The paper analyzes counterfactual invariance and its relation to conditional independence.
problem Understanding the relationship between counterfactual invariance and conditional independence.
method Theoretical analysis of existing definitions, graphical implications, and mathematical proofs.
result Counterfactual invariance implies conditional independence, but not the other way around.
Proposes a method to create fair, robust predictors that remain consistent across different scenarios.
problem Creating fair and robust machine learning models that behave consistently across different scenarios.
method Graphical criteria and a model-agnostic framework called CIP based on HSCIC.
result Demonstrates the effectiveness of CIP in enforcing counterfactual invariance across various datasets.
Study new Ricci flow invariant curvature conditions.
problem Topology of manifolds with pinched curvature.
method Provide quantitative evidence for an unpublished conjecture.
result Topology of manifolds with pinched curvature studied.
Study anti-invariant submersions from holomorphic statistical manifolds.
problem Understanding submersions in statistical manifolds.
method Introduced and analyzed anti-invariant holomorphic statistical submersions.
result Supported results with examples.
Left-invariant metrics force 2-step nilpotent groups, preserving Kähler-like conditions.
problem Existence of left-invariant pluriclosed Hermitian metrics on Lie groups.
method Analyzing left-invariant metrics on unimodular Lie groups with abelian complex structures.
result Pluriclosed flow preserves Strominger Kähler-like conditions on 2-step nilpotent Lie groups.
As a generalization of Riemannian submersions, horizontally conformal submersions, semi-invariant submersions, h-semi-invariant submersions, almost h-semi-invariant submersions, conformal semi-invariant submersions, we introduce h-conformal semi-invariant submersions and almost h-conformal semi-invariant submersions fr…
New Milnor's invariant condition for topologically slice links.
problem Conditions for topologically slice links involving Milnor's invariant.
method Different Milnor's invariant condition to handle cases not covered by previous theorem.
result New sufficient conditions for topologically slice links.
Paper provides a condition to distinguish links up to 4-moves.
problem Distinguishing links up to 4-moves is generally difficult.
method Defined a quotient of the fundamental group invariant preserved by 4-moves.
result Provides a necessary condition for triviality up to 4-moves.
Geometric invariant theory introduces stability conditions mirroring abelian category theory.
problem Stability conditions in geometric invariant theory.
method Axiomatic notion of central charge and stability condition on schemes and stacks.
result Introduction of stability conditions for polarized schemes and smooth projective varieties.
New tribrackets defined to count link homotopy invariants.
problem Counting invariants of link homotopy.
method Defined Δ-tribrackets and showed their invariants. result Counting invariants for certain tribrackets are trivial.
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.
The paper examines conditions for stochastic invariance of cones in SPDEs with jumps.
problem Stochastic invariance of cones in SPDEs with jumps.
method Sufficient conditions for stochastic invariance of closed convex cones in abstract L2-spaces. result Conditions for stochastic invariance of cones are provided and analyzed.
Proposes an alternative invariance penalty to address domain generalization issues.
problem Addressing domain generalization problems by finding invariant representations.
method Revisits the Gramian matrix of the data representation to propose an alternative invariance penalty.
result The proposed approach guarantees recovery of an invariant representation under mild conditions.
A new method evaluates invariant performance of IRM-based representations.
problem Impact of data changes on machine learning model performance.
method Proposes a novel method to evaluate invariant performance of IRM-based representations.
result Establishes a robust criterion to assess invariant performance of various representation techniques.
Proves simple type conjecture for mod 2 Seiberg-Witten invariants.
problem Proving simple type conjecture for mod 2 Seiberg-Witten invariants.
method Analyzes cohomology ring conditions to prove simple type for all smooth structures.
result Shows existence of topological 4-manifolds with mod 2 simple type.
In this paper we describe the notion of a weak lipschitzianity of a mapping on a Cq stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the …
This note is a study of nonnegativity conditions on curvature which are preserved by the Ricci flow. We focus on specific kinds of curvature conditions which we call noncoercive, these are the conditions for which nonnegative curvature and vanishing scalar curvature doesn't imply flatness. We show that, in dimensions g…
Develops tests for conditional symmetry under group actions.
problem Testing conditional symmetry in distributions under group actions.
method Nonparametric randomization tests with kernel methods and asymptotic consistency.
result Tests achieve finite-sample Type I error control and power.
