12,633 research outputs found
Kronecker Graphs: An Approach to Modeling Networks
How can we model networks with a mathematically tractable model that allows
for rigorous analysis of network properties? Networks exhibit a long list of
surprising properties: heavy tails for the degree distribution; small
diameters; and densification and shrinking diameters over time. Most present
network models either fail to match several of the above properties, are
complicated to analyze mathematically, or both. In this paper we propose a
generative model for networks that is both mathematically tractable and can
generate networks that have the above mentioned properties. Our main idea is to
use the Kronecker product to generate graphs that we refer to as "Kronecker
graphs".
First, we prove that Kronecker graphs naturally obey common network
properties. We also provide empirical evidence showing that Kronecker graphs
can effectively model the structure of real networks.
We then present KronFit, a fast and scalable algorithm for fitting the
Kronecker graph generation model to large real networks. A naive approach to
fitting would take super- exponential time. In contrast, KronFit takes linear
time, by exploiting the structure of Kronecker matrix multiplication and by
using statistical simulation techniques.
Experiments on large real and synthetic networks show that KronFit finds
accurate parameters that indeed very well mimic the properties of target
networks. Once fitted, the model parameters can be used to gain insights about
the network structure, and the resulting synthetic graphs can be used for null-
models, anonymization, extrapolations, and graph summarization
Neural Task Programming: Learning to Generalize Across Hierarchical Tasks
In this work, we propose a novel robot learning framework called Neural Task
Programming (NTP), which bridges the idea of few-shot learning from
demonstration and neural program induction. NTP takes as input a task
specification (e.g., video demonstration of a task) and recursively decomposes
it into finer sub-task specifications. These specifications are fed to a
hierarchical neural program, where bottom-level programs are callable
subroutines that interact with the environment. We validate our method in three
robot manipulation tasks. NTP achieves strong generalization across sequential
tasks that exhibit hierarchal and compositional structures. The experimental
results show that NTP learns to generalize well to- wards unseen tasks with
increasing lengths, variable topologies, and changing objectives.Comment: ICRA 201
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