CP2 uses geometric information to improve conformal prediction robustness.
problem CP fails under geometric data shifts, losing coverage guarantees.
method Integrates geometric pose information into CP via canonicalization.
result Integrating geometric information with CP ensures robustness under geometric shifts.
Problem of global integration of geometric structures arising in the theory of dynamical systems admitting the normal shift is considered. In the case when such integration is possible the problem of globalization for shift maps is studied.
Formula for the force field of Newtonian dynamical systems admitting the normal shift of hypersurfaces in Riemannian manifolds is considered. Problem of globalization for geometric structures associated with this formula is studied.
ReVol normalizes stock price features to mitigate distribution shifts, improving prediction accuracy.
problem Distribution shifts in stock price data hinder accurate prediction.
method ReVol uses normalization, attention-based estimation, and geometric Brownian motion.
result ReVol achieves an average improvement of more than 0.03 in IC and over 0.7 in SR.
New theory for Hamiltonian actions on special geometric structures.
problem Hamiltonian actions on cosymplectic groupoids.
method Developed a moment map theory for 0-shifted cosymplectic structures.
result Established a version of the Kirwan convexity theorem.
Theory of Newtonian dynamical systems admitting normal shift of hypersurfaces was first developed for the case of Riemannian manifolds. Recently it was generalized for manifolds geometric equipment of which is given by some regular Lagrangian or, equivalently, by some regular Hamiltonian dynamical system. In present pa…
Geometric observables detect financial regime shifts with high accuracy.
problem Detecting regime shifts in financial markets.
method Extracted four geometric observables from equity-index returns and evaluated them against various baseline methods.
result The Berry Phase Rate achieves an unbiased out-of-sample median Cohen's d of 0.72, significantly reducing false alarms.
M-FISHER detects and adapts to streaming data shifts with statistical validity and stability.
problem Detecting and adapting to distributional shifts in streaming data.
method Constructs an exponential martingale from non-conformity scores and applies Ville's inequality for detection. Fisher-preconditioned updates for adaptation.
result Establishes M-FISHER as a principled approach for robust, anytime-valid detection and geometrically stable adaptation.
Shifted symplectic Lie and L∞ algebroids model formal neighbourhoods of manifolds in shifted symplectic stacks, and serve as target spaces for twisted variants of classical AKSZ topological field theory. In this paper, we classify zero-, one- and two-shifted symplectic algebroids and their higher gauge symmetri…
Explicit BCH series radii found for special Banach-Malcev shift algebras.
problem Finding convergence radii for BCH series in specific algebraic structures.
method Established explicit convergence radii using continuity estimates and algebraic properties.
result Explicit formula for convergence radii derived and validated for various shift algebras.
Extended flatness approach for discrete-time systems considers forward and backward shifts.
problem Defining flatness for discrete-time systems with forward-shifts.
method Introducing backward-shifts to extend flatness definition.
result Extended flat systems maintain key properties like reachability and controllability.
Paper introduces a new metric to select optimal Graph Shift Operator for GNNs.
problem Empirical selection of Graph Shift Operator remains challenging.
method Introduces a novel alignment gain metric connecting geometric distortion to generalization bounds via spectral proxy.
result Provides a principled, computation-efficient criterion to rank and select optimal GSO.
Continues work on derived manifolds and symplectic schemes, constructing virtual classes.
problem Constructing virtual fundamental classes for derived manifolds and schemes.
method Cosection localization, reduced virtual fundamental classes, and applications to Donaldson-Thomas theory.
result Virtual fundamental classes for (−2)-shifted symplectic derived schemes are consistent with algebraic and differential geometric constructions. Structured credal learning separates covariate shift and label disagreement.
problem Uncertainty in real-world learning tasks due to covariate shift and noisy labels.
method Introduces a structured credal learning framework that explicitly separates these sources.
result Geometric bounds and decomposition reveal how covariate shifts affect label disagreement contributions.
Study uses geometric algebra to analyze credit cycles, revealing dangerous feedback loops.
problem Understanding and predicting dangerous feedback loops in credit cycles.
method Represent economic states as multi-vectors in Clifford algebra, focusing on bivector elements for rotational coupling.
result Geometric relationship between unemployment and credit contraction shifts from simple correlation to dangerous rotational dynamics during crises.
Class of Newtonian dynamical systems admitting normal blow-up of points in Riemannian manifolds is considered. Geometric interpretation for weak normality condition, which arose earlier in the theory of dynamical systems admitting the normal shift of hypersurfaces, is found.
