Constructive solid geometry (CSG) is a classical CAD representation; it models a 3D shape as a recursive assembly of solid primitives, e.g., cuboids, cylinders, etc., through Boolean operations

CSG and CAPRI-Net mentioned in Section 3 of the main paper. To prove Proposition 1, we provide an example that CAPRI-Net's sequence fails to support. CSG is able to support any CSG sequence. Each sub-figure represents a 2D implicit filed defined by the notation below. Specifically, we obtain the mesh for each primitive by performing Marching-Cube on the signed distance field produced by the quadric equation of that primitive.

The concepts of precision, and accuracy are domain and problem dependent. The simplified numeric hard and soft measures used in the fields of statistical learning, many types of machine learning, and binary or multiclass classification problems are known to be of limited use for understanding the meaningfulness of models or their relevance. Arguably, they are neither of patterns nor proofs. Further, there are no good measures or representations for analogous concepts in the cognition domain. In this research, the key issues are reflected upon, and a compositional knowledge representation approach in a minimalist general rough framework is proposed for the problem contexts. The latter is general enough to cover most application contexts, and may be applicable in the light of improved computational tools available.

Taking inspiration from Set Theory, we introduce SetCSE, an innovative information retrieval framework. SetCSE employs sets to represent complex semantics and incorporates well-defined operations for structured information querying under the provided context. Within this framework, we introduce an inter-set contrastive learning objective to enhance comprehension of sentence embedding models concerning the given semantics. Furthermore, we present a suite of operations, including SetCSE intersection, difference, and operation series, that leverage sentence embeddings of the enhanced model for complex sentence retrieval tasks. Throughout this paper, we demonstrate that SetCSE adheres to the conventions of human language expressions regarding compounded semantics, provides a significant enhancement in the discriminatory capability of underlying sentence embedding models, and enables numerous information retrieval tasks involving convoluted and intricate prompts which cannot be achieved using existing querying methods.