336 citations · 1.6k across the 53 of their papers we have counts for
54 papers
Geometric framework for biological evolution
Vitaly Vanchurin
We develop a generally covariant description of evolutionary dynamics that operates consistently in both genotype and phenotype spaces. We show that the maximum entropy principle y…
Molecular Learning Dynamics
Yaroslav Gusev, Vitaly Vanchurin
We apply the physics-learning duality to molecular systems by complementing the physical description of interacting particles with a dual learning description, where each particle…
Covariant Gradient Descent
Dmitry Guskov, Vitaly Vanchurin
We present a manifestly covariant formulation of the gradient descent method, ensuring consistency across arbitrary coordinate systems and general curved trainable spaces. The opti…
Geometric Learning Dynamics
Vitaly Vanchurin
We present a unified geometric framework for modeling learning dynamics in physical, biological, and machine learning systems. The theory reveals three fundamental regimes, each em…
Emergent field theories from neural networks
Vitaly Vanchurin
We establish a duality relation between Hamiltonian systems and neural network-based learning systems. We show that the Hamilton's equations for position and momentum variables cor…
Dataset-learning duality and emergent criticality
Ekaterina Kukleva, Vitaly Vanchurin
In artificial neural networks, the activation dynamics of non-trainable variables is strongly coupled to the learning dynamics of trainable variables. During the activation pass, t…