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Equation 9 · Part 5 · How AI for Science and Medicine Actually Works

Symbol N

hv(k+1)=ϕ(hv(k),⨁u∈N(v)ψ(hv(k),hu(k),euv)),h_v^{(k+1)} = \phi\left(h_v^{(k)}, \bigoplus_{u \in \mathcal{N}(v)} \psi\left(h_v^{(k)}, h_u^{(k)}, e_{uv}\right)\right),
N\mathcal{N}

What this part means

N is an input to the expression that computes the quantity on the left.

Its job in the formula

N is an input to the expression that computes the quantity on the left.

The passage around this formula

…propagate across the globe within a single forward pass; a decoder then reads the updated mesh back out to the original grid to produce the forecast. In general form, a message-passing update for a node v with neighbours N(v)\mathcal{N}(v) looks like hv(k+1)=ϕ(hv(k),⨁u∈N(v)ψ(hv(k),hu(k),euv))h_v^{(k+1)} = \phi\left(h_v^{(k)}, \bigoplus_{u \in \mathcal{N}(v)} \psi\left(h_v^{(k)}, h_u^{(k)}, e_{uv}\right)\right). where hv(k)h_v^{(k)} is node v ’s representation after k rounds of message passing, euve_{uv} is the edge connecting it to neighbour u , and ψ\psi and ϕ\phi are learned functions — the same general operation GNoME’s crystal-graph network applies to atoms and…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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