Improves full conformal prediction for stochastic non-conformity measures.
problem Inability of existing conditions to guarantee full conformal prediction validity under stochastic settings.
method Introduces a new sufficient condition: Conditional Independence & Permutation Invariance in Distribution.
result Corrects the insufficient condition and provides a new sufficient condition for full conformal prediction validity.
Generative model for set-valued data using permutation invariant flows.
problem Modeling set-valued data with conditional generative models.
method Conditional generative probabilistic model using continuous normalizing flows with permutation equivariant dynamics.
result Significantly outperforms non-permutation invariant baselines in log likelihood and domain-specific metrics.
The abstract discusses nonuniqueness results for specific Riemannian invariants.
problem Identifying conditions for nonhomothetic conformal rescalings with constant Riemannian invariants.
method Identifying sufficient conditions for finite and infinite geometrically distinct periodic conformal rescalings.
result Improves and establishes nonuniqueness results for various Riemannian invariants.
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.
We consider the Yamabe invariant of a compact orbifold with finitely many singular points. We prove a fundamental inequality for the estimate of the invariant from above, which also includes a criterion for the non-positivity of it. Moreover, we give a sufficient condition for the equality in the inequality. In order t…
Paper calculates Donaldson-Thomas invariants for a specific category.
problem Relating quadratic differentials to stability conditions and invariants.
method Uses string and band techniques from representation theory.
result Agrees with physics predictions for degenerate ring domains.
Necessary and sufficient conditions are given for the Palais-Smale Condition C to hold for the Yang-Mills functional for invariant connections on a principal bundle over a compact manifold of any dimension. It is assumed that the connections are invariant under the action of a compact Lie group on the manifold, and tha…
New method MRI improves machine learning models' ability to generalize to unseen data.
problem Machine learning models often fail to generalize well to out-of-distribution data.
method Introduces a new notion of invariance (MRI) and a practical version (MRI-v1) to improve model generalization.
result MRI-v1 guarantees invariant predictors and outperforms IRM-v1 in various settings.
A novel approach learns goal-conditioned policies for locomotion using batch RL.
problem Training goal-conditioned policies for rotation invariant locomotion.
method Data augmentation and Siamese framework for invariance.
result Our approach outperforms existing RL algorithms on 3D locomotion agents.
We introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and find necessary-sufficient conditions for total manifold to be locally product Riemann…
Let X be a Fano manifold. G.Tian proves that if X admits a Kaehler-Einstein metric, then it satisfies two different stability conditions: one involving the Futaki invariant of a special degeneration of X, the other Hilbert-Mumford-stability of X w.r.t. a certain polarization. He conjectures that each of these condition…
K. Habiro gave a neccesary and sufficient condition for knots to have the same Vassiliev invariants in terms of Ck-move. In this paper we give another geometric condition in terms of Brunnian local move. The proof is simple and self-contained.
This paper provides a connection between two distinct branches of research in CR geometry -- namely, analytic and geometric conditions that suffice to establish the closed range of the Cauchy-Riemann operator and CR invariants on CR manifolds. Specifically, we work on not necessarily pseudoconvex domains $Ω\subset\math…
The existence of invariant generators for distributions satisfying a compatibility condition with the symmetry algebra is proved.
In the previous work ([14]) we introduced the well-posed boundary conditions P−,L0 and P+,L1 for the odd signature operator to define the refined analytic torsion on a compact manifold with boundary. In this paper we discuss the gluing formula of the refined…
The paper explores invariant subbundles in nonholonomic mechanics.
problem Determining invariant affine subbundles in nonholonomic and constrained variational mechanics.
method Using Spencer cohomology and iterative formulae, the paper formalizes the integrability of linear partial differential equations and determines the largest invariant affine subbundle.
result Iterative formulae for determining the largest invariant affine subbundle are provided.
