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arxiv: 2604.06501 · v1 · submitted 2026-04-07 · 💻 cs.LG · cs.CL

Recognition: 2 theorem links

· Lean Theorem

Transformer See, Transformer Do: Copying as an Intermediate Step in Learning Analogical Reasoning

Philipp Hellwig , Willem Zuidema , Claire E. Stevenson , Martha Lewis
Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:38 UTC · model grok-4.3

classification 💻 cs.LG cs.CL
keywords analogical reasoningletter-string analogiestransformersmeta-learninggeneralizationcopying tasksattentioninterpretability
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The pith

Including copying tasks in training lets transformers learn letter-string analogies by attending to the most informative elements.

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

The paper establishes that transformers can master letter-string analogies when copying tasks are added to the training mix under meta-learning for compositionality. This addition steers the models toward focusing on the key relational parts of each problem rather than surface patterns. With more varied alphabets in the data, even a small three-layer encoder-decoder model generalizes to entirely new alphabets and beats most larger frontier models. The same training also supports limited transfer to combinations of previously seen transformations. Interpretability work then reveals an internal algorithm the model follows, which can be used to steer its outputs predictably.

Core claim

Letter-string analogies become learnable when guiding the models to attend to the most informative problem elements induced by including copying tasks in the training data. Furthermore, generalization to new alphabets becomes better when models are trained with more heterogeneous datasets, where our 3-layer encoder-decoder model outperforms most frontier models. The MLC approach also enables some generalization to compositions of trained transformations, but not to completely novel transformations. To understand how the model operates, we identify an algorithm that approximates the model's computations and verify this using interpretability analyses.

What carries the argument

The addition of copying tasks to the meta-learning training data, which induces attention to the most informative elements of each analogy problem.

If this is right

  • Transformers can learn to solve letter-string analogies once copying is included as an intermediate training step.
  • Greater heterogeneity in the training alphabets improves generalization to unseen alphabets.
  • A compact three-layer encoder-decoder model can exceed the performance of most larger frontier models on this generalization test.
  • The trained models transfer to some recombinations of learned transformations but fail on entirely new ones.
  • The model's internal computations can be approximated by a simple algorithm that allows precise steering of its behavior.

Where Pith is reading between the lines

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

  • The same copying-based intermediate step might improve analogical reasoning in much larger language models without requiring full retraining.
  • Human solvers of letter-string problems may also rely on an implicit copying-like focus on relational structure before mapping.
  • Applying the copying pre-training step to other structured reasoning domains could test whether it is a general route to better relational attention.

Load-bearing premise

That the copying tasks are what specifically cause the model to attend to the informative problem elements, as opposed to other features of the data or training procedure.

What would settle it

Train identical models on the letter-string task without any copying examples and check whether accuracy on new alphabets falls to the low levels seen in the original non-copying runs.

Figures

Figures reproduced from arXiv: 2604.06501 by Claire E. Stevenson, Martha Lewis, Philipp Hellwig, Willem Zuidema.

Figure 1
Figure 1. Figure 1: A forward pass through the model, with an example letter-string analogy task. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Our best model (green) outperforms most LLMs (grey) on the aggregated dataset ( [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Increasing the number of seen alphabets in training leads to better gen￾eralization to new alphabets (red and blue lines converge). Bands indicate 95% bootstrapped confidence intervals with 10 replications. Including copy tasks facilitates learning. We find that including copy tasks in the dataset gives the models a considerable boost in per￾formance on seen alphabets and seen transfor￾mations ( [PITH_FUL… view at source ↗
Figure 4
Figure 4. Figure 4: Averaged accuracies split by transformation with the best performing models with [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Models trained without copy tasks do not show information flow between example [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Illustration of the initialization step (where [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Results from our attention pattern patching. A single attention head in the second encoder layer implements the matching operation of the algorithm. We demonstrate the effects of this head are causal, by replacing the standard attention matrix A pred with A succ produced by a successor task. the letter f in our running example) across predecessor tasks, as these must be invariant if they are to represent t… view at source ↗
Figure 8
Figure 8. Figure 8: The Compute mapping and Apply mapping steps of the algorithm. The encoder builds an invariant representation for the predecessor transformation and stores it in the first letter of the example output (left). This representation is then used in the decoder cross-attention (layer 2) to move attention from letter ’b’ (layer 1) to letter ’a’ (layer 3) of the decoder. 6 Discussion & Conclusions We examined whet… view at source ↗
Figure 9
Figure 9. Figure 9: The best performing model forms distinct attention patterns for the example of [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Validation accuracy declines when providing the model with more examples to [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Elimination step of the model where token representations that attend to the EOS token (left) are subsequently wiped out (right). Analogical reasoning steps of MLC models and humans overlap We identify parallels between the matching step of the models from Section 5 and human analogy solving. Based on Johnson et al. (2025), we describe the similarities to human analogical reasoning steps in [PITH_FULL_IM… view at source ↗
Figure 12
Figure 12. Figure 12: In particular, find that (1) encoding relevant information of the domains and (2) searching for and retrieving relationships and similarities between elements closely align with the attention patterns from head #7 in the second layer of the encoder ( [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Frontier LLM performance by Transformation Type compared to our MLC trained [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Attention patterns for first layer of RASP program, locating the separators and [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Attention patterns for second layer of RASP program, locating relevant items for [PITH_FULL_IMAGE:figures/full_fig_p020_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Attention patterns for RASP program 20 [PITH_FULL_IMAGE:figures/full_fig_p020_16.png] view at source ↗
read the original abstract

Analogical reasoning is a hallmark of human intelligence, enabling us to solve new problems by transferring knowledge from one situation to another. Yet, developing artificial intelligence systems capable of robust human-like analogical reasoning has proven difficult. In this work, we train transformers using Meta-Learning for Compositionality (MLC) on an analogical reasoning task (letter-string analogies) and assess their generalization capabilities. We find that letter-string analogies become learnable when guiding the models to attend to the most informative problem elements induced by including copying tasks in the training data. Furthermore, generalization to new alphabets becomes better when models are trained with more heterogeneous datasets, where our 3-layer encoder-decoder model outperforms most frontier models. The MLC approach also enables some generalization to compositions of trained transformations, but not to completely novel transformations. To understand how the model operates, we identify an algorithm that approximates the model's computations. We verify this using interpretability analyses and show that the model can be steered precisely according to expectations derived from the algorithm. Finally, we discuss implications of our findings for generalization capabilities of larger models and parallels to human analogical reasoning.

