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