New network distance based on Laplacian flow captures structure.
problem Measuring similarity between network objects.
method Introducing Laplacian flow to define a new diffusion distance.
result Demonstrated utility and advantage over existing distances.
The paper connects neural networks to Mahalanobis distance for interpretability.
problem Lack of interpretability in neural networks.
method Establishes a connection between neural network linear layers and Mahalanobis distance.
result Provides a foundation for more interpretable neural network models.
Neural networks learn distance-based representations, not just intensity.
problem Understanding how neural networks interpret and learn from internal activations.
method Manipulated ReLU and Absolute Value activations to observe sensitivity to distance and intensity perturbations.
result Neural networks are highly sensitive to small distance-based perturbations, challenging the intensity-based interpretation.
Neural networks can learn distance metrics affecting model performance.
problem Understanding how neural networks learn and represent data.
method Experiments with six MNIST architectures, constrained to learn either distance or intensity representations.
result Distance-based learning affects model performance, validating the geometric framework.
The paper identifies clusters in the World Trade Network using communicability distances.
problem Identifying clusters in the World Trade Network.
method Uses Estrada and vibrational communicability distances to find clusters maximizing a modularity function.
result Identifies specific distance thresholds that maximize modularity, revealing unique relationships between countries.
Graph neural network learns graph distances effectively.
problem Maintaining graph distance metric properties.
method GRAPH-BERT based semi-supervised distance metric learning.
result GB-DISTANCE outperforms existing methods.
Paper analyzes neural network distances and stability, leading to a new learning rule.
problem Stability and efficiency in training deep neural networks.
method Relational trust distance and descent lemma for neural networks.
result New learning rule requires minimal learning rate tuning.
New algorithm trains generative networks using explicit optimal transport distances.
problem Training generative networks with flexible distance metrics.
method Uses an auxiliary neural network to express optimal transport map and trains generative networks with explicit transportation cost functions.
result Allows training with any transportation cost function, including image-centered distances.
Study shows effective resistance distance yields more accurate network barycenter than Hamming distance.
problem Identifying the best metric for computing the Fréchet mean network.
method Compared the effectiveness of Hamming distance and effective resistance distance in capturing network topology.
result Effective resistance distance produces a more accurate Fréchet mean network.
Permutation invariant network learns Wasserstein metrics.
problem Understanding the space of probability measures and comparing distributions.
method Permutation invariant network mapping samples to a low-dimensional space.
result Network can generalize to compute distances between unseen densities and learn moments.
Novel neural network approximates exact distance for robust classification.
problem Adversarial attacks on neural networks in safety-critical systems.
method Signed Distance Classifiers (SDCs) and Unitary-Gradient Neural Network.
result Approximates exact distance from classification boundary for certifiable predictions.
Paper finds the best way to estimate neural net distance from samples.
problem Estimating the neural net distance from samples.
method Developed minimax lower and upper bounds for the neural net distance.
result Lower and upper bounds match, validating the empirical neural net distance.
Improves molecular activity prediction using graph convolutional neural networks considering graph distances.
problem Predicting molecular activity using graph convolutional neural networks with improved distance representation.
method Proposed three improvements: modified graph distances, distance-dependent weight matrices, and weighted sum conversion.
result The proposed method slightly outperforms the original weave module in compound activity prediction.
Deep learning approximates shortest path distances in large graphs.
problem Scaling up shortest path distance computation in large networks.
method Deep learning techniques to approximate distances using vector embeddings.
result Feedforward neural networks with embeddings can approximate distances with low distortion error.
Efficiently reconstructs jump-diffusion processes from data using neural networks.
problem Reconstructing jump-diffusion processes from data.
method Temporally decoupled squared Wasserstein distance method using parameterized neural networks.
result Enhanced reconstruction of jump-diffusion processes from data.
Polynomial algorithm estimates mGH distance between unweighted graphs.
problem Efficiently measuring shape difference between unweighted graphs.
method Polynomial algorithm for mGH distance estimation.
result Algorithm finds mGH distances exactly on most scale-free graphs.
Proposes Isometric Graph Neural Networks to preserve graph distances.
problem Lack of faithful distance representation in graph neural networks.
method Introduces a new technique to modify GNNs' input space and loss function.
result Significant improvement in reflecting graph distances, as measured by KT.
