Maximum Inner Product Search (MIPS) plays an essential role in many applications ranging from information retrieval, recommender systems to natural language processing. However, exhaustive MIPS is often expensive and impractical when there are a large number of candidate items. The state-of-the-art quantization method approximated product with score-aware loss, developed by assuming that querie...

Maximum Inner Product Search (MIPS) plays an important role in many applications ranging from information retrieval, recommender systems to natural language processing and machine learning. However, exhaustive MIPS is often expensive impractical when there are a large number of candidate items. The state-of-the-art approximated product quantization with score-aware loss, which weighs more heavi...

The notion of the shell of a Hilbert space operator, which is a useful generalization (proposed by Wielandt) of the numerical range, is extended to operators in spaces with an indefinite inner product. For the most part, finite dimensional spaces are considered. Geometric properties of shells (convexity, boundedness, being a subset of a line, etc.) are described, as well as shells of operators ...