Paper Citation Record · LEDGER

Hardness of Learning Fixed Parities with Neural Networks

As of 12 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 3 inbound Pith citation observations for arXiv:2501.00817.

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

pith.paper-citation-record.v1
2501.00817 v2

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T22:49:49.794883Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

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

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T04:19:47.037946Z

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

20 of 20 outbound references displayed

verified exact0
verified fuzzy15
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

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

Outbound references

Observation b6db95a8-71c7-453d-8a14-f6e46b0171b6 · outbound

This paper cites On the non-universality of deep learning: quantifying the cost of symmetry.

Hardness of Learning Fixed Parities with Neural Networks On the non-universality of deep learning: quantifying the cost of symmetry

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:50.078039Z

Source-reported events for the cited work

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

Observation 961ea479-e4f8-4721-b7c4-e147025c7266 · outbound

This paper cites Poly-time universality and limitations of deep learning.

Hardness of Learning Fixed Parities with Neural Networks Poly-time universality and limitations of deep learning

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-10T22:49:49.716245Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2060f76f-cf0d-4fa1-89dd-31b2d1a29979 · outbound

This paper cites On the universality of deep learning.

Hardness of Learning Fixed Parities with Neural Networks On the universality of deep learning

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:50.063311Z

Source-reported events for the cited work

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

Observation 0a3aa8ef-4e84-44ec-b83b-ef325d9cd7e0 · outbound

This paper cites On the power of differentiable learning versus pac and sq learning.

Hardness of Learning Fixed Parities with Neural Networks On the power of differentiable learning versus pac and sq learning

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:50.048836Z

Source-reported events for the cited work

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

Observation b290d281-7181-4ba4-a545-4a655d115ba8 · outbound

This paper cites Noise-tolerant learning, the parity problem, and the statistical query model.

Hardness of Learning Fixed Parities with Neural Networks Noise-tolerant learning, the parity problem, and the statistical query model

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:50.032959Z

Source-reported events for the cited work

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

Observation 1d3a0ebb-c310-45b6-8a59-3049b04a2765 · outbound

This paper cites Further and stronger analogy between sampling and optimization: Langevin monte carlo and gradient descent.

Hardness of Learning Fixed Parities with Neural Networks Further and stronger analogy between sampling and optimization: Langevin monte carlo and gradient descent

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:50.019650Z

Source-reported events for the cited work

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

Observation 5176d386-74c2-4560-ae11-77a17a43d688 · outbound

This paper cites Gradient descent can take exponential time to escape saddle points.

Hardness of Learning Fixed Parities with Neural Networks Gradient descent can take exponential time to escape saddle points

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:50.005912Z

Source-reported events for the cited work

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

Observation 5349aed5-46b2-4ae2-824c-3c9f7c4705c2 · outbound

This paper cites Nonasymptotic convergence analysis for the unadjusted langevin algorithm.

Hardness of Learning Fixed Parities with Neural Networks Nonasymptotic convergence analysis for the unadjusted langevin algorithm

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:49.992723Z

Source-reported events for the cited work

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

Observation 2a1f0040-b406-4bd4-a707-fbc93bda52d8 · outbound

This paper cites Statistical algorithms and a lower bound for detecting planted cliques.

Hardness of Learning Fixed Parities with Neural Networks Statistical algorithms and a lower bound for detecting planted cliques

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:49.979654Z

Source-reported events for the cited work

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

Observation 3d634e7f-5942-4229-93b9-a1974f9732a4 · outbound

This paper cites How to escape saddle points efficiently.

Hardness of Learning Fixed Parities with Neural Networks How to escape saddle points efficiently

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-10T22:49:49.752818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9398f5bf-a446-4f32-b233-093f0d9bb9be · outbound

This paper cites Efficient noise-tolerant learning from statistical queries.

Hardness of Learning Fixed Parities with Neural Networks Efficient noise-tolerant learning from statistical queries

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:49.958817Z

Source-reported events for the cited work

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

Observation babbeeb7-08d6-42f1-8c2e-2701a87165b0 · outbound

This paper cites An introduction to computational learning theory.

Hardness of Learning Fixed Parities with Neural Networks An introduction to computational learning theory

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-10T22:49:49.760425Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55e55270-5b29-450f-ba09-5b3c9698ff14 · outbound

This paper cites On symmetry and initialization for neural networks.

Hardness of Learning Fixed Parities with Neural Networks On symmetry and initialization for neural networks

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:49.936116Z

Source-reported events for the cited work

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

Observation 84b2f23c-784a-40de-ac56-dfa09ebfb8b4 · outbound

This paper cites Analysis of Boolean Functions.

Hardness of Learning Fixed Parities with Neural Networks Analysis of Boolean Functions

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T22:49:49.768026Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f380dc3-9ec6-4dc7-9b77-20b4e2c6caf2 · outbound

This paper cites Fast learning requires good memory: A time-space lower bound for parity learning.

Hardness of Learning Fixed Parities with Neural Networks Fast learning requires good memory: A time-space lower bound for parity learning

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:49.921275Z

Source-reported events for the cited work

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

Observation 337b4323-328c-4e7c-8b91-282e4d2fd084 · outbound

This paper cites Statistical Queries and Statistical Algorithms: Foundations and Applications.

Hardness of Learning Fixed Parities with Neural Networks Statistical Queries and Statistical Algorithms: Foundations and Applications

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-10T22:49:49.776829Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c4538453-a627-4c16-8e6b-623c42ef2cc5 · outbound

This paper cites Failures of gradient-based deep learning.

Hardness of Learning Fixed Parities with Neural Networks Failures of gradient-based deep learning

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:49.907909Z

Source-reported events for the cited work

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

Observation 3809b4c9-e832-48f9-ae91-7677af5b4fe0 · outbound

This paper cites Global convergence of langevin dynamics based algorithms for nonconvex optimization.

Hardness of Learning Fixed Parities with Neural Networks Global convergence of langevin dynamics based algorithms for nonconvex optimization

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:49.894739Z

Source-reported events for the cited work

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

Observation 0002ae2d-a3eb-499a-93a2-939e4b41b240 · outbound

This paper cites New lower bounds for statistical query learning.

Hardness of Learning Fixed Parities with Neural Networks New lower bounds for statistical query learning

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:49.881203Z

Source-reported events for the cited work

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

Observation 09a9e761-7ad2-4518-9717-3c1644ea5ef4 · outbound

This paper cites Escape saddle points by a simple gradient-descent based algorithm.

Hardness of Learning Fixed Parities with Neural Networks Escape saddle points by a simple gradient-descent based algorithm

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:49:49.867492Z

Source-reported events for the cited work

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

Pith citing papers

Observation 026f25f2-02f8-4751-a1f8-636ff9b19f22 · 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 Hardness of Learning Fixed Parities with Neural Networks

Reference 165

Resolution: verified exact; arxiv_id, observed 2026-05-21T20:40:36.262167Z

Source-reported events for the cited work

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

Observation 7ac56ca2-2b13-4ac3-83b5-ac7b60fcede3 · inbound

Limitations of SGD for Multi-Index Models Beyond Statistical Queries cites this paper.

Limitations of SGD for Multi-Index Models Beyond Statistical Queries Hardness of Learning Fixed Parities with Neural Networks

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-03T04:19:47.037946Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0c4ae17-744c-453d-a63c-11733740d56d · inbound

Learning through Internalization cites this paper.

Learning through Internalization Hardness of Learning Fixed Parities with Neural Networks

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-06-26T17:49:40.655923Z

Source-reported events for the cited work

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