The Clebsch-Gordan Transform (CG transform) effectively encodes many-body interactions. Many studies have proven its accuracy in depicting atomic environments, although this comes with high computational needs. The computational burden of this challenge is hard to reduce due to the need for permutation equivariance, which limits the design space of the CG transform layer. We show that, implementing the CG transform layer on permutation-invariant inputs allows complete freedom in the design of this layer without affecting symmetry. Developing further on this premise, our idea is to create a CG transform layer that operates on permutation-invariant abstract edges generated from real edge information. We bring in group CG transform with sparse path, abstract edges shuffling, and attention enhancer to form a powerful and efficient CG transform layer. Our method, known as FreeCG, achieves State-of-The-Art (SoTA) results in force prediction for MD17, rMD17, MD22, and property prediction in QM9 datasets with notable enhancement. It introduces a novel paradigm for carrying out efficient and expressive CG transform in future geometric neural network designs.

Grid representations offer many advantages for path planning. Lookups in grids are fast, due to the uniform memory layout, and it is easy to modify grids. But, grids often have significant memory requirements, they cannot directly represent more complex surfaces, and path planning is slower due to their high granularity representation of the world. The speed of path planning on grids has been addressed using abstract representations, such as has been documented in work on Dragon Age: Origins. The abstract representation used in this game was compact, preventing permanent changes to the grid. In this paper we introduce a sparse grid representation, where grid cells are only stored where necessary. From this sparse representation we incrementally build an abstract graph which represents possible movement in the world at a high-level of granularity. This sparse representation also allows the representation of three-dimensional worlds. This representation allows the world to be incrementally changed in under a millisecond, reducing the maximum memory required to store a map and abstraction from Dragon Age: Origins by nearly one megabyte. Fundamentally, the representation allows previously allocated but unused memory to be used in ways that result in higher-quality planning and more intelligent agents.

Heuristic-search planners that use A* and related graph Parallel structured duplicate detection (PSDD) (Zhou and search algorithms must be parallelized to harness advances Hansen 2007a) is an extension of SDD that leverages the in computing power that are based on increasing use of same local structure to reduce the amount of synchronization multi-core processors. Although a graph can always be converted needed in parallel search. PSDD assigns idle processors to an equivalent tree that can be easily searched in nblocks to expand whose duplicate detection scopes are parallel, such a conversion increases the size of the search pairwise disjoint, since they can be searched in parallel without space exponentially, and the resulting overhead is hard to any synchronization. Note that two duplicate-detection justify in the context of parallel search for which the speedup scopes are disjoint if they do not share any nblocks.