SFB uses stable features to adapt unstable ones for better performance.
problem Improving classifier performance on out-of-distribution data by leveraging stable features.
method SFB learns a predictor that separates stable and unstable features, then adapts unstable predictions using stable predictions.
result SFB can learn an asymptotically-optimal predictor without test-domain labels.
Algorithm identifies and transfers unstable features to create robust classifiers.
problem Developing unbiased classifiers from input-label pairs alone.
method Contrast different data environments in source tasks to encode unstable features, then cluster target task data and minimize worst-case risk.
result Our method maintains robustness across synthetic and real-world environments.
Stable health predictions need deconfounding test set features.
problem Stability of predictions in health machine learning is compromised by selection biases.
method Deconfounding the test set features improves prediction stability across different environments.
result Improved stability achieved by deconfounding test set features.
Unstable minimal surfaces are the unstable stationary points of the Dirichlet-Integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used. The application of this method for minimal surfaces in the Euclidean spacce was presented in \cite{s3}. We…
New deep learning method preserves orientation in shape matching.
problem Symmetry issues in shape matching.
method Orientation-aware functional maps using complex functional representations and DiffusionNet.
result Stable correspondence predictions with robust orientation preservation.
Ricci flow simulations show unstable Fubini-Study metrics develop singularities.
problem Understanding the behavior of unstable perturbations in Ricci flow.
method Numerical simulations of Ricci flow starting from unstable Fubini-Study metrics.
result Ricci flow solutions from unstable Fubini-Study metrics develop local singularities.
Study finds limits for conical Kähler-Einstein metrics on unstable surfaces.
problem Optimal upper bounds for conical Kähler-Einstein metrics on K-unstable del Pezzo surfaces.
method Established optimal upper bounds for cone angles of Kähler-Einstein metrics with conical singularities.
result Optimal upper bounds for conical Kähler-Einstein metrics on K-unstable del Pezzo surfaces.
Noncompact Ricci-flat solutions have infinite unstable dimensions.
problem Understanding unstable dimensions of noncompact Ricci-flat solutions.
method Derived sufficient conditions for infinite-dimensional unstable manifolds.
result Noncompact Ricci-flat solutions have uncountably many unstable perturbations.
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.
A framework for quantifying uncertainty in feature importance values.
problem Stable interpretation of feature importance values in machine learning models.
method A novel method based on pairwise comparisons of feature importance values to produce confidence intervals for feature ranks.
result The method produces simultaneous confidence intervals for feature ranks, enabling selection of top-k important features.
Large learning rates work surprisingly well in standard parameterization, contrary to theory.
problem Theoretical limits of large learning rates do not match practical network behavior.
method Fine-grained analysis of learning rates and network behavior under cross-entropy loss.
result There are two distinct sub-regimes of unstable learning rates, with a controlled divergence regime where features continue to evolve.
New loss function helps learn unstable dynamical systems.
problem Gradient descent fails to learn unstable dynamical systems.
method Introduced a time-weighted logarithmic loss function.
result Time-weighted loss function effectively learns unstable systems.
Unstable minimal surfaces in n-space link to hyperbolic products.
problem Characterizing unstable minimal surfaces in Rn and their product counterparts. method Lifting to R-trees, deforming to hyperbolic products, and proving instability equivalence. result Unstable minimal surfaces in Rn imply unstable surfaces in product hyperbolic spaces. Segre varieties' hyperplane sections are unstable under certain conditions.
problem Stability of hyperplane sections of Segre varieties under different conditions.
method Proving instability with respect to any polarization for non-smooth or meqn cases. result Normal hyperplane sections of Segre varieties are K-unstable under specified conditions.
Humans learn a predictive model of the world and use this model to reason about future events and the consequences of actions. In contrast to most machine predictors, we exhibit an impressive ability to generalize to unseen scenarios and reason intelligently in these settings. One important aspect of this ability is ph…
Proves transitivity of real Anosov diffeomorphisms with specific properties.
problem Transitivity of real Anosov diffeomorphisms with specific properties.
method Proves transitivity using specific properties of real Anosov diffeomorphisms.
result Proves transitivity of real Anosov diffeomorphisms.
