Paper Citation Record · LEDGER

Parameter Symmetry Potentially Unifies Deep Learning Theory

As of 9 August 2026, this Paper Citation Record lists 91 of 91 outbound references and 4 inbound Pith citation observations for arXiv:2502.05300.

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

pith.paper-citation-record.v1
2502.05300 v2

Coverage vector

measured 91 of 91 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T19:58:27.272665Z

measured 95 of 95 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T15:35:24.823836Z

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

91 of 91 outbound references displayed

verified exact7
verified fuzzy38
unresolved46
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

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

Outbound references

Observation fbb9e94e-4724-4b5b-a17a-df6072a4940b · outbound

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

Parameter Symmetry Potentially Unifies Deep Learning Theory Sgd learning on neural networks: leap complexity and saddle-to-saddle dynamics

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.762761Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0fa5db58-a585-4d2d-8338-1a896c4d37d4 · outbound

This paper cites Understanding intermediate layers using linear classifier probes.

Parameter Symmetry Potentially Unifies Deep Learning Theory Understanding intermediate layers using linear classifier probes

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.840740Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cdf6a915-c7de-4b25-880b-9a5bcdc5b5ef · outbound

This paper cites Negative eigenvalues of the Hessian in deep neural networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Negative eigenvalues of the Hessian in deep neural networks

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.888569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e2b513c0-a0e9-4cac-bfff-1554ad1eabe4 · outbound

This paper cites More is different: Broken symmetry and the nature of the hierarchical structure of science.

Parameter Symmetry Potentially Unifies Deep Learning Theory More is different: Broken symmetry and the nature of the hierarchical structure of science

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.897570Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e84e0daf-8005-4e49-82d7-113abc672980 · outbound

This paper cites The prevalence of neural collapse in neural multivariate regression.

Parameter Symmetry Potentially Unifies Deep Learning Theory The prevalence of neural collapse in neural multivariate regression

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.903734Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation abd5a8bc-4def-48d5-a4e1-b72d8947100f · outbound

This paper cites Thermal forces from a micro- scopic perspective.

Parameter Symmetry Potentially Unifies Deep Learning Theory Thermal forces from a micro- scopic perspective

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.911184Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b0430263-04f5-4855-ae3f-fd4448a80077 · outbound

This paper cites Neural Networks as Kernel Learners: The Silent Alignment Effect.

Parameter Symmetry Potentially Unifies Deep Learning Theory Neural Networks as Kernel Learners: The Silent Alignment Effect

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.917872Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9793350-deb5-4771-85fc-08d0cebcbacb · outbound

This paper cites Revisiting model stitching to compare neural representations.

Parameter Symmetry Potentially Unifies Deep Learning Theory Revisiting model stitching to compare neural representations

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.927928Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 09de887b-d52e-4a54-8fa5-026717370d41 · outbound

This paper cites Nearly-tight vc-dimension and pseudodimension bounds for piecewise linear neural networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Nearly-tight vc-dimension and pseudodimension bounds for piecewise linear neural networks

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.931858Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 90b23e28-6e07-4800-a5d8-3b47a599ee1d · outbound

This paper cites Representation learning: A review and new perspectives.

Parameter Symmetry Potentially Unifies Deep Learning Theory Representation learning: A review and new perspectives

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.935606Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0fbe2ccd-20b6-4fc0-ab03-14cdeb041108 · outbound

This paper cites Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges.

Parameter Symmetry Potentially Unifies Deep Learning Theory Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.939981Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4b0e55b-3a10-42cd-98ae-e70c325ebaf6 · outbound

This paper cites Stochastic Collapse: How Gradient Noise Attracts SGD Dynamics Towards Simpler Subnetworks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Stochastic Collapse: How Gradient Noise Attracts SGD Dynamics Towards Simpler Subnetworks

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-08T19:58:27.795012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3c788795-92da-4ab6-a283-1c306e49f781 · outbound

This paper cites On Lazy Training in Differentiable Programming.

