The paper tackles automatic interpretation of manifold coordinates.
problem Finding physical meaning of abstract manifold coordinates.
method Proposes a method to explain embedding coordinates as compositions of functions from a dictionary.
result Demonstrates the effectiveness of the method on data.
Method selects interpretable circular coordinates from data.
problem Abstract circular coordinates are hard to interpret.
method Minimum-weight basis problem in vector matroid for selecting interpretable circle-valued coordinates.
result Proves consistency of cochain inner product estimator.
We explain how Itô Stochastic Differential Equations (SDEs) on manifolds may be defined using 2-jets of smooth functions. We show how this relationship can be interpreted in terms of a convergent numerical scheme. We show how jets can be used to derive graphical representations of Itô SDEs. We show how jets can be used…
Model learns Lagrangian dynamics from images for better prediction and control.
problem Lack of interpretability and applicability to high-dimensional data like images.
method Unsupervised neural network model that learns Lagrangian dynamics from images using a coordinate-aware VAE.
result Model infers interpretable Lagrangian dynamics, enabling long-term prediction and synthesis of controllers.
We construct a tangent bundle exponential map and locally autoparallel coordinates for geometries based on a general connection on the tangent bundle of a manifold. As concrete application we use these new coordinates for Finslerian geometries and obtain Finslerian geodesic coordinates. They generalise normal coordinat…
New framework learns interpretable rule ensembles without sacrificing accuracy.
problem Trade-off between accuracy and interpretability in rule ensembles.
method Introduces local interpretability and a regularizer to promote it, using coordinate descent with local search.
result Learns rule ensembles with fewer rules to explain individual predictions, maintaining comparable accuracy.
Isometry pursuit identifies orthonormal submatrices from wide matrices.
problem Identifying isometric embeddings from wide matrices.
method A convex algorithm combining normalization and multitask basis pursuit.
result The method identifies isometric embeddings from interpretable dictionaries.
New formula for implied volatility from Black-Scholes model.
problem Computing implied volatility from Black-Scholes model.
method Analytical solution using inverse Gaussian distribution.
result Explicit formulas for implied volatility with high precision.
Canonical coordinates defined for minimal time-like surfaces in n-dimensional Minkowski space.
problem Characterizing canonical coordinates on minimal time-like surfaces.
method Introducing canonical coordinates and proving their existence and uniqueness; using analysis over the algebra of double numbers.
result Canonical coordinates on minimal time-like surfaces are characterized by a natural condition for a complex function over the algebra of double numbers.
We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational, and directional. The covaria…
Algorithm learns from human demonstrations to schedule tasks efficiently.
problem Efficient resource scheduling in dynamic environments.
method Personalized apprenticeship learning framework infers decision-making criteria from heterogeneous human demonstrations.
result Achieves high accuracy in synthetic and real-world domains, outperforming baselines.
LFD method improves text classification by making features clearer and less label-leaking.
problem Creating interpretable text representations that are both predictive and understandable.
method LFD method: proposes lexical and semantic features from contrastive text pairs, screens candidates using κ, and selects features by residual gain. result LFD features achieve higher human-human and human-LLM agreement than baseline concepts and are less label-leaking.
A method for interpreting SVMs using polynomial kernels, revealing model complexity.
problem Interpreting SVMs built with truncated orthogonal polynomial kernels.
method Orthogonal Representation Contribution Analysis (ORCA) with normalized Orthogonal Kernel Contribution (OKC) indices.
result The method reveals structural aspects of model complexity not captured by predictive accuracy.
Deep autoencoder finds linear PDE coordinates for nonlinear equations.
problem Discovering linear coordinates for nonlinear PDEs.
method Residual network architecture for finding intrinsic coordinates.
result Deep learning autoencoder transforms nonlinear PDEs into linear ones.
As a contribution to interpretable machine learning research, we develop a novel optimization framework for learning accurate and sparse two-level Boolean rules. We consider rules in both conjunctive normal form (AND-of-ORs) and disjunctive normal form (OR-of-ANDs). A principled objective function is proposed to trade …
WeLa-VAE learns interpretable disentangled representations with weak supervision.
problem Learning disentangled representations without strong supervision.
method Variational inference framework with shared latent variables and modified variational lower bound.
result WeLa-VAE learns alternative disentangled representations (polar) from weak labels (distance and angle) without refined supervision.
