Paper Citation Record · LEDGER

Theoretical limitations of multi-layer Transformer

As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 18 inbound Pith citation observations for arXiv:2412.02975.

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

pith.paper-citation-record.v1
2412.02975 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 18 of 18 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-08T13:23:22.006914Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T22:06:16.211261Z

Reference resolution

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External citation measurements

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Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 54a66fe2-2e84-4fba-a26c-7fc846a45aa3 · inbound

When More is Less: Understanding Chain-of-Thought Length in LLMs cites this paper.

When More is Less: Understanding Chain-of-Thought Length in LLMs Theoretical limitations of multi-layer Transformer

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-08T13:23:22.006914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b0de0330-ed76-4636-9e78-5e132706a0e8 · inbound

Pause Tokens Strictly Increase the Expressivity of Constant-Depth Transformers cites this paper.

Pause Tokens Strictly Increase the Expressivity of Constant-Depth Transformers Theoretical limitations of multi-layer Transformer

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T13:52:57.267988Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23b29014-a63e-4589-8fc7-e3563d33c822 · inbound

Learning Compositional Functions with Transformers from Easy-to-Hard Data cites this paper.

Learning Compositional Functions with Transformers from Easy-to-Hard Data Theoretical limitations of multi-layer Transformer

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T12:46:33.978754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0892a673-8ad9-4bb9-8ba8-6a3aa63cfb42 · inbound

Transformers Meet In-Context Learning: A Universal Approximation Theory cites this paper.

Transformers Meet In-Context Learning: A Universal Approximation Theory Theoretical limitations of multi-layer Transformer

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T10:33:35.409540Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c7ad6197-2c7d-4432-9d5b-2249cf7b5a9e · inbound

Understanding Input Selectivity in Mamba: Impact on Approximation Power, Memorization, and Associative Recall Capacity cites this paper.

Understanding Input Selectivity in Mamba: Impact on Approximation Power, Memorization, and Associative Recall Capacity Theoretical limitations of multi-layer Transformer

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T01:18:51.437766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38a38488-424e-417c-9efa-9dbe9551f1bc · inbound

The Serial Scaling Hypothesis cites this paper.

The Serial Scaling Hypothesis Theoretical limitations of multi-layer Transformer

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-19T04:12:02.486141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fea037c4-e0f2-44f6-83db-7d76371b6564 · inbound

Falcon-H1: A Family of Hybrid-Head Language Models Redefining Efficiency and Performance cites this paper.

Falcon-H1: A Family of Hybrid-Head Language Models Redefining Efficiency and Performance Theoretical limitations of multi-layer Transformer

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T11:44:04.879218Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 87de76e6-4d0e-4296-a207-0af19beb2fa0 · inbound

Deep sequence models tend to memorize geometrically; it is unclear why cites this paper.

Deep sequence models tend to memorize geometrically; it is unclear why Theoretical limitations of multi-layer Transformer

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-05-21T20:40:36.194169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 06813133-1349-45ba-96d5-f3f7f8f2f588 · 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 Theoretical limitations of multi-layer Transformer

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T20:57:09.914249Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef74e4a7-f24d-426e-a99e-21cdeb40f1fb · inbound

When Do Hallucinations Arise? A Graph Perspective on the Evolution of Path Reuse and Path Compression cites this paper.

When Do Hallucinations Arise? A Graph Perspective on the Evolution of Path Reuse and Path Compression Theoretical limitations of multi-layer Transformer

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-13T13:07:00.928770Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58cf521f-8294-41cc-9335-9906260b1043 · inbound

The Power of Power Law: Asymmetry Enables Compositional Reasoning cites this paper.

The Power of Power Law: Asymmetry Enables Compositional Reasoning Theoretical limitations of multi-layer Transformer

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-11T19:31:08.240882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 346494fb-6aff-40b1-af21-3c6719f9c40d · inbound

The Power of Power Law: Asymmetry Enables Compositional Reasoning cites this paper.

The Power of Power Law: Asymmetry Enables Compositional Reasoning Theoretical limitations of multi-layer Transformer

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-12T18:26:05.728364Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f6a387a-5972-444b-ad9e-d0e0bd7ea9f1 · inbound

Continuous Latent Contexts Enable Efficient Online Learning in Transformers cites this paper.

Continuous Latent Contexts Enable Efficient Online Learning in Transformers Theoretical limitations of multi-layer Transformer

Reference 2

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T05:41:23.574147Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cb428005-a4ad-4090-8f1a-d89ede65f0a7 · inbound

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

Agentic Transformers Provably Learn to Search via Reinforcement Learning Theoretical limitations of multi-layer Transformer

Reference 24

Resolution: metadata mismatch; arxiv_id, observed 2026-06-28T23:42:49.947749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4b62c3fd-4b9e-4246-80fe-07705c18a1f7 · inbound

Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete cites this paper.

Rethinking the Role of Positional Encoding: Sliding-Window Transformers without PE Remain Turing Complete Theoretical limitations of multi-layer Transformer

Reference 8

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T22:06:16.212640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8bfa3f70-6a48-42be-9ed7-5e34a0907aa8 · inbound

Frontier Language Models Struggle to Copy: Text Can Be Better Viewed in 2D cites this paper.

Frontier Language Models Struggle to Copy: Text Can Be Better Viewed in 2D Theoretical limitations of multi-layer Transformer

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-01T21:31:00.903239Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d52774c1-9cf4-4ffe-bffc-6140e67f8c26 · inbound

Hierarchical Domain Generalization cites this paper.

Hierarchical Domain Generalization Theoretical limitations of multi-layer Transformer

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-01T20:54:05.553053Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b3d7df0-27b4-4bd4-bce4-d824ce19a4e0 · inbound

Attention-based representations for multi-task computation cites this paper.

Attention-based representations for multi-task computation Theoretical limitations of multi-layer Transformer

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-08T00:18:21.263783Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.