3,460 research outputs found
EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry
In this paper, we present a deep learning-based framework for solving
geometric construction problems through visual reasoning, which is useful for
automated geometry theorem proving. Constructible problems in geometry often
ask for the sequence of straightedge-and-compass constructions to construct a
given goal given some initial setup. Our EuclidNet framework leverages the
neural network architecture Mask R-CNN to extract the visual features from the
initial setup and goal configuration with extra points of intersection, and
then generate possible construction steps as intermediary data models that are
used as feedback in the training process for further refinement of the
construction step sequence. This process is repeated recursively until either a
solution is found, in which case we backtrack the path for a step-by-step
construction guide, or the problem is identified as unsolvable. Our EuclidNet
framework is validated on complex Japanese Sangaku geometry problems,
demonstrating its capacity to leverage backtracking for deep visual reasoning
of challenging problems.Comment: Accepted by 2nd MATH-AI Workshop at NeurIPS'2
mixing From Lattice QCD
In heavy quark limit, the lowest-lying charmed baryons with two light quarks
can form an SU(3) triplet and sextet. The in the SU(3) triplet and
in the sextet have the same quantum number and can mix due to
the finite charm quark mass and the fact the strange quark is heavier than the
up/down quark. We explore the - mixing by calculating the
two-point correlation functions of the and baryons from
lattice QCD. Based on the lattice data, we adopt two independent methods to
determine the mixing angle between and . After making the
chiral and continuum extrapolation, it is found that the mixing angle
is , which seems insufficient to account for the
large SU(3) symmetry breaking effects found in weak decays of charmed baryons
- β¦