Parameter Symmetry Potentially Unifies Deep Learning Theory On Lazy Training in Differentiable Programming

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.948535Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 39320332-5ae0-423f-86a8-b2440f25ad47 · outbound

This paper cites Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability.

Parameter Symmetry Potentially Unifies Deep Learning Theory Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.952588Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 19961cba-2e61-434a-872a-31d01e79c2c4 · outbound

This paper cites A kernel theory of modern data augmentation.

Parameter Symmetry Potentially Unifies Deep Learning Theory A kernel theory of modern data augmentation

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.956622Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f1525b9-7840-4905-96f6-892d1d58783b · outbound

This paper cites an unresolved cited work.

Parameter Symmetry Potentially Unifies Deep Learning Theory Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.960204Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11c9f8cf-a270-42f7-9359-3763d30833a2 · outbound

This paper cites An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale.

Parameter Symmetry Potentially Unifies Deep Learning Theory An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.963539Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ff311ab-441b-4304-9d1a-bbe0788ab887 · outbound

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

Parameter Symmetry Potentially Unifies Deep Learning Theory Algorithmic regularization in learning deep homogeneous models: Layers are automatically balanced

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.967069Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fdbeb665-d801-4bcc-8a41-376587748315 · outbound

This paper cites Why molecules move along a temperature gradient.

Parameter Symmetry Potentially Unifies Deep Learning Theory Why molecules move along a temperature gradient

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.970771Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cdb943ee-f0b3-468f-92d9-7f72fc7730b2 · outbound

This paper cites The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:25.973999Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a376c2a7-05d1-46ca-ba39-d57fae89a905 · outbound

This paper cites The representation theory of finite groups.

Parameter Symmetry Potentially Unifies Deep Learning Theory The representation theory of finite groups

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.006533Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4169e64c-e8f4-4592-84b0-13241ca2e1a5 · outbound

This paper cites Spontaneous Symmetry Breaking in Neural Networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Spontaneous Symmetry Breaking in Neural Networks

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-08T19:58:27.736581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6fa6e918-8115-48b7-929b-d35752a271fc · outbound

This paper cites A regularity condition of the information matrix of a multilayer perceptron network.

Parameter Symmetry Potentially Unifies Deep Learning Theory A regularity condition of the information matrix of a multilayer perceptron network

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.968538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b1dc4198-fa78-4955-899b-159ef9168f97 · outbound

This paper cites Local minima and plateaus in hierarchical structures of multilayer perceptrons.

Parameter Symmetry Potentially Unifies Deep Learning Theory Local minima and plateaus in hierarchical structures of multilayer perceptrons

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.248751Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ffae2493-54b9-48df-b30a-9c8b1ad6c152 · outbound

This paper cites On the Role of Neural Collapse in Transfer Learning.

Parameter Symmetry Potentially Unifies Deep Learning Theory On the Role of Neural Collapse in Transfer Learning

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.281082Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2da32e80-2fc6-4087-b0a0-4e39681af113 · outbound

This paper cites Norm-based Generalization Bounds for Compositionally Sparse Neural Networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Norm-based Generalization Bounds for Compositionally Sparse Neural Networks

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.287608Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4df2c74-8030-4e9d-8d83-3dfa0771e781 · outbound

This paper cites Stochastic Training is Not Necessary for Generalization.

Parameter Symmetry Potentially Unifies Deep Learning Theory Stochastic Training is Not Necessary for Generalization

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.292899Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef9fc4a5-d2b6-44de-8c06-d9a67e185918 · outbound

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

Parameter Symmetry Potentially Unifies Deep Learning Theory The Implicit Bias of Depth: How Incremental Learning Drives Generalization

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.299922Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d720ecd6-0036-4238-b7cb-07aa0aa7361b · outbound

This paper cites On the symmetries of deep learn- ing models and their internal representations.

