Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vector-valued Distance and Gyrocalculus on the Space of Symmetric
  Positive Definite Matrices   We propose the use of the vector-valued distance to compute distances and
extract geometric information from the manifold of symmetric positive definite
matrices (SPD), and develop gyrovector calculus, constructing analogs of vector
space operations in this curved space. We implement these operations and
showcase their versatility in the tasks of knowledge graph completion, item
recommendation, and question answering. In experiments, the SPD models
outperform their equivalents in Euclidean and hyperbolic space. The
vector-valued distance allows us to visualize embeddings, showing that the
models learn to disentangle representations of positive samples from negative
ones.

15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio