Paper Citation Record · LEDGER

Position: A Theory of Deep Learning Must Include Compositional Sparsity

As of 20 August 2026, this Paper Citation Record lists 75 of 75 outbound references and 5 inbound Pith citation observations for arXiv:2507.02550.

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

pith.paper-citation-record.v1
2507.02550 v1

Coverage vector

measured 75 of 75 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:35:49.377235Z

measured 80 of 80 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-30T20:55:03.949611Z

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

75 of 75 outbound references displayed

verified exact5
verified fuzzy40
unresolved30
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation e99bff07-a10d-4722-afad-72238bc9266d · outbound

This paper cites The staircase property: How hierarchical structure can guide deep learning.

Position: A Theory of Deep Learning Must Include Compositional Sparsity The staircase property: How hierarchical structure can guide deep learning

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:35:50.551112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7cdaa196-698b-4399-ac44-1105d89ca93a · outbound

This paper cites B., and Misiakiewicz, T.

Position: A Theory of Deep Learning Must Include Compositional Sparsity B., and Misiakiewicz, T

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:36:00.569728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation eb208633-a54a-4dbe-b5a0-c6fa7cffcaa3 · outbound

This paper cites SGD learning on neural networks: leap complexity and saddle-to-saddle dynamics.

Position: A Theory of Deep Learning Must Include Compositional Sparsity SGD learning on neural networks: leap complexity and saddle-to-saddle dynamics

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:42.849130Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ad3c338-a46f-4795-9beb-51881d6f4d6c · outbound

This paper cites J., Bambrick, J., Bodenstein, S.

Position: A Theory of Deep Learning Must Include Compositional Sparsity J., Bambrick, J., Bodenstein, S

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:42.930526Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d443a002-135f-450f-b756-feeb276c8daf · outbound

This paper cites Online Learning and Information Exponents : On The Importance of Batch size, and Time / Complexity Tradeoffs , June 2024 a.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Online Learning and Information Exponents : On The Importance of Batch size, and Time / Complexity Tradeoffs , June 2024 a

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:36:00.434860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d85e8884-f347-47ae-8b55-5a70f7769c9c · outbound

This paper cites Repetita Iuvant : Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions , May 2024 b.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Repetita Iuvant : Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions , May 2024 b

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:36:00.230962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 308e7920-98cb-48e9-8858-01dfa2cc7915 · outbound

This paper cites and Barak, B.

Position: A Theory of Deep Learning Must Include Compositional Sparsity and Barak, B

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:36:00.037713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 19fb3b33-3e57-4038-9fd7-f952535e9bf6 · outbound

This paper cites B., Gheissari, R., and Jagannath, A.

Position: A Theory of Deep Learning Must Include Compositional Sparsity B., Gheissari, R., and Jagannath, A

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:59.827444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 442507d7-44e7-43b5-b40a-095677094893 · outbound

This paper cites and Kohler, M.

Position: A Theory of Deep Learning Must Include Compositional Sparsity and Kohler, M

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:59.600703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6075bcdb-7196-458f-a53a-448fb0cb73ea · outbound

This paper cites Fast Feedforward Networks.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Fast Feedforward Networks

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:43.474963Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20c6c8cd-1cd4-4e03-9c35-18764ac29c6c · outbound

This paper cites Deep neural network approximation theory for high-dimensional functions, 2021.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Deep neural network approximation theory for high-dimensional functions, 2021

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:59.440412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation fa3d9f13-c2d7-4737-8c8a-4e26292769cf · outbound

This paper cites How Neural Networks Learn the Support is an Implicit Regularization Effect of SGD.

Position: A Theory of Deep Learning Must Include Compositional Sparsity How Neural Networks Learn the Support is an Implicit Regularization Effect of SGD

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:43.680310Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 527a08e8-4fb0-4857-abc9-e61bed1fe3a6 · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:35:59.268398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ca3b217e-5beb-4706-ad45-2aeb9f303f1c · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:35:59.047724Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1f699ffb-c3e5-48de-9a26-abf4dd73a5dc · outbound

This paper cites and Gerstner, W.

