Paper Citation Record · LEDGER

Theoretical limitations of multi-layer Transformer

As of 18 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 22 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 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T23:08:41.245145Z

measured 48 of 48 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 22 of 22 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T23:23:02.058863Z

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

26 of 26 outbound references displayed

verified exact0
verified fuzzy9
unresolved17
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8f07fda5-a328-49ad-9893-3c2ba0ee785a · outbound

This paper cites GPT-4 Technical Report.

Theoretical limitations of multi-layer Transformer GPT-4 Technical Report

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:39.963350Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f2fc5af2-fdf4-42f8-a517-27dab7d74f10 · outbound

This paper cites Physics of Language Models: Part 3.1, Knowledge Storage and Extraction.

Theoretical limitations of multi-layer Transformer Physics of Language Models: Part 3.1, Knowledge Storage and Extraction

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:40.164864Z

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Observation fd83f51b-5990-41df-8240-8ef4e1d69fdb · outbound

This paper cites Sparks of Artificial General Intelligence: Early experiments with GPT-4.

Theoretical limitations of multi-layer Transformer Sparks of Artificial General Intelligence: Early experiments with GPT-4

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:40.255139Z

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Observation 10638fbd-74fb-4915-8236-decd6dfc6feb · outbound

This paper cites ENTP: Encoder-only Next Token Prediction.

Theoretical limitations of multi-layer Transformer ENTP: Encoder-only Next Token Prediction

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:40.404769Z

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Observation 18246e31-ef52-4c00-a08b-9a152546daf6 · outbound

This paper cites How can s elf-attention networks recog- nize dyck-n languages? In Findings of the Association for Computational Linguistics: EMNLP 2020 , pages 4301–4306,.

Theoretical limitations of multi-layer Transformer How can s elf-attention networks recog- nize dyck-n languages? In Findings of the Association for Computational Linguistics: EMNLP 2020 , pages 4301–4306,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:08:43.528637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation dd51977d-38f1-47e5-be79-8d1b5ef5b678 · outbound

This paper cites Decoder-Only or Encoder-Decoder? Interpreting Language Model as a Regularized Encoder-Decoder.

Theoretical limitations of multi-layer Transformer Decoder-Only or Encoder-Decoder? Interpreting Language Model as a Regularized Encoder-Decoder

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:40.536263Z

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Observation cba6c8cc-72de-4319-b2e6-35671cd10e24 · outbound

This paper cites Hoza, Avishay Tal, and Roe i Tell.

Theoretical limitations of multi-layer Transformer Hoza, Avishay Tal, and Roe i Tell

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:08:43.224843Z

Source-reported events for the cited work

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Observation 3afd07c8-b8f0-4bdb-b535-0ba71ce89df0 · outbound

This paper cites Language Models are Few-Shot Learners.

Theoretical limitations of multi-layer Transformer Language Models are Few-Shot Learners

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:40.684312Z

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Observation 913378a0-8ffb-40a6-acc0-c7a4c305f34a · outbound

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

Theoretical limitations of multi-layer Transformer The Expressive Power of Transformers with Chain of Thought

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:40.697210Z

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Observation 730121a1-99d6-41a2-b410-6e86e4435012 · outbound

This paper cites Encoder vs Decoder: Comparative Analysis of Encoder and Decoder Language Models on Multilingual NLU Tasks.

Theoretical limitations of multi-layer Transformer Encoder vs Decoder: Comparative Analysis of Encoder and Decoder Language Models on Multilingual NLU Tasks

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:40.713400Z

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Observation b4da9a69-1fcc-4d76-b413-a5c075946cb7 · outbound

This paper cites The impact of depth on compositional generalizatio n in transformer language models.

Theoretical limitations of multi-layer Transformer The impact of depth on compositional generalizatio n in transformer language models

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:08:43.064020Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 769a57df-100f-465e-a3b2-5851eb4c13e3 · outbound

This paper cites Measuring and narrowing the compositionality gap in language models.

Theoretical limitations of multi-layer Transformer Measuring and narrowing the compositionality gap in language models

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:08:42.995974Z

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Observation de7ad18a-7852-42e4-a10d-7c07edc27c05 · outbound

This paper cites an unresolved cited work.

Theoretical limitations of multi-layer Transformer Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:08:42.894017Z

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Observation b9bb37d7-f136-4928-ba10-c6ccb381f3a5 · outbound

This paper cites One-layer transformers fail to solve the induction heads task.

Theoretical limitations of multi-layer Transformer One-layer transformers fail to solve the induction heads task

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:40.926187Z

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Observation a0155291-d9dd-460b-9541-e02051813e00 · outbound

This paper cites Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context.

