11,741 research outputs found
Topology and Criticality in Resonating Affleck-Kennedy-Lieb-Tasaki loop Spin Liquid States
We exploit a natural Projected Entangled-Pair State (PEPS) representation for
the resonating Affleck-Kennedy-Lieb-Tasaki loop (RAL) state. By taking
advantage of PEPS-based analytical and numerical methods, we characterize the
RAL states on various two-dimensional lattices. On square and honeycomb
lattices, these states are critical since the dimer-dimer correlations decay as
a power law. On kagome lattice, the RAL state has exponentially decaying
correlation functions, supporting the scenario of a gapped spin liquid. We
provide further evidence that the RAL state on the kagome lattice is a
spin liquid, by identifying the four topological sectors and
computing the topological entropy. Furthermore, we construct a one-parameter
family of PEPS states interpolating between the RAL state and a short-range
Resonating Valence Bond state and find a critical point, consistent with the
fact that the two states belong to two different phases. We also perform a
variational study of the spin-1 kagome Heisenberg model using this
one-parameter PEPS.Comment: 10 pages, 14 figures, published versio
Identifiability of Label Noise Transition Matrix
The noise transition matrix plays a central role in the problem of learning
with noisy labels. Among many other reasons, a large number of existing
solutions rely on access to it. Identifying and estimating the transition
matrix without ground truth labels is a critical and challenging task. When
label noise transition depends on each instance, the problem of identifying the
instance-dependent noise transition matrix becomes substantially more
challenging. Despite recent works proposing solutions for learning from
instance-dependent noisy labels, the field lacks a unified understanding of
when such a problem remains identifiable. The goal of this paper is to
characterize the identifiability of the label noise transition matrix. Building
on Kruskal's identifiability results, we are able to show the necessity of
multiple noisy labels in identifying the noise transition matrix for the
generic case at the instance level. We further instantiate the results to
explain the successes of the state-of-the-art solutions and how additional
assumptions alleviated the requirement of multiple noisy labels. Our result
also reveals that disentangled features are helpful in the above identification
task and we provide empirical evidence.Comment: Preprint. Under review. For questions please contact [email protected]
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