Low-Loss Space in Neural Networks is Continuous and Fully Connected

• URL: http://arxiv.org/abs/2505.02604v3
• Date: Wed, 11 Jun 2025 01:28:36 GMT
• Title: Low-Loss Space in Neural Networks is Continuous and Fully Connected
• Authors: Yongding Tian, Zaid Al-Ars, Maksim Kitsak, Peter Hofstee,
• Abstract summary: We show that it is possible to connect two different minima with a path consisting of intermediate points that also have low loss.<n>Our work also provides new visualization methods and opportunities to improve model generalization.
• Score: 0.8212195887472242
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Visualizations of the loss landscape in neural networks suggest that minima are isolated points. However, both theoretical and empirical studies indicate that it is possible to connect two different minima with a path consisting of intermediate points that also have low loss. In this study, we propose a new algorithm which investigates low-loss paths in the full parameter space, not only between two minima. Our experiments on LeNet5, ResNet18, and Compact Convolutional Transformer architectures consistently demonstrate the existence of such continuous paths in the parameter space. These results suggest that the low-loss region is a fully connected and continuous space in the parameter space. Our findings provide theoretical insight into neural network over-parameterization, highlighting that parameters collectively define a high-dimensional low-loss space, implying parameter redundancy exists only within individual models and not throughout the entire low-loss space. Additionally, our work also provides new visualization methods and opportunities to improve model generalization by exploring the low-loss space that is closer to the origin.