Parameter Symmetry Potentially Unifies Deep Learning Theory On the symmetries of deep learn- ing models and their internal representations

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.952586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 110c634b-c307-48a8-b6ee-8de3875bbd1e · outbound

This paper cites The Platonic Representation Hypothesis.

Parameter Symmetry Potentially Unifies Deep Learning Theory The Platonic Representation Hypothesis

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.309237Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1df1b910-eea1-4f7e-b90a-91cc327d765f · outbound

This paper cites Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift.

Parameter Symmetry Potentially Unifies Deep Learning Theory Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.313348Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 60506ad6-3c9f-420e-a2a0-29a8d19b2ab5 · outbound

This paper cites Neural Tangent Kernel: Convergence and Generalization in Neural Networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Neural Tangent Kernel: Convergence and Generalization in Neural Networks

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.366078Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0835da8-74a9-4d74-b960-dd28cc4b84d8 · outbound

This paper cites Saddle-to-Saddle Dynamics in Deep Linear Networks: Small Initialization Training, Symmetry, and Sparsity.

Parameter Symmetry Potentially Unifies Deep Learning Theory Saddle-to-Saddle Dynamics in Deep Linear Networks: Small Initialization Training, Symmetry, and Sparsity

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.454460Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6e49f4c-baf7-4153-8aad-6de5f82cba47 · outbound

This paper cites Sgd on neural networks learns functions of increasing complexity.

Parameter Symmetry Potentially Unifies Deep Learning Theory Sgd on neural networks learns functions of increasing complexity

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.941148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e6cd0852-1bdd-4edd-8e26-659ecad58608 · outbound

This paper cites Weight decay induces low-rank attention layers.

Parameter Symmetry Potentially Unifies Deep Learning Theory Weight decay induces low-rank attention layers

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.557007Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 544fad2f-adca-4135-bd67-0e9a7ef93002 · outbound

This paper cites Similarity of neural network representations revisited.

Parameter Symmetry Potentially Unifies Deep Learning Theory Similarity of neural network representations revisited

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.562736Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6250652a-1005-48bb-b201-ccfe001bf837 · outbound

This paper cites Get rich quick: exact solutions reveal how unbalanced initializations promote rapid feature learning.

Parameter Symmetry Potentially Unifies Deep Learning Theory Get rich quick: exact solutions reveal how unbalanced initializations promote rapid feature learning

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.923284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4f519f3b-3803-4bf3-9ca3-2de54a38fd3e · outbound

This paper cites Rethinking the limiting dynamics of sgd: modified loss, phase space oscillations, and anomalous diffusion.

Parameter Symmetry Potentially Unifies Deep Learning Theory Rethinking the limiting dynamics of sgd: modified loss, phase space oscillations, and anomalous diffusion

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.912293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 456c805d-9502-40e4-96f5-88fb1a94a332 · outbound

This paper cites Statistical Physics: Volume 5 , volume 5.

Parameter Symmetry Potentially Unifies Deep Learning Theory Statistical Physics: Volume 5 , volume 5

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.574614Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f5290bd-32cd-4182-bb75-fda59fc30080 · outbound

This paper cites Neural network renormalization group.

Parameter Symmetry Potentially Unifies Deep Learning Theory Neural network renormalization group

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.895037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fb754d69-c8b8-42e4-a628-e39313cb3ef2 · outbound

This paper cites Symmetry, Saddle Points, and Global Optimization Landscape of Nonconvex Matrix Factorization.

Parameter Symmetry Potentially Unifies Deep Learning Theory Symmetry, Saddle Points, and Global Optimization Landscape of Nonconvex Matrix Factorization

Reference 41

Resolution: verified exact; local_arxiv, observed 2026-08-08T19:58:27.629445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c6ddf403-17cc-4e02-b6ab-32186839424e · outbound

This paper cites Reconciling modern deep learning with traditional op- timization analyses: The intrinsic learning rate.