Position: A Theory of Deep Learning Must Include Compositional Sparsity and Gerstner, W

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:58.875851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e74d1236-8fb1-4f9a-866d-2c87da0d6f64 · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:35:58.664776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e3caacd7-685c-4619-b310-622b5a651e38 · outbound

This paper cites and Hsu, D.

Position: A Theory of Deep Learning Must Include Compositional Sparsity and Hsu, D

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:58.501369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5c0484e8-b78f-4807-8ae3-4b94923981fa · outbound

This paper cites A., Horvitz, E., Kamar, E., Lee, P., Lee, Y.

Position: A Theory of Deep Learning Must Include Compositional Sparsity A., Horvitz, E., Kamar, E., Lee, P., Lee, Y

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:58.321955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a1d838dc-cd89-4974-bbdb-d09f874ec05e · outbound

This paper cites M., Favero, A., and Wyart, M.

Position: A Theory of Deep Learning Must Include Compositional Sparsity M., Favero, A., and Wyart, M

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:44.279950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa97e1fe-a96d-4c91-941e-f750ba9f1585 · outbound

This paper cites Superposition of many models into one.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Superposition of many models into one

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:58.099368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation eb0dff58-42b0-4c61-86d7-3713a72e2ea0 · outbound

This paper cites M., Khosla, A., Pantazis, D., Torralba, A., and Oliva, A.

Position: A Theory of Deep Learning Must Include Compositional Sparsity M., Khosla, A., Pantazis, D., Torralba, A., and Oliva, A

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:57.940980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b6f41265-6ec9-4dc5-b182-8dc7bd82f80e · outbound

This paper cites Compositional Sparsity, Approximation Classes, and Parametric Transport Equations.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Compositional Sparsity, Approximation Classes, and Parametric Transport Equations

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:35:50.304551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5f63bab7-3ba4-4d82-abae-f1f0c3a7d6e6 · outbound

This paper cites F., Gou, Z., Shao, Z., Li, Z., Gao, Z., Liu, A., ..., and Zhang, Z.

Position: A Theory of Deep Learning Must Include Compositional Sparsity F., Gou, Z., Shao, Z., Li, Z., Gao, Z., Liu, A., ..., and Zhang, Z

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:57.746079Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9c6ee06e-a500-4d24-a9a9-25573103d067 · outbound

This paper cites Seeing it all: Convolutional network layers map the function of the human visual system.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Seeing it all: Convolutional network layers map the function of the human visual system

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:57.565716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a21c5af1-c143-46b1-9914-28cfb916c835 · outbound

This paper cites On the Power of Decision Trees in Auto-Regressive Language Modeling.

Position: A Theory of Deep Learning Must Include Compositional Sparsity On the Power of Decision Trees in Auto-Regressive Language Modeling

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:35:50.075447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8b518776-ef2f-4a79-b39f-86d15618409f · outbound

This paper cites The Implicit Bias of Depth: How Incremental Learning Drives Generalization.

Position: A Theory of Deep Learning Must Include Compositional Sparsity The Implicit Bias of Depth: How Incremental Learning Drives Generalization

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:44.758347Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af59e188-861f-4fa5-98bf-0dd5f415b7f5 · outbound

This paper cites How to construct random functions.

Position: A Theory of Deep Learning Must Include Compositional Sparsity How to construct random functions

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:44.802137Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76c74de4-5054-4fa1-9cb9-992d5ce82a8f · outbound

This paper cites In-context learning of large language models explained as kernel regression.

Position: A Theory of Deep Learning Must Include Compositional Sparsity In-context learning of large language models explained as kernel regression

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:57.384097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2cc0ea4a-dc28-4eac-9237-890b1b95e389 · outbound

This paper cites The Elements of Statistical Learning.

Position: A Theory of Deep Learning Must Include Compositional Sparsity The Elements of Statistical Learning

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:57.188360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b8687f2b-90dd-4c2e-8cd4-b80a5d6710af · outbound

This paper cites A., and Lenat, D.

