It has. Gradient flow or more generally flow is a well known concept in maths. Say we have a function $f:\mathbb R^n \longrightarrow \mathbb R^n$ and a function $\theta:[0,\infty)\longrightarrow \mathbb R^n$ such that the ODE $$ \partial_t \theta(t) = f(\theta(t)) $$ exists for any initial choice $\theta(0)\in\mathbb R^n$ uniquely. Then i think the naming comes from the following informal description. Lets imagine $n=2$ the $\mathbb R^2$ is a plane. Now you drop $\theta(0)$ somewhere on this plane and wait some time $t$ to see where the $\theta(0)$ will flow to. You can also draw the trajectories for multiple starting points $\theta(0)$ which will often give you an image that looks like a flow of a liquid.

In the case of the ANN $f$ would be the negative gradient of the costfunction with respect to the paramter-vector $\theta$ and gradient descent would be an approximation of the gradient flow.

It has. Gradient flow or more generally flow is a well known concept in maths. Say we have a function $f:\mathbb R^n \longrightarrow \mathbb R^n$ and a function $\theta:[0,\infty)\longrightarrow \mathbb R^n$ such that the ODE $$ \partial_t \theta(t) = f(\theta(t)) $$ exists for any initial choice $\theta(0)\in\mathbb R^n$ uniquely. Then i think the naming comes from the following informal description. Lets imagine the case $n=2$ then $\mathbb R^2$ is a plane. Now you drop $\theta(0)$ somewhere on this plane and wait some time $t$ to see where the $\theta(0)$ will flow to. You can also draw the trajectories for multiple starting points $\theta(0)$ which will often give you an image that looks like a flow of a liquid.

In the case of the ANN $f$ would be the negative gradient of the costfunction with respect to the paramter-vector $\theta$ and gradient descent would be an approximation of the gradient flow.

It has. Gradient flow or more generally flow is a well known concept in maths. Say we have a function $f:\mathbb R^n \longrightarrow \mathbb R^n$ and a function $\theta:[0,\infty)\longrightarrow \mathbb R^n$ such that the ODE $$ \partial_t \theta(t) = f(\theta(t)) $$ exists for any initial choice $\theta(0)\in\mathbb R^n$ uniquely. Then i think the naming comes from the following informal description. Let imagine $n=2$ the $\mathbb R^2$ is a plane. Now you drop $\theta(0)$ somewhere on this plane and wait some time $t$ to see where the $\theta(0)$ will flow to. You can also draw the trajectories for multiple starting points $\theta(0)$ which will often give you an image that looks like a flow of a liquid.

In the case of the ANN $f$ would be the negative gradient of the costfunction with respect to the paramter-vector $\theta$ and gradient descent would be an approximation of the gradient flow.

It has. Gradient flow or more generally flow is a well known concept in maths. Say we have a function $f:\mathbb R^n \longrightarrow \mathbb R^n$ and a function $\theta:[0,\infty)\longrightarrow \mathbb R^n$ such that the ODE $$ \partial_t \theta(t) = f(\theta(t)) $$ exists for any initial choice $\theta(0)\in\mathbb R^n$ uniquely. Then i think the naming comes from the following informal description. Lets imagine $n=2$ the $\mathbb R^2$ is a plane. Now you drop $\theta(0)$ somewhere on this plane and wait some time $t$ to see where the $\theta(0)$ will flow to. You can also draw the trajectories for multiple starting points $\theta(0)$ which will often give you an image that looks like a flow of a liquid.

In the case of the ANN $f$ would be the negative gradient of the costfunction with respect to the paramter-vector $\theta$ and gradient descent would be an approximation of the gradient flow.