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REVIEW 5 major objections 6 minor 31 references

Identifying and Mitigating the Influence of the Prior Distribution in Large Language Models

T0 review · 5 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper shows that Llama 3 often computes the correct answer to deterministic tasks even when its learned prior steers output away from it, and that lightweight finetuning of one early layer exposes that knowledge.

desk verdict A useful empirical paper with a clean prompt result and honest reporting of probing failures, but the layer-selection procedure inflates the headline fine-tuning numbers and the localization story needs a matched control. read the letter →

arxiv 2504.12585 v1 pith:522F4VHV submitted 2025-04-17 cs.CL cs.AIcs.LG

Liyi Zhang , Veniamin Veselovsky , R. Thomas McCoy , Thomas L. Griffiths This is my paper · ORCID
classification cs.CLcs.AIcs.LG
keywords largelanguagemodelspriordistributionmechanisticinterpretabilitylogitlensLoRAfinetuninghallucinationresidualstreamstratifiedevaluation
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

The paper tries to establish that an LLM's failure on deterministic tasks—counting, shift ciphers, and acronyms—is often not a failure to compute the answer, but a failure to output it because a learned prior over token sequences pulls generation toward common strings. On Llama 3, it shows the answer information is present in the residual stream and that the prior is localized to identifiable layers via logit-lens correlations. Interventions that target that influence—a one-line prompt and, more strongly, lightweight finetuning of a single early layer—substantially improve held-out accuracy, with held-out answers excluded from training so gains cannot be memorization. The same finetuning helps far less on tasks without a strong prior over answers, and after finetuning errors no longer track answer commonness. The result matters because it suggests some hallucinations are prior-driven and may be mitigable without retraining the whole model.

What carries the argument

The machinery has three parts. First, logit lens: read each layer's hidden embedding through the unembedding matrix to approximate per-layer answer logits, and correlate those with prior logits elicited from a no-input prompt; this localizes the prior to certain layers in an all-or-none pattern. Second, a stratified train/validation split in which every answer token in validation is absent from training, so high accuracy cannot come from memorizing answer–question pairs. Third, low-rank (LoRA) finetuning applied to a single early layer selected by validation performance. The argument runs: if the correct answer can be read from hidden states but the final output follows the prior, then a narrow intervention that weakens prior encoding should let the encoded answer through.

What would settle it

Run the paper's one-layer finetuning procedure with training labels randomly permuted: if held-out accuracy still rises substantially, the gain is not prior removal. Alternatively, switch off the layers identified by the correlation scan and check whether the common-token bias disappears; if it persists, the correlation is not the mechanism.

Watch

Extended reading notes

Core claim

The paper's central claim is that Llama 3 8B, on three deterministic tasks where it fails—counting letter sequences, shifting ciphertext by one, and forming acronyms—stores the information needed for the correct answer in its residual stream, but its learned prior over token sequences steers decoding toward common tokens. Evidence comes from layer-wise logit-lens correlations with the prior, which are high in some layers and absent in others; from a prompt that says "do not rely on your prior knowledge," which lifts accuracy on counting from 11.5% to 49.2% and on acronyms from 12.8% to 46.3% but barely on shift ciphers; and from lightweight LoRA finetuning of a single early layer on a stratified split, which reaches 72.3%, 99.4%, and 99.9% respectively on the three tasks while seeing no held-out answers during training. The same finetuning gives much smaller gains on multiplication and make-letters tasks, which the paper classifies as prior-insensitive, and after finetuning errors track question difficulty rather than token frequency. A linear probe fails on the stratified split, and two existing linear steering techniques fail, suggesting the prior's influence is not a simple linear direction that can be subtracted away.

Load-bearing premise

The load-bearing premise is that the layers whose internal predictions correlate with the model's prior probabilities are the causal site of prior influence, not just correlated bystanders; the paper also chooses which layer to finetune by looking at validation performance and does not compare against a randomly labeled control.

Editorial extensions

If this is right

  • Failures that look like hallucinations on counting, shift ciphers, and acronyms can be reduced by interventions that add no task-specific information, only reduce reliance on the prior.
  • Stratified held-out evaluation is necessary: random-split probing overstates what a model knows, while the stratified setup shows near-zero probe accuracy.
  • On prior-dominated tasks, one-layer finetuning with 2,000–8,000 sequences and 50 epochs is enough for high held-out accuracy.
  • Post-finetuning error correlates with question difficulty, not answer commonness, indicating the prior bias has been removed rather than masked.
  • The gains from finetuning are substantially larger on prior-dominated than prior-insensitive tasks, so the intervention is specifically prior removal.
  • The failure of linear steering methods while nonlinear finetuning succeeds suggests that prior influence is not a single linear direction in the residual stream.