Position: A Theory of Deep Learning Must Include Compositional Sparsity A., and Lenat, D

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:57.005878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 26872b84-ea83-4f3e-a85e-7c26065e903b · outbound

This paper cites Deep residual learning for image recognition.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Deep residual learning for image recognition

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:56.840878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation aa00676b-f899-4e2f-8017-62284f9613a7 · outbound

This paper cites Introduction to manifold learning.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Introduction to manifold learning

Reference 32

Resolution: verified exact; doi, observed 2026-08-06T20:35:49.676055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ca21cb50-e602-4b66-8cfd-e1c26c98645f · outbound

This paper cites An Introduction to Statistical Learning (2nd Ed.).

Position: A Theory of Deep Learning Must Include Compositional Sparsity An Introduction to Statistical Learning (2nd Ed.)

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:56.630270Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2d4f180d-c4e7-46b0-8d99-31847779dd1e · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:45.243438Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e06c74d8-5f58-4fa8-ab5c-7a2c014d8ddc · outbound

This paper cites Deep learning without poor local minima.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Deep learning without poor local minima

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:56.423948Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 05dab68f-3e64-400e-bed8-57045b46b039 · outbound

This paper cites T., Wang, J., and Weber, M.

Position: A Theory of Deep Learning Must Include Compositional Sparsity T., Wang, J., and Weber, M

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:56.278467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 72e6be2a-ccd3-4ade-b4af-b0285726b29e · outbound

This paper cites and Langer, S.

Position: A Theory of Deep Learning Must Include Compositional Sparsity and Langer, S

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:56.098996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 731184ab-0d3c-4a20-8af1-19df8db0a9cb · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:35:55.917425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7b892b69-2bd8-43f0-9bf4-92808f0f2a1b · outbound

This paper cites D., Oko, K., Suzuki, T., and Wu, D.

Position: A Theory of Deep Learning Must Include Compositional Sparsity D., Oko, K., Suzuki, T., and Wu, D

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:55.773481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c39a7277-4305-41af-8a9d-40b39ba9a403 · outbound

This paper cites How Diffusion Models Learn to Factorize and Compose.

Position: A Theory of Deep Learning Must Include Compositional Sparsity How Diffusion Models Learn to Factorize and Compose

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:45.581706Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b082c95-24fa-4b0a-aa38-b8bb59dcafa9 · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:35:55.619673Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9a3b1e9c-f6fe-44f1-9d6b-2972aaa0ce8d · outbound

This paper cites Transformers Learn Shortcuts to Automata.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Transformers Learn Shortcuts to Automata

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:45.748309Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5bf35c01-612c-46e8-86fb-028b8ecd4be8 · outbound

This paper cites Auto-Regressive Next-Token Predictors are Universal Learners.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Auto-Regressive Next-Token Predictors are Universal Learners

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:45.863740Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b872bbc7-e1f4-4728-9ac9-4f6cc2423fb4 · outbound

This paper cites Learning Boolean Functions via the Fourier Transform, pp.\ 391--424.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Learning Boolean Functions via the Fourier Transform, pp.\ 391--424

Reference 44

Resolution: verified exact; doi, observed 2026-08-06T20:35:49.554609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a523dd33-fad3-43df-b0a7-c5bcb6b8030b · outbound

This paper cites and Zhang, H.

Position: A Theory of Deep Learning Must Include Compositional Sparsity and Zhang, H

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:55.417340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f3b0230c-03cb-414f-bdf6-cc9e443e5fef · outbound

This paper cites Learning real and boolean functions: When is deep better than shallow? CBMM Memo \#45, arXiv preprint, 2016.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Learning real and boolean functions: When is deep better than shallow? CBMM Memo \#45, arXiv preprint, 2016

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:55.236917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6a5cef10-d278-4cc6-bc9d-07fefec90099 · outbound

This paper cites Characterizing Intrinsic Compositionality in Transformers with Tree Projections.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Characterizing Intrinsic Compositionality in Transformers with Tree Projections

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:46.153360Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4fc79cf-eef3-4534-b034-180672d7b69f · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 48

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:35:55.021714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 53d9b589-5bd3-466e-a452-b580c8f717f4 · outbound

This paper cites and Simon, H.

