374,870 research outputs found
Integral Geometry and Holography
We present a mathematical framework which underlies the connection between
information theory and the bulk spacetime in the AdS/CFT
correspondence. A key concept is kinematic space: an auxiliary Lorentzian
geometry whose metric is defined in terms of conditional mutual informations
and which organizes the entanglement pattern of a CFT state. When the field
theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic
space has a direct geometric meaning: it is the space of bulk geodesics studied
in integral geometry. Lengths of bulk curves are computed by kinematic volumes,
giving a precise entropic interpretation of the length of any bulk curve. We
explain how basic geometric concepts -- points, distances and angles -- are
reflected in kinematic space, allowing one to reconstruct a large class of
spatial bulk geometries from boundary entanglement entropies. In this way,
kinematic space translates between information theoretic and geometric
descriptions of a CFT state. As an example, we discuss in detail the static
slice of AdS whose kinematic space is two-dimensional de Sitter space.Comment: 23 pages + appendices, including 23 figures and an exercise sheet
with solutions; a Mathematica visualization too
Stereoscopic three-dimensional visualization applied to multimodal brain images: Clinical applications and a functional connectivity atlas
Effective visualization is central to the exploration and comprehension of brain imaging data. While MRI data are acquired in three-dimensional space, the methods for visualizing such data have rarely taken advantage of three-dimensional stereoscopic technologies. We present here results of stereoscopic visualization of clinical data, as well as an atlas of whole-brain functional connectivity. In comparison with traditional 3D rendering techniques, we demonstrate the utility of stereoscopic visualizations to provide an intuitive description of the exact location and the relative sizes of various brain landmarks, structures and lesions. In the case of resting state fMRI, stereoscopic 3D visualization facilitated comprehension of the anatomical position of complex large-scale functional connectivity patterns. Overall, stereoscopic visualization improves the intuitive visual comprehension of image contents, and brings increased dimensionality to visualization of traditional MRI data, as well as patterns of functional connectivity
Discrete Fourier Transform Improves the Prediction of the Electronic Properties of Molecules in Quantum Machine Learning
High-throughput approximations of quantum mechanics calculations and
combinatorial experiments have been traditionally used to reduce the search
space of possible molecules, drugs and materials. However, the interplay of
structural and chemical degrees of freedom introduces enormous complexity,
which the current state-of-the-art tools are not yet designed to handle. The
availability of large molecular databases generated by quantum mechanics (QM)
computations using first principles open new venues for data science to
accelerate the discovery of new compounds. In recent years, models that combine
QM with machine learning (ML) known as QM/ML models have been successful at
delivering the accuracy of QM at the speed of ML. The goals are to develop a
framework that will accelerate the extraction of knowledge and to get insights
from quantitative process-structure-property-performance relationships hidden
in materials data via a better search of the chemical compound space, and to
infer new materials with targeted properties. In this study, we show that by
integrating well-known signal processing techniques such as discrete Fourier
transform in the QM/ML pipeline, the outcomes can be significantly improved in
some cases. We also show that the spectrogram of a molecule may represent an
interesting molecular visualization tool.Comment: 4 pages, 3 figures, 2 tables. Accepted to present at 32nd IEEE
Canadian Conference in Electrical Engineering and Computer Scienc
Unlocking Feature Visualization for Deeper Networks with MAgnitude Constrained Optimization
Feature visualization has gained substantial popularity, particularly after
the influential work by Olah et al. in 2017, which established it as a crucial
tool for explainability. However, its widespread adoption has been limited due
to a reliance on tricks to generate interpretable images, and corresponding
challenges in scaling it to deeper neural networks. Here, we describe MACO, a
simple approach to address these shortcomings. The main idea is to generate
images by optimizing the phase spectrum while keeping the magnitude constant to
ensure that generated explanations lie in the space of natural images. Our
approach yields significantly better results (both qualitatively and
quantitatively) and unlocks efficient and interpretable feature visualizations
for large state-of-the-art neural networks. We also show that our approach
exhibits an attribution mechanism allowing us to augment feature visualizations
with spatial importance. We validate our method on a novel benchmark for
comparing feature visualization methods, and release its visualizations for all
classes of the ImageNet dataset on https://serre-lab.github.io/Lens/.
Overall, our approach unlocks, for the first time, feature visualizations for
large, state-of-the-art deep neural networks without resorting to any
parametric prior image model
Conditional network embeddings
Network Embeddings (NEs) map the nodes of a given network into -dimensional Euclidean space . Ideally, this mapping is such that 'similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if 'similar' means being 'more likely to be connected') or classification (if 'similar' means 'being more likely to have the same label'). In recent years various methods for NE have been introduced, all following a similar strategy: defining a notion of similarity between nodes (typically some distance measure within the network), a distance measure in the embedding space, and a loss function that penalizes large distances for similar nodes and small distances for dissimilar nodes.
A difficulty faced by existing methods is that certain networks are fundamentally hard to embed due to their structural properties: (approximate) multipartiteness, certain degree distributions, assortativity, etc. To overcome this, we introduce a conceptual innovation to the NE literature and propose to create \emph{Conditional Network Embeddings} (CNEs); embeddings that maximally add information with respect to given structural properties (e.g. node degrees, block densities, etc.). We use a simple Bayesian approach to achieve this, and propose a block stochastic gradient descent algorithm for fitting it efficiently.
We demonstrate that CNEs are superior for link prediction and multi-label classification when compared to state-of-the-art methods, and this without adding significant mathematical or computational complexity. Finally, we illustrate the potential of CNE for network visualization
Neural Relation Graph: A Unified Framework for Identifying Label Noise and Outlier Data
Diagnosing and cleaning data is a crucial step for building robust machine
learning systems. However, identifying problems within large-scale datasets
with real-world distributions is challenging due to the presence of complex
issues such as label errors, under-representation, and outliers. In this paper,
we propose a unified approach for identifying the problematic data by utilizing
a largely ignored source of information: a relational structure of data in the
feature-embedded space. To this end, we present scalable and effective
algorithms for detecting label errors and outlier data based on the relational
graph structure of data. We further introduce a visualization tool that
provides contextual information of a data point in the feature-embedded space,
serving as an effective tool for interactively diagnosing data. We evaluate the
label error and outlier/out-of-distribution (OOD) detection performances of our
approach on the large-scale image, speech, and language domain tasks, including
ImageNet, ESC-50, and MNLI. Our approach achieves state-of-the-art detection
performance on all tasks considered and demonstrates its effectiveness in
debugging large-scale real-world datasets across various domains.Comment: preprin
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