Parameter Symmetry Potentially Unifies Deep Learning Theory Reconciling modern deep learning with traditional op- timization analyses: The intrinsic learning rate

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.884853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2c4dd624-9b6d-4444-b53c-1455317097e6 · outbound

This paper cites What happens after sgd reaches zero loss?–a mathe- matical framework.

Parameter Symmetry Potentially Unifies Deep Learning Theory What happens after sgd reaches zero loss?–a mathe- matical framework

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.874676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation afd92de6-9b39-4aba-860c-ad26593f4493 · outbound

This paper cites The Empirical Impact of Neural Parameter Symmetries, or Lack Thereof.

Parameter Symmetry Potentially Unifies Deep Learning Theory The Empirical Impact of Neural Parameter Symmetries, or Lack Thereof

Reference 44

Resolution: verified exact; local_arxiv, observed 2026-08-08T19:58:27.614501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f3e0bf8a-e24f-4158-a8fb-d551e69b26b6 · outbound

This paper cites Abide by the law and follow the flow: Conserva- tion laws for gradient flows.

Parameter Symmetry Potentially Unifies Deep Learning Theory Abide by the law and follow the flow: Conserva- tion laws for gradient flows

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.828220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 898d4dc3-f6a6-426f-9513-e5db7676fbcf · outbound

This paper cites Invariant and Equivariant Graph Networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Invariant and Equivariant Graph Networks

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.601242Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfda142d-1c66-4908-9c0c-dda9b81177a0 · outbound

This paper cites The tunnel effect: Building data representations in deep neural networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory The tunnel effect: Building data representations in deep neural networks

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.694619Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0db7458a-be17-4815-bfa6-e78cff579db5 · outbound

This paper cites Charge symmetry, quarks and mesons.

Parameter Symmetry Potentially Unifies Deep Learning Theory Charge symmetry, quarks and mesons

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.605574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation baf69777-51bf-421a-b154-3fdc7476cd58 · outbound

This paper cites Deep neural networks have an inbuilt occam’s razor.

Parameter Symmetry Potentially Unifies Deep Learning Theory Deep neural networks have an inbuilt occam’s razor

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.593785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 18a02589-0534-4f8f-b85a-64cbb8e78447 · outbound

This paper cites Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.724182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2aebb79-c594-4e82-9bf2-3c550279583c · outbound

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

Parameter Symmetry Potentially Unifies Deep Learning Theory In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.794022Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 67a462be-6771-4795-b213-328be8f3b68d · outbound

This paper cites On connected sublevel sets in deep learning.

Parameter Symmetry Potentially Unifies Deep Learning Theory On connected sublevel sets in deep learning

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.582580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation dbf40799-3e8b-4468-a31b-500aa07e46c2 · outbound

This paper cites Neural networks should be wide enough to learn disconnected decision regions.

Parameter Symmetry Potentially Unifies Deep Learning Theory Neural networks should be wide enough to learn disconnected decision regions

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.572413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0b336871-9644-47a4-906e-8f30d510ecc8 · outbound

This paper cites Prevalence of neural collapse during the terminal phase of deep learning training.

Parameter Symmetry Potentially Unifies Deep Learning Theory Prevalence of neural collapse during the terminal phase of deep learning training

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.560677Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 60496c21-2dc2-40c2-a278-1da106efc2c7 · outbound

This paper cites An introduction to quantum field theory.

Parameter Symmetry Potentially Unifies Deep Learning Theory An introduction to quantum field theory

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.549195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 32e4a70b-92df-4506-b716-770f59b22ddf · outbound

This paper cites On Generalization Bounds for Neural Networks with Low Rank Layers.

Parameter Symmetry Potentially Unifies Deep Learning Theory On Generalization Bounds for Neural Networks with Low Rank Layers

Reference 56

Resolution: verified exact; local_arxiv, observed 2026-08-08T19:58:27.570879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 618f192e-4796-40b4-aa21-f9bb670883da · outbound

This paper cites Cosmology and broken discrete symmetry.