Theoretical limitations of multi-layer Transformer Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:40.988082Z

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Observation a517fd89-f493-4e04-8813-7229279dcb12 · outbound

This paper cites RNNs are not Transformers (Yet): The Key Bottleneck on In-context Retrieval.

Theoretical limitations of multi-layer Transformer RNNs are not Transformers (Yet): The Key Bottleneck on In-context Retrieval

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:41.006808Z

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Observation 1a97bfc1-598d-46af-99a3-a3d58a1cc152 · outbound

This paper cites Emergent Abilities of Large Language Models.

Theoretical limitations of multi-layer Transformer Emergent Abilities of Large Language Models

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:41.082304Z

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Observation ae0062f6-dad7-4894-af4b-43a6f88b7815 · outbound

This paper cites Do large language models latently perform multi-hop reasoning? In Association for Com- putational Linguistics: ACL-IJCNLP 2024 ,.

Theoretical limitations of multi-layer Transformer Do large language models latently perform multi-hop reasoning? In Association for Com- putational Linguistics: ACL-IJCNLP 2024 ,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:08:42.688922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6bd2eb1e-1304-462a-9ca9-02f8863f88f7 · outbound

This paper cites A Theory for Emergence of Complex Skills in Language Models.

Theoretical limitations of multi-layer Transformer A Theory for Emergence of Complex Skills in Language Models

Reference 2016

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:40.040192Z

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Observation 81157387-3bb9-453e-87e4-67309dafc729 · outbound

This paper cites On medium-unifor mity and circuit lower bounds.

Theoretical limitations of multi-layer Transformer On medium-unifor mity and circuit lower bounds

Reference 2017

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:08:42.762856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e5e1eadc-763a-4a0b-8720-b1e6e87826e5 · outbound

This paper cites Bootstrapping results for t hreshold circuits ”just beyond” known lower bounds.

Theoretical limitations of multi-layer Transformer Bootstrapping results for t hreshold circuits ”just beyond” known lower bounds

Reference 2018

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:08:43.599277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9e1afbf5-a0a7-487b-9d7a-1552cbb80b11 · outbound

This paper cites Mixture of Parrots: Experts improve memorization more than reasoning.

Theoretical limitations of multi-layer Transformer Mixture of Parrots: Experts improve memorization more than reasoning

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:40.634905Z

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Observation ed83ac09-1faf-479a-9d54-1594fc7debb5 · outbound

This paper cites Rnns can generate bounded hierarchical languages with opti mal memory.

Theoretical limitations of multi-layer Transformer Rnns can generate bounded hierarchical languages with opti mal memory

Reference 2020

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:08:43.365175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 29394370-e257-4826-bf3f-2f6312204bde · outbound

This paper cites Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process.

Theoretical limitations of multi-layer Transformer Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:41.245145Z

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Observation 1148aad9-b8ca-4c71-a0b0-68ab6c76928b · outbound

This paper cites Chan, and R.

Theoretical limitations of multi-layer Transformer Chan, and R

Reference 2023

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:08:43.760560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d4209ae2-08da-4405-a76b-c77e42ddd1be · outbound

This paper cites Physics of Language Models: Part 1, Learning Hierarchical Language Structures.

Theoretical limitations of multi-layer Transformer Physics of Language Models: Part 1, Learning Hierarchical Language Structures

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-11T23:08:40.089817Z

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Pith citing papers

Observation 20fcc26d-e5b9-4c05-9573-cc7ab0ef6084 · inbound

Lower bounds on transformers with infinite precision cites this paper.

Lower bounds on transformers with infinite precision Theoretical limitations of multi-layer Transformer

Reference 2

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Observation bb59aa56-0181-4f9f-a88c-00d741943aa3 · inbound

Ehrenfeucht-Haussler Rank and Chain of Thought cites this paper.

Ehrenfeucht-Haussler Rank and Chain of Thought Theoretical limitations of multi-layer Transformer

Reference 3

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Observation 2fff638b-a1a9-4bbf-af5d-92983cb89be9 · inbound

Lower Bounds for Chain-of-Thought Reasoning in Hard-Attention Transformers cites this paper.

Lower Bounds for Chain-of-Thought Reasoning in Hard-Attention Transformers Theoretical limitations of multi-layer Transformer

Reference 3

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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

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Observation d07a529e-cc28-44a6-85b0-053c7761745c · inbound

Chain-of-Thought Tokens are Computer Program Variables cites this paper.

Chain-of-Thought Tokens are Computer Program Variables Theoretical limitations of multi-layer Transformer

Reference 1

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Source-reported events for the cited work

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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

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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

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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

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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

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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

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