Paper Citation Record · LEDGER

A Solvable Model of Neural Scaling Laws

As of 12 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 39 inbound Pith citation observations for arXiv:2210.16859.

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

pith.paper-citation-record.v1
2210.16859 v1

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measured 0 of 0 reference resolution

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measured 39 of 39 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 39 of 39 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-12T12:01:21.856440Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T17:20:00.933699Z

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Outbound references

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Pith citing papers

Observation d39f3736-b790-422d-8ea4-6ea9458ad96e · inbound

A solvable generative model with a linear, one-step denoiser cites this paper.

A solvable generative model with a linear, one-step denoiser A Solvable Model of Neural Scaling Laws

Reference 24

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Observation 68cedbfe-4907-42f7-a302-b485f98f843d · inbound

Neural Scaling Laws Rooted in the Data Distribution cites this paper.

Neural Scaling Laws Rooted in the Data Distribution A Solvable Model of Neural Scaling Laws

Reference 41

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Observation 7949c896-d677-4046-9656-48ce083b9489 · inbound

Physics of Skill Learning cites this paper.

Physics of Skill Learning A Solvable Model of Neural Scaling Laws

Reference 51

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Observation 5af9d93b-3a82-4376-a6d4-72db98944c31 · inbound

Phase Transitions in Large Language Models and the $O(N)$ Model cites this paper.

Phase Transitions in Large Language Models and the $O(N)$ Model A Solvable Model of Neural Scaling Laws

Reference 17

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Observation 2dc43d41-29b2-4d25-8cd5-f5c519b3891f · inbound

Scaling Laws for Upcycling Mixture-of-Experts Language Models cites this paper.

Scaling Laws for Upcycling Mixture-of-Experts Language Models A Solvable Model of Neural Scaling Laws

Reference 43

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Observation 893a05cf-e463-4ab3-825d-0372c0b52dec · inbound

Superposition Yields Robust Neural Scaling cites this paper.

Superposition Yields Robust Neural Scaling A Solvable Model of Neural Scaling Laws

Reference 18

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Observation f0eff303-0a79-4b5f-8810-45bc0ad8a5f2 · inbound

Dimension-adapted Momentum Outscales SGD cites this paper.

Dimension-adapted Momentum Outscales SGD A Solvable Model of Neural Scaling Laws

Reference 69

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Observation 1cce0274-4132-4d29-be3c-11cb913f1980 · inbound

X-Factor: Quality Is a Dataset-Intrinsic Property cites this paper.

X-Factor: Quality Is a Dataset-Intrinsic Property A Solvable Model of Neural Scaling Laws

Reference 9

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Observation f3770cae-fe95-4738-ab7f-9f70102b2849 · inbound

Models of Heavy-Tailed Mechanistic Universality cites this paper.

Models of Heavy-Tailed Mechanistic Universality A Solvable Model of Neural Scaling Laws

Reference 2011

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Observation 46b99037-ca04-4263-8baf-ef25ccbe84e9 · inbound

Scaling Laws and Spectra of Shallow Neural Networks in the Feature Learning Regime cites this paper.

Scaling Laws and Spectra of Shallow Neural Networks in the Feature Learning Regime A Solvable Model of Neural Scaling Laws

Reference 42

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Observation efedc4cb-28ea-41ec-9c0d-bce98d09b9f7 · inbound

From Zipf's Law to Neural Scaling through Heaps' Law and Hilberg's Hypothesis cites this paper.

From Zipf's Law to Neural Scaling through Heaps' Law and Hilberg's Hypothesis A Solvable Model of Neural Scaling Laws

Reference 65

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Observation 586d93f0-6620-4dd7-8d48-38a7159a6a97 · inbound

Revisiting Training Scale: An Empirical Study of Token Count, Power Consumption, and Parameter Efficiency cites this paper.

Revisiting Training Scale: An Empirical Study of Token Count, Power Consumption, and Parameter Efficiency A Solvable Model of Neural Scaling Laws

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T11:25:09.558686Z

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Observation 706bb2b3-eea6-47fd-8fee-67402b30fe57 · inbound

Universal One-third Time Scaling in Learning Peaked Distributions cites this paper.

Universal One-third Time Scaling in Learning Peaked Distributions A Solvable Model of Neural Scaling Laws

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T05:01:12.953666Z

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Observation 392ddaf4-955f-4e2e-99cb-68ce2c54c86b · inbound

Inverse Depth Scaling From Most Layers Being Similar cites this paper.