Parameter Symmetry Potentially Unifies Deep Learning Theory Cosmology and broken discrete symmetry

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.537985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 703716d4-3c5a-4dd8-8cd9-1c9da2b03824 · outbound

This paper cites Neural collapse in deep homogeneous classifiers and the role of weight decay.

Parameter Symmetry Potentially Unifies Deep Learning Theory Neural collapse in deep homogeneous classifiers and the role of weight decay

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.527888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 73154d2c-26e7-4dd7-87d0-85267098e1ab · outbound

This paper cites Feature learning in deep classifiers through intermediate neural collapse.

Parameter Symmetry Potentially Unifies Deep Learning Theory Feature learning in deep classifiers through intermediate neural collapse

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.517575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e379ef95-079f-4e57-ab90-9bc29f88a4a2 · outbound

This paper cites Exact solutions to the nonlinear dynamics of learning in deep linear neural networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.835795Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8b10588b-ee63-4d89-aa7b-ea3ed7c11c06 · outbound

This paper cites On the Stepwise Nature of Self-Supervised Learning.

Parameter Symmetry Potentially Unifies Deep Learning Theory On the Stepwise Nature of Self-Supervised Learning

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.839502Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 10a9c39c-b4f6-44ff-bcda-4d942355da75 · outbound

This paper cites Geometry of the loss landscape in overparameterized neural networks: Symmetries and invariances.

Parameter Symmetry Potentially Unifies Deep Learning Theory Geometry of the loss landscape in overparameterized neural networks: Symmetries and invariances

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.506504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3bc75599-3baf-4d5f-b66d-7cd7fac037ac · outbound

This paper cites On the Origin of Implicit Regularization in Stochastic Gradient Descent.

Parameter Symmetry Potentially Unifies Deep Learning Theory On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.846533Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a5d911d4-e216-452e-98c7-84ce07ac8792 · outbound

This paper cites Noether’s learning dynamics: Role of symmetry breaking in neural networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Noether’s learning dynamics: Role of symmetry breaking in neural networks

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.496013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f675996b-90c8-4c06-b8fd-aa2866ec6b66 · outbound

This paper cites Optimizing mode connectivity via neuron alignment.Advances in Neural Information Processing Systems, 33:15300– 15311, 2020.

Parameter Symmetry Potentially Unifies Deep Learning Theory Optimizing mode connectivity via neuron alignment.Advances in Neural Information Processing Systems, 33:15300– 15311, 2020

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.458441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1c54e815-9fbc-4ddf-8101-e43ade21467d · outbound

This paper cites Equivalences between sparse models and neural networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Equivalences between sparse models and neural networks

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.378434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d514f935-1d64-400e-9fbb-14c1375cb4af · outbound

This paper cites The information bottleneck method.

Parameter Symmetry Potentially Unifies Deep Learning Theory The information bottleneck method

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:27.030727Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 62d34c9b-fee2-402a-b445-9d74a027b254 · outbound

This paper cites Deep learning and the information bottleneck principle.

Parameter Symmetry Potentially Unifies Deep Learning Theory Deep learning and the information bottleneck principle

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.278050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bc1831b4-c7d1-473b-b4f4-2df82f419471 · outbound

This paper cites Attention is all you need.

Parameter Symmetry Potentially Unifies Deep Learning Theory Attention is all you need

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:27.051405Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8b11102-9b4e-4e8c-ac4f-2ed442b955ce · outbound

This paper cites Asymptotic equivalence of bayes cross validation and widely applicable information criterion in singular learning theory.

Parameter Symmetry Potentially Unifies Deep Learning Theory Asymptotic equivalence of bayes cross validation and widely applicable information criterion in singular learning theory

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.248119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e1210920-b7e8-4909-8da9-7114c1221a0b · outbound

This paper cites Linguistic Collapse: Neural Collapse in (Large) Language Models.

