Paper Citation Record · LEDGER

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias

As of 17 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 2 inbound Pith citation observations for arXiv:2505.00926.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2505.00926 v3

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T04:39:55.113761Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T20:57:10.776717Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-06-28T23:42:49.961290Z

Reference resolution

30 of 30 outbound references displayed

verified exact2
verified fuzzy2
unresolved26
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cdcfbd51-fa8a-40ac-97a3-b0915cb0119c · outbound

This paper cites Training Dynamics of Multi-Head Softmax Attention for In-Context Learning: Emergence, Convergence, and Optimality.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Training Dynamics of Multi-Head Softmax Attention for In-Context Learning: Emergence, Convergence, and Optimality

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:54.990906Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18158418-9dd5-489e-8a7a-012a1f23fc06 · outbound

This paper cites Transformers Implement Functional Gradient Descent to Learn Non-Linear Functions In Context.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Transformers Implement Functional Gradient Descent to Learn Non-Linear Functions In Context

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:54.995663Z

Source-reported events for the cited work

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Observation 799d9f0c-6b1f-413f-b6b3-c91d44b9317d · outbound

This paper cites Overcoming a Theoretical Limitation of Self-Attention.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Overcoming a Theoretical Limitation of Self-Attention

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.000654Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7bf4afd-cb6f-4825-8f2a-7f3396c30c9d · outbound

This paper cites On the Optimization and Generalization of Multi-head Attention.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias On the Optimization and Generalization of Multi-head Attention

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.010451Z

Source-reported events for the cited work

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Observation 8f1bf8ba-7431-4872-8a8b-7c2865077a0f · outbound

This paper cites BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.014925Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3232a6ae-4d9f-43c1-aee1-9f9a9fff8c40 · outbound

This paper cites On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.024520Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1de9036-333e-45a3-826a-9c832158e0a3 · outbound

This paper cites In-Context Convergence of Transformers.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias In-Context Convergence of Transformers

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.033194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11777658-631e-4e64-a941-589384b125ef · outbound

This paper cites A Theoretical Analysis of Self-Supervised Learning for Vision Transformers.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias A Theoretical Analysis of Self-Supervised Learning for Vision Transformers

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.038985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 456a1a31-bddc-4d14-ade5-db6d5590bd62 · outbound

This paper cites Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscape.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscape

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.048091Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06b3ef20-65e2-4861-94a3-5e285381d92a · outbound

This paper cites A Theoretical Understanding of Shallow Vision Transformers: Learning, Generalization, and Sample Complexity.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias A Theoretical Understanding of Shallow Vision Transformers: Learning, Generalization, and Sample Complexity

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.052535Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a87cda34-ab35-4ad1-91e6-5dfdb3acde01 · outbound

This paper cites Training Nonlinear Transformers for Chain-of-Thought Inference: A Theoretical Generalization Analysis.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Training Nonlinear Transformers for Chain-of-Thought Inference: A Theoretical Generalization Analysis

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.057589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b139b00c-2f00-4bc6-aeb4-4bcc0712611d · outbound

This paper cites One Step of Gradient Descent is Provably the Optimal In-Context Learner with One Layer of Linear Self-Attention.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias One Step of Gradient Descent is Provably the Optimal In-Context Learner with One Layer of Linear Self-Attention

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.061423Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3849a41a-2628-416c-a463-68a4e5478a53 · outbound

This paper cites The Expressive Power of Transformers with Chain of Thought.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias The Expressive Power of Transformers with Chain of Thought

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.065880Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 579ba2f9-5294-4944-a8ef-4175aa5d9664 · outbound

This paper cites an unresolved cited work.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-16T04:39:55.504372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 27895490-f6d5-404a-ac19-e0b2a9814f1a · outbound

This paper cites Benign Overfitting in Token Selection of Attention Mechanism.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Benign Overfitting in Token Selection of Attention Mechanism

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.078557Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 439fd820-6ffa-4b94-a19f-4ca19600d8d0 · outbound

This paper cites Implicit Regularization of Gradient Flow on One-Layer Softmax Attention.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Implicit Regularization of Gradient Flow on One-Layer Softmax Attention

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.082521Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c15a587-fc9f-4354-9f9f-9ef84f2a3456 · outbound

This paper cites Transformers as Support Vector Machines.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Transformers as Support Vector Machines

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.086987Z

Source-reported events for the cited work

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Observation 379d2c9c-b268-487a-aa25-0cdb2c8605b7 · outbound