Reading between the lines

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

  • If the localization is causal, the same layer-targeted finetuning could be tested on other failure modes with a known probabilistic bias, such as fact retrieval where high-frequency answers win, though the paper does not test that.
  • The authors did not ablate the identified prior-correlated layers to show they are necessary; that ablation would be the test that turns localization into causation.
  • The stratified design could be extended to other open-weight models to see whether the early-layer locus is architecture-specific or a general feature of transformer language models.
  • The failure of linear steering methods suggests a nonlinear, layer-specific representation-editing method beyond finetuning might reproduce the effect at inference time, which the paper leaves open.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 6 minor

Summary. This paper studies three deterministic tasks—counting letters, shift ciphers, and acronym construction—on Llama 3 8B, where model outputs are biased toward high-probability token sequences. Using a logit-lens analysis, the authors report that individual layers show an all-or-none pattern of Spearman correlation with prior logits, suggesting localized encoding of the prior. They then test two interventions: adding 'do not rely on your prior knowledge' to the prompt, and LoRA fine-tuning either the full model or a single selected layer under a stratified train/validation split that excludes validation answer tokens from training. They report that prompting improves accuracy on counting and acronyms, and that fine-tuning the best-performing layer reaches 72.3–99.9% validation accuracy on the three tasks, with larger gains than on two 'prior-insensitive' tasks (multiplication and make-letters). They interpret these results as evidence that the correct answers are already encoded in the residual stream and that the prior's influence can be localized and removed.

Significance. If the central claim holds, the paper makes a useful contribution: it provides a concrete setting in which a pretrained LLM's failures on simple deterministic tasks can be reduced by lightweight interventions, and it offers a template for separating 'known but not expressed' knowledge from genuine task inability. The use of a stratified split to prevent answer-token memorization is a thoughtful design choice, and the probing failure result is an honest negative result that strengthens the field's understanding of probe-based claims. The paper also ships code and uses an open model, which supports reproducibility. However, the current evidence does not yet establish the stronger mechanistic claims: the headline fine-tuning numbers are obtained by selecting the best of 32 layers on the validation split, and no experiment connects the fine-tuned layers to the layers identified as prior-correlated in the localization analysis. The comparison against prior-insensitive tasks is also confounded by floor effects. These are addressable with additional experiments, so the paper is on the right track but needs revision.

