t-SNE loses important features in data visualization.
problem t-SNE's loss of important features in data visualization.
method Established mathematical framework to understand t-SNE's loss in different scenarios.
result t-SNE loses important features of data in various scenarios.
The paper explains knowledge distillation by analyzing visual concepts in DNNs.
problem Understanding how knowledge distillation affects the learning of visual concepts in deep neural networks.
method The paper proposes three hypotheses and designs mathematical metrics to evaluate feature representations of DNNs.
result The hypotheses were verified through experiments on various DNNs.
Virtual reality brings non-Euclidean geometry to life.
problem Understanding non-Euclidean geometry is challenging.
method Interactive visualizations in virtual reality.
result Users can experience non-Euclidean geometry firsthand.
New model for visual cortex border completion using bicycle wheel motions.
problem Understanding border completion in the visual cortex V1.
method Sub-Riemannian Hamiltonian formalism and bicycle wheel analogy.
result Analogies between visual cortex border completion and bicycle wheel motions.
Unified view of SOMs and SNE from a common framework.
problem Comparing and understanding SOMs and SNE.
method Unified mathematical framework, quantitative comparison on datasets.
result SOMs and SNE can be derived from a common framework.
Model explains optical illusions using geometric sub-Riemannian geodesics.
problem Understanding and explaining geometrical optical illusions.
method Neuro-mathematical model based on sub-Riemannian geodesics in the Roto-Translation Group.
result Illusory contours are described as geodesics in a new metric.
A novel method visualizes higher-dimensional spaces using hyperbolic geometry.
problem Challenges in visualizing higher-dimensional spaces.
method Interactive visualization of higher-dimensional grids based on hyperbolic geometry.
result Our method shows the whole higher-dimensional space at once and avoids disadvantages of previous methods.
The paper topologically characterizes near force-free magnetic fields using Giroux correspondence.
problem Characterizing near force-free magnetic fields.
method Using Giroux correspondence and topological tools.
result Conditions for sufficiency of topological characterization of force-free magnetic fields.
New method addresses crowding in high-dimensional data visualization.
problem Crowding issue in visualizing high-dimensional data.
method Adjusting capacity of high-dimensional balls and estimating correlation dimension.
result Mitigates crowding in various distance metrics.
Computational topology shows knots can converge to stick knots.
problem Understanding convergence of smooth knots to stick knots.
method Computational experiments and mathematical visualization.
result Sufficient conditions for isotopic equivalence of knots.
This paper proves t-SNE can recover well-separated clusters, improving visualization and embedding quality.
problem The lack of mathematical foundations and inner workings of t-SNE.
method Proves t-SNE's ability to recover well-separated clusters, using early exaggeration phase and rigorous analysis.
result t-SNE in the early exaggeration phase can be rigorously analyzed and provides novel ways to set parameters.
Unified regularization framework for visualizing CNNs.
problem Visualizing concepts learned by convolutional neural networks.
method Mathematical framework unifying regularization methods, Sobolev gradients.
result Sobolev filters provide sharper reconstructions and better control over scales.
New model explains visual illusions using sub-Riemannian geometry.
problem Mathematical modeling of Poggendorff-type visual illusions.
method Cortical-inspired sub-Riemannian model with sub-Laplacian evolution.
result Sub-Riemannian kernel enhances visual misperceptions and biases.
Adds a precortical module to CNNs for improved robustness to light variations.
problem Robustness of CNNs to global light intensity and contrast variations.
method Developed a mathematical model of the mammalian visual pathway, inspired by CNNs, and added a preliminary convolutional module.
result Significantly more robust CNNs achieved with added module on MNIST, FashionMNIST, and SVHN databases.
The paper explores squircles and their 3D applications.
problem None explicitly stated; focuses on squircle equations and 3D surfaces.
method Examined and discussed squircle equations, then developed 3D surfaces based on these shapes.
result Developed 3D surfaces based on squircle equations.
New puzzles from geometry and topology.
problem Exploring puzzles from geometric and topological concepts.
method Construction from square-tiled shapes, discussion of underlying mathematics.
result Puzzles naturally associated to puzzle spaces.
GradVis visualizes and analyzes deep neural network optimization surfaces efficiently.
problem Understanding and optimizing deep neural network training landscapes.
method Developed an open-source library GradVis for efficient visualization and analysis of optimization surfaces.
result GradVis enables plotting of optimization surfaces and trajectories for large networks.
