Paper Citation Record · LEDGER

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning

As of 7 August 2026, this Paper Citation Record lists 56 of 56 outbound references and 1 inbound Pith citation observation for arXiv:2607.03347.

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

pith.paper-citation-record.v1
2607.03347 v1

Coverage vector

measured 56 of 56 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-12T03:07:54.001891Z

measured 57 of 57 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T03:14:39.949582Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-01T06:16:24.888925Z

Reference resolution

56 of 56 outbound references displayed

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verified fuzzy0
unresolved56
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1e189931-d8b0-4636-96cc-3cd3c2c91b3f · outbound

This paper cites The merged-staircase property: a necessary and nearly sufficient condition for sgd learning of sparse functions on two-layer neural networks.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning The merged-staircase property: a necessary and nearly sufficient condition for sgd learning of sparse functions on two-layer neural networks

Reference 1

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Observation 0e586882-d6b2-4375-a9cb-a217fe67804c · outbound

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

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Sgd learning on neural networks: leap complexity and saddle-to-saddle dynamics

Reference 2

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Observation 7b7f9449-49ca-42fb-bc53-dbcb512f610c · outbound

This paper cites Stochastic Interpolants: A Unifying Framework for Flows and Diffusions.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Stochastic Interpolants: A Unifying Framework for Flows and Diffusions

Reference 3

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Observation 1bd1a306-596c-438b-91de-3937bd310e48 · outbound

This paper cites Algorithmic thresholds for tensor PCA.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Algorithmic thresholds for tensor PCA

Reference 4

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Observation 5d03e1b8-7763-4cca-9b8f-93d50653d714 · outbound

This paper cites Online stochastic gradient descent on non-convex losses from high-dimensional inference, 2021.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Online stochastic gradient descent on non-convex losses from high-dimensional inference, 2021

Reference 5

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Observation 17702635-14b3-45c6-8244-65cc42eecf14 · outbound

This paper cites Langevin dynamics for high-dimensional optimization: the case of multi-spiked tensor PCA.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Langevin dynamics for high-dimensional optimization: the case of multi-spiked tensor PCA

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-12T03:07:54.001891Z

Source-reported events for the cited work

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Observation 6ddbd7ea-4418-4d34-8867-b7c21b60114f · outbound

This paper cites Quality over quantity in attention layers: When adding more heads hurts.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Quality over quantity in attention layers: When adding more heads hurts

Reference 7

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Observation 27c9abfe-9802-446f-8f08-1d7542a0e5d8 · outbound

This paper cites What Can ResNet Learn Efficiently, Going Beyond Kernels? 2019.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning What Can ResNet Learn Efficiently, Going Beyond Kernels? 2019

Reference 8

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Observation fe5b2f85-cf19-46e6-b8e4-7e497dac8d1e · outbound

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

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Online stochastic gradient descent on non-convex losses from high-dimensional inference

Reference 9

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Observation de88921c-de4e-4e10-bd47-5423f2d41b3d · outbound

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

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning On Learning Gaussian Multi-index Models with Gradient Flow

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-12T03:07:54.001891Z

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Observation 99d5487b-c554-404b-b6f0-16132bef76c3 · outbound

This paper cites Survey on algorithms for multi-index models, 2025.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Survey on algorithms for multi-index models, 2025

Reference 11

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Observation 5c55191c-98fd-4c9d-9a3f-9300099d7e4d · outbound

This paper cites Optimal errors and phase transitions in high-dimensional generalized linear models.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Optimal errors and phase transitions in high-dimensional generalized linear models

Reference 12

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Observation 9905aa8e-01fa-4c3f-8532-630dea663ceb · outbound

This paper cites Invariant scattering convolution networks.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Invariant scattering convolution networks

Reference 13

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Observation 55862490-2eb4-4819-bf2a-5964496201ef · outbound

This paper cites Resnets of all shapes and sizes: Convergence of training dynamics in the large-scale limit.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Resnets of all shapes and sizes: Convergence of training dynamics in the large-scale limit

Reference 14

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Observation 224dbd56-d443-4942-9f16-35eb234a55ad · outbound

This paper cites The hidden width of deep resnets: Tight error bounds and phase diagrams.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning The hidden width of deep resnets: Tight error bounds and phase diagrams