major comments (5)
  1. [Table 1; Figure 2; Section 4.2] The 'Finetune-layer' row reports the accuracy of the best-performing layer selected on the validation split. With 32 layers, taking the maximum validation accuracy inflates the reported numbers relative to the expected accuracy of a fixed layer on a truly held-out test set; the manuscript does not report a nested split in which layer selection is made on training/validation data and the selected layer is evaluated on a disjoint test set. As a result, the headline held-out accuracies (72.3–99.9%) and the claim that finetuning is 'lightweight' are not yet established. Please report test-set accuracy of the selected layer and include a null baseline such as finetuning the same layer with shuffled labels.
  2. [Abstract; Section 4.1; Section 4.2] The abstract says 'lightweight finetuning of these layers,' referring to the layers identified as prior-correlated via logit lens, but the experiments select the best-performing layer independently of the correlation analysis. No experiment shows that the best-performing layer coincides with or is even related to the layers with high prior correlation in Figure 3. The mechanistic link between localization and mitigation is therefore missing. Please report finetuning results for fixed layers chosen from the prior-correlation analysis (e.g., a layer with high correlation, a layer with low correlation, and a random layer), evaluated on a disjoint test set.
  3. [Section 4.3; Figure 2; Table 1] The comparison between prior-dominated and prior-insensitive tasks is confounded by baseline accuracy. Multiplication and make-letters start near 0% accuracy, so they have more room for absolute improvement; larger absolute gains on prior-dominated tasks do not by themselves show that the intervention removes prior influence. Table 1 includes only the three prior-dominated tasks, so the reader cannot see the actual baselines and gains for the two control tasks. Please report all numbers and use a baseline-adjusted measure (e.g., improvement relative to the maximum possible improvement) or match tasks on baseline accuracy.
  4. [Section 4.2; Section 3.4.2] The central claim that 'the information required to produce a correct response is contained within the representations' is supported primarily by the fact that finetuning improves accuracy, since the probing evidence fails in the stratified setup. Finetuning can also learn the task from the training data rather than eliciting pre-existing representations. To support the 'already encoded' interpretation, please add a control in which the same finetuning recipe is applied with randomized answer labels (or to a held-in but non-prior task) and show that accuracy does not reach the reported levels; alternatively, demonstrate that the correct answer is linearly decodable from the selected layer under the stratified split with an appropriate control task.
  5. [Abstract; Figure 4; Section 4.3] The abstract claims that 'the error after finetuning is no longer correlated with the prior,' but the only supporting evidence is Figure 4, which shows counting accuracy by sequence length for one task. Please provide a quantitative test of the correlation between post-finetuning errors and prior token probabilities for all three prior-dominated tasks, with a significance test and, ideally, a comparison to the pre-finetuning correlation.
minor comments (6)
  1. [Figure 2 caption] The caption says 'six tasks' but the figure shows five; please correct the count.
  2. [Section 4.1] The 'all-or-none' pattern is based on a p<0.05 threshold without multiple-comparison correction; please report effect sizes or adjusted p-values to support the claim.
  3. [Figure 3] The color legend is ambiguous ('dots colored in red have more answer logits with negative correlation'); please clarify the exact criterion for red versus blue.
  4. [Appendix A; Table 3] 'We take motivation from this approach an ablate out the unigram direction' contains a typo ('an' should be 'and'), and Table 3 reports no standard errors for the steering results.
  5. [Table 1] The entries 'Finetune' and 'Finetune-layer' are not defined in the table; please state whether 'Finetune' refers to whole-model LoRA or all-layer LoRA and specify the layer-selection protocol.
  6. [Reproducibility Statement] The URL for torchtune has a typo ('https//github.com' should be 'https://github.com').

Circularity Check

1 steps flagged · score 6.0 of 10

Best-layer finetuning accuracy is selected on the validation set and reported on that same set, making the headline 'held-out' numbers a maximum-over-layers artifact.

  1. fitted input called prediction [Table 1 caption; Figure 2 caption; Section 4.2 'Finetuning'; abstract's 'held-out answers' claim.]
    "Finetune-layer refers to performance obtained by only finetuning the best-performing layer. ... Accuracy of finetuned (blue) and original (red) models on six tasks (shown here is the best layer's performance in each individual task)."

    The layer index is chosen by maximizing validation accuracy across 32 layers, and the accuracy of that same validation split is then reported as the Finetune-layer result. Because the validation labels were used to select the layer, the reported 'validation accuracy' is by construction the maximum over 32 fitted models, not an unbiased estimate of held-out performance. With 32 candidates, even a null model will produce a spuriously high maximum. The abstract's 'held-out answers' overstates the result: the held-out set has already influenced model selection. The additional claim that finetuning 'these layers' (the logit-lens prior-correlated layers) works is not established because the best-performing layer is not shown to coincide with the prior-correlated layers.

full rationale

The main non-circular evidence is substantial: the paper reproduces the prior-sensitivity phenomenon itself (Figure 1, Figure 4a) rather than relying solely on self-citations, the prompting results are genuine behavioral interventions with no parameter fitting, and whole-model finetuning (the 'Finetune' row of Table 1: 37.5%, 99.2%, 97.5%) already supports the latent-competence claim without layer selection. The logit-lens localization is operational (correlating internal predictions with the same model's no-input guesses) and is not circular by construction. The one concrete circular step is the 'Finetune-layer' result: the best layer is selected on the validation set and the validation accuracy of that selected layer is presented as the headline outcome. This is a fitted-input-called-prediction pattern, since the reported percentage is the maximum over 32 layer-specific fits and is therefore optimistically biased. The paper does not use a separate test split after layer selection, nor does it fix the layer from the prior-localization analysis, so the highlighted 72.3-99.9% accuracies and the mechanistic link to the localized prior are not cleanly established. This partial circularity affects an emphasized result, but it does not collapse the whole derivation, because the non-selected finetuning and prompting results retain independent content.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The main dependency is the use of the model's own prior distribution as the explanatory variable, which is measured from the model itself. The causal interpretation from correlation is the key assumption. No new entities are introduced.

