-3} (one-sided Mann–Whitney) while the main text states p<10^{-16}. Please reconcile these numbers or state the exact p-values.
  3. [Appendix H] The abbreviation 'MSAR' is used without definition. If it means Markov-switching autoregressive, please spell it out.
  4. [Figure 2] The caption uses 'H(pS)' in what appears to be a typo for H(p_M).

Circularity Check

0 steps flagged

No significant circularity: the core decomposition is an algebraic identity and empirical claims use external verifier labels.

full rationale

The derivation chain starts with Eq. (1)-(3), where δ = log p_M - log p_O and E[δ^2] = KL(p_M || p_O)^2 + Var[δ]. This is an exact algebraic identity, not a fitted output. 'Bias' and 'risk' are names for the two moments, and the statement that H(p_M) enters only the bias term follows directly from Eq. (3). The empirical content - scaling of knowledge gap and degradation, risk share, persistence asymmetry, snowballing, bridge occupancy, and the contraction result - is measured against public benchmarks and a Claude web-search verifier's claim labels, not against quantities constructed to reproduce the target conclusion. The manipulation check in Fig. 6 confirms that Eq. (4) changes the realized variance to the target dose while keeping mean drift about 11 orders of magnitude below the bias, so the 35-74% reduction in web-verified hallucinations is not prediction by construction: the outcome uses a verifier independent of the δ moments, with bootstrap CIs excluding zero. The oracle-as-truth framing is an external-validity assumption, not a circular reduction. The paper's Limitations explicitly concede that verifier error could propagate and that the causal test uses a co-resident oracle to both detect onset and define the contraction, and Appendix D provides oracle-size and oracle-family robustness. The only same-author citation (Chakrabarti and Balachundhar 2025) appears as one of three motivating facts and again in Related Work and Discussion, but no equation or experiment depends on its truth; it is not load-bearing. No circular step was found. The score of 2 reflects only the presence of that non-load-bearing self-citation, not a derivation that reduces to its inputs.

Axiom & Free-Parameter Ledger

3 free parameters · 7 axioms · 1 invented entities

The central claim rests on exact algebra, but also on the oracle-as-truth assumption, a heuristic autoregressive conversion, fitted latent states, post-hoc intervention hyperparameters, and an external web verifier. The oracle and verifier assumptions are explicitly acknowledged in the Limitations.

free parameters (3)
  • Intervention trigger, window, and dose (Z, K, ρ; λ, ν solved per step) = Z=2; best K ∈ {0,1,2}; best ρ=0.5
    The headline 35–74% reduction selects the best arm post hoc over the causal K≥0 grid (Table F.2), so these are fitted hyperparameters, not predictions.
  • Three-state Markov-switching parameters (µ_oc, σ_oc, transition probabilities) = µ_oc 2.36→0.81 nats; σ_oc 2.75→1.56; entry/self-transition ≈0.42–0.45
    The precarious-regime bridge and the label-free AUROC 0.68–0.71 risk marker depend on this fitted latent-state model.
  • GLMM random-intercept logistic fit (β0, βpos, τ_resp) = βpos significant at 20 of 22 fits; τ_resp 1.04–3.01
    The knowledge-degradation column of Table 1 is read off this fitted mixed-effects model, not from raw rates directly.
axioms (7)
  • standard math Variance decomposition: E[δ²] = (Eδ)² + Var[δ].
    Used in Equation (2); exact and uncontroversial.
  • standard math KL identity: KL(p_M∥p_O) = H(p_M,p_O) − H(p_M).
    Used to rewrite bias² as (oracle surprise − felt uncertainty)² in Equation (3).
  • domain assumption The oracle p_O is a valid proxy for factual truth.
    Every gap and risk measurement is disagreement with a larger model; if the oracle is wrong about a fact, the paper mislabels the model's disagreement as hallucination. Entered at Section 2, Equation (1), and only partially mitigated by oracle-robustness checks.
  • ad hoc to paper Autoregressive sampling at onset converts one-step risk into downstream bias.
    Prediction 2 in Section 2.3 is asserted as a mechanistic claim; no formal derivation is given, and the causal interpretation rests on it.
  • domain assumption Teacher-forced moment analyses characterize free-run behavior.
    The moment decompositions are computed from p_M and p_O directly; the paper argues decoding invariance but the free-run connection is assumed.
  • domain assumption The Claude web-search verifier labels are accurate enough.
    All support/unsupported labels come from a public verifier API; the authors acknowledge verifier error could propagate and offer the white-box AUROC as partial corroboration.
  • ad hoc to paper The BIC-selected three-state Markov-switching model identifies meaningful decoding regimes.
    The precarious/diverged/grounded states are fitted latent states; the bridge effect and detector-blindness results depend on this modeling choice.
invented entities (1)
  • Precarious regime (confident-but-high-risk decoding state) independent evidence
    purpose: A latent state that bridges consecutive fabrications and is claimed to be invisible to self-monitoring.
    It is a fitted construct, but it has a falsifiable handle: state occupancy separates supported from unsupported tokens at AUROC 0.68–0.71 without verifier labels (Table H.1).

