Paper Citation Record · LEDGER

Joint Learning in the Gaussian Single Index Model

As of 9 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 1 inbound Pith citation observation for arXiv:2505.21336.

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

pith.paper-citation-record.v1
2505.21336 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:44:29.686799Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T08:40:30.522134Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

34 of 34 outbound references displayed

verified exact2
verified fuzzy21
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fbed67ba-2021-47de-9fc2-1219507365f4 · outbound

This paper cites Sgd learning on neural networks: leap complexity and saddle-to-saddle dynamics.Proceedings of Machine Learning Research, 195:1–72, 2023.

Joint Learning in the Gaussian Single Index Model Sgd learning on neural networks: leap complexity and saddle-to-saddle dynamics.Proceedings of Machine Learning Research, 195:1–72, 2023

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:35.537452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dcce8d70-e5e1-4ecc-98e1-cb0be55a1554 · outbound

This paper cites MIT press, 2024.

Joint Learning in the Gaussian Single Index Model MIT press, 2024

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T13:44:26.252343Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cd593e90-d378-49e7-9390-c283c39afc3e · outbound

This paper cites Springer Science & Business Media, 2013.

Joint Learning in the Gaussian Single Index Model Springer Science & Business Media, 2013

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T13:44:26.455602Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dc6f7fe5-f537-4db6-8cd6-da0129f72e2a · outbound

This paper cites Online stochastic gradient descent on non-convex losses from high-dimensional inference.J.

Joint Learning in the Gaussian Single Index Model Online stochastic gradient descent on non-convex losses from high-dimensional inference.J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:35.337836Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d70e9f2b-726d-4f1b-ade9-67db1b2b3f04 · outbound

This paper cites High-dimensional limit theorems for sgd: Effective dynamics and critical scaling.Advances in neural information processing systems, 35:25349–25362, 2022.

Joint Learning in the Gaussian Single Index Model High-dimensional limit theorems for sgd: Effective dynamics and critical scaling.Advances in neural information processing systems, 35:25349–25362, 2022

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T13:44:26.664262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 226f2a21-777d-4d4d-b23b-32baff655f06 · outbound

This paper cites Learning time-scales in two-layers neural networks.Found Comput Math, 2024.

Joint Learning in the Gaussian Single Index Model Learning time-scales in two-layers neural networks.Found Comput Math, 2024

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:35.081413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 214cd6bd-e5e6-4498-b2bc-95ca76dc3eaf · outbound

This paper cites On Learning Gaussian Multi-index Models with Gradient Flow.

Joint Learning in the Gaussian Single Index Model On Learning Gaussian Multi-index Models with Gradient Flow

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T13:44:26.951223Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c34d923f-12e2-4f5f-9fea-3c52c20ad14a · outbound

This paper cites Gaussian measures.American Mathematical Soc., 36(62), 1998.

Joint Learning in the Gaussian Single Index Model Gaussian measures.American Mathematical Soc., 36(62), 1998

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:34.813982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 83cda6d9-26cc-4899-aa8c-76e2197518ac · outbound

This paper cites Survey on Algorithms for multi-index models.

Joint Learning in the Gaussian Single Index Model Survey on Algorithms for multi-index models

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T13:44:27.216117Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86b72982-a0e9-4d41-b9df-95803c47436d · outbound

This paper cites an unresolved cited work.

Joint Learning in the Gaussian Single Index Model Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:44:34.592551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 229f46fc-3ec0-4500-8456-549876720943 · outbound

This paper cites Computational-Statistical Gaps in Gaussian Single-Index Models.

Joint Learning in the Gaussian Single Index Model Computational-Statistical Gaps in Gaussian Single-Index Models

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T13:44:27.432955Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72048da5-749e-49cf-ae95-f54c49f52d7f · outbound

This paper cites Learning two-layer neural networks, one (giant) step at a time.Journal of Machine Learning Research, 2024.

Joint Learning in the Gaussian Single Index Model Learning two-layer neural networks, one (giant) step at a time.Journal of Machine Learning Research, 2024

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:34.329529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fb1e26fc-787d-4b2e-b99e-8d21cb92c401 · outbound

This paper cites Learning single-index models in gaussian space.

Joint Learning in the Gaussian Single Index Model Learning single-index models in gaussian space

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:34.065418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e8362529-2c32-4ddc-8f44-2c2899e6cbb1 · outbound

This paper cites Nonparametric Linear Feature Learning in Regression Through Regularisation.

Joint Learning in the Gaussian Single Index Model Nonparametric Linear Feature Learning in Regression Through Regularisation

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:44:30.195528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 08ab7037-e6d6-4616-8eeb-0206939a9c0b · outbound

This paper cites Agnostic learning of a single neuron with gradient descent.

Joint Learning in the Gaussian Single Index Model Agnostic learning of a single neuron with gradient descent

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:33.848962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c7f5e7fa-12e7-4d66-abca-dcd70ddc8b76 · outbound

This paper cites High-dimensional integration on rd, weighted hermite spaces, and orthogonal transforms.Journal of Complexity, 31(2):174–205, 2015.

Joint Learning in the Gaussian Single Index Model High-dimensional integration on rd, weighted hermite spaces, and orthogonal transforms.Journal of Complexity, 31(2):174–205, 2015

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:33.633684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d0ae15ed-aed4-47fb-93f8-152143b604ab · outbound

This paper cites Efficient learning of generalized linear and single index models with isotonic regression.