Geometrically interprets cup products and defines combinatorial Pin structures.
problem Understanding Steenrod's cup products and their geometric interpretation.
method Constructs vector fields and combinatorial frames to interpret cochain-level formulas.
result Geometrically interprets cup products and defines Pin structures combinatorially.
In the framework of geometric quantization we extend the Bohr-Sommerfeld rules to a full quantization theory which resembles Heisenberg's matrix theory. This extension is possible because Bohr-Sommerfeld rules not only provide an orthogonal basis in the space of quantum states, but also give a lattice structure to this…
Study shows how to count and equidistribute cusped Hitchin representations with entropy gaps.
problem Counting and equidistribution of cusped Hitchin representations.
method Renewal theorem of Kesseböhmer and Kombrink applied to count and equidistribute.
result Entropy gaps at infinity allow for counting and equidistribution results.
In this article, existence results concerning temporal functions with additional properties on a globally hyperbolic manifold are obtained. These properties are certain bounds on geometric quantities as lapse and shift. The results are linked to completeness properties and the existence of closed isometric embeddings i…
Two approaches improve conformal Bayes for label shift, one post-hoc and one in-training.
problem Improving prediction sets for target domain under label shift.
method Two complementary approaches: post-hoc calibration and in-training adaptation.
result In-training adaptation achieves up to 43% width reduction at unchanged coverage.
The paper establishes a Lagrangian correspondence linking different geometric structures on complex varieties.
problem Identifying relationships between different geometric structures on complex varieties.
method Using perfect complexes and shifted symplectic geometries, the paper establishes a Lagrangian correspondence.
result A Lagrangian correspondence between shifted symplectic geometries of flat and Higgs perfect complexes.
Bayesian Scattering offers a simple baseline for image data uncertainty.
problem Lack of interpretable, mathematically grounded uncertainty quantification methods for image data.
method Coupling wavelet scattering transform with a simple probabilistic head.
result Bayesian Scattering provides sensible uncertainty estimates under distribution shifts.
Conformal Bayes under label shift: post-hoc calibration vs. in-training adaptation
problem Bayesian prediction sets under label shift
method Post-hoc calibration vs. In-training adaptation
result Both strategies achieve valid coverage equally in an unbiased training regime
The BPS decomposition theorem splits cohomology of symmetric stacks into invariant parts.
problem Decomposing the cohomology of smooth symmetric stacks into invariant parts.
method Using cohomological Hall induction and intersection cohomology of moduli spaces.
result Establishes the BPS decomposition theorem for various symplectic stacks.
Paper solves Christoffel-Minkowski and Weingarten curvature problems in hyperbolic space.
problem Christoffel-Minkowski and Weingarten curvature problems in hyperbolic space.
method Proved existence of solutions using a new full rank theorem.
result Existence of smooth, origin-symmetric, strictly horospherically convex solutions.
TopoGeoScore selects robust checkpoints using only source-domain representations.
problem Selecting robust checkpoints without target-domain labels or samples.
method Constructs class-conditional mutual k-nearest-neighbour graphs and extracts three interpretable signals.
result Source representations contain measurable global-local-topological evidence of robustness.
The paper studies curvature flows in hyperbolic space and proves geometric inequalities.
problem Proving geometric inequalities in hyperbolic space using curvature flows.
method Locally constrained curvature flows, h-convexity, and shifted principal curvatures.
result Established new sharp geometric inequalities comparing curvature integrals to quermassintegrals.
We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal. Geometric examples include the shifted de Rham complex of a Poisson manifold and the subcomplex of differential forms on a symplectic manifold vanishing on a Lagrang…
In this paper, we formulate a new local move on virtual knot diagram, called arc shift move. Further, we extend it to another local move called region arc shift defined on a region of a virtual knot diagram. We establish that these arc shift and region arc shift moves are unknotting operations by showing that any virtu…
New framework uses geometry of embeddings to predict robustness.
problem Monitoring robustness in models without OOD labels.
method Constructs graphs from embeddings, measures spectral complexity and curvature.
result Representation geometry predicts robustness reliably.
New deep network derived from rate reduction principles, explaining features and efficiency.
problem Understanding and optimizing deep learning architectures.
method Gradient ascent scheme for rate reduction leading to multi-layer deep network.
result Explicitly constructed multi-layer network with precise optimization and interpretation.
