Pith. sign in

REVIEW 5 major objections 4 minor 1 cited by

Understanding Hidden Computations in Chain-of-Thought Reasoning

T0 review · 5 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A transformer trained to output filler tokens still stores the true reasoning tokens in lower-ranked logits, and a modified greedy decoder can surface them without losing task accuracy.

desk verdict The rank-2 recovery idea is plausible and cheap to test, but the paper never reports the measurements that would support it — it reads as an abstract rather than a paper. read the letter →

arxiv 2412.04537 v1 pith:YYQTYRNY submitted 2024-12-05 cs.CL cs.LG

Aryasomayajula Ram Bharadwaj This is my paper · ORCID
classification cs.CLcs.LG
keywords chain-of-thoughtreasoninghiddencomputationlogitlenstokenrankinggreedydecoding3SUMtasktransformerinterpretabilityfillertokens
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 asks what a transformer is really computing when it is trained to output filler characters instead of a visible chain of thought. Using the logit lens, the author shows that in a small transformer trained on a synthetic 3SUM-style task, early layers predict the numerical reasoning tokens and the final layer overwrites them with filler tokens. The original reasoning tokens survive as the second-ranked choices at decoding time. A modified greedy decoder that skips the filler token and outputs the highest-ranked non-filler token recovers the hidden reasoning steps while keeping task accuracy intact. The point is that visible chain-of-thought is not a reliable guide to what the model has computed, and hidden computations can be surfaced without retraining.

What carries the argument

The load-bearing tool is the logit lens, which projects each layer's hidden state $h_l$ onto vocabulary logits via the unembedding matrix $W_{\text{out}}$, turning internal activations into a probability distribution over tokens at every layer. Alongside it, token-ranking analysis inspects the top-$k$ candidates at each decoding step. In this model the filler token wins at the last layer while the true reasoning token sits at rank 2, and the modified decoding algorithm exploits that ordering by selecting the highest-ranked non-filler token whenever the filler token is on top.

What would settle it

Take the same trained model and a held-out set with known ground-truth reasoning chains, then measure how often the highest-ranked non-filler token equals the true next reasoning token. If that token-level recovery accuracy is near chance while task accuracy stays high, the central claim fails. A second, sharper test is to retrain with a random or nonlinear output embedding; if the rank-2 pattern disappears while accuracy is unchanged, the pattern was an artifact of the logit-lens projection.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is that hidden reasoning steps in a transformer trained with filler chain-of-thought are not lost: they are computed in early layers and then masked by filler tokens in the final layer. Evidence comes from layer-wise projections $z_l = h_l W_{\text{out}}$ and from token rankings during autoregressive decoding, where the true chain-of-thought tokens appear as rank-2 candidates beneath the filler token. Replacing each filler token with the highest-ranked non-filler token during greedy decoding recovers the original reasoning sequence and preserves performance on the 3SUM task. The paper concludes that the hidden characters can be recovered without loss of performance.

Load-bearing premise

The whole analysis rests on believing that projecting a layer's hidden state through the output embedding matrix shows what token that layer is 'thinking about'; if that projection is not a faithful view, the recovered rank-2 tokens could be artifacts of the projection rather than the original reasoning steps.

Editorial extensions

If this is right

  • If the claim holds, model outputs that consist of filler or placeholder tokens can still be audited for the reasoning that produced them, without retraining or changing the model.
  • Task accuracy on filler chain-of-thought training is not evidence that no internal reasoning occurred; the reasoning can be present and merely hidden in lower-ranked logits.
  • Rank-ordered token inspection becomes a practical, cheap method for extracting hidden intermediate steps from small transformers on algorithmic tasks.
  • The recovery-by-rank-2 observation gives a concrete target for studying when and how transformers overwrite computed information during output formatting.