Position: A Theory of Deep Learning Must Include Compositional Sparsity and Simon, H

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:46.323598Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a2faf52c-60b9-4365-b77f-f9cc50e680a3 · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 50

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:35:54.877809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 53accd1a-8ac0-4098-896b-b80c2c4a3632 · outbound

This paper cites Gpt-4 technical report.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Gpt-4 technical report

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:54.699287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1bd8dbf2-7bf2-4c65-8658-540cb9037e13 · outbound

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

Position: A Theory of Deep Learning Must Include Compositional Sparsity The impact of depth on compositional generalization in transformer language models

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:54.525671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3ee6e408-b621-4560-b9ed-c18a3c5add67 · outbound

This paper cites On efficiently computable functions, deep networks and sparse compositionality.

Position: A Theory of Deep Learning Must Include Compositional Sparsity On efficiently computable functions, deep networks and sparse compositionality

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:54.401350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3f6dfcf2-09aa-442c-92d5-a62911b0a53f · outbound

This paper cites and Fraser, M.

Position: A Theory of Deep Learning Must Include Compositional Sparsity and Fraser, M

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:46.837693Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57e211e7-3e12-425a-920c-0e8c70aab84a · outbound

This paper cites Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:54.219378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 62a9519f-7ade-4681-88d2-ac007bf95290 · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 56

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:35:54.011847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5de9dea2-4a07-4ecf-88a0-20a7a30923f6 · outbound

This paper cites Language models are unsupervised multitask learners.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Language models are unsupervised multitask learners

Reference 57

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:47.302129Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b94ad60-0589-408d-a197-5b2699f0ada7 · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:47.434826Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b6fdb02-357d-4b19-8c97-c32a4c5abcbf · outbound

This paper cites P., Dupont, E., Ruiz, F.

Position: A Theory of Deep Learning Must Include Compositional Sparsity P., Dupont, E., Ruiz, F

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:53.778454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 75bc159f-009c-421a-8d10-d5932b7a78b3 · outbound

This paper cites Nonparametric regression using deep neural networks with ReLU activation function.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Nonparametric regression using deep neural networks with ReLU activation function

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:53.541956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 820de09c-dec8-4782-85fa-b439b175fbcf · outbound

This paper cites J., Guez, A., Sifre, L., van den Driessche, G., Schrittwieser, J., Antonoglou, I., Panneershelvam, V., Lanctot, M., Dieleman, S., Grewe, D., Nand, D., et al.

Position: A Theory of Deep Learning Must Include Compositional Sparsity J., Guez, A., Sifre, L., van den Driessche, G., Schrittwieser, J., Antonoglou, I., Panneershelvam, V., Lanctot, M., Dieleman, S., Grewe, D., Nand, D., et al

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:53.348298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a318c086-e97c-474a-8e25-6b42054f15bd · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:48.078364Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8bed4428-2811-4aa4-983e-93ecccb2865d · outbound

This paper cites A general reinforcement learning algorithm that masters chess, shogi, and go through self-play.

Position: A Theory of Deep Learning Must Include Compositional Sparsity A general reinforcement learning algorithm that masters chess, shogi, and go through self-play

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:48.214114Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d3bb53d1-a788-4c58-af60-6608a47867c5 · outbound

This paper cites How sparse attention approximates exact attention?your attention is naturally \ n c\ -sparse.

Position: A Theory of Deep Learning Must Include Compositional Sparsity How sparse attention approximates exact attention?your attention is naturally \ n c\ -sparse

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:53.097686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9af30030-b52c-4c81-bfab-9e1ad4549106 · outbound

This paper cites and Krause, A.