Inverse Depth Scaling From Most Layers Being Similar A Solvable Model of Neural Scaling Laws

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T04:07:46.211483Z

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Observation a5599f16-4da7-48d5-be98-7e5da2768231 · inbound

Dynamics of neural scaling laws in random feature regression with powerlaw-distributed kernel eigenvalues cites this paper.

Dynamics of neural scaling laws in random feature regression with powerlaw-distributed kernel eigenvalues A Solvable Model of Neural Scaling Laws

Reference 24

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Observation ec6d1a16-ab5b-4e79-883d-4835848206c5 · inbound

A Limit Theory of Foundation Models: A Mathematical Approach to Understanding Emergent Intelligence and Scaling Laws cites this paper.

A Limit Theory of Foundation Models: A Mathematical Approach to Understanding Emergent Intelligence and Scaling Laws A Solvable Model of Neural Scaling Laws

Reference 83

Resolution: verified exact; arxiv_id, observed 2026-05-13T07:27:28.948778Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ddefce1b-ea3c-4e47-b034-664aa894c2cd · inbound

A Limit Theory of Foundation Models: A Mathematical Approach to Understanding Emergent Intelligence and Scaling Laws cites this paper.

A Limit Theory of Foundation Models: A Mathematical Approach to Understanding Emergent Intelligence and Scaling Laws A Solvable Model of Neural Scaling Laws

Reference 84

Resolution: verified exact; arxiv_id, observed 2026-07-01T09:05:36.341948Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 34fa947e-f693-4fbb-8bf1-1ef2b54ea95f · inbound

High-Dimensional Statistics: Reflections on Progress and Open Problems cites this paper.

High-Dimensional Statistics: Reflections on Progress and Open Problems A Solvable Model of Neural Scaling Laws

Reference 71

Resolution: verified exact; arxiv_id, observed 2026-05-11T18:36:06.580939Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3c5b22b2-cd9d-46bc-aa1a-362c3bea1570 · inbound

High-Dimensional Statistics: Reflections on Progress and Open Problems cites this paper.

High-Dimensional Statistics: Reflections on Progress and Open Problems A Solvable Model of Neural Scaling Laws

Reference 71

Resolution: verified exact; arxiv_id, observed 2026-06-30T23:35:08.037828Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 455cdc7e-d189-4d5d-a330-2b1064372718 · inbound

Spectral Lens: Activation and Gradient Spectra as Diagnostics of LLM Optimization cites this paper.

Spectral Lens: Activation and Gradient Spectra as Diagnostics of LLM Optimization A Solvable Model of Neural Scaling Laws

Reference 25

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T21:26:13.379542Z

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Observation 74622cf9-2406-4f7f-b7db-f74cc4f1bbdd · inbound

Criticality and Saturation in Orthogonal Neural Networks cites this paper.

Criticality and Saturation in Orthogonal Neural Networks A Solvable Model of Neural Scaling Laws

Reference 19

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Observation e2e80ef0-64a6-429e-aa11-992b9c369aa2 · inbound

Practical Scaling Laws: Converting Compute into Performance in a Data-Constrained World cites this paper.

Practical Scaling Laws: Converting Compute into Performance in a Data-Constrained World A Solvable Model of Neural Scaling Laws

Reference 34

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Observation f05e73b5-cd1c-4d70-ae65-4b8829b98afa · inbound

Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model cites this paper.

Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model A Solvable Model of Neural Scaling Laws

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-05-15T01:39:38.388073Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 01751d39-b00b-4dbf-abc3-0407f78ed107 · inbound

A Boundary-Layer Mechanism for One-Third Scaling in Online Softmax Classification cites this paper.

A Boundary-Layer Mechanism for One-Third Scaling in Online Softmax Classification A Solvable Model of Neural Scaling Laws

Reference 8

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Observation 52b5c0d9-0e37-4125-aa5b-174c4f144906 · inbound

Asymmetric Scaling Laws from Sparse Features cites this paper.

Asymmetric Scaling Laws from Sparse Features A Solvable Model of Neural Scaling Laws

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-05-25T03:20:17.080193Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 52bbb7af-9e6a-4712-880f-d25a5410c7ef · inbound

From One-Pass SGD to Data Reuse: Mini-Batch Scaling Laws in Sketched Linear Regression cites this paper.