Estimating signals with linear recurrence relations under Gaussian noise is nearly as hard as sparse signals.
problem Estimating discrete-time signals with unknown linear recurrence relations in Gaussian noise.
method Analyzing shift-invariant subspaces and their Fourier coefficients as reproducing filters.
result The statistical complexity is nearly the same as for s-sparse signals, and the estimator is tractable. Geometric focusing affects dispersive estimates for Schrödinger and wave equations.
problem Long-time decay rate in dispersive estimates for Schrödinger and wave equations on non-trapping asymptotically conic manifolds and exact metric cones.
method Classifying the long-time decay rate in dispersive estimates for the Schrödinger and wave equations on non-trapping asymptotically conic manifolds and exact metric cones in terms of the intensity of geometric focusing.
result Each multiplicity of conjugate points within distance π on Y = ∂X0 leads to a |t|1/2-loss in the long-time decay order and a half-order shift in the regularity index in the dispersive estimate for the Schrödinger equation.
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.
Study on unknotting twisted knots using arc shift and region arc shift moves.
problem Unknotting twisted knots and finding bounds for region arc shift number.
method Introduced arc shift move and region arc shift move for twisted knots.
result Found families of twisted knots with specific arc shift and region arc shift numbers.
Study detects concept shift in online data using martingales.
problem Detecting concept shift in online datasets.
method Exchangeable martingales and conformal prediction techniques.
result Decomposes concept shift into detectable components.
The paper proves geometric inequalities and their stabilities for curves in hyperbolic space.
problem Geometric inequalities and their stabilities for curves in hyperbolic space.
method Curve flow for shifted principal curvatures, Heintze-Karcher type inequality for h-convex curves.
result Geometric inequalities and their stabilities for curves in hyperbolic space.
We construct a categorification of the quantum sl_3 projectors, the sl_3 analog of the Jones-Wenzl projectors, as the stable limit of the complexes assigned to k-twist torus braids (as k goes to infinity) in a suitably shifted version of Morrison and Nieh's geometric formulation of sl_3 link homology (math.GT/0612754).…
Paper proposes SJS model to estimate model performance under covariate and label shifts.
problem Estimating model performance when both covariates and labels shift.
method Sparse Joint Shift (SJS) model and SEES algorithm.
result SEES achieves significant shift estimation error improvements over existing approaches.
Geometric approach improves probabilistic robustness in neural networks.
problem Widespread lack of robustness in deep neural networks to adversarial examples.
method Geometric view on Probabilistically Robust Learning (PRL) and introduction of new perimeters.
result Existence of solutions and properties of modified PRL models.
Extends FJS analysis to general label spaces, including classification and regression.
problem Distribution shift in general label spaces, including covariate and label shifts.
method Proposes a framework for analyzing FJS in general label spaces and generalizes existing results.
result Generalizes FJS analysis to general label spaces, including classification and regression.
Paper tackles high-dimensional quantile regression with distribution shift using transfer learning.
problem Efficiency of knowledge transfer is severely impacted by distribution shift in high-dimensional regression.
method Proposes a novel transferable set and framework for three types of distribution shift: parameter, covariate, and residual.
result Establishes estimation error bounds and source detection consistency for the proposed method.
Unified learning bound for covariate and concept shifts.
problem Generalization under distribution shift in machine learning.
method Support-agnostic definitions of covariate and concept shifts using entropic optimal transport, leading to a unified error bound applicable to various loss functions and label spaces.
result Development of estimators for shifts with concentration guarantees and the DataShifts algorithm for quantifying and estimating the error bound.
Proposes SGShift to identify shifted features causing model performance degradation under concept shift.
problem Concept shift leading to miscalibration in ML models across domains.
method SGShift method for identifying sparse set of shifted features using feature selection and statistical tools.
result SGShift identifies shifted features more accurately than baseline methods, requires few samples in the shifted domain, and is robust to complex cases.
New contact structures defined on differentiable stacks.
problem Defining contact structures on differentiable stacks.
method Introducing 0-shifted and +1-shifted contact structures. result Shifted contact structures provide new insights into geometry.
Graphs models are vulnerable to distribution shifts, which this work explains and mitigates.
problem Graph Neural Networks (GNNs) are susceptible to distribution shift, leading to performance degradation.
method Theoretical analysis quantifying conditional shift, proposing an approach to estimate and minimize it.
result The proposed approach demonstrates up to 10% absolute ROC AUC improvement under various distribution shifts.
RLSbench benchmarks domain adaptation under label proportion shifts, revealing widespread failures and proposing a two-step meta-algorithm.
problem Domain adaptation under label proportion shifts is poorly understood and inconsistent across methods.
method RLSbench introduces a large-scale benchmark with 500 distribution shift pairs. It proposes a two-step meta-algorithm to improve domain adaptation methods under label proportion shifts.
result The two-step meta-algorithm improves domain adaptation methods by 2-10% accuracy points under large label proportion shifts.