Parameter Symmetry Potentially Unifies Deep Learning Theory Linguistic Collapse: Neural Collapse in (Large) Language Models

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:27.058975Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0b57a276-0e39-441c-97ff-e589130f5877 · outbound

This paper cites The janus effects of sgd vs gd: high noise and low rank.

Parameter Symmetry Potentially Unifies Deep Learning Theory The janus effects of sgd vs gd: high noise and low rank

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.236617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 67aeef13-5422-4f85-8dce-df450fb2d042 · outbound

This paper cites Removed for anonymity.

Parameter Symmetry Potentially Unifies Deep Learning Theory Removed for anonymity

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.225989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 97d1b892-f228-43fb-9d0b-1162e6f74a0b · outbound

This paper cites Three Mechanisms of Feature Learning in a Linear Network.

Parameter Symmetry Potentially Unifies Deep Learning Theory Three Mechanisms of Feature Learning in a Linear Network

Reference 74

Resolution: verified exact; local_arxiv, observed 2026-08-08T19:58:27.504143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e1193183-e1e0-4a58-92e4-fb33b9683e8f · outbound

This paper cites Performance-optimized hierarchical models predict neural responses in higher visual cortex.

Parameter Symmetry Potentially Unifies Deep Learning Theory Performance-optimized hierarchical models predict neural responses in higher visual cortex

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.214127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c537dd00-9eef-43a2-9640-cbb631fcc321 · outbound

This paper cites Feature Learning in Infinite-Width Neural Networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Feature Learning in Infinite-Width Neural Networks

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:27.079130Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1ad77583-9e71-477a-aeff-8cca6dce8487 · outbound

This paper cites Visualizing and understanding convolutional networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Visualizing and understanding convolutional networks

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.202908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ce01cb2b-f913-43a3-be7a-43c305ea4658 · outbound

This paper cites Understanding deep learning requires rethinking generalization.

Parameter Symmetry Potentially Unifies Deep Learning Theory Understanding deep learning requires rethinking generalization

Reference 78

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:27.086235Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation afd32a63-f25f-46c0-a847-6ae1a945278b · outbound

This paper cites Symmetry teleportation for accelerated opti- mization.

Parameter Symmetry Potentially Unifies Deep Learning Theory Symmetry teleportation for accelerated opti- mization

Reference 79

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.184718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6c11d115-8c1b-4c79-9f52-197843f2b0f3 · outbound

This paper cites Understanding mode connectivity via param- eter space symmetry.

Parameter Symmetry Potentially Unifies Deep Learning Theory Understanding mode connectivity via param- eter space symmetry

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.174227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0e132255-ffe7-4f2a-ae40-fefbecd25cd5 · outbound

This paper cites Improving Convergence and Generalization Using Parameter Symmetries.

Parameter Symmetry Potentially Unifies Deep Learning Theory Improving Convergence and Generalization Using Parameter Symmetries

Reference 81

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:27.096742Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 31cb38e9-0646-4d01-a54a-715e3bad237f · outbound

This paper cites Quadratic models for understanding catapult dynamics of neural networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Quadratic models for understanding catapult dynamics of neural networks

Reference 82

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:27.100942Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfcde326-caec-4264-a254-6f58443deeb0 · outbound

This paper cites Symmetry induces structure and constraint of learning.

Parameter Symmetry Potentially Unifies Deep Learning Theory Symmetry induces structure and constraint of learning

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.163906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c4a11f64-bc11-4224-ab6d-2b3d5c51fbc2 · outbound

This paper cites Formation of representations in neural networks.

Parameter Symmetry Potentially Unifies Deep Learning Theory Formation of representations in neural networks

Reference 84

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.153538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1fc5c95f-ee4a-4f0f-a201-fd92e0e64528 · outbound

This paper cites The probabilistic stability of stochastic gradient descent, 2023.

