Paper Citation Record · LEDGER

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning

As of 15 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 2 inbound Pith citation observations for arXiv:2505.22308.

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

pith.paper-citation-record.v1
2505.22308 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:14:28.634005Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T17:31:49.264777Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-12T07:11:25.690518Z

Reference resolution

36 of 36 outbound references displayed

verified exact6
verified fuzzy8
unresolved20
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b1b2825d-eda5-42b1-9cc4-47842dad1b99 · outbound

This paper cites Transferring Inductive Biases through Knowledge Distillation.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Transferring Inductive Biases through Knowledge Distillation

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:24.874183Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3625d6de-dd67-4a70-9a44-e49158854701 · outbound

This paper cites REVERSED ADDITION.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning REVERSED ADDITION

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:31.112266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 95d800d4-9c64-4006-ac34-4bf227f73b02 · outbound

This paper cites Meta-Learning Neural Mechanisms rather than Bayesian Priors.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Meta-Learning Neural Mechanisms rather than Bayesian Priors

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:14:30.454365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 92d5d0dd-6ef4-41b3-8637-9538820c95e0 · outbound

This paper cites General Intelligence Requires Reward-based Pretraining.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning General Intelligence Requires Reward-based Pretraining

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:14:30.219287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e6bf7406-b0b7-4a91-ba40-abbf7e83c1cf · outbound

This paper cites Between Circuits and Chomsky: Pre-pretraining on Formal Languages Imparts Linguistic Biases.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Between Circuits and Chomsky: Pre-pretraining on Formal Languages Imparts Linguistic Biases

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:25.498615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca75d691-e10e-464b-9417-560a316942db · outbound

This paper cites Scaling Laws for Neural Language Models.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Scaling Laws for Neural Language Models

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:25.555854Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce33c289-0ea5-433b-848a-339799a778f5 · outbound

This paper cites Modeling rapid language learning by distilling Bayesian priors into artificial neural networks.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Modeling rapid language learning by distilling Bayesian priors into artificial neural networks

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:25.627169Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd77af24-af1f-4158-afa4-5c52b7356c06 · outbound

This paper cites Transformers Can Do Bayesian Inference.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Transformers Can Do Bayesian Inference

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:25.641616Z

Source-reported events for the cited work

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Observation dbccbc5f-9eba-440e-8e61-2d76c5bf1207 · outbound

This paper cites Scaling Backwards: Minimal Synthetic Pre-training?.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Scaling Backwards: Minimal Synthetic Pre-training?

Reference 14

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T13:14:29.886160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a10a90ee-67a1-4874-896b-313c880b4aa6 · outbound

This paper cites Injecting structural hints: Using language models to study inductive biases in language learning.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Injecting structural hints: Using language models to study inductive biases in language learning

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:25.938487Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f626fef6-0c33-4241-9f59-6ac83b318122 · outbound

This paper cites How Does Code Pretraining Affect Language Model Task Performance?.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning How Does Code Pretraining Affect Language Model Task Performance?

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:26.122419Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3160d337-b882-4a74-9685-0a84327393a6 · outbound

This paper cites Procedural Knowledge in Pretraining Drives Reasoning in Large Language Models.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Procedural Knowledge in Pretraining Drives Reasoning in Large Language Models

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:26.413691Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28d032f0-c492-4955-b7c8-7b66e8f9b5a1 · outbound

This paper cites Mimetic Initialization of Self-Attention Layers.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Mimetic Initialization of Self-Attention Layers

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:26.536645Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d39d4ff9-402a-467a-b7d4-02db4e3196bc · outbound

This paper cites Visual Pre-training for Navigation: What Can We Learn from Noise?.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Visual Pre-training for Navigation: What Can We Learn from Noise?

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:26.636172Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a227dc90-bdce-4ee6-84be-e0a97a2f16cb · outbound

This paper cites Pre-training with Synthetic Data Helps Offline Reinforcement Learning.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Pre-training with Synthetic Data Helps Offline Reinforcement Learning

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:14:29.283058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 492a3a35-69f9-4641-84cf-7144cecc80f7 · outbound

This paper cites Initializing Models with Larger Ones.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Initializing Models with Larger Ones

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:26.797297Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20fa538f-7c97-471f-a9e3-a64eb288af94 · outbound

This paper cites Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:26.870092Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ce8af13-93b6-4638-bbba-024f6a8d03df · outbound

This paper cites Instilling Inductive Biases with Subnetworks.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Instilling Inductive Biases with Subnetworks

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:14:28.911580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ec09404a-d0cb-4785-9c12-312a70d7c026 · outbound