Paper proposes a method to train generative networks with minimized Wasserstein distance.
problem Training generative networks to match target distributions accurately.
method Gradual, semi-discrete approach via explicit Wasserstein minimization.
result The approach minimizes Wasserstein distance to both empirical and population target distributions.
Develops a private synthetic graph generator using Gromov-Wasserstein distance.
problem Creating private synthetic networks for complex data.
method Random connection model, fused Gromov-Wasserstein distance, differential privacy.
result Effective algorithm for generating private synthetic graphs with theoretical guarantees.
A new method compares synthetic power networks to actual ones using multiscale flat norm.
problem Comparing synthetic power networks to actual ones due to lack of correspondence.
method Proposes a multiscale flat norm approach to compute distance between networks.
result The flat norm distance captures variations more accurately than Hausdorff distance.
Many mobile robots rely on 2D laser scanners for localization, mapping, and navigation. However, those sensors are unable to correctly provide distance to obstacles such as glass panels and tables whose actual occupancy is invisible at the height the sensor is measuring. In this work, instead of estimating the distance…
The paper analyzes how well classes are separated in neural network feature space.
problem Understanding class separability in neural network feature space.
method Theoretical analysis of intra-class and inter-class distances in feature space.
result A lower bound for the probability of inter-class distance being greater than intra-class distance as a function of loss value.
This work develops a generic framework, called the bag-of-paths (BoP), for link and network data analysis. The central idea is to assign a probability distribution on the set of all paths in a network. More precisely, a Gibbs-Boltzmann distribution is defined over a bag of paths in a network, that is, on a representati…
Novel neural network approach on hyperbolic and SPD spaces.
problem Developing neural networks on symmetric spaces of noncompact type.
method Unified formulation of distance from a point to a hyperplane.
result Closed-form expression for point-to-hyperplane distance in higher-rank spaces.
Wasserstein distance improves GANs by reducing training difficulties.
problem Training difficulties and arbitrary hyperparameters in GANs.
method Estimating Wasserstein distance for generative modeling.
result Various ways to estimate Wasserstein distance for generative models.
Researchers compare brain connectomes using geodesic distance on manifold for twin pairs.
problem Assessing functional similarity in brain networks between monozygotic and dizygotic twins.
method Using fMRI data, the researchers compared functional networks between mono- and dizygotic twin pairs by measuring similarity with geodesic distance on graph Laplacians.
result Functional networks are more similar in monozygotic twins compared to dizygotic twins, and similarity is higher for task-relevant networks.
Paper explains distance-based classifiers using neural network structures.
problem Making distance-based classifiers explainable.
method Uncovering latent neural network structures in distance-based classifiers.
result Novel explanation approach outperforms baselines.
We propose fast approximations for the generalized sliced-Wasserstein distance.
problem Efficient approximation of the generalized sliced-Wasserstein distance in high dimensions.
method Deterministic approximations using random projections and concentration of measure results.
result One-dimensional projections of high-dimensional random vectors are approximately Gaussian.
Generates valid Euclidean distance matrices for molecular structures.
problem Generating point clouds in arbitrary rotations and translations is challenging.
method Developed a neural network architecture that produces valid Euclidean distance matrices invariant to rotations and translations.
result The architecture can generate molecular structures in a one-shot fashion by producing Euclidean distance matrices with a three-dimensional embedding.
SGD-trained deep networks generalize well due to regularization of distance from initialization.
problem Why deep networks generalize well despite increasing number of parameters.
method Introduced a notion of effective model capacity dependent on initialization.
result Distance from initialization regularizes model capacity, leading to generalization.
Proposes Topology Distance for evaluating GANs.
problem Challenges in evaluating GANs' goodness.
method Builds Vietoris-Rips complex on image features and defines TD based on latent manifold comparisons.
result Demonstrates TD's superiority over existing metrics.
New method improves Wasserstein distance for large-scale data.
problem High computational cost of Wasserstein distance for large-scale machine learning.
method Augmented Sliced Wasserstein Distances (ASWDs) using neural network mappings.
result ASWDs significantly outperform other Wasserstein variants in synthetic and real-world problems.
Efficiently approximates neural network function space distance.
problem Estimating the average discrepancy between neural network outputs.
method Linearized Activation Function TRick (LAFTR) for ReLU networks.
result Parametric approximation outperforms nonparametric methods in memory and accuracy.