Related papers

• NExT-OMNI: Towards Any-to-Any Omnimodal Foundation Models with Discrete Flow Matching [64.10695425442164]
  We introduce NExT-OMNI, an open-source omnimodal foundation model that achieves unified modeling through discrete flow paradigms.<n>Trained on large-scale interleaved text, image, video, and audio data, NExT-OMNI delivers competitive performance on multimodal generation and understanding benchmarks.<n>To advance further research, we release training details, data protocols, and open-source both the code and model checkpoints.
  arXiv  Detail & Related papers  (2025-10-15T16:25:18Z)
• In-Context Learning for Gradient-Free Receiver Adaptation: Principles, Applications, and Theory [54.92893355284945]
  Deep learning-based wireless receivers offer the potential to dynamically adapt to varying channel environments.<n>Current adaptation strategies, including joint training, hypernetwork-based methods, and meta-learning, either demonstrate limited flexibility or necessitate explicit optimization through gradient descent.<n>This paper presents gradient-free adaptation techniques rooted in the emerging paradigm of in-context learning (ICL)
  arXiv  Detail & Related papers  (2025-06-18T06:43:55Z)
• Simplicity Bias via Global Convergence of Sharpness Minimization [43.658859631741024]
  We show that label noise SGD always minimizes the sharpness on the manifold of models with zero loss for two-layer networks. We also find a novel property of the trace of Hessian of the loss at approximate stationary points on the manifold of zero loss.
  arXiv  Detail & Related papers  (2024-10-21T18:10:37Z)
• A simple connection from loss flatness to compressed neural representations [3.5502600490147196]
  Sharpness, a geometric measure in the parameter space that reflects the flatness of the loss landscape, has long been studied for its potential connections to neural network behavior.<n>In this paper, we investigate how sharpness influences the local geometric features of neural representations in feature space.
  arXiv  Detail & Related papers  (2023-10-03T03:36:29Z)
• The Underlying Correlated Dynamics in Neural Training [6.385006149689549]
  Training of neural networks is a computationally intensive task. We propose a model based on the correlation of the parameters' dynamics, which dramatically reduces the dimensionality. This representation enhances the understanding of the underlying training dynamics and can pave the way for designing better acceleration techniques.
  arXiv  Detail & Related papers  (2022-12-18T08:34:11Z)
• Learning Low Dimensional State Spaces with Overparameterized Recurrent Neural Nets [57.06026574261203]
  We provide theoretical evidence for learning low-dimensional state spaces, which can also model long-term memory. Experiments corroborate our theory, demonstrating extrapolation via learning low-dimensional state spaces with both linear and non-linear RNNs.
  arXiv  Detail & Related papers  (2022-10-25T14:45:15Z)
• FuNNscope: Visual microscope for interactively exploring the loss landscape of fully connected neural networks [77.34726150561087]
  We show how to explore high-dimensional landscape characteristics of neural networks. We generalize observations on small neural networks to more complex systems. An interactive dashboard opens up a number of possible application networks.
  arXiv  Detail & Related papers  (2022-04-09T16:41:53Z)
• On the Omnipresence of Spurious Local Minima in Certain Neural Network Training Problems [0.0]
  We study the loss landscape of training problems for deep artificial neural networks with a one-dimensional real output. It is shown that such problems possess a continuum of spurious (i.e., not globally optimal) local minima for all target functions that are not affine.
  arXiv  Detail & Related papers  (2022-02-23T14:41:54Z)
• Deep Networks on Toroids: Removing Symmetries Reveals the Structure of Flat Regions in the Landscape Geometry [3.712728573432119]
  We develop a standardized parameterization in which all symmetries are removed, resulting in a toroidal topology. We derive a meaningful notion of the flatness of minimizers and of the geodesic paths connecting them. We also find that minimizers found by variants of gradient descent can be connected by zero-error paths with a single bend.
  arXiv  Detail & Related papers  (2022-02-07T09:57:54Z)
• Neighborhood Region Smoothing Regularization for Finding Flat Minima In Deep Neural Networks [16.4654807047138]
  We propose an effective regularization technique, called Neighborhood Region Smoothing (NRS) NRS tries to regularize the neighborhood region in weight space to yield approximate outputs. We empirically show that the minima found by NRS would have relatively smaller Hessian eigenvalues compared to the conventional method.
  arXiv  Detail & Related papers  (2022-01-16T15:11:00Z)
• InfoNeRF: Ray Entropy Minimization for Few-Shot Neural Volume Rendering [55.70938412352287]
  We present an information-theoretic regularization technique for few-shot novel view synthesis based on neural implicit representation. The proposed approach minimizes potential reconstruction inconsistency that happens due to insufficient viewpoints. We achieve consistently improved performance compared to existing neural view synthesis methods by large margins on multiple standard benchmarks.
  arXiv  Detail & Related papers  (2021-12-31T11:56:01Z)
• Connections between Numerical Algorithms for PDEs and Neural Networks [8.660429288575369]
  We investigate numerous structural connections between numerical algorithms for partial differential equations (PDEs) and neural networks. Our goal is to transfer the rich set of mathematical foundations from the world of PDEs to neural networks.
  arXiv  Detail & Related papers  (2021-07-30T16:42:45Z)
• On Connectivity of Solutions in Deep Learning: The Role of Over-parameterization and Feature Quality [21.13299067136635]
  We present a novel condition for ensuring the connectivity of two arbitrary points in parameter space. This condition is provably milder than dropout stability, and it provides a connection between the problem of finding low-loss paths and the memorization capacity of neural nets.
  arXiv  Detail & Related papers  (2021-02-18T23:44:08Z)
• Topological obstructions in neural networks learning [67.8848058842671]
  We study global properties of the loss gradient function flow. We use topological data analysis of the loss function and its Morse complex to relate local behavior along gradient trajectories with global properties of the loss surface.
  arXiv  Detail & Related papers  (2020-12-31T18:53:25Z)
• Modeling from Features: a Mean-field Framework for Over-parameterized Deep Neural Networks [54.27962244835622]
  This paper proposes a new mean-field framework for over- parameterized deep neural networks (DNNs) In this framework, a DNN is represented by probability measures and functions over its features in the continuous limit. We illustrate the framework via the standard DNN and the Residual Network (Res-Net) architectures.
  arXiv  Detail & Related papers  (2020-07-03T01:37:16Z)
• Effective Version Space Reduction for Convolutional Neural Networks [61.84773892603885]
  In active learning, sampling bias could pose a serious inconsistency problem and hinder the algorithm from finding the optimal hypothesis. We examine active learning with convolutional neural networks through the principled lens of version space reduction.
  arXiv  Detail & Related papers  (2020-06-22T17:40:03Z)
• An Ode to an ODE [78.97367880223254]
  We present a new paradigm for Neural ODE algorithms, called ODEtoODE, where time-dependent parameters of the main flow evolve according to a matrix flow on the group O(d) This nested system of two flows provides stability and effectiveness of training and provably solves the gradient vanishing-explosion problem.
  arXiv  Detail & Related papers  (2020-06-19T22:05:19Z)
• Dynamic Hierarchical Mimicking Towards Consistent Optimization Objectives [73.15276998621582]
  We propose a generic feature learning mechanism to advance CNN training with enhanced generalization ability. Partially inspired by DSN, we fork delicately designed side branches from the intermediate layers of a given neural network. Experiments on both category and instance recognition tasks demonstrate the substantial improvements of our proposed method.
  arXiv  Detail & Related papers  (2020-03-24T09:56:13Z)
• Unpaired Multi-modal Segmentation via Knowledge Distillation [77.39798870702174]
  We propose a novel learning scheme for unpaired cross-modality image segmentation. In our method, we heavily reuse network parameters, by sharing all convolutional kernels across CT and MRI. We have extensively validated our approach on two multi-class segmentation problems.
  arXiv  Detail & Related papers  (2020-01-06T20:03:17Z)
• Avoiding Spurious Local Minima in Deep Quadratic Networks [0.0]
  We characterize the landscape of the mean squared nonlinear error for networks with neural activation functions. We prove that deepized neural networks with quadratic activations benefit from similar landscape properties.
  arXiv  Detail & Related papers  (2019-12-31T22:31:11Z)
• Model Fusion via Optimal Transport [64.13185244219353]
  We present a layer-wise model fusion algorithm for neural networks. We show that this can successfully yield "one-shot" knowledge transfer between neural networks trained on heterogeneous non-i.i.d. data.
  arXiv  Detail & Related papers  (2019-10-12T22:07:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.