Study embeds PC matrices into Grassmannian manifold for geometric interpretation.
problem Understanding algebraic consistency of pairwise comparisons matrices.
method Leverages Plücker coordinates and geometric interpretation of Grassmannian manifold.
result Algebraic consistency condition is equivalent to geometric consistency in G(2,n). Introduces Plücker coordinates for a complex projective octonion plane, solving an overdetermined system of relations.
problem Understanding the complex projective octonion plane and its quotient space EIII.
method Introduces Plücker coordinates and uses Clifford algebra to solve the overdetermined system of relations.
result Shows that EIII can be decomposed into F4-orbits and provides detailed analysis near the subvariety X∞.
Proposes DR-ME test for interpretable distributional treatment effects.
problem Detects invisible differences in treatment effects on distributional outcomes.
method Semiparametrically efficient finite-location test using kernel witnesses and orthogonal features.
result DR-ME reveals causal-discrepancy coordinates and has noncentral chi-square local power.
The Newlander-Nirenberg theorem links complex coordinates to the vanishing of the Nijenhuis tensor.
problem Existence of complex coordinates associated with almost complex structures.
method Simple explicit proof and supersymmetric interpretation.
result The vanishing of the Nijenhuis tensor is both necessary and sufficient for complex coordinates to exist.
TarMAC targets and coordinates multi-agent communication for cooperative tasks.
problem Coordinating multi-agent reinforcement learning in partially observable environments.
method Targeted multi-round communication approach without supervision.
result Improved performance and sample efficiency in diverse environments.
Interprets SL3-web intersections on surfaces.
problem Interpreting SL3-web intersections on surfaces.
method Intersection pairing between reduced SL3-webs and tropical sets.
result Provides a new proof of flip equivariance.
New method deflates manifolds to visualize high-dimensional data.
problem Failure of nonlinear dimensionality reduction methods on simple manifolds.
method Iterative deflation of differential operators using single-coordinate estimates.
result Empirically, recovers novel embeddings on real-world and synthetic datasets.
New algorithm for robust circular coordinates in recurrent time series data.
problem Inefficient and sensitive methods for finding circular coordinates on recurrent data.
method Subsampling, aligning, and averaging to correct uneven sampling density.
result More robust and efficient circular coordinates for neuronal recordings.
A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted to represent internal structure of matter (e.g. classical or quantum spin). The …
New adaptive stepsize method for stochastic approximation converges to target point.
problem Finding optimal step sizes for stochastic approximation algorithms.
method Adaptive block-coordinate stepsizes using online estimates of second moment.
result New method converges almost surely to a small neighborhood of the target point.
RC flow learns molecular kinetics in low dimensions.
problem Discovering interpretable low-dimensional models of molecular kinetics.
method Normalizing flow for coordinate transformation and Brownian dynamics for kinetics approximation.
result Tractable and trainable model of reduced kinetics in continuous time and space.
NDM incorporates geometric structure into neural networks for better optimization and interpretability.
problem Efficient and interpretable deep learning architectures.
method NDM is a neural network architecture that explicitly incorporates geometric structure into its design, using a Coordinate Layer, Geometric Layer, and Evolution Layer.
result NDM provides intrinsic regularization, enhancing generalization and robustness.
Optimizes explanations for linear models to enhance trust and interpretability.
problem Lack of well-defined interpretability for linear models and ad hoc approaches.
method Optimization framework using coordinate updates on coefficients.
result Derives a family of interpretability metrics for linear models.
Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of nonlinear systems using standard linear theory. The Koopman operator has emerged…
node2coords learns interpretable graph node representations robust to graph perturbations.
problem Need representations that capture graph structure and are robust to perturbations.
method Proposes a graph representation learning algorithm using Wasserstein barycenters.
result Learned representations are interpretable and stable to graph perturbations.
Study identifies 1,012 persistent wallet cohorts on Solana pump.fun, showing coordinated buying behavior.
problem Understanding coordinated buying behavior on Solana pump.fun.
method Two-stage detection pipeline: first-buyer-window extraction followed by persistent-cohort surfacing via graph co-occurrence.
result 1,012 persistent wallet cohorts identified, showing systematic co-buying across multiple launches.