The paper introduces a statistical distance matrix for better feature representation and clustering.
problem Lack of detailed distance representation between feature elements.
method Extended traditional statistical distance to a matrix form (statistical distance matrix) and applied hierarchical clustering.
result The statistical distance matrix with clustering (Information Mandala) provides clearer and geometrically arranged feature representations.
Deep neural networks can approximate any target probability distribution given certain conditions.
problem Approximating complex probability distributions with deep neural networks.
method Proving the existence of a deep neural network mapping that approximates a target distribution under various integral probability metrics.
result Upper bounds on the size of the neural network in terms of dimension and approximation error for different metrics.
This work proposes unsupervised learning by predicting random distances in neural networks.
problem Lack of labelled data in unsupervised learning tasks.
method Train neural networks to predict random distances in a randomly projected space, optimizing for genuine class structures.
result Learned representations outperform state-of-the-art methods in anomaly detection and clustering.
Quantum Earth Mover's distance improves stability and efficiency in quantum learning.
problem Quantum learning's loss landscapes often lead to poor local minima and gradients.
method Introduced the quantum Earth Mover's (EM) distance and proposed a quantum Wasserstein generative adversarial network (qWGAN).
result The quantum EM distance makes quantum learning more stable and efficient.
Enhanced travel time prediction using deep neural networks and road network information.
problem Improving travel time estimation using deep learning models.
method Proposes incorporating road network information into deep learning models for travel time prediction.
result Improved travel time prediction, especially with limited training data.
HighwayGraph models long-distance node relations in GNNs with improved performance.
problem Limited-layer information propagation in GNNs hinders long-distance node relation modeling.
method Proposes two solutions: implicit and explicit modeling of long-distance node relations using shallow GNN architectures and a self-training framework.
result HighwayGraph achieves consistent and significant improvements over four GNNs on three benchmark datasets.
GRNF embeds graphs into vectors preserving distances.
problem Representing graph data in a vector space while preserving distances.
method Graph Random Neural Features (GRNF) using graph neural networks.
result GRNF preserves graph metric structure and distances.
This paper proposes a new method for embedding sequences using Wasserstein distances.
problem Embedding sequences in a metric space for better pattern recognition.
method Develops a deep learning model that embeds sequences as distributions and uses Wasserstein distances for comparison.
result Distributional embeddings using Wasserstein distances outperform traditional vector embeddings.
To optimize a neural network one often thinks of optimizing its parameters, but it is ultimately a matter of optimizing the function that maps inputs to outputs. Since a change in the parameters might serve as a poor proxy for the change in the function, it is of some concern that primacy is given to parameters but tha…
Preference are central to decision making by both machines and humans. Representing, learning, and reasoning with preferences is an important area of study both within computer science and across the sciences. When working with preferences it is necessary to understand and compute the distance between sets of objects, …
K-DAREK improves KKANs for efficient function approximation with robust error bounds.
problem Efficient function approximation with uncertainty quantification for large-scale problems.
method Developed a novel learning algorithm, K-DAREK, for KKANs.
result Established robust error bounds that are distance-aware, improving efficiency and scalability.
Authors disagree with recent findings on random Gaussian weights in DNNs.
problem The relationship between angle and distance shrinkage in DNNs with random Gaussian weights is incorrect.
method Comparison of recent findings with new observations on random Gaussian weights in DNNs.
result Theorem 3 and Figure 5 in the recent paper are not accurate.
As a highlighting research topic in the multimedia area, cross-media retrieval aims to capture the complex correlations among multiple media types. Learning better shared representation and distance metric for multimedia data is important to boost the cross-media retrieval. Motivated by the strong ability of deep neura…
New metric captures individual neuron tuning across neural networks.
problem Need a metric that respects individual neuron tuning across different neural networks.
method Derived a 'soft' permutation-based metric using optimal transport theory.
result Metric avoids counter-intuitive outcomes and captures geometric insights.
Unified pipeline classifies time series using complex networks and persistent homology.
problem Classifying univariate time series using various graph constructions and metrics.
method Time series to graph, graph to dissimilarity matrix, filtration to persistence diagrams, vectorization to features.
result Persistence-based features are robust to noise and optimal graph type depends on signal structure.