Reading between the lines

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

  • If the same rank-skipping pattern holds in larger models, auditing systems that emit placeholder or redacted intermediate text could surface the genuine computation underneath, changing what such outputs can be taken to conceal.
  • A direct extension would be to test the modified decoder on natural-language reasoning tasks, where reasoning tokens are not a fixed synthetic vocabulary; the paper's small-model setting does not guarantee the pattern transfers.
  • The paper hints at induction heads as the overwriting mechanism; one could test that by ablating attention heads and checking whether the rank-2 recovery disappears.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 4 minor

Summary. The paper studies a 4-layer transformer trained from scratch on synthetic 3SUM-style instances in which the chain of thought is replaced by filler tokens. It applies the logit lens and token-ranking analysis to argue that the hidden non-filler reasoning tokens can be recovered by replacing filler tokens with the highest-ranked non-filler token during greedy decoding, 'without loss of performance.' The manuscript presents qualitative descriptions and placeholder figures, but contains no quantitative results such as recovery rates, task accuracies, or error bars.

Significance. If established, the result would be a useful interpretability contribution: it would show that a small transformer trained on filler CoT retains the underlying reasoning tokens in lower-ranked logits, and that a simple decoding modification can expose them. The paper also connects to prior work on hidden computation and unfaithful CoT, which is an appropriate framing. However, the value is conditional on the missing empirical support; as submitted, the significance cannot be assessed because the central claims are asserted rather than demonstrated.

major comments (5)
  1. [Section 6.3, Figures 1 and 2] The central claim that the modified decoder 'significantly outperformed' random replacement and recovers hidden characters 'without loss of performance' is never quantified. No recovery accuracy, no final-task accuracy, and no standard errors are reported, and the figures referenced (Figures 1 and 2) are absent from the submission. These quantities are the evidentiary core of the paper.
  2. [Section 5.1.1 and Section 5.3.1] The corruption rate is set to 4/3, which is not a valid probability (a rate should lie in [0,1] or be expressed as a percentage). This makes the data-generation procedure ill-defined and impossible to reproduce as written, and it undermines all dataset-dependent results.
  3. [Section 6.2] The token-ranking analysis reports that 'the second-ranked token often corresponded to the numerical tokens representing the hidden reasoning steps,' but 'often' is never quantified. The paper does not report the frequency with which the ground-truth token appears at rank 2 (or any rank) under standard greedy decoding, so the step from ranking observations to a recovery method is not validated.
  4. [Section 5.7 and Section 6.3] The modified decoding algorithm changes the conditioning distribution at inference time by replacing filler tokens with non-filler tokens, whereas the model was trained on filler-token sequences. The paper never reports final-answer accuracy under this modified decoding distribution, so the central claim of 'without loss of performance' is not demonstrated.
  5. [Section 5.5] The logit-lens projection z_l = h_l W_out is applied to a small, randomly initialized, from-scratch trained model, but the paper gives no validation that the output embedding matrix supports meaningful vocabulary-space inspection for this model. Without such validation or a suitable control, the observed rank-2 patterns could be projection artifacts rather than recovered reasoning tokens.
minor comments (4)
  1. [Section 5.1.1] The headings 'T rue Instances' and 'T riple Listing' contain stray spaces; these should be corrected.
  2. [Section 8] The code availability statement says the code is 'available on GitHub here' but no URL is provided, so the experiments cannot be independently checked.
  3. [Figures 1 and 2] The figures are placeholders with no plots or data; they should either be included as real figures or removed if the results are not yet available.
  4. [Conclusion] The conclusion states that the paper 'demonstrated' the recovery claim, but the body contains only qualitative observations; the wording should be tempered to match the evidence actually presented.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the recovery claim is under-evidenced but not input-equivalent.

full rationale

The paper's derivation chain does not reduce to its own inputs by construction. The recovery method in §5.7 is a fixed decoding rule: whenever the top-ranked token is a filler token, select the highest-ranked non-filler token. The claim that this recovers the original CoT tokens is an empirical assertion about token rankings, not an identity forced by the algorithm's definition. The dataset generation in §5.3 provides ground-truth CoT annotations (e.g., the example 'A B C 15 75 22 2 ...'), so agreement with those annotations could in principle falsify the claim; the paper simply does not report recovery rates, task accuracies, or standard errors. That is an evidentiary gap, not circularity. No parameter is fitted to a subset of the data and then renamed a prediction, and no load-bearing result is imported from a self-citation: the only closely related prior work, Pfau et al. [2], is not authored by the present paper's author. The logit lens premise in §5.5 is an interpretive assumption about how to inspect representations, and it is not itself equivalent to the recovered-token conclusion. The unquantified 'often' in §6.2, the missing figures, and the invalid corruption rate of 4/3 in §5.3.1 are correctness and reproducibility concerns, not circular steps. Therefore the appropriate finding is no significant circularity.