Improved SINDy autoencoder for identifying noisy dynamical systems.
problem Robust identification of noisy dynamical systems from data.
method Incorporates noise-separating neural network structures into SINDy autoencoder architecture.
result Accurately recovers latent dynamics and estimates measurement noise from noisy observations.
Locally symplectic structure found on Kerr space-time.
problem Understanding Kerr space-time using geodesics.
method Identifying locally conformally symplectic structure using characteristic classes and Kerr-Schild coordinates.
result Definition of cobordism category of contact 3-manifolds and locally conformally symplectic cobordisms.
Signed-permutation coordinate transport improves model alignment across checkpoints.
problem Improper alignment of coordinate-indexed objects across model checkpoints.
method Introduces sign-marginalized Hungarian matching and coordinate-preserving transport.
result Recovering signed-permutation gauge improves coordinate alignment and model performance.
Elie Cartan's general equivalence problem is recast in the language of Lie algebroids. The resulting formalism, being coordinate and model-free, allows for a full geometric interpretation of Cartan's method of equivalence via reduction and prolongation. We show how to construct certain normal forms (Cartan algebroids) …
New algorithm for low-rank optimal transport with improved interpretability and efficiency.
problem Quadratic scaling of optimal transport coupling matrix for massive datasets.
method Factor Relaxation with Latent Coupling (FRLC) algorithm.
result Superior performance on diverse applications including graph clustering and spatial transcriptomics.
The paper analyzes LIME for tabular data and proves its behavior in large samples.
problem Understanding the behavior of LIME in tabular data settings.
method Theoretical analysis of LIME's behavior in tabular data, proving its properties in the large sample limit.
result LIME provides explanations proportional to the coefficients of the function in linear cases, but can produce misleading explanations for partition-based models.
Integrable Killing tensors are used to classify orthogonal coordinates in which the classical Hamilton-Jacobi equation can be solved by a separation of variables. We completely solve the Nijenhuis integrability conditions for Killing tensors on the sphere S3 and give a set of isometry invariants for the integrabilit…
Curvature interpretation for WDVV equation in Frobenius manifolds.
problem Understanding the WDVV equation in statistical manifolds.
method Analyzing the curvature of statistical manifolds and their tangent spaces.
result WDVV equation is equivalent to zero sectional K-curvature. New algorithm improves mean-variance optimization with finite-sample guarantees.
problem Dynamic risk management in various fields.
method Stochastic block coordinate ascent policy search.
result Finite-sample error bound analysis and convergence rate for randomly picked solutions.
FIRE extracts interpretable rules from tree ensembles.
problem Building sparse and interpretable rule sets from tree ensembles.
method Optimization-based framework with fusion regularization and sparsity-inducing penalties.
result FIRE outperforms state-of-the-art rule ensemble algorithms.
In this paper we continue the investigation of Loday's Leibniz cohomology as a new invariant for differentiable manifolds. In particular the Leibniz coboundary of a k-tensor (in the sense of differential geometry) is computed in a local coordinate chart and then interpreted in terms of the calculus of variations. For e…
New kernel interprets 3D anisotropic data with rotations and improved predictions.
problem Capturing rotated anisotropy in 3D spatial fields.
method Introduces a Lie-algebraic kernel with three principal length-scales and an explicit rotation.
result Posterior recovers rotated anisotropy and improves prediction over axis-aligned kernels.
Construct geometric interpretation of Heston model using group quantization.
problem Geometric interpretation of Heston model
method Lifted local Lie groupoid formulation
result Geometric interpretation of Heston pricing operator and Riccati equations
Clusterpath estimator simplifies graphical model interpretation for large datasets.
problem Difficulty in interpreting graphical models with many variables.
method Clusterpath estimator that groups variables for block-structured precision matrix.
result CGGM outperforms other methods in variable clustering and practical applications.
Characterizes monodromy groups for projective structures on surfaces with specified poles.
problem Characterizing monodromy groups for meromorphic projective structures on surfaces with specific singularities.
method Geometric interpretation of Fock-Goncharov coordinates and recent results on moduli spaces of representations.
result Proves the analogue of a theorem for closed surfaces and settles a long-standing question.
A new method calculates intrinsic effective sample size for manifold-valued data.
problem Challenges in choosing effective sample size for manifold-valued data.
method Proposes an intrinsic effective sample size based on kernel discrepancy.
result Establishes an exact finite-sample risk interpretation and consistency of the estimator.