Paper Citation Record · LEDGER

How are linear representations learned? Exact solutions to the dynamics of abstraction

As of 19 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2607.08843.

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

pith.paper-citation-record.v1
2607.08843 v1

Coverage vector

measured 50 of 50 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-13T06:19:30.027337Z

measured 50 of 50 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

50 of 50 outbound references displayed

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verified fuzzy0
unresolved50
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malformed identifier0
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External citation measurements

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Outbound references

Observation 30c6bb84-d694-451c-bfe9-addd39f84650 · outbound

This paper cites Linguistic Regularities in Continuous Space Word Representations.

How are linear representations learned? Exact solutions to the dynamics of abstraction Linguistic Regularities in Continuous Space Word Representations

Reference 1

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Observation fd4f8eb0-375e-4397-aab1-6c786969f6ab · outbound

This paper cites Emergent Linear Representations in World Models of Self-Supervised Sequence Models.

How are linear representations learned? Exact solutions to the dynamics of abstraction Emergent Linear Representations in World Models of Self-Supervised Sequence Models

Reference 2

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Observation 252022a9-0203-40a8-aa44-4da326c6249a · outbound

This paper cites The Linear Representation Hypothesis and the Geometry of Large Language Models.

How are linear representations learned? Exact solutions to the dynamics of abstraction The Linear Representation Hypothesis and the Geometry of Large Language Models

Reference 3

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Observation fac94f7f-e3a6-44e7-913f-73aaaacc5b06 · outbound

This paper cites On the Origins of Linear Representations in Large Language Models.

How are linear representations learned? Exact solutions to the dynamics of abstraction On the Origins of Linear Representations in Large Language Models

Reference 4

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Observation fe0fa536-efc1-47cb-93b3-95c739fa632e · outbound

This paper cites The Geometry of Categorical and Hierarchical Concepts in Large Language Models.

How are linear representations learned? Exact solutions to the dynamics of abstraction The Geometry of Categorical and Hierarchical Concepts in Large Language Models

Reference 5

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Observation 22ac3703-ed4e-4c5b-9896-eda2f0d148da · outbound

This paper cites Benna, Mattia Rigotti, Jérôme Munuera, Stefano Fusi, and C.

How are linear representations learned? Exact solutions to the dynamics of abstraction Benna, Mattia Rigotti, Jérôme Munuera, Stefano Fusi, and C

Reference 6

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Observation be575075-af3c-4313-8b73-0a3e85523cc0 · outbound

This paper cites Rodgers, Randy M.

How are linear representations learned? Exact solutions to the dynamics of abstraction Rodgers, Randy M

Reference 7

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Observation a42811b6-ba57-42e9-8544-d81eb6d34bb0 · outbound

This paper cites Shin, Wenbo Tang, and Shantanu P.

How are linear representations learned? Exact solutions to the dynamics of abstraction Shin, Wenbo Tang, and Shantanu P

Reference 8

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Observation 6fc8b8dd-e75c-48c0-a890-a65845aa9b7d · outbound

This paper cites Neural representational geometries reflect behavioral differences in monkeys and recurrent neural networks.Nature Communications, 15(1):6479, August 2024.

How are linear representations learned? Exact solutions to the dynamics of abstraction Neural representational geometries reflect behavioral differences in monkeys and recurrent neural networks.Nature Communications, 15(1):6479, August 2024

Reference 9

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Observation e282ee65-6909-4cd3-8545-7396ea5e823d · outbound

This paper cites Courellis, Juri Minxha, Araceli R.

How are linear representations learned? Exact solutions to the dynamics of abstraction Courellis, Juri Minxha, Araceli R

Reference 10

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Observation cf602ec4-8883-46a8-91b7-a5a3f705427f · outbound

This paper cites Boyle, Lorenzo Posani, Sarah Irfan, Steven A.

How are linear representations learned? Exact solutions to the dynamics of abstraction Boyle, Lorenzo Posani, Sarah Irfan, Steven A

Reference 11

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Observation 64dbde20-d3e1-48c7-b431-af0a4caa3c3d · outbound

This paper cites an unresolved cited work.

