Neural SDE
A class of generative models that parameterize the drift and/or diffusion terms of a stochastic differential equation with neural networks, in the standard form dX_t = f_θ(X_t,t)dt + g_φ(X_t,t)dW_t.
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A divergence-kernel-based method can jointly optimize the drift field, diffusion field, and initial Gaussian distribution of a neural SDE, and is trained directly using a loss function that depends on the terminal density.
A neural SDE refers to a class of models that parameterize the drift and/or diffusion terms of a stochastic differential equation with neural networks, with the standard form dX_t = f_θ(X_t, t)dt + g_φ(X_t, t)dW_t.
Training neural SDEs typically requires simulating paths or solving the Fokker-Planck equation to obtain the terminal density, which is computationally expensive.
This paper bypasses explicit path simulation through the divergence kernel loss, making joint training feasible.
The significance of this work lies in providing a new training paradigm for generative models: treating the diffusion term of the SDE also as a learnable component and directly optimizing the terminal density.
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A divergence-kernel-based method can jointly optimize the drift field, diffusion field, and initial Gaussian distribution of a neural SDE, and is trained directly using a loss function that depends on the terminal density.
50%UnverifiedA neural SDE refers to a class of models that parameterize the drift and/or diffusion terms of a stochastic differential equation with neural networks, with the standard form dX_t = f_θ(X_t, t)dt + g_φ(X_t, t)dW_t.
50%UnverifiedTraining neural SDEs typically requires simulating paths or solving the Fokker-Planck equation to obtain the terminal density, which is computationally expensive.
50%UnverifiedThis paper bypasses explicit path simulation through the divergence kernel loss, making joint training feasible.
50%UnverifiedThe significance of this work lies in providing a new training paradigm for generative models: treating the diffusion term of the SDE also as a learnable component and directly optimizing the terminal density.
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