777 research outputs found
Algorithms and Adaptivity Gaps for Stochastic k-TSP
Given a metric and a , the classic
\textsf{k-TSP} problem is to find a tour originating at the
of minimum length that visits at least nodes in . In this work,
motivated by applications where the input to an optimization problem is
uncertain, we study two stochastic versions of \textsf{k-TSP}.
In Stoch-Reward -TSP, originally defined by Ene-Nagarajan-Saket [ENS17],
each vertex in the given metric contains a stochastic reward .
The goal is to adaptively find a tour of minimum expected length that collects
at least reward ; here "adaptively" means our next decision may depend on
previous outcomes. Ene et al. give an -approximation adaptive
algorithm for this problem, and left open if there is an -approximation
algorithm. We totally resolve their open question and even give an
-approximation \emph{non-adaptive} algorithm for this problem.
We also introduce and obtain similar results for the Stoch-Cost -TSP
problem. In this problem each vertex has a stochastic cost , and the
goal is to visit and select at least vertices to minimize the expected
\emph{sum} of tour length and cost of selected vertices. This problem
generalizes the Price of Information framework [Singla18] from deterministic
probing costs to metric probing costs.
Our techniques are based on two crucial ideas: "repetitions" and "critical
scaling". We show using Freedman's and Jogdeo-Samuels' inequalities that for
our problems, if we truncate the random variables at an ideal threshold and
repeat, then their expected values form a good surrogate. Unfortunately, this
ideal threshold is adaptive as it depends on how far we are from achieving our
target , so we truncate at various different scales and identify a
"critical" scale.Comment: ITCS 202
Forward and Inverse Approximation Theory for Linear Temporal Convolutional Networks
We present a theoretical analysis of the approximation properties of
convolutional architectures when applied to the modeling of temporal sequences.
Specifically, we prove an approximation rate estimate (Jackson-type result) and
an inverse approximation theorem (Bernstein-type result), which together
provide a comprehensive characterization of the types of sequential
relationships that can be efficiently captured by a temporal convolutional
architecture. The rate estimate improves upon a previous result via the
introduction of a refined complexity measure, whereas the inverse approximation
theorem is new
Approximation theory of transformer networks for sequence modeling
The transformer is a widely applied architecture in sequence modeling
applications, but the theoretical understanding of its working principles is
limited. In this work, we investigate the ability of transformers to
approximate sequential relationships. We first prove a universal approximation
theorem for the transformer hypothesis space. From its derivation, we identify
a novel notion of regularity under which we can prove an explicit approximation
rate estimate. This estimate reveals key structural properties of the
transformer and suggests the types of sequence relationships that the
transformer is adapted to approximating. In particular, it allows us to
concretely discuss the structural bias between the transformer and classical
sequence modeling methods, such as recurrent neural networks. Our findings are
supported by numerical experiments
TextureNet: Consistent Local Parametrizations for Learning from High-Resolution Signals on Meshes
We introduce, TextureNet, a neural network architecture designed to extract
features from high-resolution signals associated with 3D surface meshes (e.g.,
color texture maps). The key idea is to utilize a 4-rotational symmetric
(4-RoSy) field to define a domain for convolution on a surface. Though 4-RoSy
fields have several properties favorable for convolution on surfaces (low
distortion, few singularities, consistent parameterization, etc.), orientations
are ambiguous up to 4-fold rotation at any sample point. So, we introduce a new
convolutional operator invariant to the 4-RoSy ambiguity and use it in a
network to extract features from high-resolution signals on geodesic
neighborhoods of a surface. In comparison to alternatives, such as PointNet
based methods which lack a notion of orientation, the coherent structure given
by these neighborhoods results in significantly stronger features. As an
example application, we demonstrate the benefits of our architecture for 3D
semantic segmentation of textured 3D meshes. The results show that our method
outperforms all existing methods on the basis of mean IoU by a significant
margin in both geometry-only (6.4%) and RGB+Geometry (6.9-8.2%) settings
Natural Graph Wavelet Packet Dictionaries
We introduce a set of novel multiscale basis transforms for signals on graphs
that utilize their "dual" domains by incorporating the "natural" distances
between graph Laplacian eigenvectors, rather than simply using the eigenvalue
ordering. These basis dictionaries can be seen as generalizations of the
classical Shannon wavelet packet dictionary to arbitrary graphs, and do not
rely on the frequency interpretation of Laplacian eigenvalues. We describe the
algorithms (involving either vector rotations or orthogonalizations) to
construct these basis dictionaries, use them to efficiently approximate graph
signals through the best basis search, and demonstrate the strengths of these
basis dictionaries for graph signals measured on sunflower graphs and street
networks
Soybean seedling detection and counting from UAV images based on an improved YOLOv8 Network
The utilization of unmanned aerial vehicle (UAV) for soybean seedling detection is an effective way to estimate soybean yield, which plays a crucial role in agricultural planning and decision-making. However, the soybean seedlings objects in the UAV image are small, in clusters, and occluded each other, which makes it very challenging to achieve accurate object detection and counting. To address these issues, we optimize the YOLOv8 model and propose a GAS-YOLOv8 network, aiming to enhance the detection accuracy for the task of soybean seedling detection based on UAV images. Firstly, a global attention mechanism (GAM) is incorporated into the neck module of YOLOv8, which reallocates weights and prioritizes global information to more effectively extract soybean seedling features. Secondly, the CIOU loss function is replaced with the SIOU loss, which includes an angle loss term to guide the regression of bounding boxes. Experimental results show that, on the soybean seedling dataset, the proposed GAS-YOLOv8 model achieves a 1.3% improvement in [email protected] and a 6% enhancement in detection performance in dense seedling areas, when compared to the baseline model YOLOv8s.When compared to other object detection models (YOLOv5, Faster R-CNN, etc.), the GAS-YOLOv8 model similarly achieved the best detection performance. These results demonstrate the effectiveness of the GAS-YOLOv8 in detecting dense soybean seedlings, providing more accurate theoretical support for subsequent yield estimation
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