Deep neural nets on 1-D data are convex Lasso models with reflection features.
problem Training neural networks on 1-D data.
method Proving equivalence to convex Lasso problems with discrete, explicitly defined dictionary matrices.
result Reflection features in neural networks with certain activations.
Deep neural networks favor symmetric structures, enabling multilevel symmetries.
problem Understanding and optimizing deep neural networks.
method Formulating DNN training as convex Lasso problems with geometric algebra.
result Deep networks inherently favor symmetric structures, enabling multilevel symmetries.
Decision trees are a popular technique in statistical data classification. They recursively partition the feature space into disjoint sub-regions until each sub-region becomes homogeneous with respect to a particular class. The basic Classification and Regression Tree (CART) algorithm partitions the feature space using…
We show that a tensor field of any rank integrates to zero over all broken rays if and only if it is a symmetrized covariant derivative of a lower order tensor which satisfies a symmetry condition at the reflecting part of the boundary and vanishes on the rest. This is done in a geometry with non-positive sectional cur…
Study characterizes cryospheric spectral feature space using joint PC+t-SNE approach.
problem Characterize cryospheric spectral feature space for remote sensing applications.
method Compare and contrast two approaches for identifying feature space basis vectors via dimensionality reduction (PCA and t-SNE).
result Joint characterization reveals distinct continua and clusters of ice reflectance properties.
Study examines how machine learning attribution methods reflect risk in finance.
problem Ensuring machine learning attribution methods accurately reflect underlying risks in finance.
method Examined Shapley value and Integrated Gradients, and derived axioms from asset pricing domain knowledge.
result Neither Shapley value nor Integrated Gradients can satisfy all axioms for reflecting risks accurately.
For technology (like serious games) that aims to deliver interactive learning, it is important to address relevant mental experiences such as reflective thinking during problem solving. To facilitate research in this direction, we present the weDraw-1 Movement Dataset of body movement sensor data and reflective thinkin…
Reflective Hamiltonian Monte Carlo struggles with high-dimensional sampling.
problem Slow mixing in reflective Hamiltonian Monte Carlo with inexact reflections.
method Quantifying instantaneous non-uniformity with Sinkhorn divergence; analyzing particle motion in spheres and cubes; constructing low-dimensional toy models.
result Particles spontaneously unmix, leading to resonances in particle density.
The paper models SOFR and EFFR dynamics, reconciling diffusive and piecewise paths.
problem Updating interest rate models for SOFR, which is becoming a key benchmark.
method Calibrates a model to SOFR and EFFR futures prices, reconciling diffusive and piecewise paths.
result The model reflects key empirical features of SOFR dynamics and reconciles diffusive and piecewise paths.
In this paper, we present a family of a control-stopping games which arise naturally in equilibrium-based models of market microstructure, as well as in other models with strategic buyers and sellers. A distinctive feature of this family of games is the fact that the agents do not have any exogenously given fundamental…
Method evaluates classification uncertainty with adaptively chosen features.
problem Finding a balance between model efficiency and fairness.
method Adaptively selects features for equalized coverage in classification.
result Valid and effective method demonstrated on simulated and real data.
First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made---for the continuous-time case---in Mallat, 2012, and Wiatowski and Bölcskei, 2015. This paper considers the discrete case, introduces new convolutional neural network architectures, and proposes a mathemati…
Interpretable machine-learning models can be unstable under multicollinearity, leading to oscillatory weights that do not reflect meaningful contributions.
problem Interpretable machine-learning models can be unstable under multicollinearity.
method Theoretical analysis of eigenmodes of the feature correlation matrix.
result Small-eigenvalue modes associated with multicollinearity amplify fluctuations in the weights and generate oscillatory patterns that do not necessarily reflect meaningful contributions.
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves to evaluation of whether or not a time series is multifractal and width of the …
Very often features come with their own vectorial descriptions which provide detailed information about their properties. We refer to these vectorial descriptions as feature side-information. In the standard learning scenario, input is represented as a vector of features and the feature side-information is most often i…
Two new methods assess feature importance for fairness in machine learning models.
problem Understanding how features influence fairness in machine learning models.
method Two model-agnostic approaches: permutation and occlusion.
result Simple, scalable, and interpretable methods to quantify feature importance for fairness.