How are linear representations learned? Exact solutions to the dynamics of abstraction Unresolved cited work

Reference 12

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Observation eaa97cbb-fa31-43a2-8766-d6b1caacc3a0 · outbound

This paper cites Schoonover, Andrew J.

How are linear representations learned? Exact solutions to the dynamics of abstraction Schoonover, Andrew J

Reference 13

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Observation a618b0e9-6ab8-47c6-96d7-5ce7574e489d · outbound

This paper cites Finding Neurons in a Haystack: Case Studies with Sparse Probing.

How are linear representations learned? Exact solutions to the dynamics of abstraction Finding Neurons in a Haystack: Case Studies with Sparse Probing

Reference 14

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Observation d961e035-f4eb-415e-aa6a-4a1e2ff84e5f · outbound

This paper cites De- tecting Strategic Deception with Linear Probes.

How are linear representations learned? Exact solutions to the dynamics of abstraction De- tecting Strategic Deception with Linear Probes

Reference 15

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Observation fab6a33c-284f-4540-8774-98da733686c6 · outbound

This paper cites Vazquez, Ulisse Mini, and Monte MacDiarmid.

How are linear representations learned? Exact solutions to the dynamics of abstraction Vazquez, Ulisse Mini, and Monte MacDiarmid

Reference 16

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Observation 0a2f29c7-27ad-45f8-bb8c-e5f8828926cf · outbound

This paper cites Steering Language Models With Activation Engineering.

How are linear representations learned? Exact solutions to the dynamics of abstraction Steering Language Models With Activation Engineering

Reference 17

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Observation 408f0310-6202-47cb-9108-f1f9cc268c8c · outbound

This paper cites Inference-Time Intervention: Eliciting Truthful Answers from a Language Model.

How are linear representations learned? Exact solutions to the dynamics of abstraction Inference-Time Intervention: Eliciting Truthful Answers from a Language Model

Reference 18

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Observation 867a9b4b-68ac-4052-943b-2ed7bc5bcd44 · outbound

This paper cites Compositional generalization through abstract representations in human and artificial neural networks.

How are linear representations learned? Exact solutions to the dynamics of abstraction Compositional generalization through abstract representations in human and artificial neural networks

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-13T06:19:30.027337Z

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Observation 6ca20dc2-15d5-4370-95b7-cca9dc34a4ce · outbound

This paper cites Jeffrey Johnston, and Stefano Fusi.

How are linear representations learned? Exact solutions to the dynamics of abstraction Jeffrey Johnston, and Stefano Fusi

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-13T06:19:30.027337Z

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Observation fe9e551c-316a-40ae-ac13-7bf498f29b6b · outbound

This paper cites Task structure and nonlinearity jointly determine learned representational geometry.

How are linear representations learned? Exact solutions to the dynamics of abstraction Task structure and nonlinearity jointly determine learned representational geometry

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-13T06:19:30.027337Z

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Observation 668e7407-41d5-4093-900a-1e324272b670 · outbound

This paper cites Disentangling by Factorising.

How are linear representations learned? Exact solutions to the dynamics of abstraction Disentangling by Factorising

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-13T06:19:30.027337Z

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Observation 19519842-3938-408c-ad17-556f27a8339f · outbound

This paper cites Jeffrey Johnston and Stefano Fusi.

How are linear representations learned? Exact solutions to the dynamics of abstraction Jeffrey Johnston and Stefano Fusi

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-13T06:19:30.027337Z

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Observation 2e203a87-be7e-4755-a0f6-65d68dd83f6c · outbound

This paper cites Mickiewicz, James L.

How are linear representations learned? Exact solutions to the dynamics of abstraction Mickiewicz, James L

Reference 24

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Observation 4d1defce-f80b-47ad-9940-d68174449412 · outbound

This paper cites Exact solutions to the nonlinear dynamics of learning in deep linear neural networks.