Assumptions & free parameters 8 free parameters · 4 assumptions · 0 invented entities

The central claim depends on a from-scratch 4-layer transformer, a synthetic 3SUM dataset with several hand-set parameters, and interpretability assumptions about logit lens and token rankings. No quantitative ground truth is provided to break the loop between the observed rank-2 tokens and the claimed hidden reasoning steps.

free parameters (8)
  • Corruption rate = 4/3 (as stated)
    Chosen to generate corrupted instances in Sections 5.1.1 and 5.3.1; a rate above 1 is not a valid probability, so the actual corruption procedure is undefined.
  • True instance rate = 50%
    Balanced label distribution chosen in Section 5.3.1; affects task difficulty.
  • CoT rate = 50%
    Fraction of training samples with chain-of-thought annotations in Section 5.3.1; the mixture of filler and visible CoT is central to the recovery setup, but its exact role is not analyzed.
  • No filler rate = 0%
    Stated in Section 5.3.1; combined with CoT rate 50%, the training data composition is under-specified.
  • Sequence length = 7 tuples
    Input length in Section 5.1; affects combinatorial difficulty.
  • Tuple dimension = 3
    Tuple dimension in Section 5.1; defines the 3SUM variant.
  • Modulus = 10
    Arithmetic modulus in Section 5.1; defines the sum-to-zero condition.
  • Model scale = 4 layers, 384 hidden, 6 heads, ~34M parameters
    Architecture chosen in Section 4.1; the authors note in Limitations that findings may not transfer to larger models, making this a load-bearing scope choice.
assumptions (4)
  • domain assumption Logit lens validity: projecting hidden states through the output embedding matrix reveals meaningful intermediate token predictions.
    Invoked in Section 5.5 for the layer-wise analysis; no control or alternative probe validates this for a from-scratch 4-layer model.
  • domain assumption Filler CoT training leads to hidden computation as described by Pfau et al. [2].
    The paper adopts [2]'s phenomenon as its starting point without reproducing or quantifying it in its own model.
  • domain assumption Instance-adaptive CoT in Section 5.2 creates genuine sequential dependencies that make filler tokens carry cached intermediate results.
    The recovery interpretation assumes the model must compute earlier dimensions before later ones; if the model can solve the task in parallel or ignore the dependency, rank-2 tokens need not be cached reasoning.
  • domain assumption Token probability rankings at decoding steps reflect internal computation rather than output-format artifacts.
    The token ranking analysis in Section 5.6 treats the second-ranked non-filler token as the hidden reasoning token; this is the interpretability premise behind the modified decoding algorithm.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Understanding Hidden Computations in Chain-of-Thought Reasoning." pith.science (2026). https://pith.science/paper/YYQTYRNY

@misc{pith2026241204537,
  author       = {Pith},
  title        = {Pith review of: Understanding Hidden Computations in Chain-of-Thought Reasoning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YYQTYRNY}},
  note         = {Machine review of arXiv:2412.04537}
}
read the original abstract

Chain-of-Thought (CoT) prompting has significantly enhanced the reasoning abilities of large language models. However, recent studies have shown that models can still perform complex reasoning tasks even when the CoT is replaced with filler(hidden) characters (e.g., "..."), leaving open questions about how models internally process and represent reasoning steps. In this paper, we investigate methods to decode these hidden characters in transformer models trained with filler CoT sequences. By analyzing layer-wise representations using the logit lens method and examining token rankings, we demonstrate that the hidden characters can be recovered without loss of performance. Our findings provide insights into the internal mechanisms of transformer models and open avenues for improving interpretability and transparency in language model reasoning.

Figures

Figures reproduced from arXiv: 2412.04537 by the authors.