For decades, the sphere eversion has been a classic subject for mathematical visualization. The 1998 video "The Optiverse" shows geometrically optimal eversions created by minimizing elastic bending energy. We contrast these minimax eversions with earlier ones, including those by Morin, Phillips, Max, and Thurston. The…
A new model of V1 using orientation, frequency, and phase.
problem Understanding the complex behavior of V1 simple cells.
method Developed a sub-Riemannian model based on Gabor functions.
result The model enhances images using orientation, frequency, and phase.
New EM algorithms for weighted-data clustering improve audio-visual scene analysis.
problem Improving clustering of weighted data in heterogeneous environments.
method Proposed weighted-data Gaussian mixture model and two EM algorithms.
result Validation shows improved clustering in audio-visual scenes.
Study uses crochet to visualize non-Euclidean geometry.
problem Understanding non-Euclidean surfaces through physical models.
method Parametrization of crochet models to represent Lobachevskian surface.
result Crochet models reflect non-Euclidean geometry characteristics.
Francy enhances GAP for interactive discrete math with web technologies.
problem Lack of abstraction and portability in XGAP for GAP.
method Develops Francy, a graphical semantics package for GAP, integrating web technologies.
result Enhanced usability and accessibility of GAP with rich graphical environment.
Proposes GPCA module for channel attention in CNNs using Gaussian processes.
problem Improving performance in visual tasks through effective channel selection.
method Integrates Gaussian processes into channel attention mechanisms for probabilistic modeling of channel correlations.
result Demonstrates improved performance of GPCA module in end-to-end CNN training.
Unified optimization framework for matrix seriation.
problem Discovering latent structure in relational data.
method Mathematical optimization models for seriation.
result Optimization models enhance solution quality and interpretability.
Study quantifies how LLMs capture higher-order statistical structure using cumulant expansion.
problem Understanding how LLMs internalize statistical structure during next-token prediction.
method Cumulant-expansion framework treating softmax entropy as perturbation around center distribution.
result Cumulants reveal distinct signatures for mathematical vs. general text prompts, quantifying feature-learning dynamics.
The article develops a mathematical theory for uniformly distributing points on surfaces.
problem Creating representative point clouds on surfaces and higher-dimensional manifolds.
method Using Cauchy Crofton formula and its generalizations from Integral Geometry.
result A rigorous mathematical theory for point clouds on various manifolds.
Neighbor embeddings balance attraction and repulsion to visualize data.
problem Visualizing high-dimensional datasets with trade-offs between continuous and discrete structures.
method Neighbor embeddings combine attractive and repulsive forces to visualize data.
result Changing the exaggeration parameter in t-SNE yields a spectrum of embeddings with a trade-off between continuous and discrete structures.
ParaMonte::Python streamlines Bayesian data analysis with fast Monte Carlo and MCMC routines.
problem Efficiently sampling posterior distributions in Bayesian modeling and data science.
method Serial and MPI-parallelized Markov Chain Monte Carlo (MCMC) routines.
result Automated model calibration and uncertainty quantification in Bayesian analysis.
This paper studies the transition from disequilibrium to equilibrium in financial markets.
problem Modeling financial markets as disequilibrium models and analyzing their transition to equilibrium.
method Mathematical analysis using asymptotic limits and Tikhonov-Fenichel reduction.
result Stability of the reduced equilibrium model and economic implications are discussed.
Introduces basic facts on early vision's functional architecture.
problem Accessibility of early vision's functional architecture for non-specialists.
method Survey of three neurogeometric models and discussion of the conformal model.
result Synthesis of symplectic and spherical models into the conformal model.
In this article, we will formulate a mathematical framework that allows us to treat character animations as points on infinite dimensional Hilbert manifolds. Constructing geodesic paths between animations on those manifolds allows us to derive a distance function to measure similarities of different motions. This appro…
These lectures were a part of the geometry course held during the Fall 2011 Mathematics Advanced Study Semesters (MASS) Program at Penn State (\url{http://www.math.psu.edu/mass/}). The lectures are meant to be accessible to advanced undergraduate and early graduate students in mathematics. We have placed a great emphas…
KANs replace fixed MLP weights with learnable edge functions, improving accuracy and interpretability.
problem Lack of interpretability and scalability in MLPs.
method KANs use learnable activation functions on edges instead of fixed weights, replacing weights with spline functions.
result KANs outperform MLPs in accuracy and interpretability with smaller models.