This paper cites JoMA: Demystifying Multilayer Transformers via JOint Dynamics of MLP and Attention.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias JoMA: Demystifying Multilayer Transformers via JOint Dynamics of MLP and Attention

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.092241Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a95aef2-5781-4583-a80b-64ac21e2cd4e · outbound

This paper cites Implicit Bias and Fast Convergence Rates for Self-attention.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Implicit Bias and Fast Convergence Rates for Self-attention

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.096841Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 471940bf-60e2-48b6-bc36-428bcb39696a · outbound

This paper cites From Sparse Dependence to Sparse Attention: Unveiling How Chain-of-Thought Enhances Transformer Sample Efficiency.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias From Sparse Dependence to Sparse Attention: Unveiling How Chain-of-Thought Enhances Transformer Sample Efficiency

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.101972Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2aebcc4d-0092-45f9-8b07-40dd5df9ed25 · outbound

This paper cites Trained Transformers Learn Linear Models In-Context.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Trained Transformers Learn Linear Models In-Context

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.105878Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b0c9f10c-2b93-4a6e-91aa-7cbb25e75fc3 · outbound

This paper cites Auxiliary Lemmas and Equations Lemma A.1 (Gao & Pavel (2017)).

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Auxiliary Lemmas and Equations Lemma A.1 (Gao & Pavel (2017))

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:39:55.490887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 704aca31-5cd0-4508-b99a-4b474790b8d9 · outbound

This paper cites This can be done by noting that⟨u2,Ew 1 −E2 ℓ⟩≥ Ω(η) forℓ̸=ℓ0.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias This can be done by noting that⟨u2,Ew 1 −E2 ℓ⟩≥ Ω(η) forℓ̸=ℓ0

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:39:55.478138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0beb3973-5f06-4848-9285-64e2c0825a93 · outbound

This paper cites Implicit Bias in Leaky ReLU Networks Trained on High-Dimensional Data.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Implicit Bias in Leaky ReLU Networks Trained on High-Dimensional Data

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.019942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 67f1ecc1-9c23-48f5-b26a-ca3dbb3303aa · outbound

This paper cites How Transformers Learn Causal Structure with Gradient Descent.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias How Transformers Learn Causal Structure with Gradient Descent

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.074860Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd26e19c-2269-43b7-b139-cc5fea7b213b · outbound

This paper cites Why are Sensitive Functions Hard for Transformers?.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Why are Sensitive Functions Hard for Transformers?

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:55.028824Z

Source-reported events for the cited work

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Observation 267c3f93-77d8-43d0-ba85-389b4d88ce17 · outbound

This paper cites Unveil Benign Overfitting for Transformer in Vision: Training Dynamics, Convergence, and Generalization.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Unveil Benign Overfitting for Transformer in Vision: Training Dynamics, Convergence, and Generalization

Reference 2021

Resolution: verified exact; local_arxiv, observed 2026-08-16T04:39:55.311900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation fb8d970e-59c1-4cb6-a089-55a7073a6925 · outbound

This paper cites Superiority of Multi-Head Attention in In-Context Linear Regression.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Superiority of Multi-Head Attention in In-Context Linear Regression

Reference 2022

Resolution: verified exact; local_arxiv, observed 2026-08-16T04:39:55.407581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6d55574b-e675-4f26-ac77-97799f6e2fa2 · outbound

This paper cites Provably learning a multi-head attention layer.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias Provably learning a multi-head attention layer

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:54.985634Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8fbe3cd4-788c-44c5-8cde-21f2c77b66ea · outbound

This paper cites On the Ability and Limitations of Transformers to Recognize Formal Languages.

How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias On the Ability and Limitations of Transformers to Recognize Formal Languages

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-16T04:39:54.980591Z

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Pith citing papers

Observation b54f4b11-435e-45a8-9ac1-9f884743d67c · inbound

Transformers with RL or SFT Provably Learn Sparse Boolean Functions, But Differently cites this paper.

Transformers with RL or SFT Provably Learn Sparse Boolean Functions, But Differently How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T20:57:10.776717Z

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Observation 16c8f18c-5384-421d-95be-6c837185879a · inbound

Agentic Transformers Provably Learn to Search via Reinforcement Learning cites this paper.

Agentic Transformers Provably Learn to Search via Reinforcement Learning How Transformers Learn Regular Language Recognition: A Theoretical Study on Training Dynamics and Implicit Bias

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-06-28T23:42:49.962665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.