Figure 1
Figure 1. Percentage of filler tokens among top predictions across layers [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Comparison of decoding methods: Our method achieves higher accuracy in recovering hidden [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Greedy Decoding: The model outputs filler tokens followed by the final answer [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Greedy Decoding with Rank-2 Tokens [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Our Method: Greedy Decoding with Filler Tokens Replaced by Rank-2 Tokens (Recovering hidden [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: Random Token Replacement: Replacing Filler Tokens with Random Tokens [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Pause Tokens Strictly Increase the Expressivity of Constant-Depth Transformers

    cs.LG 2025-05 reject novelty 5.0 of 10

    The paper claims pause tokens strictly increase constant-precision, constant-depth Transformer expressivity from a subset of AC0 to AC0 (and log-precision to TC0), but the constant-precision proof is not sound as written.

Reference graph

Works this paper leans on

8 extracted references · 2 canonical work pages · cited by 1 Pith paper

  1. [1]

    Chain-of-thought prompting elicits reasoning in large language models.arXiv preprint arXiv:2201.11903, 2022

    Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Brian Ichter, Fei Xia, Ed Chi, Quoc Le, and Denny Zhou. Chain-of-thought prompting elicits reasoning in large language models.arXiv preprint arXiv:2201.11903, 2022

    arXiv 2022

  2. [2]

    Jacob Pfau, William Merrill, and Samuel R. Bowman. Let’s think dot by dot: Hidden computation in transformer language models. arXiv preprint arXiv:2308.07317 , 2023

    arXiv 2023

  3. [3]

    Interpreting GPT: the logit lens

    Nostalgebraist. Interpreting GPT: the logit lens. https://www.lesswrong.com/posts/ AcKRB8wDpdaN6v6ru/interpreting-gpt-the-logit-lens, 2020

    work page 2020

  4. [4]

    A mathematical framework for transformer circuits

    Nelson Elhage, Neel Nanda, Catherine Olsson, Nicholas Schiefer, Skyler Hallinan, Stanislav Fort, Danny Hernandez, and Chris Olah. A mathematical framework for transformer circuits. https: //transformer-circuits.pub/2021/framework/index.html, 2021

    work page 2021

  5. [5]

    Bluck, Azhar Golriz, Morgan Funtowicz, Lucas Sbarra, Aurelien Rodriguez, et al

    Hugo Touvron, Thibaut Lavril, Gautier Izacard, Edouard Grave, Matthieu Lin, Pierre H. Bluck, Azhar Golriz, Morgan Funtowicz, Lucas Sbarra, Aurelien Rodriguez, et al. LLaMA: Open and efficient foun- dation language models. arXiv preprint arXiv:2302.13971 , 2023

    arXiv 2023

  6. [6]

    Bowman, and Ethan Perez

    Tamera Lanham, Anna Chen, Ansh Radhakrishnan, Benoit Steiner, Carson Denison, Danny Hernandez, Dustin Li, Esin Durmus, Evan Hubinger, Jackson Kernion, Kamil˙ e Lukoši¯ ut˙ e, Karina Nguyen, Newton Cheng, Nicholas Joseph, Nicholas Schiefer, Oliver Rausch, Robin Larson, Sam McCandlish, Sandipan Kundu, Shannon Yang, Thomas Henighan, Timothy Maxwell, Timothy ...

    arXiv 2023

  7. [7]

    Bowman, and Ethan Perez

    Ansh Radhakrishnan, Karina Nguyen, Anna Chen, Carol Chen, Carson Denison, Danny Hernandez, Esin Durmus, Evan Hubinger, Jackson Kernion, Kamil˙ e Lukoši¯ ut˙ e, Newton Cheng, Nicholas Joseph, Nicholas Schiefer, Oliver Rausch, Sam McCandlish, Sheer El Showk, Tamera Lanham, Tim Maxwell, Venkatesa Chandrasekaran, Zac Hatfield-Dodds, Jared Kaplan, Jan Brauner,...

    arXiv 2023

  8. [8]

    Miles Turpin, Julian Michael, Ethan Perez, and Samuel R. Bowman. Language Models Don’t Al- ways Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting.arXiv preprint arXiv:2305.04388, 2023. https://arxiv.org/abs/2305.04388. 12

    arXiv 2023

Pith tools

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