free parameters (3)
  • loRA rank / alpha = rank=8, alpha=16
    These are standard hyperparameters, but their values affect the fine-tuning results and are not derived from theory. They are chosen by the authors, not fitted to the target data, hence not counted as fitted parameters.
  • learning rate = 1e-4
    A fixed hyperparameter; not fitted to the target tasks.
  • number of epochs = 50
    A fixed hyperparameter; not fitted.
assumptions (3)
  • domain assumption The logit-lens method gives a faithful proxy for the model's internal predictions at each layer.
    Used in Section 4.1 to localize the prior. This is a known method, but its faithfulness for interpreting these specific layers is assumed.
  • domain assumption The Spearman correlation between prior logits and logit-lens outputs measures the influence of the prior.
    The correlation analysis assumes that a correlation at a layer indicates that the prior is encoded there, and that this encodes a causal influence. The paper does not establish causality.
  • domain assumption The tasks are representative of prior-dominated failures.
    The choice of counting, shift-cipher, and acronyms is motivated by McCoy et al. (2023), but the generality of the findings to other prior-dominated tasks is assumed.

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Cite this review

Pith. "Pith review of Identifying and Mitigating the Influence of the Prior Distribution in Large Language Models." pith.science (2026). https://pith.science/paper/522F4VHV

@misc{pith2026250412585,
  author       = {Pith},
  title        = {Pith review of: Identifying and Mitigating the Influence of the Prior Distribution in Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/522F4VHV}},
  note         = {Machine review of arXiv:2504.12585}
}
read the original abstract

Large language models (LLMs) sometimes fail to respond appropriately to deterministic tasks -- such as counting or forming acronyms -- because the implicit prior distribution they have learned over sequences of tokens influences their responses. In this work, we show that, in at least some cases, LLMs actually compute the information needed to perform these tasks correctly, and we identify some interventions that can allow them to access this information to improve their performance. First, we show that simply prompting the language model to not rely on its prior knowledge leads to dramatic improvements in prior-dominated tasks. We then use mechanistic interpretability techniques to localize the prior within the LLM and manipulate the extent to which that prior influences its responses. Specifically, we show that it is possible to identify layers of the underlying neural network that correlate with the prior probability of a response and that lightweight finetuning of these layers with basic prompts on prior-dominated tasks achieves high performance on held-out answers. These results suggest that the information required to produce a correct response is contained within the representations of the problems formed by the models. Furthermore, we show that this finetuning is significantly more effective for prior-dominated tasks, and that the error after finetuning is no longer correlated with the prior. Our results suggest that it may be possible to define effective methods for manipulating the extent to which LLMs rely upon their priors in solving problems, potentially increasing their performance in settings where LLMs hallucinate for reasons related to the prior probability of token sequences.

Figures

Figures reproduced from arXiv: 2504.12585 by the authors.

Figure 1
Figure 1. Influence of the prior on LLAMA 3’s performance for deterministic tasks. (a): Although LLAMA 3 reasons through the correct characters, it outputs a more likely token ‘in’, instead of the correct ‘inf’ (which is the first token of the correct answer ‘infidel’), followed by ‘field’. (b): Performance of the pretrained LLM LLAMA 3 on three prior-related tasks. For counting, the common set is multiples of 10 from 20 to 1… view at source ↗
Figure 2
Figure 2. Accuracy of finetuned (blue) and original (red) models on six tasks (shown here is [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Percentage of questions (vertical axis) where the LLM answer logits have a positive [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Accuracy of LLAMA 3 (y-axis) when asked to count different lengths of sequences of letters (x-axis). The original LLM performance is biased towards common numbers such as multiples of ten (marked by grey dash lines). The finetuned performance is instead correlated with…
Figure 5
Figure 5. Figure 5: Prompt and ground truth examples of each task (shift-cipher example is included [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]

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    Iman Mirzadeh, Keivan Alizadeh, Hooman Shahrokhi, Oncel Tuzel, Samy Bengio, and Mehrdad Farajtabar. GSM-Symbolic: Understanding the limitations of mathematical reasoning in large language models. arXiv preprint arXiv:2410.05229,

    arXiv

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.