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There are many surprising and perhaps counter-intuitive properties of optimization of deep neural networks. We propose and experimentally verify a unified phenomenological model of the loss landscape that incorporates many of them. High…

Machine Learning · Computer Science 2019-06-12 Stanislav Fort , Stanislaw Jastrzebski

Characterizing the loss of a neural network with respect to model parameters, i.e., the loss landscape, can provide valuable insights into properties of that model. Various methods for visualizing loss landscapes have been proposed, but…

Deep learning involves navigating a high-dimensional loss landscape over the neural network parameter space. Over the course of training, complex computational structures form and re-form inside the neural network, leading to shifts in…

Machine Learning · Computer Science 2025-08-04 Jesse Hoogland , George Wang , Matthew Farrugia-Roberts , Liam Carroll , Susan Wei , Daniel Murfet

We extend the concept of loss landscape mode connectivity to the input space of deep neural networks. Mode connectivity was originally studied within parameter space, where it describes the existence of low-loss paths between different…

Machine Learning · Computer Science 2024-09-10 Jakub Vrabel , Ori Shem-Ur , Yaron Oz , David Krueger

Model merging combines the parameters of multiple neural networks into a single model without additional training. As fine-tuned large language models (LLMs) proliferate, merging offers a computationally efficient alternative to ensembles…

Computation and Language · Computer Science 2026-03-31 Mingyang Song , Mao Zheng

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…

Disordered Systems and Neural Networks · Physics 2020-03-18 Simon Becker , Yao Zhang , Alpha A. Lee

The ability to explain decisions made by machine learning models remains one of the most significant hurdles towards widespread adoption of AI in highly sensitive areas such as medicine, cybersecurity or autonomous driving. Great interest…

Machine Learning · Computer Science 2024-12-17 Maximilian P Niroomand , David J Wales

Model merging combines knowledge from separately fine-tuned models, yet the factors driving its success remain poorly understood. While recent work treats mergeability as an intrinsic property of the models, we show with an…

Machine Learning · Computer Science 2026-05-27 Luca Zhou , Bo Zhao , Rose Yu , Emanuele Rodolà

Understanding the geometry of neural network loss landscapes is a central question in deep learning, with implications for generalization and optimization. A striking phenomenon is linear mode connectivity (LMC), where independently trained…

Machine Learning · Computer Science 2025-11-14 Alexander Theus , Alessandro Cabodi , Sotiris Anagnostidis , Antonio Orvieto , Sidak Pal Singh , Valentina Boeva

Despite their effective use in various fields, many aspects of neural networks are poorly understood. One important way to investigate the characteristics of neural networks is to explore the loss landscape. However, most models produce a…

Machine Learning · Computer Science 2022-04-12 Aleksandar Doknic , Torsten Möller

In machine learning, a loss function measures the difference between model predictions and ground-truth (or target) values. For neural network models, visualizing how this loss changes as model parameters are varied can provide insights…

Neural networks have greatly boosted performance in computer vision by learning powerful representations of input data. The drawback of end-to-end training for maximal overall performance are black-box models whose hidden representations…

Computer Vision and Pattern Recognition · Computer Science 2020-04-29 Patrick Esser , Robin Rombach , Björn Ommer

Deep model fusion/merging is an emerging technique that merges the parameters or predictions of multiple deep learning models into a single one. It combines the abilities of different models to make up for the biases and errors of a single…

Machine Learning · Computer Science 2023-09-28 Weishi Li , Yong Peng , Miao Zhang , Liang Ding , Han Hu , Li Shen

Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…

Machine Learning · Computer Science 2025-03-11 Michael Wienczkowski , Addisu Desta , Paschal Ugochukwu

The loss landscapes of deep neural networks are not well understood due to their high nonconvexity. Empirically, the local minima of these loss functions can be connected by a learned curve in model space, along which the loss remains…

Machine Learning · Computer Science 2020-12-11 N. Joseph Tatro , Pin-Yu Chen , Payel Das , Igor Melnyk , Prasanna Sattigeri , Rongjie Lai

As the discipline has evolved, research in machine learning has been focused more and more on creating more powerful neural networks, without regard for the interpretability of these networks. Such "black-box models" yield state-of-the-art…

Machine Learning · Computer Science 2021-09-02 Lachlan O'Neill , Simon Angus , Satya Borgohain , Nader Chmait , David L. Dowe

The clear understanding of the non-convex landscape of neural network is a complex incomplete problem. This paper studies the landscape of linear (residual) network, the simplified version of the nonlinear network. By treating the gradient…

Algebraic Geometry · Mathematics 2021-02-09 Xiuyi Yang

The proliferation of deep neural networks in various domains has seen an increased need for interpretability of these models. Preliminary work done along this line and papers that surveyed such, are focused on high-level representation…

Computation and Language · Computer Science 2022-08-17 Hassan Sajjad , Nadir Durrani , Fahim Dalvi

Recent work has established clear links between the generalization performance of trained neural networks and the geometry of their loss landscape near the local minima to which they converge. This suggests that qualitative and quantitative…

Machine Learning · Computer Science 2022-01-28 Stefan Horoi , Jessie Huang , Bastian Rieck , Guillaume Lajoie , Guy Wolf , Smita Krishnaswamy

Decomposing a deep neural network's learned representations into interpretable features could greatly enhance its safety and reliability. To better understand features, we adopt a geometric perspective, viewing them as a learned coordinate…

Machine Learning · Computer Science 2025-04-30 Aryeh Brill
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