Publication

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Related publications (30)

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The probability of detecting technosignatures (i.e., evidence of technological activity beyond Earth) increases with their longevity, or the time interval over which they manifest. Therefore, the assumed distribution of longevities has some bearing on the ...

Iop Publishing Ltd2024

Residual-based attention in physics-informed neural networks

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Driven by the need for more efficient and seamless integration of physical models and data, physics -informed neural networks (PINNs) have seen a surge of interest in recent years. However, ensuring the reliability of their convergence and accuracy remains ...

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Optimization Algorithms for Decentralized, Distributed and Collaborative Machine Learning

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Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...

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Experimental characterization and stochastic models for time-dependent rupture of thin-ply composite laminates

Thin-laminate composites with thicknesses below 200 mu m hold significant promise for future, larger, and lighter deployable structures. This paper presents a study of the time-dependent failure behavior of thin carbon-fiber laminates under bending, focusi ...

2024

Mean value theorems for collections of lattices with a prescribed group of symmetries

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Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...

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Generalization of Scaled Deep ResNets in the Mean-Field Regime

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Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

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Robot Learning using Tensor Networks

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In various robotics applications, the selection of function approximation methods greatly influences the feasibility and computational efficiency of algorithms. Tensor Networks (TNs), also referred to as tensor decomposition techniques, present a versatile ...

EPFL2024

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Nicolas Henri Bernard Flammarion, Hristo Georgiev Papazov, Scott William Pesme

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

\gamma

and momentum parameter

\beta

that allows u ...

2024

Stochastic pairwise preference convergence in Bayesian agents

Max-Olivier Hongler

Beliefs inform the behaviour of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack critical theory to ...

2024

Spatiotemporal energy‐density distribution of time‐reversed electromagnetic fields

Farhad Rachidi-Haeri, Marcos Rubinstein, Hamidreza Karami, Elias Per Joachim Le Boudec, Nicolas Mora Parra

Time reversal exploits the invariance of electromagnetic wave propagation in reciprocal and lossless media to localize radiating sources. Time-reversed measurements are back-propagated in a simulated domain and converge to the unknown source location. The ...

2024

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Nicolas Henri Bernard Flammarion, Hristo Georgiev Papazov, Scott William Pesme

\gamma

and momentum parameter

\beta

that allows u ...

2024