Study on geometric properties of h-conformal semi-invariant submersions.
problem Exploring geometric characteristics of h-conformal semi-invariant submersions.
method Investigation of quaternionic Kähler manifolds and Riemannian manifolds, focusing on integrability of distributions and foliations.
result Established necessary and sufficient conditions for total geodesic submersions and twisted product manifolds.
Invariant measures found for contact Hamiltonian systems split into Reeb and Liouville dynamics.
problem Finding invariant measures for contact Hamiltonian systems.
method Splitting the system into Reeb and Liouville dynamics; using invariant measures and symplectic sandwiches.
result Invariant measure found for Reeb dynamics; characterization of Liouville dynamics invariant measure.
New invariant for spin 3-manifolds using super 3-cocycles.
problem Constructing an invariant for spin 3-manifolds.
method State sum construction based on super 3-cocycles and combinatorial representation.
result The invariant is sensitive to the spin structure.
We define a bordism invariant for the fiberwise intersection theory. Under some certain conditions, this invariant is an obstruction for the theory.
We find Einstein metrics on homogeneous HKT manifolds.
problem Characterizing and finding Einstein metrics on homogeneous HKT manifolds.
method Characterization and construction of invariant HKT-Einstein metrics.
result Existence and uniqueness of invariant HKT-Einstein metrics.
We obtain some results on symmetries of sub-Riemannian surfaces. In case of contact sub-Riemannian surface we base on invariants found by Hughen \cite{Hughen}. Using these invariants, we find conditions under which a sub-Riemannian surface does not admit symmetries. If a surface admits symmetries, we show how invariant…
Compact metrics on Heisenberg manifolds have a specific condition for being relatively compact.
problem Conditions for relatively compact sets of left invariant metrics on Heisenberg manifolds.
method Necessary and sufficient condition for relatively compact sets of left invariant metrics.
result A condition for a set of left invariant metrics to be relatively compact in the moduli space.
The paper studies Clairaut maps on Sasakian manifolds.
problem Investigating Clairaut maps on Sasakian manifolds.
method Analyzing necessary and sufficient conditions for geodesics and biharmonicity.
result Conditions for Clairaut anti-invariant Riemannian maps on Sasakian manifolds.
We use the theory of dual of Fréchet-Schwartz (DFS) spaces to establish a sufficient condition for top-degree solvability for the differential complex associated to a hypocomplex locally integrable structure. As an application, we show that the top-degree cohomology of left-invariant hypocomplex structures on a compact…
Dynamic risk measures follow law invariance principles over time.
problem Tackles dynamic risk measurement principles.
method Shows equivalence between adapted law invariance and recursive one-step conditional-law representation for time-consistent risk measures.
result Identifies adapted law invariance as the dynamic counterpart of ordinary law invariance.
We consider a subset S of the complex Lie algebra $\so(n,\C)$ and the cone C(S) of curvature operators which are nonnegative on S. We show that C(S) defines a Ricci flow invariant curvature condition if S is invariant under $\Ad_{\SO(n,\C)}$. The analogue for Kähler curvature operators holds as well. Although…
CIRCE measures conditional independence for learning invariant features.
problem Learning invariant features while being conditionally independent of a distractor.
method CIRCE is a measure of conditional independence applied as a regularizer in feature learning.
result CIRCE provides a zero value if and only if features are conditionally independent of the distractor given the target.
Study on SASI-lightlike submanifolds in indefinite Kaehler manifolds.
problem Characterizing and understanding SASI-lightlike submanifolds in indefinite Kaehler manifolds.
method Introduced and analyzed SASI-lightlike submanifolds, derived conditions for metric connection, and investigated integrability of distributions.
result Found necessary and sufficient conditions for the induced connection to be a metric connection on SASI-lightlike submanifolds.
Associated to every generalized complex structure is a differential Gerstenhaber algebra (DGA). When the generalized complex structure deforms, so does the associated DGA. In this paper, we identify the infinitesimal conditions when the DGA is invariant as the generalized complex structure deforms. We prove that the in…