This paper cites Intelligence at the Edge of Chaos.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Intelligence at the Edge of Chaos

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:27.128137Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 04f57d2a-75dc-4271-9424-167f1741aba3 · outbound

This paper cites But recent results also question the value of the data, showing that some benefits of pretraining are attributable to the optimization objective more than the actual data.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning But recent results also question the value of the data, showing that some benefits of pretraining are attributable to the optimization objective more than the actual data

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:33.107476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f31d0e48-eb80-40ac-bd70-61ef9d90fed2 · outbound

This paper cites an unresolved cited work.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:14:32.813420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 98fe74e4-b88c-4408-ba00-af62a0536f8a · outbound

This paper cites Partial transfer from pretrained transformers.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Partial transfer from pretrained transformers

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:32.603605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 237a342a-b295-49c5-9ade-7b4d0b6f143f · outbound

This paper cites mimetic initialization.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning mimetic initialization

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:32.392827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 30aa9289-380a-4cc7-bde4-3e05b808d31f · outbound

This paper cites Goodale et al.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Goodale et al

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:32.202176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 93fd55b2-4eaf-4b51-9c72-384025ae8349 · outbound

This paper cites As stated by Hu et al.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning As stated by Hu et al

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:32.001433Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f3cf8ee7-9b7d-43c7-96b8-33c357f5dcd0 · outbound

This paper cites an unresolved cited work.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:14:31.570998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 14e761fb-7dd9-459c-b51e-03a8ca34f39c · outbound

This paper cites This setup effectively simulates infinite data.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning This setup effectively simulates infinite data

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:31.364349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8eb0e7be-7fc0-4bab-80c0-a08d310435f3 · outbound

This paper cites For example, given an input sequence 6 3 5 and separator |, the expected output is 3 5 6.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning For example, given an input sequence 6 3 5 and separator |, the expected output is 3 5 6

Reference 100

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T13:14:30.932762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation df944879-a8f0-451d-b492-c4e8fd8a7cc5 · outbound

This paper cites (2024), where data is procedurally generated from Elementary Cellular Automata (ECA) using Rule 110, a Class IV rule known for its complex, Turing- complete behavior.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning (2024), where data is procedurally generated from Elementary Cellular Automata (ECA) using Rule 110, a Class IV rule known for its complex, Turing- complete behavior

Reference 110

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:31.744540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0d48b379-35cc-44f6-98f9-1f5f20b5a267 · outbound

This paper cites Pretraining with Artificial Language: Studying Transferable Knowledge in Language Models.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Pretraining with Artificial Language: Studying Transferable Knowledge in Language Models

Reference 2019

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:14:29.583690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0e11be88-ab40-4bbd-96f0-2148f08cb111 · outbound

This paper cites To Code, or Not To Code? Exploring Impact of Code in Pre-training.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning To Code, or Not To Code? Exploring Impact of Code in Pre-training

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:24.938053Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76f7e039-4c91-4ccc-83f4-eed6796f4e04 · outbound

This paper cites Procedural Image Programs for Representation Learning.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Procedural Image Programs for Representation Learning

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:25.071849Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2ad212d8-b944-4178-8d4d-5d1b7c075383 · outbound

This paper cites Emergent properties with repeated examples.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Emergent properties with repeated examples

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:25.167243Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7412de9-a583-4bf4-8cec-43376413809c · outbound

This paper cites DoGE: Domain Reweighting with Generalization Estimation.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning DoGE: Domain Reweighting with Generalization Estimation

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:25.236291Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a555c366-167d-4fcb-8e53-15c2132cc67a · outbound

This paper cites Learning to See by Looking at Noise.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Learning to See by Looking at Noise

Reference 2024

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:14:30.679490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 86706279-418f-4f33-829f-e5aa1726c826 · outbound

This paper cites Learning Universal Predictors.

Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning Learning Universal Predictors

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-07T13:14:25.350545Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 62030f58-7b87-407a-b593-e6793d47850c · inbound

Synthetic Pre-Pre-Training Improves Language Model Robustness to Noisy Pre-Training Data cites this paper.

Synthetic Pre-Pre-Training Improves Language Model Robustness to Noisy Pre-Training Data Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning

Reference 62

Resolution: verified exact; arxiv_id, observed 2026-05-12T07:11:25.693145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 59b69caf-52d7-4753-b0a3-63054497bf75 · inbound

Can Transformers Really Do It All? On the Compatibility of Inductive Biases Across Tasks cites this paper.

Can Transformers Really Do It All? On the Compatibility of Inductive Biases Across Tasks Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-01T17:31:49.264777Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.