ResearchTrend.AI
  • Communities
  • Connect sessions
  • AI calendar
  • Organizations
  • Join Slack
  • Contact Sales
Papers
Communities
Social Events
Terms and Conditions
Pricing
Contact Sales
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2026 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 2006.09313
  4. Cited By
Hausdorff Dimension, Heavy Tails, and Generalization in Neural Networks
v1v2v3 (latest)

Hausdorff Dimension, Heavy Tails, and Generalization in Neural Networks

16 June 2020
Umut Simsekli
Ozan Sener
George Deligiannidis
Murat A. Erdogdu
ArXiv (abs)PDFHTML

Papers citing "Hausdorff Dimension, Heavy Tails, and Generalization in Neural Networks"

49 / 49 papers shown
Geometric Properties of Neural Multivariate Regression
Geometric Properties of Neural Multivariate Regression
George Andriopoulos
Zixuan Dong
Bimarsha Adhikari
Keith Ross
187
1
0
01 Oct 2025
Optimal Condition for Initialization Variance in Deep Neural Networks: An SGD Dynamics Perspective
Optimal Condition for Initialization Variance in Deep Neural Networks: An SGD Dynamics Perspective
Hiroshi Horii
Sothea Has
140
0
0
18 Aug 2025
Eigenspectrum Analysis of Neural Networks without Aspect Ratio Bias
Eigenspectrum Analysis of Neural Networks without Aspect Ratio Bias
Yuanzhe Hu
Kinshuk Goel
Vlad Killiakov
Yaoqing Yang
511
5
0
06 Jun 2025
Generalization Guarantees for Multi-View Representation Learning and Application to Regularization via Gaussian Product Mixture Prior
Generalization Guarantees for Multi-View Representation Learning and Application to Regularization via Gaussian Product Mixture Prior
Romain Chor
Abdellatif Zaidi
Piotr Krasnowski
331
2
0
25 Apr 2025
Short-PHD: Detecting Short LLM-generated Text with Topological Data Analysis After Off-topic Content Insertion
Short-PHD: Detecting Short LLM-generated Text with Topological Data Analysis After Off-topic Content Insertion
Dongjun Wei
Minjia Mao
Xiao Fang
Michael Chau
DeLMO
374
4
0
01 Apr 2025
Almost Bayesian: The Fractal Dynamics of Stochastic Gradient Descent
Almost Bayesian: The Fractal Dynamics of Stochastic Gradient Descent
Max Hennick
Stijn De Baerdemacker
277
3
0
28 Mar 2025
Generalization Guarantees for Representation Learning via Data-Dependent Gaussian Mixture Priors
Generalization Guarantees for Representation Learning via Data-Dependent Gaussian Mixture PriorsInternational Conference on Learning Representations (ICLR), 2025
Romain Chor
Milad Sefidgaran
Piotr Krasnowski
611
3
0
21 Feb 2025
Model Balancing Helps Low-data Training and Fine-tuning
Model Balancing Helps Low-data Training and Fine-tuningConference on Empirical Methods in Natural Language Processing (EMNLP), 2024
Zihang Liu
Yihan Hu
Tianyu Pang
Yefan Zhou
Pu Ren
Yaoqing Yang
256
10
0
16 Oct 2024
From Spikes to Heavy Tails: Unveiling the Spectral Evolution of Neural Networks
From Spikes to Heavy Tails: Unveiling the Spectral Evolution of Neural Networks
Vignesh Kothapalli
Tianyu Pang
Shenyang Deng
Zongmin Liu
Yaoqing Yang
454
4
0
07 Jun 2024
Slicing Mutual Information Generalization Bounds for Neural Networks
Slicing Mutual Information Generalization Bounds for Neural Networks
Kimia Nadjahi
Kristjan Greenewald
Rickard Brüel-Gabrielsson
Justin Solomon
266
5
0
06 Jun 2024
On the Limitations of Fractal Dimension as a Measure of Generalization
On the Limitations of Fractal Dimension as a Measure of Generalization
Charlie Tan
Inés García-Redondo
Qiquan Wang
M. Bronstein
Anthea Monod
AI4CE
