Paper Citation Record · LEDGER

How Transformers Learn Causal Structure with Gradient Descent

As of 22 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 16 inbound Pith citation observations for arXiv:2402.14735.

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

pith.paper-citation-record.v1
2402.14735 v2

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 16 of 16 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 16 of 16 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T04:39:55.074860Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

5
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 2a8c7430-2f72-4c3c-876f-d16d315c907c · inbound

Transformers with Sparse Attention for Granger Causality cites this paper.

Transformers with Sparse Attention for Granger Causality How Transformers Learn Causal Structure with Gradient Descent

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-12T16:44:59.240801Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c183ed2-280b-45ad-925c-ea1580ad48cc · inbound

Rethinking Associative Memory Mechanism in Induction Head cites this paper.

Rethinking Associative Memory Mechanism in Induction Head How Transformers Learn Causal Structure with Gradient Descent

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-11T15:06:30.765076Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4b8a0cc-5aff-4b01-91e0-42c87d69b3f1 · inbound

Metastable Dynamics of Chain-of-Thought Reasoning: Provable Benefits of Search, RL and Distillation cites this paper.

Metastable Dynamics of Chain-of-Thought Reasoning: Provable Benefits of Search, RL and Distillation How Transformers Learn Causal Structure with Gradient Descent

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-09T17:37:40.730834Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 64b2ac71-9cd4-42de-b4fe-26e85ddf615e · inbound

Transformers and Their Roles as Time Series Foundation Models cites this paper.

Transformers and Their Roles as Time Series Foundation Models How Transformers Learn Causal Structure with Gradient Descent

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-09T05:01:32.372660Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 096930cc-88e8-41d1-8ee2-b3f090ea8a2c · inbound

Spectral Journey: How Transformers Predict the Shortest Path cites this paper.

Spectral Journey: How Transformers Predict the Shortest Path How Transformers Learn Causal Structure with Gradient Descent

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-07T23:44:10.834946Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

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

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 ff75ee10-68d8-4aa0-8153-f544be1c01b3 · inbound

Transformers as Multi-task Learners: Decoupling Features in Hidden Markov Models cites this paper.

Transformers as Multi-task Learners: Decoupling Features in Hidden Markov Models How Transformers Learn Causal Structure with Gradient Descent

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T11:40:57.895555Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e6ad2f75-2630-4327-84e0-ed74ac02d5f6 · inbound

The Features at Convergence Theorem: a first-principles alternative to the Neural Feature Ansatz for how networks learn representations cites this paper.

The Features at Convergence Theorem: a first-principles alternative to the Neural Feature Ansatz for how networks learn representations How Transformers Learn Causal Structure with Gradient Descent

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-06T19:31:21.883499Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f83e290-35b7-4ccd-80a0-69c93bc572ee · inbound

Provable Knowledge Acquisition and Extraction in One-Layer Transformers cites this paper.

Provable Knowledge Acquisition and Extraction in One-Layer Transformers How Transformers Learn Causal Structure with Gradient Descent

Reference 27

Resolution: metadata mismatch; arxiv_id, observed 2026-05-21T23:10:44.830980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7ff6388f-9ea2-47c8-bb47-61d49b1e97cd · inbound

Learning In-context n-grams with Transformers: Sub-n-grams Are Near-stationary Points cites this paper.

Learning In-context n-grams with Transformers: Sub-n-grams Are Near-stationary Points How Transformers Learn Causal Structure with Gradient Descent

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T17:26:36.890264Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3d1807cc-20b7-44dc-b906-a36d47a21dcd · inbound

Fast Wasserstein rates for estimating probability distributions of probabilistic graphical models cites this paper.

Fast Wasserstein rates for estimating probability distributions of probabilistic graphical models How Transformers Learn Causal Structure with Gradient Descent

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-22T12:51:33.487252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6936fe17-362f-450a-b57f-52294ab5cbd8 · inbound

A Global Characterization of $f$-Divergences Yielding PSD Mutual-Information Matrices cites this paper.

A Global Characterization of $f$-Divergences Yielding PSD Mutual-Information Matrices How Transformers Learn Causal Structure with Gradient Descent

Reference 4

Resolution: metadata mismatch; arxiv_id, observed 2026-05-16T14:27:59.464866Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 17079616-3aae-4d65-863d-992f1b4ff796 · inbound

Visual prompting reimagined: The power of the Activation Prompts cites this paper.

Visual prompting reimagined: The power of the Activation Prompts How Transformers Learn Causal Structure with Gradient Descent

Reference 64

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T23:45:54.010348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3b4e5ebb-8cb4-4630-a8bb-253aef7587e7 · inbound

CausalDetox: Causal Head Selection and Intervention for Language Model Detoxification cites this paper.

CausalDetox: Causal Head Selection and Intervention for Language Model Detoxification How Transformers Learn Causal Structure with Gradient Descent

Reference 5

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T12:05:21.985681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a30481fc-c454-4a69-a8ad-fd407bac2e32 · inbound

Why Muon Outperforms Adam: A Curvature Perspective cites this paper.

Why Muon Outperforms Adam: A Curvature Perspective How Transformers Learn Causal Structure with Gradient Descent

Reference 62

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T07:16:44.441942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d0e6d8b0-b8aa-481b-aeca-d8473989c797 · inbound

Rigorous uncertainty quantification of probabilistic AI weather forecasts with conformal prediction cites this paper.

Rigorous uncertainty quantification of probabilistic AI weather forecasts with conformal prediction How Transformers Learn Causal Structure with Gradient Descent

Reference 79

Resolution: metadata mismatch; arxiv_id, observed 2026-06-26T18:29:41.671020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.