Parameter Symmetry Potentially Unifies Deep Learning Theory The probabilistic stability of stochastic gradient descent, 2023

Reference 85

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.142672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 64140146-7ba7-4918-934b-3957c4774f2d · outbound

This paper cites Parameter symmetry and noise equilibrium of stochastic gradient descent.

Parameter Symmetry Potentially Unifies Deep Learning Theory Parameter symmetry and noise equilibrium of stochastic gradient descent

Reference 86

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.131090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation aba9f7ed-3c4f-4259-be47-2b4a08e10013 · outbound

This paper cites Neural thermodynamics i: Entropic forces in deep and universal representation learning.

Parameter Symmetry Potentially Unifies Deep Learning Theory Neural thermodynamics i: Entropic forces in deep and universal representation learning

Reference 87

Resolution: verified exact; raw_fallback, observed 2026-08-08T19:58:27.389789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1f65beb9-de34-45fb-9379-d3b809dae6a2 · outbound

This paper cites Remove symmetries to control model expressivity.

Parameter Symmetry Potentially Unifies Deep Learning Theory Remove symmetries to control model expressivity

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:28.082683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation afeaa83c-6586-4a35-a8ec-e4d68a06e506 · outbound

This paper cites an unresolved cited work.

Parameter Symmetry Potentially Unifies Deep Learning Theory Unresolved cited work

Reference 89

Resolution: unresolved; raw_fallback, observed 2026-08-08T19:58:28.029857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d153e544-46d9-4131-b1c8-ddbf21638d23 · outbound

This paper cites Here, A ∶= PG ∑x∇θf(x, θ0)T∇θf(x, θ0)PG and A+ denotes the Moore–Penrose inverse of A.

Parameter Symmetry Potentially Unifies Deep Learning Theory Here, A ∶= PG ∑x∇θf(x, θ0)T∇θf(x, θ0)PG and A+ denotes the Moore–Penrose inverse of A

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:27.963863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7c9dc0bf-cb19-4a5b-ad97-1d34d7d79b35 · outbound

This paper cites (21) Therefore, g(x, θ) simplifies to a kernel model g(x, θ)=∇θ0 f(x, θ0)PGθ.

Parameter Symmetry Potentially Unifies Deep Learning Theory (21) Therefore, g(x, θ) simplifies to a kernel model g(x, θ)=∇θ0 f(x, θ0)PGθ

Reference 91

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T19:58:27.918485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

Observation fb451b88-15e2-4900-b577-343e509179c3 · inbound

Thermodynamic Irreversibility of Training Algorithms cites this paper.

Thermodynamic Irreversibility of Training Algorithms Parameter Symmetry Potentially Unifies Deep Learning Theory

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-22T04:41:04.261521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 304ba9d5-e647-474b-b3e4-323991dfb6b5 · inbound

Beyond Structural Symmetries: Linear Mode Connectivity via Neuron Identifiability cites this paper.

Beyond Structural Symmetries: Linear Mode Connectivity via Neuron Identifiability Parameter Symmetry Potentially Unifies Deep Learning Theory

Reference 39

Resolution: verified exact; arxiv_id, observed 2026-06-28T07:31:44.820712Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c2521a33-80e7-40bc-b476-70eada18c351 · inbound

Observable- and Positional-Encoding-Dependent Symmetry Readout from Neural Network Weights cites this paper.

Observable- and Positional-Encoding-Dependent Symmetry Readout from Neural Network Weights Parameter Symmetry Potentially Unifies Deep Learning Theory

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-12T04:51:08.903724Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bba359f4-e947-4753-9606-1fc1a34c5940 · inbound

PAC--Bayes Bounds on Quotient Parameter Spaces: Geometry-induced Implicit-Bias Priors cites this paper.

PAC--Bayes Bounds on Quotient Parameter Spaces: Geometry-induced Implicit-Bias Priors Parameter Symmetry Potentially Unifies Deep Learning Theory

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T15:35:24.823836Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.