reviewed 2026-08-02 · how reviews work

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Cite this review

Pith. "Pith review of Reliability Scales Inversely: Hallucinations Snowball Faster in Bigger Language Models." pith.science (2026). https://pith.science/paper/E43A3EKY

@misc{pith2026260718292,
  author       = {Pith},
  title        = {Pith review of: Reliability Scales Inversely: Hallucinations Snowball Faster in Bigger Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E43A3EKY}},
  note         = {Machine review of arXiv:2607.18292}
}
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abstract

Bigger language models are less reliable. Across three families, three benchmarks and six rungs, including in-the-wild chat logs, scaling closes the start-of-response knowledge gap up to $7\times$ while within-response knowledge degradation grows up to $39\times$. We trace that residual to one variable, the per-position disagreement $\delta = \log p_M - \log p_O$ against a stronger oracle, whose second moment splits exactly into bias$^2$ $\mathrm{KL}(p_M \,\|\, p_O)^2$ and decoding risk $\mathrm{Var}[\delta]$. That split is an interpretability statement before it is a statistical one: the model's self-readable uncertainty $H(p_M)$ enters only the bias term, so the risk term has no model-readable component. Risk also takes a growing share of the squared error with scale, $31\%$ to $49\%$ from $1.7$B to $14$B. At a fabrication $H(p_M)$ relaxes within one token while risk persists up to $23\times$ longer, leaving a confident-but-precarious regime that bridges consecutive fabrications ($+69\%$ at $14$B). Contracting that risk at fixed $\mathrm{KL}$ removes $35$-$74\%$ of web-verified hallucinations across six rungs and three families. Semantic entropy fires $\approx$$30\%$ less on that branch ($p\!<\!10^{-16}$) though it carries nearly $4\times$ the fabrications. Bigger models snowball mistakes faster, through a failure mode that is dominant, self-perpetuating, causal and invisible to the model itself.

Figures

Figures reproduced from arXiv: 2607.18292 by Kushal Chakrabarti.

Figure 1
Figure 1. Figure 1: Reliability scales inversely; long-form hal￾lucination is compounding risk. (a) On LongFact++ free-run claims across the Qwen3 family (0.6–32B), the start-of-response knowledge gap (left) decreases while knowledge degradation over the full response (right) trends upward, so initial answers become truer but au￾toregressively decay faster as models scale (Section 3.1). (b) A KL-preserving risk contraction (b… view at source ↗
Figure 2
Figure 2. Figure 2: At fabrication onset every channel spikes, but the model’s self-readable uncertainty collapses within a token while the oracle-referenced decoding risk self-perpetuates. (a) Onset-aligned free-run LongFact++ trajectories (per Qwen3 rung, 0.6–8B vs. Qwen3-14B oracle; 95% CIs): the bias gap KL(pM∥pO) (red), entropy H(pM) (green) and decoding risk p Var[δ] (yellow) spike at the first unsupported claim (t=t ⋆ … view at source ↗
Figure 3
Figure 3. Figure 3: The variance side of hallucination strengthens with scale in two ways. (a) the across-claim compound￾ing (relative risk RR that a fabrication begets the next) rises monotonically with Qwen3 model size, and (b) the per-position oracle-gap tail (excess kurtosis of δt) sits far above the Gaussian baseline and rises monotonically while the mean gap shrinks in both Llama-3.2 and Qwen3 (OLMo-3 corroborating at 7… view at source ↗
Figure 4
Figure 4. Figure 4: Decoding risk is a growing share of the per-position error with scale. Teacher-forced δt = log pM(y ∗ t ) − log pO(y ∗ t ) (Qwen3 vs. Qwen3-32B; 14,629 tokens/model, 58 biographies; 0.6B omitted). Top: realized-token δt density, leptokurtic with scale. Middle/bottom: the distributional bias2 (KL(pM∥pO) 2 t ) and risk (VarpM [δ]t) terms (nats2 ); both shrink, but the bias2 term faster, so risk’s share of E[… view at source ↗
Figure 5
Figure 5. Figure 5: An over-confident risk regime increasingly bridges adjacent fabrications. The y-axis is the rela￾tive likelihood that a bridge token is in the precarious regime (Figure 2b) when one fabrication leads to an￾other rather than to a supported claim: P (prec|U→U) P (prec|U→S) − 1. Each point is one model scale (x, log), over adjacent pairs (gap ≤ 10 tokens, sample n ≥ 100) in mixed responses. 5 Related Work Err… view at source ↗
Figure 6
Figure 6. Figure 6: Manipulation check: the contraction moves variance and nothing else. Left: realized per-fired-step variance fraction Varqλ [δ]/V0 vs target dose ρ, per rung — points on the identity mean variance fell to the dose (realized 0.50–0.77 at ρ=0.5–0.75). Right: bias drift |Eqλ [δ] − µ| (box = IQR, whiskers = 5–95%) against the |µ| barrier (red) the contraction must not cross. Median drift is ≤ 10−11 nats, ∼11 or… view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 2, 2026.