How are linear representations learned? Exact solutions to the dynamics of abstraction Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-13T06:19:30.027337Z

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Observation 77a0de79-c247-41a5-9db8-f6e490ec4bf7 · outbound

This paper cites An analytic theory of generalization dynamics and transfer learning in deep linear networks.

How are linear representations learned? Exact solutions to the dynamics of abstraction An analytic theory of generalization dynamics and transfer learning in deep linear networks

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-13T06:19:30.027337Z

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Observation 2accb746-4c48-4451-81dc-dd8b1a97f352 · outbound

This paper cites an unresolved cited work.

How are linear representations learned? Exact solutions to the dynamics of abstraction Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-13T06:19:30.027337Z

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Observation 138b986a-0070-410c-a1b1-413c811a4a4e · outbound

This paper cites Position: Solve Layerwise Linear Models First to Understand Neural Dynamical Phenomena (Neural Collapse, Emergence, Lazy/Rich Regime, and Grokking).

How are linear representations learned? Exact solutions to the dynamics of abstraction Position: Solve Layerwise Linear Models First to Understand Neural Dynamical Phenomena (Neural Collapse, Emergence, Lazy/Rich Regime, and Grokking)

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-13T06:19:30.027337Z

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Observation 323c044c-2d29-4f78-868e-714ef08b1163 · outbound

This paper cites There Will Be a Scientific Theory of Deep Learning.

How are linear representations learned? Exact solutions to the dynamics of abstraction There Will Be a Scientific Theory of Deep Learning

Reference 29

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Observation ae8e7888-1544-4781-bee7-2256cff180f8 · outbound

This paper cites Exact learning dynam- ics of deep linear networks with prior knowledge.Advances in Neural Information Processing Systems, 35:6615–6629, December 2022.

How are linear representations learned? Exact solutions to the dynamics of abstraction Exact learning dynam- ics of deep linear networks with prior knowledge.Advances in Neural Information Processing Systems, 35:6615–6629, December 2022

Reference 30

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Observation b0a81c82-badd-4a6b-829e-e1e2999aa7d3 · outbound

This paper cites From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks.

How are linear representations learned? Exact solutions to the dynamics of abstraction From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Reference 31

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Observation f6fffcc5-70af-4be1-a907-cbf987a3b59d · outbound

This paper cites Korchinski, Dhruva Karkada, Yasaman Bahri, and Matthieu Wyart.

How are linear representations learned? Exact solutions to the dynamics of abstraction Korchinski, Dhruva Karkada, Yasaman Bahri, and Matthieu Wyart

Reference 32

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Observation 7fa246b4-a1fc-4a84-a822-f595badc9917 · outbound

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How are linear representations learned? Exact solutions to the dynamics of abstraction Unresolved cited work

Reference 33

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Observation bc45e45a-1030-4d8f-82d0-a8cb4379dfaf · outbound

This paper cites Du, Wei Hu, Zhiyuan Li, and Ruosong Wang.

How are linear representations learned? Exact solutions to the dynamics of abstraction Du, Wei Hu, Zhiyuan Li, and Ruosong Wang

Reference 34

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Observation a4789879-1abd-4478-8700-df0e4a44e4e8 · outbound

This paper cites Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks.

How are linear representations learned? Exact solutions to the dynamics of abstraction Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks

Reference 35

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Observation 426ea73a-23d6-4685-9315-7ced04b2844a · outbound

This paper cites Ultra-fast feature learning for the training of two-layer neural networks in the two-timescale regime.

How are linear representations learned? Exact solutions to the dynamics of abstraction Ultra-fast feature learning for the training of two-layer neural networks in the two-timescale regime

Reference 36

Resolution: unresolved; no resolver link, observed 2026-07-13T06:19:30.027337Z

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Observation 538507ff-581f-452b-9dbd-3eaa31527630 · outbound

This paper cites Leveraging the two timescale regime to demonstrate convergence of neural networks.

