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arxiv: 2604.18839 · v1 · submitted 2026-04-20 · 💻 cs.LG · cs.AI

Recognition: unknown

One Step Forward and K Steps Back: Better Reasoning with Denoising Recursion Models

Chris Cameron , Wangzheng Wang , Nikita Ivanov , Ashmita Bhattacharyya , Didier Ch\'etelat , Yingxue Zhang
Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:52 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords denoising recursion modelslooped transformersARC-AGIiterative refinementnoise corruptionreasoningcurriculum learningnon-greedy generation
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The pith

Denoising Recursion Models reverse noise over multiple recursive steps to improve performance on ARC-AGI reasoning tasks.

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

Looped transformers can refine predictions iteratively but struggle to learn long trajectories when only the final answer is supervised. The paper proposes corrupting inputs with noise and training the model to undo this corruption across several recursive steps of the shared transformer block. This multi-step reversal creates intermediate training examples, aligns the training process with how the model is deployed at test time, and encourages the model to consider future states rather than making immediate corrections. Experiments on the ARC-AGI benchmark show this approach outperforms the Tiny Recursion Model.

Core claim

Denoising Recursion Models corrupt data with varying magnitudes of noise and train the model to reverse the corruption over multiple recursive steps. This provides a tractable curriculum of intermediate states while better aligning training with testing and incentivizing non-greedy, forward-looking generation.

What carries the argument

Denoising Recursion Model, which trains a shared transformer to reverse noise corruption in multiple recursive steps.

If this is right

  • Long refinement trajectories for difficult problems become easier to learn through the provided intermediate states.
  • Training behavior matches testing behavior more closely by using multi-step reversal.
  • Non-greedy generation is incentivized as the model learns to plan over multiple steps.
  • Superior performance is achieved compared to the Tiny Recursion Model on ARC-AGI.

Where Pith is reading between the lines

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

  • Such models could be applied to other iterative tasks where building structure from noise is key, like image generation or planning.
  • Adjusting the number of recursive steps during training might offer a way to control the difficulty of the curriculum dynamically.
  • This suggests potential for improving parameter-efficient deep reasoning in other looped neural architectures.

Load-bearing premise

Training to reverse noise over multiple recursive steps will supply a useful curriculum, align train and test distributions, and incentivize non-greedy behavior without new optimization instabilities.

What would settle it

Running the Denoising Recursion Model on ARC-AGI and observing no performance gain over the Tiny Recursion Model would disprove the benefit of the multi-step approach.

Figures

Figures reproduced from arXiv: 2604.18839 by Ashmita Bhattacharyya, Chris Cameron, Didier Ch\'etelat, Nikita Ivanov, Wangzheng Wang, Yingxue Zhang.

Figure 1
Figure 1. Figure 1: Architectural comparison between (a) backward-training (e.g., TRM), (b) forward-training [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Example of ARC-AGI task. Two input-output grids examples for the task transformation: [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Various examples of the flavours of reasoning needed to solved ARC-AGI-2 tasks. [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Successful convergence on the ARC-AGI 2 task [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Successful solution on the ARC-AGI 2 task [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Failure to converge to a correct answer on a ARC-AGI 2 task [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of training logic between TRM and DRM (with TRM base). Text in red [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Pass@k exact-match accuracy on ARC2-Eval for three methods (TRM baseline, SPRM, [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Extreme robustness to overfitting. TRM validation accuracy continues to improve even after training surpasses 99% per-pixel accuracy across the grid. (left) 1–exact-match accuracy, 1–per-cell accuracy, (middle) validation per-cell accuracy, (right) validation pass@2. We note that standard masked diffusion corresponds to DRM with k = 1 and no warm-up loops. The fact that DRM at k = 1 achieves 31.8% accuracy… view at source ↗
Figure 10
Figure 10. Figure 10: Unlooped transformer has better training loss than TRM baseline (left)) but worse training [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Training dynamics comparison between TRM and SPRM. (left) training exact accuracy [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Single z (no scratchpad latent state) performed as good as the TRM baseline. becomes an update where both transitions reuse a single module f: zL ← f(zL, zH + x), zH ← f(zH, zL). A natural question is whether this scratchpad zL is truly necessary. In Jolicoeur-Martineau (2025)’s ablations, they test a more aggressive simplification that only depends on zH zH ← f(zH, x), zH ← f(zH). which performed substan… view at source ↗
read the original abstract

Looped transformers scale computational depth without increasing parameter count by repeatedly applying a shared transformer block and can be used for iterative refinement, where each loop rewrites a full fixed-size prediction in parallel. On difficult problems, such as those that require search-like computation, reaching a highly structured solution starting from noise can require long refinement trajectories. Learning such trajectories is challenging when training specifies only the target solution and provides no supervision over the intermediate refinement path. Diffusion models tackle this issue by corrupting data with varying magnitudes of noise and training the model to reverse it in a \textit{single step}. However, this process misaligns training and testing behaviour. We introduce Denoising Recursion Models, a method that similarly corrupts data with noise but trains the model to reverse the corruption over \textit{multiple} recursive steps. This strategy provides a tractable curriculum of intermediate states, while better aligning training with testing and incentivizing non-greedy, forward-looking generation. Through extensive experiments, we show this approach outperforms the Tiny Recursion Model (TRM) on ARC-AGI, where it recently achieved breakthrough performance.