262
2
0
04 Jun 2024
Uniform Generalization Bounds on Data-Dependent Hypothesis Sets via PAC-Bayesian Theory on Random Sets
Uniform Generalization Bounds on Data-Dependent Hypothesis Sets via PAC-Bayesian Theory on Random Sets
Benjamin Dupuis
Paul Viallard
George Deligiannidis
Umut Simsekli
381
6
0
26 Apr 2024
Tracking the Median of Gradients with a Stochastic Proximal Point Method
Tracking the Median of Gradients with a Stochastic Proximal Point Method
Fabian Schaipp
Guillaume Garrigos
Umut Simsekli
Robert M. Gower
376
1
0
20 Feb 2024
Tighter Generalisation Bounds via Interpolation
Tighter Generalisation Bounds via Interpolation
Paul Viallard
Maxime Haddouche
Umut Simsekli
Benjamin Guedj
347
4
0
07 Feb 2024
Minimum Description Length and Generalization Guarantees for
  Representation Learning
Minimum Description Length and Generalization Guarantees for Representation LearningNeural Information Processing Systems (NeurIPS), 2024
Romain Chor
Abdellatif Zaidi
Piotr Krasnowski
376
13
0
05 Feb 2024
Emergence of heavy tails in homogenized stochastic gradient descent
Emergence of heavy tails in homogenized stochastic gradient descent
Zhe Jiao
Martin Keller-Ressel
213
3
0
02 Feb 2024
From Mutual Information to Expected Dynamics: New Generalization Bounds
  for Heavy-Tailed SGD
From Mutual Information to Expected Dynamics: New Generalization Bounds for Heavy-Tailed SGD
Benjamin Dupuis
Paul Viallard
367
4
0
01 Dec 2023
Temperature Balancing, Layer-wise Weight Analysis, and Neural Network
  Training
Temperature Balancing, Layer-wise Weight Analysis, and Neural Network TrainingNeural Information Processing Systems (NeurIPS), 2023
Yefan Zhou
Tianyu Pang
Keqin Liu
Charles H. Martin
Michael W. Mahoney
Yaoqing Yang
476
18
0
01 Dec 2023
Approximate Heavy Tails in Offline (Multi-Pass) Stochastic Gradient
  Descent
Approximate Heavy Tails in Offline (Multi-Pass) Stochastic Gradient DescentNeural Information Processing Systems (NeurIPS), 2023
Krunoslav Lehman Pavasovic
Alain Durmus
Umut Simsekli
OffRL
237
3
0
27 Oct 2023
Generalization Guarantees via Algorithm-dependent Rademacher Complexity
Generalization Guarantees via Algorithm-dependent Rademacher ComplexityAnnual Conference Computational Learning Theory (COLT), 2023
Sarah Sachs
T. Erven
Liam Hodgkinson
Rajiv Khanna
Umut Simsekli
322
7
0
04 Jul 2023
Deep neural networks architectures from the perspective of manifold
  learning
Deep neural networks architectures from the perspective of manifold learning
German Magai
AAMLAI4CE
273
9
0
06 Jun 2023
Metric Space Magnitude and Generalisation in Neural Networks
Metric Space Magnitude and Generalisation in Neural Networks
R. Andreeva
K. Limbeck
Bastian Rieck
Rik Sarkar
OOD
266
13
0
09 May 2023
Heavy-Tailed Regularization of Weight Matrices in Deep Neural Networks
Heavy-Tailed Regularization of Weight Matrices in Deep Neural NetworksInternational Conference on Artificial Neural Networks (ICANN), 2023
Xuanzhe Xiao
Zengyi Li
Chuanlong Xie
Fengwei Zhou
373
5
0
06 Apr 2023
Efficient Sampling of Stochastic Differential Equations with Positive
  Semi-Definite Models
Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite ModelsNeural Information Processing Systems (NeurIPS), 2023
Anant Raj
Umut Simsekli
Alessandro Rudi
DiffM
457
3
0
30 Mar 2023
Heterogeneous Neuronal and Synaptic Dynamics for Spike-Efficient
  Unsupervised Learning: Theory and Design Principles