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 / 1 minor

Summary. The paper trains small transformer models using Meta-Learning for Compositionality (MLC) on letter-string analogy tasks. It claims that including copying tasks in the training data guides the models to attend to the most informative problem elements, thereby making analogical reasoning learnable. Generalization to new alphabets improves with more heterogeneous training datasets, and a 3-layer encoder-decoder model outperforms most frontier models on this metric. The approach yields partial generalization to compositions of trained transformations but not to entirely novel ones. Interpretability analyses identify an algorithm approximating the model's computations, which is verified and used to steer model behavior.

Significance. If the empirical findings and causal attribution hold after proper controls, the work would demonstrate that auxiliary copying tasks can serve as an effective intermediate step for inducing structured attention patterns that support analogical reasoning in transformers. The mechanistic interpretability component, including the identified algorithm and steering experiments, strengthens the contribution by providing falsifiable, verifiable insights rather than purely black-box performance claims. This could inform training strategies for compositionality and generalization in larger models and draw parallels to human analogical reasoning.

major comments (2)
  1. [Abstract / Results] Abstract and Results: The central claim that copying tasks specifically induce attention to the most informative elements (rather than MLC meta-learning, dataset heterogeneity, or total training volume) lacks isolating controls. No experiments are described that hold data size, diversity, and training procedure fixed while toggling only the presence/absence of copying tasks versus other auxiliary objectives, making the causal attribution load-bearing but unsupported.
  2. [Abstract] Abstract: The statement that the 3-layer encoder-decoder 'outperforms most frontier models' on new-alphabet generalization requires explicit details on the exact frontier models tested, evaluation metrics, number of trials, statistical tests, and error bars to assess whether the comparison is robust and not driven by differences in training regime or evaluation protocol.
minor comments (1)
  1. [Abstract] The abstract provides high-level findings but omits key methodological details (datasets, statistical tests, baselines, error analysis) that would allow readers to evaluate the strength of the reported generalization results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback, which highlights important aspects of our causal claims and reporting. We address each major comment below and will revise the manuscript accordingly to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Abstract / Results] Abstract and Results: The central claim that copying tasks specifically induce attention to the most informative elements (rather than MLC meta-learning, dataset heterogeneity, or total training volume) lacks isolating controls. No experiments are described that hold data size, diversity, and training procedure fixed while toggling only the presence/absence of copying tasks versus other auxiliary objectives, making the causal attribution load-bearing but unsupported.

    Authors: We agree that stronger isolation of the copying task's role would bolster the causal attribution. Our current experiments compare MLC training with and without copying tasks (while varying dataset heterogeneity), and the mechanistic analyses link copying-induced attention patterns to improved analogy performance. However, we did not test against matched alternative auxiliary objectives. In the revision, we will add new control experiments that hold total data volume, diversity, and training procedure fixed while comparing copying tasks to other auxiliaries (e.g., random masking or repetition tasks). This will allow direct assessment of whether copying specifically drives the observed attention and generalization benefits. revision: yes

  2. Referee: [Abstract] Abstract: The statement that the 3-layer encoder-decoder 'outperforms most frontier models' on new-alphabet generalization requires explicit details on the exact frontier models tested, evaluation metrics, number of trials, statistical tests, and error bars to assess whether the comparison is robust and not driven by differences in training regime or evaluation protocol.

    Authors: We acknowledge that the abstract statement requires supporting details for proper evaluation. The main text reports comparisons to specific models (including GPT-4, Claude-3, and Gemini) using exact-match accuracy on held-out alphabets, with results averaged over multiple random seeds. In the revised version, we will expand both the abstract and results section to explicitly list the frontier models, the precise metrics and protocols, the number of evaluation trials, any statistical tests applied, and error bars. We will also clarify training and evaluation differences to ensure the comparison is transparent and reproducible. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical training results on letter-string analogies do not reduce to inputs by construction

full rationale

The paper reports experimental outcomes from training 3-layer encoder-decoder transformers via MLC on letter-string analogy tasks, with and without copying subtasks, and measures generalization to new alphabets and compositions. No equations, derivations, fitted parameters, or first-principles claims appear; the central findings (learnability induced by copying tasks, better generalization with heterogeneous data) are presented as direct results of the reported training regimes and test evaluations rather than any self-referential reduction or renamed fit. Any MLC reference is external methodological context and does not substitute for the empirical isolation or verification steps described.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review is based on abstract only; no specific free parameters, axioms, or invented entities are identifiable from the provided text.

pith-pipeline@v0.9.0 · 5505 in / 1141 out tokens · 48509 ms · 2026-05-10T18:38:35.650013+00:00 · methodology

discussion (0)

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    on the dataset with 20 permuted alphabets (copy tasks included). Figure 10 and Table 5 show that increasing the number of examples worsens the overall accuracy of 62.5% when trained with one example per task to an overall accuracy of 37.1% when trained with 5 examples per task. Figure 10: Validation accuracy declines when providing the model with more exa...

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