This program is designed to provide decision-makers, policymakers and professional working in policy with a foundational understanding of AI technology.
We use cookies to analyze the browsing and usage of our website and to personalize your experience. You can disable these technologies at any time, but this may limit certain functionalities of the site. Read our Privacy Policy for more information.
Setting cookies
You can enable and disable the types of cookies you wish to accept. However certain choices you make could affect the services offered on our sites (e.g. suggestions, personalised ads, etc.).
Essential cookies
These cookies are necessary for the operation of the site and cannot be deactivated. (Still active)
Analytics cookies
Do you accept the use of cookies to measure the audience of our sites?
Multimedia Player
Do you accept the use of cookies to display and allow you to watch the video content hosted by our partners (YouTube, etc.)?
The energy landscape of high-dimensional non-convex optimization problems is crucial to understanding the effectiveness of modern deep neura… (see more)l network architectures. Recent works have experimentally shown that two different solutions found after two runs of a stochastic training are often connected by very simple continuous paths (e.g., linear) modulo a permutation of the weights. In this paper, we provide a framework theoretically explaining this empirical observation. Based on convergence rates in Wasserstein distance of empirical measures, we show that, with high probability, two wide enough two-layer neural networks trained with stochastic gradient descent are linearly connected. Additionally, we express upper and lower bounds on the width of each layer of two deep neural networks with independent neuron weights to be linearly connected. Finally, we empirically demonstrate the validity of our approach by showing how the dimension of the support of the weight distribution of neurons, which dictates Wasserstein convergence rates is correlated with linear mode connectivity.
The energy landscape of high-dimensional non-convex optimization problems is crucial to understanding the effectiveness of modern deep neura… (see more)l network architectures. Recent works have experimentally shown that two different solutions found after two runs of a stochastic training are often connected by very simple continuous paths (e.g., linear) modulo a permutation of the weights. In this paper, we provide a framework theoretically explaining this empirical observation. Based on convergence rates in Wasserstein distance of empirical measures, we show that, with high probability, two wide enough two-layer neural networks trained with stochastic gradient descent are linearly connected. Additionally, we express upper and lower bounds on the width of each layer of two deep neural networks with independent neuron weights to be linearly connected. Finally, we empirically demonstrate the validity of our approach by showing how the dimension of the support of the weight distribution of neurons, which dictates Wasserstein convergence rates is correlated with linear mode connectivity.
The Strong Lottery Ticket Hypothesis (SLTH) stipulates the existence of a subnetwork within a sufficiently overparameterized (dense) neural … (see more)network that -- when initialized randomly and without any training -- achieves the accuracy of a fully trained target network. Recent works by Da Cunha et. al 2022; Burkholz 2022 demonstrate that the SLTH can be extended to translation equivariant networks -- i.e. CNNs -- with the same level of overparametrization as needed for the SLTs in dense networks. However, modern neural networks are capable of incorporating more than just translation symmetry, and developing general equivariant architectures such as rotation and permutation has been a powerful design principle. In this paper, we generalize the SLTH to functions that preserve the action of the group