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@unpublished{Beneventano_2023_On,
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 title = {On the Trajectories of {SGD} Without Replacement},
 year = {2023},
 month = {dec},
 url = {https://arxiv.org/abs/2312.16143},
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@unpublished{Montanari_2024_On,
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@unpublished{Urbani_2024_Statistical,
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@unpublished{Vivo_2024_Random,
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 volume = {32},
 pages = {},
 url = {https://proceedings.neurips.cc/paper_files/paper/2019/file/fbad540b2f3b5638a9be9aa6a4d8e450-Paper.pdf},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {Wallach, H. and Larochelle, H. and Beygelzimer, A. and d'Alché-Buc, F. and Fox, E. and Garnett, R.}
}

@inproceedings{SaraoMannelli_2019_Passed,
 author = {Sarao Mannelli, Stefano and Krzakala, Florent and Urbani, Pierfrancesco and Zdeborová, Lenka},
 title = {Passed \& Spurious: Descent Algorithms and Local Minima in Spiked Matrix-Tensor Models},
 publisher = {PMLR},
 year = {2019},
 month = {09--15 Jun},
 volume = {97},
 pages = {4333--4342},
 url = {https://proceedings.mlr.press/v97/mannelli19a.html},
 abstract = {In this work we analyse quantitatively the interplay between the loss landscape and performance of descent algorithms in a prototypical inference problem, the spiked matrix-tensor model. We study a loss function that is the negative log-likelihood of the model. We analyse the number of local minima at a fixed distance from the signal/spike with the Kac-Rice formula, and locate trivialization of the landscape at large signal-to-noise ratios. We evaluate analytically the performance of a gradient flow algorithm using integro-differential PDEs as developed in physics of disordered systems for the Langevin dynamics. We analyze the performance of an approximate message passing algorithm estimating the maximum likelihood configuration via its state evolution. We conclude by comparing the above results: while we observe a drastic slow down of the gradient flow dynamics even in the region where the landscape is trivial, both the analyzed algorithms are shown to perform well even in the part of the region of parameters where spurious local minima are present.},
 booktitle = {Proceedings of the 36th International Conference on Machine Learning},
 editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
 pdf = {https://proceedings.mlr.press/v97/mannelli19a/mannelli19a.pdf},
 series = {Proceedings of Machine Learning Research}
}

@unpublished{ElAlaoui_2020_Algorithmic,
 author = {El Alaoui, Ahmed and Montanari, Andrea},
 title = {Algorithmic Thresholds in Mean Field Spin Glasses},
 year = {2020},
 month = {Sept},
 url = {https://arxiv.org/abs/2009.11481},
 archiveprefix = {arXiv},
 date = {2020-09-24T04:22:42Z},
 eprint = {2009.11481},
 eprintclass = {cond-mat.stat-mech},
 eprinttype = {arxiv},
 note = {ArXiv preprint},
 primaryclass = {cond-mat.stat-mech}
}

@article{ElAlaoui_2021_Optimization,
 author = {El Alaoui, Ahmed and Montanari, Andrea and Sellke, Mark},
 title = {Optimization of mean-field spin glasses},
 journal = {The Annals of Probability},
 publisher = {Institute of Mathematical Statistics},
 year = {2021},
 month = {11},
 number = {6},
 volume = {49},
 pages = {2922--2960},
 url = {https://doi.org/10.1214%2F21-aop1519},
 doi = {10.1214/21-aop1519}
}

@article{Gamarnik_2021-10_The,
 author = {Gamarnik, David},
 title = {The overlap gap property: A topological barrier to optimizing over random structures},
 journal = {Proceedings of the National Academy of Sciences},
 publisher = {Proceedings of the National Academy of Sciences},
 year = {2021},
 month = {October},
 number = {41},
 volume = {118},
 pages = {e2108492118},
 url = {https://dx.doi.org/10.1073/pnas.2108492118},
 doi = {10.1073/pnas.2108492118},
 issn = {1091-6490}
}

