Slide 6
Slide 6 text
6
Message passing with spherical representation
𝑴"#
' = 𝜙()**+,)
𝒎"#
' , ⃗
𝑟"#
, ⃗
𝑟"-
, 𝜃#"-,
⃗
𝑟"#
",.
𝒉"#
'/. = 𝜙012+3)
𝒉 𝒉"
', 𝒉#
', 𝑴"#
'
𝒎"#
'/. = 𝜙012+3)
𝒎 𝒉"
', 𝒉#
', 𝒎"#
' , 𝑴"#
'
𝒆'()
!",& = 𝑗*
⃗
𝑟!"
𝑌*+
⃗
𝑟!"
!,&/ ⃗
𝑟!"
!,&
J. Gasteiger et al., arXiv abs/2106.08903 (2021).
𝒉"
) : node embedding (invariant)
𝒎"#
) : edge embedding (invariant)
⃗
𝑟"#
",% : Transformed relative vector from central atom 𝑖 to 𝑗.
ü𝜙,-../0-
→ Bilinear product between 𝒆'()
!",& and 𝒎!"
* .
Maintain invariance by adding all
transformed vectors.
ü𝜙123/4-
→ same as GemNet
Generate Spherical representation 𝒆
𝐒𝐁𝐅
𝒊𝒋,𝒕
Message & Update functions
6