Study of small growth invariants in Goursat distributions.
problem Understanding local invariants of Goursat distributions.
method Analysis of the small growth sequence and its relation to structural invariants.
result Relate small growth invariants to structural invariants of Goursat distributions.
Study structural invariants of Goursat distributions related to curve singularities.
problem Understanding local invariants of Goursat distributions.
method Investigate structural invariants akin to curve singularities on surfaces.
result Relate structural invariants to small growth invariants in the sequel.
IRM learns representations invariant to training distributions for better generalization.
problem Learning generalizable models across different training distributions.
method IRM learns a data representation that remains consistent across multiple training distributions, ensuring an optimal classifier matches across them.
result IRM enables out-of-distribution generalization by learning invariant correlations.
Paper studies invariant distributions of bi-Hamiltonian structures.
problem Integrability of invariant distributions in bi-Hamiltonian structures.
method Description and investigation of invariant distributions.
result All invariant distributions of non-degenerate bi-Hamiltonian structures are described.
Study finds homogeneous spaces with geodesic orbits but no integrable distributions.
problem Characterizing homogeneous spaces with specific geometric properties.
method Examined Lie groups with compact stabilizers and classified spaces based on geodesic orbits and integrable distributions.
result Identified homogeneous spaces with geodesic orbits but lacking integrable invariant distributions.
New probabilistic invariants bound classical topological complexity and category.
problem Bounding classical topological complexity and category.
method Developed probabilistic variants of one-category and diagonal topological complexity.
result Identified new invariants with distributional category and complexity on Eilenberg-Mac Lane spaces.
This paper tackles domain generalization by learning invariant class conditional distributions.
problem Learning invariant representations across different domains with varying distributions.
method Proposes a conditional invariant representation to ensure invariance of class conditional distributions.
result Guarantees invariance of the joint distribution P(h(X),Y) if class prior P(Y) remains invariant. New approach combines invariance and information bottleneck for OOD generalization.
problem OOD generalization failures in classification tasks.
method Revisit linear regression tasks, prove information bottleneck constraint necessary, propose combined approach.
result Combined invariance and information bottleneck approach improves OOD generalization.
New framework learns sufficient invariant features robustly across distribution shifts.
problem Learning robust models under distribution shifts between training and test datasets.
method Sufficient Invariant Learning (SIL) framework and Adaptive Sharpness-aware Group Distributionally Robust Optimization (ASGDRO) algorithm.
result Empirical evaluations confirm ASGDRO's robustness against distribution shifts.
Efficiently estimates densities of multidimensional shift-invariant distributions.
problem Density estimation for shift-invariant multidimensional distributions.
method Efficient algorithms for learning any distribution in the class from samples, using total variation distance.
result Shift-invariant distributions can be learned efficiently with a number of samples and time proportional to 1/εd+2 and 1/ε2d+2 respectively. Quantum invariant derived from ternary cohomology of self-distributive structures.
problem Defining and proving a quantum invariant from ternary cohomology.
method Constructing a ribbon category from a TSD set, showing it coincides with the cocycle invariant.
result The ribbon cocycle invariant is a quantum invariant.
This paper develops methods for obtaining distribution-free prediction regions for invariant representations.
problem Distributional shifts in machine learning models.
method Invariant risk minimization and weighted conformity scores.
result Proves the effectiveness of adaptive conformal intervals for uncertainty estimation.
Estimates model performance under distribution shift using domain-invariant predictors.
problem Poor performance of models on test distributions different from training distributions.
method Uses domain-invariant predictors as a proxy for unknown target labels.
result Shows that the complexity of latent representations influences target risk.
The existence of invariant generators for distributions satisfying a compatibility condition with the symmetry algebra is proved.
Symmetry distribution in naturally reductive nilpotent Lie groups matches invariant induced by fixed vectors.
problem Understanding symmetry distribution in naturally reductive nilpotent Lie groups.
method Analyzing the invariant distribution induced by fixed vectors of isotropy.
result Symmetry distribution matches the invariant induced by fixed vectors.
Novel framework improves graph learning for out-of-distribution generalization.
problem Graph out-of-distribution generalization challenges in neural networks.
method Invariant Graph Learning based on Information bottleneck theory (InfoIGL).
result Achieves state-of-the-art performance in graph classification tasks under OOD generalization.