From One-Pass SGD to Data Reuse: Mini-Batch Scaling Laws in Sketched Linear Regression A Solvable Model of Neural Scaling Laws

Reference 8

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Observation a7c9d649-fa35-42af-be95-3929dfd0b698 · inbound

Why Larger Models Learn More: Effects of Capacity, Interference, and Rare-Task Retention cites this paper.

Why Larger Models Learn More: Effects of Capacity, Interference, and Rare-Task Retention A Solvable Model of Neural Scaling Laws

Reference 37

Resolution: verified exact; arxiv_id, observed 2026-06-29T08:43:15.227113Z

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Observation 63f67eaa-c963-4c30-8734-04f8ed929025 · inbound

Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail cites this paper.

Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail A Solvable Model of Neural Scaling Laws

Reference 6

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T19:16:00.259743Z

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Observation c21a7f9c-28dc-4b3f-a419-03510d521d4e · inbound

Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail cites this paper.

Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail A Solvable Model of Neural Scaling Laws

Reference 2024

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Observation 5b61f59a-8012-40bc-a051-e7dc6210cee5 · inbound

Explaining Data Mixing Scaling Laws cites this paper.

Explaining Data Mixing Scaling Laws A Solvable Model of Neural Scaling Laws

Reference 12

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T20:37:22.531196Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ca8fb948-ab66-41a5-bc28-248b95aad65d · inbound

Explaining Data Mixing Scaling Laws cites this paper.

Explaining Data Mixing Scaling Laws A Solvable Model of Neural Scaling Laws

Reference 12

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Observation ba1ae0eb-8755-4317-8800-e76e3826fd45 · inbound

Explaining Data Mixing Scaling Laws cites this paper.

Explaining Data Mixing Scaling Laws A Solvable Model of Neural Scaling Laws

Reference 12

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Observation 8f7991e6-4252-4f1a-af20-46b88b5b547c · inbound

Learning Dynamics of Chain-of-Thought State Tracking in a Solvable Transformer Model cites this paper.

Learning Dynamics of Chain-of-Thought State Tracking in a Solvable Transformer Model A Solvable Model of Neural Scaling Laws

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-07-03T23:39:05.180523Z

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Observation 0a001962-c6cb-4676-a358-1d41f1b3e69c · inbound

Critical Percolation as a Synthetic Data Model for Interpretability cites this paper.

Critical Percolation as a Synthetic Data Model for Interpretability A Solvable Model of Neural Scaling Laws

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-07-04T03:49:29.695396Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c8c4096d-4fe0-44eb-ae14-2a4c644aca69 · inbound

Neural Scaling Universality: If Exponents Are Fixed, Time to Understand Coefficients cites this paper.

Neural Scaling Universality: If Exponents Are Fixed, Time to Understand Coefficients A Solvable Model of Neural Scaling Laws

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-07-04T17:20:00.939107Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 74022b10-892a-4b42-be71-47966e8a1cbc · inbound

Sketched Linear Contrastive Learning: Approximation, Optimization, and Statistical Scaling cites this paper.

Sketched Linear Contrastive Learning: Approximation, Optimization, and Statistical Scaling A Solvable Model of Neural Scaling Laws

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-07-04T12:59:52.807788Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5f263e16-e6de-488a-a758-dbc2ea191c3a · inbound

How Width and Data Shape Generalization Scaling Laws in Quadratic Neural Networks cites this paper.

How Width and Data Shape Generalization Scaling Laws in Quadratic Neural Networks A Solvable Model of Neural Scaling Laws

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:51.287189Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d6b6d756-f7c7-4d20-959b-7c76bd133b01 · inbound

Smooth Scaling Laws Hide Stepwise Token Learning cites this paper.

Smooth Scaling Laws Hide Stepwise Token Learning A Solvable Model of Neural Scaling Laws

Reference 6

Resolution: metadata mismatch; arxiv_id, observed 2026-06-30T08:14:26.563121Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e9147c95-3363-4ae1-b99e-a08da0610c7e · inbound

Smooth Scaling Laws Hide Stepwise Token Learning cites this paper.

Smooth Scaling Laws Hide Stepwise Token Learning A Solvable Model of Neural Scaling Laws

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-13T07:15:03.029543Z

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Unavailable: canonical work link unavailable.