Heterogeneous Neuronal and Synaptic Dynamics for Spike-Efficient Unsupervised Learning: Theory and Design PrinciplesInternational Conference on Learning Representations (ICLR), 2023
Biswadeep Chakraborty
Saibal Mukhopadhyay
252
14
0
22 Feb 2023
Cyclic and Randomized Stepsizes Invoke Heavier Tails in SGD than
  Constant Stepsize
Cyclic and Randomized Stepsizes Invoke Heavier Tails in SGD than Constant Stepsize
Mert Gurbuzbalaban
Yuanhan Hu
Umut Simsekli
Lingjiong Zhu
LRM
390
2
0
10 Feb 2023
Generalization Bounds with Data-dependent Fractal Dimensions
Generalization Bounds with Data-dependent Fractal DimensionsInternational Conference on Machine Learning (ICML), 2023
Benjamin Dupuis
George Deligiannidis
Umut cSimcsekli
AI4CE
253
16
0
06 Feb 2023
Algorithmic Stability of Heavy-Tailed SGD with General Loss Functions
Algorithmic Stability of Heavy-Tailed SGD with General Loss FunctionsInternational Conference on Machine Learning (ICML), 2023
Anant Raj
Lingjiong Zhu
Mert Gurbuzbalaban
Umut Simsekli
276
21
0
27 Jan 2023
Two Facets of SDE Under an Information-Theoretic Lens: Generalization of
  SGD via Training Trajectories and via Terminal States
Two Facets of SDE Under an Information-Theoretic Lens: Generalization of SGD via Training Trajectories and via Terminal StatesConference on Uncertainty in Artificial Intelligence (UAI), 2022
Ziqiao Wang
Yongyi Mao
383
12
0
19 Nov 2022
Neural Networks Efficiently Learn Low-Dimensional Representations with
  SGD
Neural Networks Efficiently Learn Low-Dimensional Representations with SGDInternational Conference on Learning Representations (ICLR), 2022
Alireza Mousavi-Hosseini
Sejun Park
M. Girotti
Ioannis Mitliagkas
Murat A. Erdogdu
MLT
650
65
0
29 Sep 2022
Generalization Bounds for Stochastic Gradient Descent via Localized
  $\varepsilon$-Covers
Generalization Bounds for Stochastic Gradient Descent via Localized ε\varepsilonε-CoversNeural Information Processing Systems (NeurIPS), 2022
Sejun Park
Umut Simsekli
Murat A. Erdogdu
231
10
0
19 Sep 2022
Trajectory-dependent Generalization Bounds for Deep Neural Networks via
  Fractional Brownian Motion
Trajectory-dependent Generalization Bounds for Deep Neural Networks via Fractional Brownian Motion
Chengli Tan
Jiang Zhang
Junmin Liu
255
1
0
09 Jun 2022
Rate-Distortion Theoretic Bounds on Generalization Error for Distributed
  Learning
Rate-Distortion Theoretic Bounds on Generalization Error for Distributed LearningNeural Information Processing Systems (NeurIPS), 2022
Romain Chor
Abdellatif Zaidi
Milad Sefidgaran
FedML
336
18
0
06 Jun 2022
Algorithmic Stability of Heavy-Tailed Stochastic Gradient Descent on
  Least Squares
Algorithmic Stability of Heavy-Tailed Stochastic Gradient Descent on Least SquaresInternational Conference on Algorithmic Learning Theory (ALT), 2022
Anant Raj
Melih Barsbey
Mert Gurbuzbalaban
Lingjiong Zhu
Umut Simsekli
299
13
0
02 Jun 2022
Generalization Bounds for Gradient Methods via Discrete and Continuous
  Prior
Generalization Bounds for Gradient Methods via Discrete and Continuous PriorNeural Information Processing Systems (NeurIPS), 2022
Jun Yu Li
Xu Luo
Jian Li
378
4
0
27 May 2022
Chaotic Regularization and Heavy-Tailed Limits for Deterministic
  Gradient Descent
Chaotic Regularization and Heavy-Tailed Limits for Deterministic Gradient DescentNeural Information Processing Systems (NeurIPS), 2022
Soon Hoe Lim
Yijun Wan
Umut cSimcsekli
296
14
0
23 May 2022
Heavy-Tail Phenomenon in Decentralized SGD
Heavy-Tail Phenomenon in Decentralized SGDIISE Transactions (IISE Trans.), 2022