Reference 15

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Observation 3827d155-278d-4b55-830c-408150666751 · outbound

This paper cites Asymptotics of feature learning in two-layer networks after one gradient-step.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Asymptotics of feature learning in two-layer networks after one gradient-step

Reference 16

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Observation ba82f010-0f3a-408f-bdb0-ad67b80f2db2 · outbound

This paper cites How deep neural networks learn compositional data: The random hierarchy model.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning How deep neural networks learn compositional data: The random hierarchy model

Reference 17

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Observation ddf54aa8-65ce-478c-b050-e941a49a5c6b · outbound

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The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Unresolved cited work

Reference 18

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Observation dc9142df-5779-4086-9c03-ed23e1d2e25a · outbound

This paper cites On the expressive power of deep learning: A tensor analysis.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning On the expressive power of deep learning: A tensor analysis

Reference 19

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Observation fab2baeb-eb7d-4dab-ab17-2cfdda614289 · outbound

This paper cites Mse analysis of online sgd for the multiscale single index model.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Mse analysis of online sgd for the multiscale single index model

Reference 20

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Observation eb0dd3d1-3ec5-4a26-bc10-b12f855bcfd3 · outbound

This paper cites Donoho and Michael J.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Donoho and Michael J

Reference 21

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Observation 8f2a42aa-4244-4558-ab75-48474a215ab7 · outbound

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

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Learning single-index models in gaussian space

Reference 22

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Observation db64cf4b-848b-44b4-bdc4-79ed4fc670d3 · outbound

This paper cites Statistical query lower bounds for tensor pca.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Statistical query lower bounds for tensor pca

Reference 23

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Observation 35c1a2cd-d361-4f9c-bc7f-b499cafbcb1c · outbound

This paper cites How Two-Layer Neural Networks Learn, One (Giant) Step at a Time.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning How Two-Layer Neural Networks Learn, One (Giant) Step at a Time

Reference 25

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Observation 11139e03-0d24-46c7-b45c-3d606d79053e · outbound

This paper cites The Generative Leap: Sharp Sample Complexity for Efficiently Learning Gaussian Multi-Index Models.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning The Generative Leap: Sharp Sample Complexity for Efficiently Learning Gaussian Multi-Index Models

Reference 26

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Observation 448810d9-aa3a-458d-98d2-59195f5c400d · outbound

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

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Computational-Statistical Gaps in Gaussian Single-Index Models

Reference 27

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Observation 6dad2d0f-388c-4ff1-bc82-e95119aa2c9f · outbound

This paper cites The computational advantage of depth: Learning high-dimensional hierarchical functions with gradient descent, 2025.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning The computational advantage of depth: Learning high-dimensional hierarchical functions with gradient descent, 2025

Reference 28

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Observation 58028eba-f86d-4ee3-b355-65d7dc52a2e9 · outbound

This paper cites The power of depth for feedforward neural networks.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning The power of depth for feedforward neural networks

Reference 29

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Observation 1d4ced3a-1e33-4e99-a49d-3d2be0bf127f · outbound

This paper cites Sharp recovery thresholds of tensor pca spectral algorithms.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Sharp recovery thresholds of tensor pca spectral algorithms

Reference 30

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Observation 1d2a2009-1b94-4635-a8ca-d695fe74b9e8 · outbound

This paper cites Universality of high-dimensional scaling limits of stochastic gradient descent.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Universality of high-dimensional scaling limits of stochastic gradient descent

Reference 31

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Observation 98fcd980-a143-437b-9ac2-4dfd400ae819 · outbound

This paper cites Learning One-hidden-layer Neural Networks with Landscape Design.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Learning One-hidden-layer Neural Networks with Landscape Design

Reference 32

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Observation df4dfe2e-bd66-4655-ad78-dd0e58f55ed1 · outbound

This paper cites A mathematical perspective on transformers.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning A mathematical perspective on transformers

Reference 33

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Observation 68cc769c-2eb5-4c8b-b142-5b06b7559858 · outbound

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The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Deep residual learning for image recognition, 2015

Reference 34

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This paper cites On the Complexity of Learning Sparse Functions with Statistical and Gradient Queries.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning On the Complexity of Learning Sparse Functions with Statistical and Gradient Queries

