374,870 research outputs found

    Integral Geometry and Holography

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    We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3_3/CFT2_2 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 AdS3_3 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

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    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

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    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

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    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

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    Network Embeddings (NEs) map the nodes of a given network into dd-dimensional Euclidean space Rd\mathbb{R}^d. 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

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    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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