We consider the SO(3) Witten-Reshetikhin-Turaev quantum invariants of random 3-manifolds. When the level r is prime, we show that the asymptotic distribution of the absolute value of these invariants is given by the standard Rayleigh distribution and independent of the choice of level. Hence the probability that the qu…
Conditions for metallic structures to induce integrable distributions and geodesic invariance.
problem Conditions for metallic structures to induce integrable and geodesically invariant distributions.
method Analyzing tensor fields and adapted connections associated with metallic structures.
result Chen-type inequality for metallic distributions and conditions for metallic maps to preserve these distributions.
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that all possible differences between samples are of interest -- discovered difference…
The study defines and analyzes semi-invariant submanifolds in complex contact metric manifolds.
problem Characterizing semi-invariant submanifolds in complex contact metric manifolds.
method Definition and derivation of relations, integrability conditions of distributions.
result Obtained useful relations and integrability conditions for semi-invariant submanifolds.
This research focuses on invariant probabilistic predictions, showing they are not robust under distribution shifts.
problem The challenge of creating robust probabilistic predictions that remain consistent under distribution shifts.
method A causality-inspired framework to investigate invariance and robustness of probabilistic predictions with respect to proper scoring rules.
result Arbitrary distribution shifts do not admit invariant and robust probabilistic predictions, unlike point predictions.
A new method learns graph distributions invariant to node ordering.
problem Graphs are hard to model due to node ordering invariance issues.
method Score-based generative modeling with permutation equivariant graph neural network.
result The method achieves better or comparable graph generation results.
Study finds a method to discover causal relationships that are invariant to marginal distributions.
problem Current causal discovery methods are sensitive to marginal distributions, leading to unreliable results.
method Proposes a non-parametric estimator that marginalizes the marginals to find intrinsic causal relationships.
result The proposed method yields causal estimators competitive with current methodologies and emphasizes uncertainty.
Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X)=n, ran…
The distribution of Chern-Simons invariants on 3-manifolds resembles quadratic residues.
problem Distribution of Chern-Simons invariants on 3-manifolds.
method Analyzing the values of the Chern-Simons function on conjugacy classes of representations.
result Chern-Simons invariants tend to become equidistributed on the circle with white noise fluctuations.
Constructs portfolios based on Hellinger distance to normal, finding market invariance.
problem Finding a market invariant for portfolio construction.
method Uses Hellinger distance to normal distribution for portfolio construction and analysis.
result Minimum Hellinger distance varies drastically between markets, suggesting market invariance.
Employing the Klein-Gordon equation, we propose a generalized Black-Scholes equation. In addition, we found a limit where this generalized equation is invariant under conformal transformations, in particular invariant under scale transformations. In this limit, we show that the stock prices distribution is given by a C…
The distributional category bounds manifold invariants and imposes constraints.
problem Bounding manifold invariants and understanding constraints.
method Using geometric conditions like non-negative Ricci curvature, the distributional category bounds invariants such as the first Betti number and macroscopic dimension.
result Equality of bounds imposes specific constraints on the manifold.
GALA framework learns invariant graph representations via environment augmentation with minimal assumptions.
problem Learning invariant graph representations from different environments without additional assumptions.
method Developed GALA framework with minimal assumptions of variation sufficiency and consistency. Uses an assistant model to differentiate graph environment changes.
result Extracting maximally invariant subgraphs to proxy predictions identifies underlying invariant subgraphs for successful out-of-distribution generalization.
Simplified proofs and new distributions on anti-quasi-Sasakian manifolds.
problem Properties of anti-quasi-Sasakian manifolds.
method Simplified proofs and discussion of new invariant distributions.
result New invariant distributions exist on every anti-quasi-Sasakian manifold.
Defines g-expectation of distributions and its applications.
problem Defining g-expectation of distributions. method Two special cases of nonlinear g and law-invariant g-expectation. result Explicit derivation of g-expectation of distributions. RIA method improves OoD generalization for covariate shift.
problem Improving out-of-distribution generalization under covariate shift.
method Adversarial label invariant graph data augmentations for OoD generalization.
result RIA method achieves high accuracy compared to OoD baselines.
Normal geodesic flows flows of Carnot-Caratheodory are discussed from the point of view of the theory of Hamiltonian systems. The geodesic flows corresponding to left-invariant metrics and left- and -right-invariant rank 2 distributions on the three-dimensional Heisenberg group are analysed as integrable systems. The f…
A new method improves cross-domain sentiment analysis by learning weighted domain-invariant representations.
problem Label distribution changes across domains harm domain adaptation in DIRL.
method Proposes WDIRL, a modification to DIRL that learns weighted domain-invariant representations.
result Empirical studies show the effectiveness of WDIRL in cross-domain sentiment analysis.