@inproceedings{Wang_2023_Plateau,
 author = {Wang, Xiang and Wang, Annie N. and Zhou, Mo and Ge, Rong},
 title = {Plateau in Monotonic Linear Interpolation --- A ``Biased'' View of Loss Landscape for Deep Networks},
 year = {2023},
 url = {https://openreview.net/forum?id=z289SIQOQna},
 booktitle = {The Eleventh International Conference on Learning Representations }
}

@inproceedings{Vlaar_2022_What,
 author = {Vlaar, Tiffany J and Frankle, Jonathan},
 title = {What Can Linear Interpolation of Neural Network Loss Landscapes Tell Us?},
 publisher = {PMLR},
 year = {2022},
 month = {17--23 Jul},
 volume = {162},
 pages = {22325--22341},
 url = {https://proceedings.mlr.press/v162/vlaar22a.html},
 abstract = {Studying neural network loss landscapes provides insights into the nature of the underlying optimization problems. Unfortunately, loss landscapes are notoriously difficult to visualize in a human-comprehensible fashion. One common way to address this problem is to plot linear slices of the landscape, for example from the initial state of the network to the final state after optimization. On the basis of this analysis, prior work has drawn broader conclusions about the difficulty of the optimization problem. In this paper, we put inferences of this kind to the test, systematically evaluating how linear interpolation and final performance vary when altering the data, choice of initialization, and other optimizer and architecture design choices. Further, we use linear interpolation to study the role played by individual layers and substructures of the network. We find that certain layers are more sensitive to the choice of initialization, but that the shape of the linear path is not indicative of the changes in test accuracy of the model. Our results cast doubt on the broader intuition that the presence or absence of barriers when interpolating necessarily relates to the success of optimization.},
 booktitle = {Proceedings of the 39th International Conference on Machine Learning},
 editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
 pdf = {https://proceedings.mlr.press/v162/vlaar22a/vlaar22a.pdf},
 series = {Proceedings of Machine Learning Research}
}

@unpublished{Goodfellow_2014_Qualitatively,
 author = {Goodfellow, Ian J. and Vinyals, Oriol and Saxe, Andrew M.},
 title = {Qualitatively characterizing neural network optimization problems},
 year = {2014},
 month = {dec},
 url = {http://arxiv.org/abs/1412.6544},
 date = {2014-12-19T21:55:01Z},
 eprint = {1412.6544},
 note = {ArXiv preprint},
 eprintclass = {cs.NE},
 eprinttype = {arxiv},
 urldate = {2025-02-13T19:29:53.705054Z}
}

@inproceedings{Draxler_2018_Essentially,
 author = {Draxler, Felix and Veschgini, Kambis and Salmhofer, Manfred and Hamprecht, Fred},
 title = {Essentially No Barriers in Neural Network Energy Landscape},
 publisher = {PMLR},
 year = {2018},
 month = {10--15 Jul},
 volume = {80},
 pages = {1309--1318},
 url = {https://proceedings.mlr.press/v80/draxler18a.html},
 abstract = {Training neural networks involves finding minima of a high-dimensional non-convex loss function. Relaxing from linear interpolations, we construct continuous paths between minima of recent neural network architectures on CIFAR10 and CIFAR100. Surprisingly, the paths are essentially flat in both the training and test landscapes. This implies that minima are perhaps best seen as points on a single connected manifold of low loss, rather than as the bottoms of distinct valleys.},
 booktitle = {Proceedings of the 35th International Conference on Machine Learning},
 editor = {Dy, Jennifer and Krause, Andreas},
 pdf = {http://proceedings.mlr.press/v80/draxler18a/draxler18a.pdf},
 series = {Proceedings of Machine Learning Research}
}

@unpublished{Frankle_2020_Revisiting,
 author = {Frankle, Jonathan},
 title = {Revisiting ``Qualitatively Characterizing Neural Network Optimization Problems''},
 year = {2020},
 month = {dec},
 url = {http://arxiv.org/abs/2012.06898},
 date = {2020-12-12T20:01:33Z},
 eprint = {2012.06898},
 note = {ArXiv preprint},
 eprintclass = {cs.LG},
 eprinttype = {arxiv},
 urldate = {2025-02-13T19:32:17.287212Z}
}