Study shows instability of specific cone solutions in high-dimensional spaces.
problem Unstable solutions of minimal graphs in high codimension.
method Min-max technique applied to Euclidean spaces.
result First examples of non-smooth unstable minimal graphs.
This work examines the stability of GD and SGD near minima, revealing nonlinear dynamics that differ from linear analysis.
problem The stability of optimization algorithms like GD and SGD near minima is not well understood.
method The authors derive an exact criterion for stable oscillations of GD near minima in the multivariate setting, considering high-order derivatives.
result Nonlinear dynamics can diverge in expectation even if a single batch is unstable, challenging linear analysis.
In this note we show that the bi-invariant Einstein metric on the compact Lie group G2 is dynamically unstable as a fixed point of the Ricci flow. This completes the stability analysis for the bi-invariant metrics on the compact, connected, simple Lie groups. Interestingly, G2 is the only unstable exceptional…
Survey of computations for Riemann surface moduli spaces, focusing on unstable homology.
problem Computing unstable homology of moduli spaces of Riemann surfaces.
method Integral, mod-2, and rational coefficient computations; use of homology operations.
result Explicit generators of unstable homology for most cases determined.
Constructs a family to handle unstable fibers on complex surfaces.
problem Handling unstable fibers on complex surfaces.
method Uses Teichmüller theory to construct a degenerating family over the moduli space.
result Any fibered complex surface with unstable fibers can be pulled back from the constructed family.
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.
We study the structure of the smooth manifold which is defined as the intersection of a stable manifold and an unstable manifold for an invariant Morse-Smale function.
In this paper, we introduce a non linear ODE method to construct CMC surfaces in Riemannian manifolds with symmetry. As an application we construct unstable CMC spheres and outlying CMC spheres in asymptotically Schwarzschild manifolds with metrics like gij=(1+l1)2δij+O(l−2). The existence of uns…
Neuroimage analysis usually involves learning thousands or even millions of variables using only a limited number of samples. In this regard, sparse models, e.g. the lasso, are applied to select the optimal features and achieve high diagnosis accuracy. The lasso, however, usually results in independent unstable feature…
New proof associates partitions to isotopic pseudo-Anosov homeomorphisms.
problem Stable and unstable foliations for pseudo-Anosov homeomorphisms.
method Geometric realization of Fathi's result for isotopic homeomorphisms.
result Associated stable and unstable partitions for isotopic pseudo-Anosov homeomorphisms.
We show that the pair (X,−KX) is K-unstable for a del Pezzo manifold X of degree five with dimension four or five. This disprove a conjecture of Odaka and Okada.
New model captures asymmetric rough volatility with Zumbach effect.
problem Capturing asymmetric rough volatility and Zumbach effect.
method Proposes a bivariate QHawkes process to model asymmetric buying and selling actions.
result Derives a super-rough-Heston model preserving the Zumbach effect.
A novel framework interprets driving patterns using Action phases clustering.
problem Challenges in comprehending driving heterogeneity from underlying behavior mechanisms.
method Resampling and Downsampling Method (RDM) followed by iterative clustering calibration.
result Six driving patterns identified in real-world datasets, revealing dynamic nature of driving.
A crypto coin designed to provide a stabilization instrument backed up by minded like financial investments instruments to maintain the purchase value of savings across time, in order to construct new tools for unstable economies.
We show that a strict, nearly Kähler 6-manifold with either second or third Betti number nonzero is linearly unstable with respect to the ν-entropy of Perelman and hence is dynamically unstable for the Ricci flow.
In this paper we conjecture the stability and vanishing of a large piece of the unstable rational cohomology of SL_n Z, of mapping class groups, and of Aut(F_n).
Ensemble models provide more accurate feature importance estimates than single models.
problem Inaccurate variable importance estimates due to model instability and stochasticity.
method Theoretical analysis and validation on benchmarks and real data.
result Ensembling at the model level reduces excess risk and provides more accurate variable-importance estimates.
This article deals with stability issues related to geodesic X-ray transforms, where an interplay between the (attenuation type) weight in the transform and the underlying geometry strongly impact whether the problem is stable or unstable. In the unstable case, we also explain what types of artifacts are expected in te…
New algorithms improve Langevin Monte Carlo efficiency.
problem High computational cost of classical Langevin Monte Carlo.
method Integrates ensemble feature into LMC, constraining gradient approximations.
result Constrained Ensemble Langevin Monte Carlo reduces gradient computation.