Study invariant connections on multivariate Gaussian distributions.
problem Understanding statistical connections on multivariate Gaussian distributions.
method Investigate invariant connections on N0n with the Fisher metric. result Explicitly determined invariant connections and their moduli spaces.
Study curvature invariants in sub-Riemannian manifolds.
problem Understand curvature invariants in sub-Riemannian geometry.
method Prove geometrical inequalities for submanifolds with orthogonal distributions.
result Inequalities for submanifolds with orthogonal distributions are derived.
The paper studies invariant functions and their relation to Landsberg surfaces.
problem Investigating the geometry of invariant functions and their applications to Landsberg surfaces.
method Investigating the geometry of S-invariant functions and their associated vertical subdistribution, and relating the holonomy distribution to these subdistributions. result For Landsberg surfaces, if the flag curvature is S-invariant, it is constant, and the surface is Riemannian. Proposes FSM-IRL to learn invariant network representations considering feature and structural shifts.
problem Spatial heterogeneity and temporal dynamics lead to OOD generalization issues in geographic networks.
method Introduces FSM-IRL model that accounts for feature and structural distribution shifts using causal attention and reweighting.
result Demonstrates strong learning capabilities on geographic and social network datasets in OOD scenarios.
The paper studies distributions on surfaces and their connection to twistor spaces.
problem Understanding distributions invariant under geodesic flows on surfaces.
method Analyzes transport equations on unit tangent bundles and connects to twistor spaces.
result Holomorphic distributions form a unital algebra and are bijectively related to functions on twistor space.
Boosted Control Functions improve prediction under distributional shifts.
problem Prediction under distributional shifts in the presence of hidden confounding.
method Boosted Control Function (BCF) and ControlTwicing algorithm.
result BCF allows for distribution generalization and invariance under nonlinear, non-identifiable structural functions.
In 1979, M. Kashiwara and M. Vergne formulated a conjecture on a Lie group G which implies that the Duflo isomorphism of Z(g) and S(g)^g extends to a natural module isomorphism between the spaces of germs of invariant distributions on G and g=Lie(G), respectively. They also proved their conjecture for G solvable. Using…
Study geometric inequalities for CR-submanifolds using curvature invariants.
problem Geometric inequalities for CR-submanifolds in almost Hermitian spaces.
method Comparing mutual curvature invariants with Chen-type invariants and proving geometric inequalities.
result Proved geometric inequalities with intermediate mean curvature squared for CR-submanifolds.
Paper tackles label noise in transfer learning, proposing a new framework.
problem Label noise in source domain affects learning of invariant representations and correcting label shift.
method Proposes Denoising Conditional Invariant Component (DCIC) framework to handle noisy labels.
result Proposed framework ensures extraction of invariant representations and unbiased estimation of target domain labels.
In this paper, we first study the Poisson reductions of controlled Hamiltonian (CH) system and symmetric CH system by controllability distributions. These reductions are the extension of Poisson reductions by distribution for Poisson manifolds to that for phase spaces of CH systems with external force and control. We g…
Study on weaving knots W(3,n) confirms they are fibered and provides normal distribution evidence.
problem Investigate polynomial knot invariants and homologies of weaving knots.
method Compute polynomial knot invariants and homologies for W(3,n), analyze Khovanov homology ranks.
result W(3,n) are fibered knots and Khovanov homology ranks asymptotically follow a normal distribution.
New connections found on zero-mean multivariate normal distributions.
problem Characterizing statistical connections on zero-mean multivariate normal distributions.
method Investigating invariant conjugate symmetric statistical connections on the submanifold of zero-mean multivariate normal distributions.
result Invariant connections on zero-mean multivariate normal distributions are not uniquely characterized by invariance under the general linear group action.
Some new results on geometry of classical parabolic Monge-Ampère equations (PMA) are presented. PMAs are either \emph{integrable}, or \emph{nonintegrable} according to integrability of its characteristic distribution. All integrable PMAs are locally equivalent to the equation uxx=0. We study nonintegrable PMAs by …
Proposes a method to predict responses from covariates over time.
problem Predicting responses from covariates with changing conditional distributions over time.
method Invariant Subspace Decomposition (ISD) framework that splits the conditional distribution into time-invariant and time-dependent components.
result The decomposition can be used for zero-shot and time-adaptation prediction tasks.