This paper improves neural network explanations by quantifying and visualizing semantic compositions.
problem Improving neural network explanations for natural language processing tasks.
method Proposes a formal way to quantify word and phrase importance, introduces SCD and SOC algorithms.
result Our algorithms outperform prior methods in explaining neural network predictions.
Our project improves function approximation by seeking nonlinear analogues.
problem High-dimensional models are difficult to quantify due to sparse or expensive observations.
method Active Manifolds approach, seeking nonlinear projections to approximate the function.
result Improved estimation accuracy and accessible visualization.
GADGET framework decomposes global feature effects using recursive partitioning.
problem Misleading global feature effects when feature interactions are present.
method Generalized additive decomposition of global effects (GADGET) based on recursive partitioning.
result Minimizes interaction-related heterogeneity of local feature effects.
regvis.net offers a visual survey of regulatory visualization.
problem Lack of a comprehensive resource for regulatory visualization.
method Collection and manual tagging of 80+ publications, creation of a searchable webpage.
result First publication set tailored for regulatory visualization.
Algorithm transfers visual concepts to answer out-of-vocabulary questions.
problem Leveraging off-the-shelf visual and linguistic data for out-of-vocabulary answers in visual question answering.
method Unsupervised task discovery for learning task conditional visual classifier, then transferring to visual question answering models.
result Algorithm generalizes to out-of-vocabulary answers successfully.
Net2Vis automates CNN visualization for publications.
problem Lack of consistent visual representations in deep learning papers.
method Proposes a visual grammar and automated system for generating publication-ready CNN visualizations.
result Reduces time and ambiguity in generating network visualizations.
Convolutional networks outperform shallow classifiers on certain tasks due to hierarchical structure.
problem Understanding why convolutional networks outperform shallow classifiers on specific tasks.
method Approximation theory, visual tasks with deterministic scrambling, and network performance evaluation.
result Hierarchical structure is crucial for convolutional networks' performance on certain tasks, but not all.
BERT captures linguistic features in separate semantic and syntactic subspaces.
problem Understanding how transformer models like BERT represent linguistic features internally.
method Qualitative and quantitative investigations of BERT's internal representations.
result Evidence of a fine-grained geometric representation of word senses and syntactic representations.
Proposes a spectral method to assess and combine multiple data visualizations.
problem Evaluating and combining the strengths of different data visualization algorithms.
method Spectral method for assessing and combining multiple visualizations.
result Proposes a visualization eigenscore to quantify relative performance and a consensus visualization.
AV-CPL uses continuous pseudo-labels for AVSR combining labeled and unlabeled data.
problem Improving AVSR performance with labeled and unlabeled data.
method Semi-supervised method using continuous pseudo-labels generated by the same AVSR model.
result Significant improvements in VSR performance on LRS3 dataset.
This report synthesizes research advances in integrating machine learning with visual analytics.
problem Underexplored combination of machine learning and data visualization in visual analytics.
method Synthesizing research advances to highlight the progress and challenges.
result Opportunities and challenges identified for future research in machine learning and visual analytics.
Visualizes futures markets using particle physics tools.
problem Understanding high-velocity data in futures markets.
method Uses ROOT, an open-source data-analysis tool, to reconstruct and visualize message-based data.
result Allows stakeholders to gain a better understanding of markets and monitor effectively.
New report on machine learning visualization techniques and trends.
problem Improving trust in machine learning models through visualization.
method Analysis of peer-reviewed articles on machine learning visualization techniques.
result Rapid growth in machine learning visualization techniques over the past three years.
The abstract discusses how humans use visualizations in machine learning.
problem The reliance on human involvement in AI systems and analytics.
method Review of seven steps in the ML process and different visualization techniques.
result Different visualizations are used at various stages of the ML process.
Grad-CAM visualizes CNN predictions to explain model decisions.
problem Making CNN models transparent and understandable.
method Using class-specific gradient information to localize important regions.
result Improved understanding of CNN-based models, including image captioning and VQA.