Reference 35

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This paper cites Beating the Perils of Non-Convexity: Guaranteed Training of Neural Networks using Tensor Methods.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Beating the Perils of Non-Convexity: Guaranteed Training of Neural Networks using Tensor Methods

Reference 36

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Observation 7226c86a-18af-4a19-9138-d61bb3b7e84f · outbound

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The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Bayesian inference with finitely wide neural networks

Reference 37

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Observation 6a23b49c-016b-41b3-b019-fe30f78db91d · outbound

This paper cites Flow matching for generative modeling.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Flow matching for generative modeling

Reference 38

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Observation 812e76a9-9bca-4176-b65b-dcb7bbfa0c55 · outbound

This paper cites Statistical-computational trade-offs in learning multi-index models via harmonic analysis.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Statistical-computational trade-offs in learning multi-index models via harmonic analysis

Reference 39

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Observation 14f4c00f-5905-4364-806f-ed66dfc54319 · outbound

This paper cites Understanding deep convolutional networks.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Understanding deep convolutional networks

Reference 40

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This paper cites Fundamental limits of weak recovery with applications to phase retrieval.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Fundamental limits of weak recovery with applications to phase retrieval

Reference 41

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Observation 4d8c3723-2ebd-4607-80c0-853a98bb94fe · outbound

This paper cites A statistical model for tensor pca.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning A statistical model for tensor pca

Reference 42

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Observation 549fc86d-1ae8-4492-b080-d9113dbe5c1a · outbound

This paper cites Phase transitions for feature learning in neural networks, 2026.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Phase transitions for feature learning in neural networks, 2026

Reference 43

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This paper cites The connection between approximation, depth separation and learnability in neural networks.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning The connection between approximation, depth separation and learnability in neural networks

Reference 44

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This paper cites Provable guarantees for nonlinear feature learning in three-layer neural networks.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Provable guarantees for nonlinear feature learning in three-layer neural networks

Reference 45

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This paper cites Improving the gaussian approximation in neural networks: Para-gaussians and edgeworth expansions, 2024.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Improving the gaussian approximation in neural networks: Para-gaussians and edgeworth expansions, 2024

Reference 46

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This paper cites Learning a deep convolutional neural network via tensor decomposition.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Learning a deep convolutional neural network via tensor decomposition

Reference 47

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Observation 22a3c2af-3e01-40aa-8d99-955b6e50e368 · outbound

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The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Unresolved cited work

Reference 48

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This paper cites A statistical model for tensor pca.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning A statistical model for tensor pca

Reference 49

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The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Deep unsupervised learning using nonequilibrium thermodynamics

Reference 50

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The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Optimization-based separations for neural networks

Reference 51

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This paper cites Serre, L.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Serre, L

Reference 52

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This paper cites Deep learning of compositional targets with hierarchical spectral methods.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Deep learning of compositional targets with hierarchical spectral methods

Reference 53

Resolution: unresolved; no resolver link, observed 2026-07-12T03:07:54.001891Z

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Observation 0efe9933-7ea8-4b52-889e-b12f06060fa4 · outbound

This paper cites Benefits of depth in neural networks.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Benefits of depth in neural networks

Reference 54

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Observation 7d2d2aad-ec86-46d6-a0d8-7783135c88d3 · outbound

This paper cites Attention is all you need.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Attention is all you need

Reference 55

Resolution: unresolved; no resolver link, observed 2026-07-12T03:07:54.001891Z

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Observation 6f7b4851-ce27-4b2b-9316-eb32bff46b7b · outbound

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The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Unresolved cited work

Reference 56

Resolution: unresolved; no resolver link, observed 2026-07-12T03:07:54.001891Z

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Observation f2d2a4ef-3fbe-469c-af2f-38d49de85b38 · outbound

This paper cites Exponential separations in symmetric neural networks.

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning Exponential separations in symmetric neural networks

Reference 57

Resolution: unresolved; no resolver link, observed 2026-07-12T03:07:54.001891Z

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Pith citing papers

Observation 1b1e3e37-0966-4b0d-a65c-e758d6955df8 · inbound

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks cites this paper.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-01T03:19:17.644733Z

Source-reported events for the cited work

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