DIVI clusters noisy high-dimensional data with stable feature gating.
problem Challenging clustering in high-dimensional noisy data.
method Data-informed variational clustering framework combining global feature gating and adaptive structure growth.
result DIVI performs competitively under severe feature noise and remains computationally feasible.
The paper proves regularity of states on manifolds with unstable dynamics.
problem Propagation of regularity in dynamical systems with unstable manifolds.
method Leafwise semiclassical pseudodifferential calculus adapted to foliated spaces.
result Pollicott-Ruelle resonant states are smooth over entire manifolds if smooth on unstable leaves.
We give examples of smooth surfaces with negative first Chern class which are slope unstable with respect to certain polarisations, and so have Kahler classes that do not admit any constant scalar curvature Kahler metrics. We also compare this to the work of Song-Weinkove on the J-flow.
Node2vec embeddings are unstable and unstable with parameter choices.
problem Stability and robustness of node2vec embeddings for graph classification.
method Analysis of node2vec embeddings from multiple perspectives.
result Node2vec embeddings are unstable with respect to parameter choices.
CTRF combines logged data and randomized experiments for robust prediction.
problem Robust prediction models to handle distributional shifts between training and testing data.
method CTRF uses existing training data and a small amount of randomized experiment data to train a robust model.
result CTRF produces robust predictions and outperforms baseline methods in the presence of feature shifts.
We construct Hodge filtered function spaces associated to infinite loop spaces. For Brown-Peterson cohomology, we show that the corresponding Hodge filtered spaces satisfy an analog of Wilson's unstable splitting. As a consequence, we obtain an analog of Quillen's theorem for Hodge filtered Brown-Peterson cohomology fo…
The paper shows measures equidistribute on affine submanifolds with a rate.
problem Understanding equidistribution of measures on affine invariant submanifolds.
method Analyzing unstable foliations and using results from homogeneous dynamics.
result Measures of large dimension equidistribute on affine invariant submanifolds with an effective rate.
The paper explores maximal destabilizers for both K-stability and Chow-stability in unstable situations.
problem Exploring maximal destabilizers for K-stability and Chow-stability in unstable situations.
method Using non-Archimedean pluripotential theory and idealistic assumptions, the paper provides a route to show that maximal K-destabilizers are quantized by maximal Chow-destabilizers.
result Maximal K-destabilizers are quantized by maximal Chow-destabilizers.
A new method corrects weight values to improve treatment effect estimation.
problem Estimating heterogeneous treatment effects in high-dimensional data with sample selection bias.
method Differentiable Pareto-Smoothed Weighting (DPSW) framework.
result Our method outperforms existing methods in treatment effect estimation.
Study finds Kähler-Einstein metrics on two Pasquier varieties.
problem Existence of Kähler-Einstein metrics on specific varieties.
method Analyzes Pasquier's two-orbits varieties to find metrics.
result New example of K-unstable Fano manifold with Picard number one.
Combines RFs and GLMs for better accuracy and interpretable feature importance.
problem Inability to interpret random forests (RFs) due to black box nature and unstable feature importance methods.
method Reinterprets decision trees and MDI as linear regression and R² values, combining RFs and GLMs in RF+.
result MDI+ outperforms existing feature importance measures in identifying signal features and stability.
AEN-SAEs address feature starvation in sparse autoencoders by stabilizing the geometric alignment of sparse coding.
problem Feature starvation in sparse autoencoders, leading to unstable and misaligned representations.
method Adaptive Elastic Net SAEs (AEN-SAEs) combine ℓ2 and ℓ1 terms to stabilize the sparse coding map and control feature interactions. result AEN-SAEs mitigate feature starvation without heuristic resampling, maintaining competitive reconstruction abilities.
CV inference can be invalid for relatively unstable model comparisons.
problem The validity of cross-validation for model comparison is questioned when models are relatively unstable.
method The study proves that simple, individually stable models can generate relatively unstable comparisons, invalidating CV inference.
result The Lasso and soft-thresholding generate relatively unstable comparisons, invalidating CV inferences.