Mert Gurbuzbalaban
Yuanhan Hu
Umut Simsekli
Kun Yuan
Lingjiong Zhu
399
14
0
13 May 2022
Topology and geometry of data manifold in deep learning
Topology and geometry of data manifold in deep learning
German Magai
A. Ayzenberg
AAML
297
13
0
19 Apr 2022
Predicting the generalization gap in neural networks using topological
  data analysis
Predicting the generalization gap in neural networks using topological data analysisNeurocomputing (Neurocomputing), 2022
Rubén Ballester
Xavier Arnal Clemente
Carles Casacuberta
Meysam Madadi
C. Corneanu
Sergio Escalera
326
12
0
23 Mar 2022
Rate-Distortion Theoretic Generalization Bounds for Stochastic Learning
  Algorithms
Rate-Distortion Theoretic Generalization Bounds for Stochastic Learning AlgorithmsAnnual Conference Computational Learning Theory (COLT), 2022
Romain Chor
A. Gohari
Gaël Richard
Umut Simsekli
342
28
0
04 Mar 2022
On the Hidden Biases of Policy Mirror Ascent in Continuous Action Spaces
On the Hidden Biases of Policy Mirror Ascent in Continuous Action SpacesInternational Conference on Machine Learning (ICML), 2022
Amrit Singh Bedi
Souradip Chakraborty
Anjaly Parayil
Brian M Sadler
Erfaun Noorani
Alec Koppel
392
20
0
28 Jan 2022
Intrinsic Dimension, Persistent Homology and Generalization in Neural
  Networks
Intrinsic Dimension, Persistent Homology and Generalization in Neural NetworksNeural Information Processing Systems (NeurIPS), 2021
Tolga Birdal
Aaron Lou
Leonidas Guibas
Umut cSimcsekli
300
86
0
25 Nov 2021
On the Sample Complexity and Metastability of Heavy-tailed Policy Search
  in Continuous Control
On the Sample Complexity and Metastability of Heavy-tailed Policy Search in Continuous Control
Amrit Singh Bedi
Anjaly Parayil
Junyu Zhang
Mengdi Wang
Alec Koppel
215
20
0
15 Jun 2021
Fractal Structure and Generalization Properties of Stochastic
  Optimization Algorithms
Fractal Structure and Generalization Properties of Stochastic Optimization AlgorithmsNeural Information Processing Systems (NeurIPS), 2021
A. Camuto
George Deligiannidis
Murat A. Erdogdu
Mert Gurbuzbalaban
Umut cSimcsekli
Lingjiong Zhu
179
32
0
09 Jun 2021
Heavy Tails in SGD and Compressibility of Overparametrized Neural
  Networks
Heavy Tails in SGD and Compressibility of Overparametrized Neural NetworksNeural Information Processing Systems (NeurIPS), 2021
Melih Barsbey
Romain Chor
Murat A. Erdogdu
Gaël Richard
Umut Simsekli
311
51
0
07 Jun 2021
Characterization of Generalizability of Spike Timing Dependent
  Plasticity trained Spiking Neural Networks
Characterization of Generalizability of Spike Timing Dependent Plasticity trained Spiking Neural NetworksFrontiers in Neuroscience (Front. Neurosci.), 2021
Biswadeep Chakraborty
Saibal Mukhopadhyay
285
18
0
31 May 2021
A Fully Spiking Hybrid Neural Network for Energy-Efficient Object
  Detection
A Fully Spiking Hybrid Neural Network for Energy-Efficient Object DetectionIEEE Transactions on Image Processing (TIP), 2021
Biswadeep Chakraborty
Xueyuan She
Saibal Mukhopadhyay
293
61
0
21 Apr 2021
Strength of Minibatch Noise in SGD
Strength of Minibatch Noise in SGDInternational Conference on Learning Representations (ICLR), 2021
Liu Ziyin
Kangqiao Liu
Takashi Mori
Masakuni Ueda
ODLMLT
395
44
0
10 Feb 2021
Noise and Fluctuation of Finite Learning Rate Stochastic Gradient
  Descent
Noise and Fluctuation of Finite Learning Rate Stochastic Gradient Descent
Kangqiao Liu
Liu Ziyin
Masakuni Ueda
MLT
553
45
0
07 Dec 2020
1
Page 1 of 1