Paper Citation Record · LEDGER

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks

As of 15 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 1 inbound Pith citation observation for arXiv:2502.05668.

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

pith.paper-citation-record.v1
2502.05668 v3

Coverage vector

measured 55 of 55 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T18:38:57.105705Z

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-30T07:05:09.767632Z

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

Source: arxiv_reference, observed 2026-06-30T07:14:21.720119Z

Reference resolution

55 of 55 outbound references displayed

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External citation measurements

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Outbound references

Observation 7fbd825b-9009-4509-a187-5b9ecde6c088 · outbound

This paper cites an unresolved cited work.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Unresolved cited work

Reference 1

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This paper cites Reconciling modern machine-learning practice and the classical bias--variance trade-off.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Reconciling modern machine-learning practice and the classical bias--variance trade-off

Reference 2

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This paper cites Dynamics of stochastic approximation algorithms.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Dynamics of stochastic approximation algorithms

Reference 3

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This paper cites Stochastic approximations and differential inclusions.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Stochastic approximations and differential inclusions

Reference 4

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This paper cites Semianalytic and subanalytic sets.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Semianalytic and subanalytic sets

Reference 5

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This paper cites Bolte, A.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Bolte, A

Reference 6

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Observation 8939745b-0806-4ad0-9121-ff69cb25b8c3 · outbound

This paper cites Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning

Reference 7

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This paper cites Subgradient sampling for nonsmooth nonconvex minimization.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Subgradient sampling for nonsmooth nonconvex minimization

Reference 8

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This paper cites Stochastic approximation: a dynamical systems viewpoint, volume 9.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Stochastic approximation: a dynamical systems viewpoint, volume 9

Reference 9

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This paper cites The ode method for convergence of stochastic approximation and reinforcement learning.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks The ode method for convergence of stochastic approximation and reinforcement learning

Reference 10

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Observation fe38cc36-f071-4e8b-88a9-ce8d4d06dc1b · outbound

This paper cites An introduction to optimization on smooth manifolds.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks An introduction to optimization on smooth manifolds

Reference 11

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Observation f3966ade-874b-4499-b74f-cfd57faf6315 · outbound

This paper cites Large stepsize gradient descent for non-homogeneous two-layer networks: Margin improvement and fast optimization.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Large stepsize gradient descent for non-homogeneous two-layer networks: Margin improvement and fast optimization

Reference 12

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Observation 5c94012c-62d7-46ea-94fb-deae84c99267 · outbound

This paper cites Implicit bias of gradient descent for wide two-layer neural networks trained with the logistic loss.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Implicit bias of gradient descent for wide two-layer neural networks trained with the logistic loss

Reference 13

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Observation 2ac8ba6a-21da-4f1d-bc8c-145c61d206a9 · outbound

This paper cites Nonsmooth analysis and control theory, volume 178.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Nonsmooth analysis and control theory, volume 178

Reference 14

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Observation 7a6a4062-a337-475f-93a1-03269016620d · outbound

This paper cites An introduction to o-minimal geometry.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks An introduction to o-minimal geometry

Reference 15

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Observation a38c5ba8-b4b5-4bbc-bbe2-578bce8d9ad8 · outbound

This paper cites Stochastic subgradient method converges on tame functions.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Stochastic subgradient method converges on tame functions

Reference 16

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Observation db68b9eb-f9c8-4dcb-a050-99801f471346 · outbound

This paper cites Curves of descent.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Curves of descent

Reference 17

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Observation d0ad4bc6-fa09-4f43-a6b5-2de151bcff96 · outbound

This paper cites Algorithmic regularization in learning deep homogeneous models: Layers are automatically balanced.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Algorithmic regularization in learning deep homogeneous models: Layers are automatically balanced

Reference 18

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Observation 9a389864-f43c-45ee-a055-01dd65abd8fe · outbound

This paper cites Stochastic methods for composite and weakly convex optimization problems.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Stochastic methods for composite and weakly convex optimization problems

Reference 19

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Observation ef1cc023-19d9-4b1b-8c95-beb4d6c0832d · outbound

This paper cites The little book of deep learning.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks The little book of deep learning

Reference 20

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This paper cites Complements of subanalytic sets and existential formulas for analytic functions.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Complements of subanalytic sets and existential formulas for analytic functions

Reference 21

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Observation 1e93a0a1-2866-43a0-a7d9-176bd12d7fe6 · outbound

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The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Projections of semi-analytic sets

Reference 22

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Observation 2da008c0-3f64-4ec3-a2fa-7024081c2154 · outbound

This paper cites Deep learning, volume 196.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Deep learning, volume 196

Reference 23

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Observation 48bae627-5ca6-4aa2-9a01-b72070a9a39f · outbound

This paper cites Lee, Daniel Soudry, and Nathan Srebro.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Lee, Daniel Soudry, and Nathan Srebro

Reference 24

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Observation 0d88e792-9acd-4924-a275-6afd390abce2 · outbound

This paper cites Implicit bias of gradient descent on linear convolutional networks.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Implicit bias of gradient descent on linear convolutional networks

Reference 25

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Observation a6e19c96-d9f1-4f7c-b6de-5cd1dcfed0f7 · outbound

This paper cites An invitation to tame optimization.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks An invitation to tame optimization

Reference 26

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Observation 81ba1b4d-0540-4949-8afb-97aac81c8c58 · outbound

This paper cites Gradient descent aligns the layers of deep linear networks.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Gradient descent aligns the layers of deep linear networks