A discrete subgroup of the group of isometries of the hyperbolic space is called reflective if up to a finite index it is generated by reflections in hyperplanes. The main result of this paper is a complete classification of the reflective (and quasi-reflective) subgroups among the Bianchi groups and their extensions.
New method produces reflections with nonseparating fixed points.
problem Constructing hyperbolic manifolds with reflective symmetries.
method Standard method for constructing closed hyperbolic manifolds.
result Fixed point sets of reflections are nonseparating.
Survey explores interactions between four conformal dynamics branches.
problem Understanding complex dynamics through different mathematical concepts.
method Examples and general results with technical tools.
result Dynamical relations between Schwarz reflection parameter spaces and anti-rational maps/ reflection groups.
One reflection suffices for orthogonal weights, reducing GPU usage.
problem Efficiently computing orthogonal weight matrices without high GPU utilization.
method Use an auxiliary neural network to compute one reflection instead of many.
result One reflection is sufficient for orthogonal weights, improving GPU utilization.
Researchers quantify the relationship between feature depth and performance in deep neural networks.
problem Understanding how depth affects feature extraction and generalization in deep neural networks.
method Adaptive analysis of feature-depth trade-offs in deep nets, proving optimal generalization performance.
result Optimal generalization performance achieved through empirical risk minimization on deep nets.
We consider the two problems of predicting links in a dynamic graph sequence and predicting functions defined at each node of the graph. In many applications, the solution of one problem is useful for solving the other. Indeed, if these functions reflect node features, then they are related through the graph structure.…
Minimal surfaces in 3-sphere created by reflections from polygons, with new examples based on pentagons.
problem Constructing minimal surfaces in 3-sphere using reflections.
method Minimal n-gon solves free boundary problem; curvature lines combinatorics investigated. result New examples of minimal reflection surfaces based on pentagons.
Adaptive PI by reweighting nonconformity scores improves model uncertainty reflection.
problem CP methods using a constant correction for all test points ignore individual uncertainties.
method QRF learns distribution of nonconformity scores and assigns weights to samples.
result PI lengths more aligned with model uncertainty and improved adaptiveness.
Study thin hyperbolic reflection groups and their properties.
problem Characterize and enumerate thin hyperbolic reflection groups.
method Analyze Zariski dense subgroups of hyperbolic isometries, apply Vinberg algorithm.
result All thin hyperbolic reflection groups are enumerable.
We consider the problem of estimating a ranking on a set of items from noisy pairwise comparisons given item features. We address the fact that pairwise comparison data often reflects irrational choice, e.g. intransitivity. Our key observation is that two items compared in isolation from other items may be compared bas…
Minimal surfaces reflect across spheres, proving annulus uniqueness.
problem Uniqueness of free boundary minimal annuli in balls.
method Reflection principle applied to minimal surfaces meeting spheres at 90 degrees.
result Every embedded free boundary minimal annulus in a ball is the critical catenoid.
Hausdorff reflection keeps space shape intact.
problem Preserving shape type in spaces.
method Hausdorff reflection method.
result Hausdorff reflection preserves shape type.
Graph cross network improves graph classification accuracy.
problem Improving graph classification accuracy.
method Graph cross network (GXN) with vertex infomax pooling (VIPool) and feature-crossing layer.
result Improves graph classification accuracy by 2.12% and 1.15%.
Glare is a phenomenon that occurs when the scene has a reflection of a light source or has one in it. This luminescence can hide useful information from the image, making text recognition virtually impossible. In this paper, we propose an approach to detect glare in images taken by users via mobile devices. Our method …
Study extends reflective submanifold theory to compact homogeneous spaces.
problem Characterize reflective submanifolds in compact isotropy irreducible spaces.
method Extend previous results to infinite-dimensional Hilbert spaces.
result Inverse image of reflective submanifolds is also reflective.
New reflection groups derived from torus knots with finite meridians.
problem Understanding reflection groups derived from torus knot groups with finite meridians.
method Using the theory of J-groups and Coxeter groups, study quotients of torus knot groups.
result Classification of toric reflection groups and their properties.
