You’re looking for group equivariance - there is some work in group equivariant neural networks. You might find the very recent paper on Clifford Group-Equivari

You’re looking for group equivariance - there is some work in group equivariant neural networks. You might find the very recent paper on Clifford Group-Equivariant networks interesting - it applies to not only Euclidean spacetime transformations but even Minkowskian spacetime. You might also be interested in implementations for novel view synthesis such as instantngp and other NERF-type models. InstantNGP is actually ludicrously simple relative to most recent neural architectures, imo. With respect to the reversal problem, I wonder how strongly this would still hold for eg encoder-decoder (eg T5) or “order-free autoregressive” models (eg sigma-GPT from last week)