Reference 27

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The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Risk and parameter convergence of logistic regression

Reference 28

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The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Directional convergence and alignment in deep learning

Reference 29

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This paper cites Global stability of first-order methods for coercive tame functions.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Global stability of first-order methods for coercive tame functions

Reference 30

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Observation 29b04d98-57a6-48a7-ac36-3a128c0802d6 · outbound

This paper cites The Asymmetric Maximum Margin Bias of Quasi-Homogeneous Neural Networks.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks The Asymmetric Maximum Margin Bias of Quasi-Homogeneous Neural Networks

Reference 31

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Observation 5b3c22b2-59c4-45c5-a512-5c9754de0259 · outbound

This paper cites An Introduction to Differential Manifolds.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks An Introduction to Differential Manifolds

Reference 32

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The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Nonsmooth nonconvex stochastic heavy ball

Reference 33

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Observation d654da66-7c8a-437d-a93c-2fb12654215e · outbound

This paper cites Training invariances and the low-rank phenomenon: beyond linear networks.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Training invariances and the low-rank phenomenon: beyond linear networks

Reference 34

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Observation 3a8c4171-8fbe-4620-96b2-495caac1ff02 · outbound

This paper cites Gradient descent maximizes the margin of homogeneous neural networks.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Gradient descent maximizes the margin of homogeneous neural networks

Reference 35

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The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Analysis of nonsmooth stochastic approximation: the differential inclusion approach

Reference 36

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This paper cites Lexicographic and depth-sensitive margins in homogeneous and non-homogeneous deep models.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Lexicographic and depth-sensitive margins in homogeneous and non-homogeneous deep models

Reference 37

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This paper cites Convergence of gradient descent on separable data.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Convergence of gradient descent on separable data

Reference 38

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Observation 8a7d30e8-3b4b-4801-88d8-6d2c5c0b77e8 · outbound

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The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Stochastic gradient descent on separable data: Exact convergence with a fixed learning rate

Reference 39

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This paper cites In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning

Reference 40

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The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Automatic differentiation in pytorch

Reference 41

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This paper cites A generalization of the borkar-meyn theorem for stochastic recursive inclusions.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks A generalization of the borkar-meyn theorem for stochastic recursive inclusions

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:38:57.913688Z

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Observation aad8fb48-f1af-4f9e-bd80-c6ba042d94d4 · outbound

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The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks The measure of the critical values of differentiable maps

Reference 43

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Observation df8e8f68-f04a-4122-bdcf-7644a6b32d27 · outbound

This paper cites The implicit bias of gradient descent on separable data.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks The implicit bias of gradient descent on separable data

Reference 44

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The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks A decision method for elementary algebra and geometry

Reference 45

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This paper cites Tame topology and o-minimal structures, volume 248.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Tame topology and o-minimal structures, volume 248

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:38:57.878862Z

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Observation 99b34755-0249-4fee-9118-e63f978e1fcb · outbound

This paper cites Geometric categories and o-minimal structures.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Geometric categories and o-minimal structures

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:38:57.861574Z

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Observation bb0c2ed5-7f49-40ff-9392-b8510455cb3f · outbound

This paper cites The elementary theory of restricted analytic fields with exponentiation.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks The elementary theory of restricted analytic fields with exponentiation

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:38:57.846335Z

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Observation 98c4737c-70c0-4c61-b57d-23f1f2f5f51e · outbound

This paper cites Statistical learning theory.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Statistical learning theory

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:38:57.736656Z

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Observation dfc36c98-a3b7-473e-87c0-e2624bf85633 · outbound

This paper cites On the implicit bias in deep-learning algorithms.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks On the implicit bias in deep-learning algorithms

Reference 50

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Observation 1f2c7d03-ad75-40fc-b2fe-a9a3a226391b · outbound

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The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks On margin maximization in linear and relu networks

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:38:57.589078Z

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Observation 93f113f2-3cda-4fb2-8414-80abb7aebd87 · outbound

This paper cites The implicit bias for adaptive optimization algorithms on homogeneous neural networks.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks The implicit bias for adaptive optimization algorithms on homogeneous neural networks

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:38:57.574800Z

Source-reported events for the cited work

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Observation 14db0bdc-5cbd-42c0-a0b7-af8dfce8fc0c · outbound

This paper cites Model completeness results for expansions of the ordered field of real numbers by restricted pfaffian functions and the exponential function.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Model completeness results for expansions of the ordered field of real numbers by restricted pfaffian functions and the exponential function

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T18:38:57.559818Z

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Observation 6804c035-5aaf-44cb-a657-2d55be3cbbc6 · outbound

This paper cites A Unifying View on Implicit Bias in Training Linear Neural Networks.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks A Unifying View on Implicit Bias in Training Linear Neural Networks

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-08T18:38:56.984487Z

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Observation 3e3b6691-8f37-4cc8-a5e7-8800f3dc51fb · outbound

This paper cites Understanding deep learning (still) requires rethinking generalization.

The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks Understanding deep learning (still) requires rethinking generalization

Reference 55

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Pith citing papers

Observation deb5d617-a54b-408f-8faa-fc0a7131ccc2 · inbound

Convergence of Continual Learning in Homogeneous Deep Networks cites this paper.

Convergence of Continual Learning in Homogeneous Deep Networks The late-stage training dynamics of (stochastic) subgradient descent on homogeneous neural networks

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-06-30T07:14:21.722003Z

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