Predicting interactions between structured entities lies at the core of numerous tasks such as drug regimen and new material design. In recent years, graph neural networks have become attractive. They represent structured entities as graphs and then extract features from each individual graph using graph convolution op…
Study compares price patterns of cryptocurrencies and stocks using machine learning.
problem Investor behavior in cryptocurrencies vs. stocks.
method Machine learning models (LR, RF, SVM) classify price time series of cryptocurrencies and stocks.
result Cryptocurrencies and stocks have distinct price patterns, explained by various statistical features.
Proposes a framework to assess feature importance without algorithm constraints.
problem Lack of a general framework for assessing feature importance across different algorithms.
method Develops a nonparametric framework for algorithm-agnostic variable importance assessment.
result Valid confidence intervals and testing strategies for variable importance.
We review a method for click-through rate prediction based on the work of Menon et al. [11], which combines collaborative filtering and matrix factorization with a side-information model and fuses the outputs to proper probabilities in [0,1]. In addition we provide details, both for the modeling as well as the experime…
Deep networks learn features suddenly, akin to a phase transition.
problem Understanding sudden feature learning in deep networks.
method Adaptive kernel approach applied to two teacher-student models.
result Feature learning and Grokking are analogous to a first-order phase transition.
A hyperbolic lattice is called \textit{1.2-reflective} if the subgroup of its automorphism group generated by all 1- and 2-reflections is of finite index. The main result of this article is a complete classification of 1.2-reflective maximal anisotropic lattices of rank 4.
A hyperbolic reflection group is a discrete group generated by reflections in the faces of an n-dimensional hyperbolic polyhedron. This survey article is dedicated to the study of arithmetic hyperbolic reflection groups with an emphasis on the results that were obtained in the last ten years and on the open problems.
We propose a semantic segmentation model that exploits rotation and reflection symmetries. We demonstrate significant gains in sample efficiency due to increased weight sharing, as well as improvements in robustness to symmetry transformations. The group equivariant CNN framework is extended for segmentation by introdu…
This paper compares self-reflection and budget tuning for LLMs, revealing domain-specific performance gains.
problem Improving inference-time performance of LLMs without retraining, balancing quality, cost, and latency.
method Systematic comparison of self-reflection and budget tuning across mathematical reasoning and translation tasks, evaluating various LLMs and model families.
result Substantial domain-dependent variation in self-reflection effectiveness, with up to 220% performance gains in mathematical reasoning.
FinVision uses LLM agents to predict stock markets by processing various financial data types.
problem Challenges in integrating diverse financial data for accurate stock market prediction.
method Multi-agent framework with LLMs specialized in different financial data types and a reflection module.
result The reflection module enhances decision-making capabilities for financial trading.
Study how models represent features in naturalistic learning problems.
problem Understanding which features models use and ignore in naturalistic tasks.
method Synthetic datasets with controlled task-relevance of features, training models to recognize both easy and hard features.
result Models preferentially represent task-relevant features and suppress task-irrelevant ones over training.
This paper describes caustics of wave fronts reflected by a surface.
problem Understanding the geometry of caustics formed by wave fronts reflected by a surface.
method Purely geometric description of caustics, clarifying their dependence on surface characteristics.
result Clarifies the geometry and topology of caustics formed by wave fronts after reflection from a mirror surface.
Picard modular groups are shown to be generated by complex reflections.
problem Understanding the structure of Picard modular groups using reflections.
method Using presentations from previous works to show generation by reflections.
result Picard modular groups mPU(2,1,Od) are generated by complex reflections. A hyperbolic lattice is called \textit{(1,2)-reflective} if its automorphism group is generated by 1- and 2-reflections up to finite index. In this paper we prove that the fundamental polyhedron of a Q-arithmetic cocompact reflection group in the three-dimensional Lobachevsky space contains an edge s…
XGBoost fails to accurately identify relevant features, while interpretable methods do.
problem Accurately identifying relevant features in black-box models like XGBoost.
method Comparison of variable importance methods (CART, Optimal Trees, XGBoost, SHAP) across various experiments.
result Interpretable methods outperform black-box models in feature selection accuracy.
Survey data imputation methods impact feature selection and importance assessment.
problem Impact of different imputation methods on feature selection and importance assessment in survey data.
method Investigated eight imputation methods (listwise deletion, MICE, missRanger, mixGBoost) and three learners (Random Forest, XGBoost, linear model) in a simulation study.
result Different imputation methods yield varying feature selection and importance assessments.