Position: A Theory of Deep Learning Must Include Compositional Sparsity and Krause, A

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:52.871723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 0840e7a4-581c-4a4c-9758-e4d7727af747 · outbound

This paper cites H., Wu, Y., Le, Q.

Position: A Theory of Deep Learning Must Include Compositional Sparsity H., Wu, Y., Le, Q

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-06T20:35:48.615249Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b558b9c-d1a2-4aac-8494-1aac998b0b61 · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 67

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:35:52.666672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ddcfaf34-3b60-4574-8a6a-fc8463b7b1d3 · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 68

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:35:52.370428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 0745daa3-2f6d-4db5-b793-ad5cd5902ec2 · outbound

This paper cites M., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.

Position: A Theory of Deep Learning Must Include Compositional Sparsity M., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:52.124579Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e71a933a-0aff-46f0-84db-9a680a601d64 · outbound

This paper cites and Belinkov, Y.

Position: A Theory of Deep Learning Must Include Compositional Sparsity and Belinkov, Y

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:51.909365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c3d7c163-7644-4388-abf8-4c3b4bc90192 · outbound

This paper cites H., Xia, F., Le, Q., and Zhou, D.

Position: A Theory of Deep Learning Must Include Compositional Sparsity H., Xia, F., Le, Q., and Zhou, D

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:51.657602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6d7a7c77-01ad-407d-88ba-bf5047774d2e · outbound

This paper cites an unresolved cited work.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Unresolved cited work

Reference 72

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:35:51.438853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3bafaca6-ce83-42fb-a7b4-b03ce3a05a02 · outbound

This paper cites F., Solomon, E.

Position: A Theory of Deep Learning Must Include Compositional Sparsity F., Solomon, E

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:51.163429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e372e614-dc5c-4e90-a76a-6aeb54ba28c2 · outbound

This paper cites L., Cao, Y., and Narasimhan, K.

Position: A Theory of Deep Learning Must Include Compositional Sparsity L., Cao, Y., and Narasimhan, K

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:50.956001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 0c017c28-23e7-48d8-bd84-39a6e78e2187 · outbound

This paper cites Symmetry induces structure and constraint of learning.

Position: A Theory of Deep Learning Must Include Compositional Sparsity Symmetry induces structure and constraint of learning

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:35:50.757280Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

Observation 874bfd00-bb95-45fc-8c44-9e0058a67dff · inbound

From Mechanistic to Compositional Interpretability cites this paper.

From Mechanistic to Compositional Interpretability Position: A Theory of Deep Learning Must Include Compositional Sparsity

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-12T02:46:18.513779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9c70c116-e10a-4ea2-b64e-b0bf3286452f · inbound

Compositional Sparsity as an Inductive Bias for Neural Architecture Design cites this paper.

Compositional Sparsity as an Inductive Bias for Neural Architecture Design Position: A Theory of Deep Learning Must Include Compositional Sparsity

Reference 6

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T14:35:46.881494Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2cb45454-5812-42e6-b4ba-d9335a0d6b1e · inbound

Learning Sparse Compositional Functions with Norm-Constrained Neural Networks cites this paper.

Learning Sparse Compositional Functions with Norm-Constrained Neural Networks Position: A Theory of Deep Learning Must Include Compositional Sparsity

Reference 24

Resolution: metadata mismatch; arxiv_id, observed 2026-06-29T20:33:58.324454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 954a043a-8377-4f1d-ba2a-c1fdece242eb · inbound

Compositionality Emerges in a Narrow Depth-Connectivity Regime: Architecture Constraints and Solution Manifolds cites this paper.

Compositionality Emerges in a Narrow Depth-Connectivity Regime: Architecture Constraints and Solution Manifolds Position: A Theory of Deep Learning Must Include Compositional Sparsity

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-07-04T03:09:29.761198Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f3510f5b-4d76-4733-bbdc-0ec6a85ce116 · inbound

Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximation cites this paper.

Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximation Position: A Theory of Deep Learning Must Include Compositional Sparsity

Reference 7

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T13:19:50.617560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.