Joint Learning in the Gaussian Single Index Model Efficient learning of generalized linear and single index models with isotonic regression

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:33.400208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ea73b9b5-bf26-4e6f-a026-fb815345ce5f · outbound

This paper cites The isotron algorithm: High-dimensional isotonic regression.

Joint Learning in the Gaussian Single Index Model The isotron algorithm: High-dimensional isotonic regression

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:33.132741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 190523c7-5dfd-4c13-955b-1ef8015c5765 · outbound

This paper cites Phase retrieval in high dimensions: Statistical and computational phase transitions.

Joint Learning in the Gaussian Single Index Model Phase retrieval in high dimensions: Statistical and computational phase transitions

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:32.909471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 448d0b7b-598a-480c-8264-de2ecab0f62e · outbound

This paper cites The landscape of empirical risk for nonconvex losses.

Joint Learning in the Gaussian Single Index Model The landscape of empirical risk for nonconvex losses

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:32.678787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5d4e427a-cfb6-40e1-832d-d4f14dc89c9c · outbound

This paper cites Random features for large-scale kernel machines.Advances in neural information processing systems, 20, 2007.

Joint Learning in the Gaussian Single Index Model Random features for large-scale kernel machines.Advances in neural information processing systems, 20, 2007

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T13:44:28.538441Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 34f306c0-4ded-41bc-ac10-3f3e5c52b059 · outbound

This paper cites Exact solution for on-line learning in multilayer neural networks.

Joint Learning in the Gaussian Single Index Model Exact solution for on-line learning in multilayer neural networks

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T13:44:28.617700Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation abebb385-8bbd-4ab5-9fd8-9a37afbfbb4d · outbound

This paper cites Kernel techniques: from machine learning to meshless methods.

Joint Learning in the Gaussian Single Index Model Kernel techniques: from machine learning to meshless methods

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:32.441687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7ca5ea4b-5a25-4c12-9356-a42d44117dce · outbound

This paper cites Stochastic Differential Equations models for Least-Squares Stochastic Gradient Descent.

Joint Learning in the Gaussian Single Index Model Stochastic Differential Equations models for Least-Squares Stochastic Gradient Descent

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-07T13:44:28.799808Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea8ee283-c3a3-488d-b9d0-f33a166592a5 · outbound

This paper cites MIT press, 2002.

Joint Learning in the Gaussian Single Index Model MIT press, 2002

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:32.142624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a734563e-dfa5-4e8c-b229-d9de11ff0f09 · outbound

This paper cites Learning kernel-based halfspaces with the zero-one loss.SIAM J.

Joint Learning in the Gaussian Single Index Model Learning kernel-based halfspaces with the zero-one loss.SIAM J

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:31.961499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1d5c5a20-d6aa-4dea-97f6-a8e4dfe0efb5 · outbound

This paper cites Learning relus via gradient descent.Advances in neural information processing systems, 2017.

Joint Learning in the Gaussian Single Index Model Learning relus via gradient descent.Advances in neural information processing systems, 2017

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:31.688692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 426fa6da-3f54-47bc-99e8-8e0202b0646b · outbound

This paper cites Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks.

Joint Learning in the Gaussian Single Index Model Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T13:44:29.158300Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6518ba48-ca61-4b8e-8233-4ac28d84334e · outbound

This paper cites Learning a single neuron for non-monotonic activation functions.

Joint Learning in the Gaussian Single Index Model Learning a single neuron for non-monotonic activation functions

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:31.410971Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7db72e21-dabf-48ce-9b63-fd0cdd2f54c0 · outbound

This paper cites Learning a single neuron with gradient methods.

Joint Learning in the Gaussian Single Index Model Learning a single neuron with gradient methods

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:31.184157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9df17beb-135f-412a-b150-b949bbacf001 · outbound

This paper cites Symmetric Single Index Learning.

Joint Learning in the Gaussian Single Index Model Symmetric Single Index Learning

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:44:29.910938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d9aec454-26d3-4cbc-872e-c11c7dafc478 · outbound

This paper cites On single-index models beyond gaussian data.

Joint Learning in the Gaussian Single Index Model On single-index models beyond gaussian data

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:30.980576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 33bd5c4a-89a3-458d-b57f-268dd1ede831 · outbound

This paper cites We now prove that, after timeT, both mt and a1,t remain uniformly bounded away from zero.

Joint Learning in the Gaussian Single Index Model We now prove that, after timeT, both mt and a1,t remain uniformly bounded away from zero

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:30.741168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 23605da6-b50c-4c5f-91a1-5340cba45ff8 · outbound

This paper cites We now prove that an arbitrary number of coefficientsak,t adopt the sign of their target values (the sign ofa∗ kmk t).

Joint Learning in the Gaussian Single Index Model We now prove that an arbitrary number of coefficientsak,t adopt the sign of their target values (the sign ofa∗ kmk t)

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:44:30.507254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

Observation 89feaad8-ecdb-459d-8973-e4e00d026582 · inbound

Singular perturbations and hierarchical learning in two-layer neural networks cites this paper.

Singular perturbations and hierarchical learning in two-layer neural networks Joint Learning in the Gaussian Single Index Model

Reference 32

Resolution: unresolved; no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.