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 introduces Denoising Recursion Models, which extend looped transformers by corrupting inputs with noise and training a shared transformer block to reverse the corruption over multiple recursive steps (rather than one). This is argued to supply an intermediate-state curriculum, better align training and test distributions, and incentivize non-greedy behavior. The central claim is that the resulting models outperform the Tiny Recursion Model (TRM) on ARC-AGI, as demonstrated through extensive experiments.

Significance. If the empirical results hold under rigorous controls, the work could advance training of parameter-efficient iterative refinement architectures for search-like reasoning tasks. By integrating multi-step denoising into recursion, it addresses the lack of intermediate supervision in looped models while potentially avoiding some train-test misalignment issues of standard diffusion approaches.

major comments (2)
  1. [§4 (Experiments)] §4 (Experiments): The manuscript asserts outperformance on ARC-AGI via 'extensive experiments' but the provided description supplies no quantitative metrics, matched baselines, ablation results on recursion depth K, statistical tests, or controls for hyperparameter tuning budgets. This renders the central empirical claim unverifiable and leaves open whether multi-step denoising yields net gains or merely requires compensatory tuning.
  2. [§3 (Method)] §3 (Method): The claim that training to reverse noise over K recursive steps 'automatically' supplies a useful curriculum, aligns distributions, and avoids greedy behavior without introducing compounding prediction errors or gradient instabilities is presented without supporting analysis, loss diagnostics across depth, or sensitivity studies. This assumption is load-bearing for the proposed advantage over single-step or standard recursion.
minor comments (2)
  1. [Abstract] Abstract: Including at least one key performance number or comparison would help substantiate the outperformance claim for readers.
  2. [Notation] Notation and figures: Ensure the noise schedule, recursion update rule, and loss formulation are defined with explicit equations and that any diagrams of the K-step process are clearly labeled.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and for acknowledging the potential of integrating multi-step denoising into looped transformers for reasoning tasks. We address the two major comments below with specific plans for revision. We believe these changes will enhance the verifiability of our empirical claims and the supporting analysis for our methodological assumptions.

read point-by-point responses

  1. Referee: [§4 (Experiments)] The manuscript asserts outperformance on ARC-AGI via 'extensive experiments' but the provided description supplies no quantitative metrics, matched baselines, ablation results on recursion depth K, statistical tests, or controls for hyperparameter tuning budgets. This renders the central empirical claim unverifiable and leaves open whether multi-step denoising yields net gains or merely requires compensatory tuning.

    Authors: We acknowledge that the summary in Section 4 could be expanded for greater clarity and verifiability. The full manuscript does include quantitative comparisons in Tables 1–3 reporting ARC-AGI accuracy improvements over TRM and other baselines, along with some matched controls. However, we agree that explicit ablations on recursion depth K, statistical significance (e.g., standard deviations over seeds), and details on hyperparameter tuning budgets are necessary to rule out compensatory tuning effects. We will revise Section 4 to add these elements, including a dedicated ablation table for K=1 to K=8, multiple-run statistics, and a description of the tuning protocol used for all models. revision: yes

  2. Referee: [§3 (Method)] The claim that training to reverse noise over K recursive steps 'automatically' supplies a useful curriculum, aligns distributions, and avoids greedy behavior without introducing compounding prediction errors or gradient instabilities is presented without supporting analysis, loss diagnostics across depth, or sensitivity studies. This assumption is load-bearing for the proposed advantage over single-step or standard recursion.

    Authors: Section 3 presents a conceptual rationale: multi-step noise reversal creates a curriculum of progressively cleaner intermediate states, the shared recursive process aligns train and test distributions, and forward-looking reversal discourages greedy local corrections. We did not include loss-per-depth diagnostics or sensitivity plots in the initial submission. We agree this supporting analysis would strengthen the paper and will add it in revision, specifically loss curves across recursion steps, gradient norm statistics to address stability, and performance sensitivity as a function of K to demonstrate the absence of compounding errors. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical claims rest on experiments, not definitional reduction

full rationale

The paper proposes Denoising Recursion Models as a training strategy for looped transformers, describing how noise corruption followed by multi-step reversal supplies a curriculum and alignment by design. However, the central result—outperformance over TRM on ARC-AGI—is asserted via 'extensive experiments' rather than any derivation, equation, or fitted parameter that reduces to the method's own inputs. No self-citations, uniqueness theorems, or ansatzes are invoked to force conclusions; the argument remains externally falsifiable through the reported empirical comparisons and does not contain load-bearing steps that collapse by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard machine-learning assumptions about the benefits of curriculum learning and train-test alignment in iterative models, plus the empirical observation that single-step denoising misaligns with looped inference. No new physical or mathematical axioms are introduced.

axioms (2)
  • domain assumption Looped transformers can perform iterative refinement by repeatedly applying a shared block to rewrite a fixed-size prediction.
    Background premise stated in the opening sentences of the abstract.
  • domain assumption Single-step noise reversal in diffusion-style training misaligns with the multi-step inference behavior of looped models.
    Explicitly claimed as the core problem the new method addresses.

pith-pipeline@v0.9.0 · 5513 in / 1449 out tokens · 42154 ms · 2026-05-10T04:52:47.647147+00:00 · methodology

discussion (0)

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Reference graph

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