How are linear representations learned? Exact solutions to the dynamics of abstraction Leveraging the two timescale regime to demonstrate convergence of neural networks

Reference 37

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Observation 8f421669-c9b0-4bb9-96e3-7a41559a4b0c · outbound

This paper cites A Convergence Analysis of Gradient Descent for Deep Linear Neural Networks.

How are linear representations learned? Exact solutions to the dynamics of abstraction A Convergence Analysis of Gradient Descent for Deep Linear Neural Networks

Reference 38

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Observation f4d49287-3728-41a2-821c-617f29b5b18c · outbound

This paper cites Kernel Methods for Deep Learning.

How are linear representations learned? Exact solutions to the dynamics of abstraction Kernel Methods for Deep Learning

Reference 39

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Observation 484c21b6-4f43-48a3-b947-f0de95864923 · outbound

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How are linear representations learned? Exact solutions to the dynamics of abstraction Computing with Infinite Networks

Reference 40

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Observation 270d1a44-ff3e-4b87-a98f-1b56fdbe7116 · outbound

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How are linear representations learned? Exact solutions to the dynamics of abstraction DINOv3

Reference 41

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Observation 1d88c27d-a04e-47d7-b716-2162c93801a9 · outbound

This paper cites Gemma: Open Models Based on Gemini Research and Technology.

How are linear representations learned? Exact solutions to the dynamics of abstraction Gemma: Open Models Based on Gemini Research and Technology

Reference 42

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Observation 3af46104-04b0-44b1-a32d-d61afcbcd6b9 · outbound

This paper cites Majaj, Ha Hong, Ethan A.

How are linear representations learned? Exact solutions to the dynamics of abstraction Majaj, Ha Hong, Ethan A

Reference 43

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Observation ee37bed6-06b7-4bbd-8cb0-0b7e1a24bd64 · outbound

This paper cites Analogies Explained: Towards Understanding Word Embeddings.

How are linear representations learned? Exact solutions to the dynamics of abstraction Analogies Explained: Towards Understanding Word Embeddings

Reference 44

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Observation 8d4e6d2c-cd01-498b-ae38-524cf0ebbf01 · outbound

This paper cites Simon, Yasaman Bahri, and Michael R.

How are linear representations learned? Exact solutions to the dynamics of abstraction Simon, Yasaman Bahri, and Michael R

Reference 45

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Observation 6c3a31e5-8379-4b21-b5e3-1901ae827d18 · outbound

This paper cites Korchinski, Andres Nava, Matthieu Wyart, and Yasaman Bahri.

How are linear representations learned? Exact solutions to the dynamics of abstraction Korchinski, Andres Nava, Matthieu Wyart, and Yasaman Bahri

Reference 46

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Observation e983af7e-7745-4273-b3af-19362473c766 · outbound

This paper cites Separable nonlinear least squares: The variable projection method and its applications.Inverse Problems, 19(2):R1, February 2003.

How are linear representations learned? Exact solutions to the dynamics of abstraction Separable nonlinear least squares: The variable projection method and its applications.Inverse Problems, 19(2):R1, February 2003

Reference 47

Resolution: unresolved; no resolver link, observed 2026-07-13T06:19:30.027337Z

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Observation 3221e9e8-2691-434a-8689-51d828adc212 · outbound

This paper cites Training Two-Layered Feedforward Networks With Variable Projection Method.IEEE Transactions on Neural Networks, 19(2):371–375, February 2008.

How are linear representations learned? Exact solutions to the dynamics of abstraction Training Two-Layered Feedforward Networks With Variable Projection Method.IEEE Transactions on Neural Networks, 19(2):371–375, February 2008

Reference 48

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Observation fba0e60b-0607-4333-bef3-df41bbe2f552 · outbound

This paper cites abstract.

How are linear representations learned? Exact solutions to the dynamics of abstraction abstract

Reference 49

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Observation a94ce804-dbbd-418f-93b7-2f4c838c8e39 · outbound

This paper cites Each concept is instantiated by 80 ordered word pairs comprising common words.

How are linear representations learned? Exact solutions to the dynamics of abstraction Each concept is instantiated by 80 ordered word pairs comprising common words

Reference 50

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