Slice-based Learning improves model performance on critical data subsets.
problem Low performance on critical data subsets in machine learning models.
method Proposes a new programming model (Slice-based Learning) that uses slicing functions to specify critical data subsets and combines these with an attention mechanism.
result Improves model performance by up to 19.0 F1 on slices and 4.6 F1 overall.
Defines weak geodesics on specific subsets of manifolds.
problem Characterizing geodesics on prox-regular subsets of Riemannian manifolds.
method Defining weak geodesics as continuous curves with weak regularities, and characterizing them as viscosity critical points of the energy functional.
result Characterizes weak geodesics on prox-regular subsets of Riemannian manifolds.
In this paper we consider the compactness of β-symplectic critical surfaces in a Kähler surface. Let M be a compact Kähler surface and Σi⊂M be a sequence of closed βi-symplectic critical surfaces with βi→β0∈(0,∞). Suppose the quantity ∫Σicosqαi1dμi (for some q>4) a…
Proposes a method to partition univariate data into unimodal subsets.
problem Partitioning univariate multimodal data into unimodal subsets.
method Recursive splitting around valley points of the data density using properties of critical points on the convex hull of the ecdf plot.
result Obtains a hierarchical statistical model of the initial dataset as a mixture of UMMs.
We give a necessary condition for a closed subset of R3 to be the set of critical points of some smooth function. In particular we obtain that for example neither the Whitehead continuum nor the p-adic solenoid are such a critical sets.
Necessary and sufficient condition is given for a set A⊂R1 to be a subset of the critical values set for a Ck function f:Rm→R1.
Proves critical exponent for Θ−positive representations in discrete subgroups.
problem Determining the critical exponent for Θ−positive representations. method Analyzes discrete subgroups Γ⊂PSL(2,R) and their geometric properties. result Equality of critical exponent holds if and only if Γ is a lattice for geometrically finite Γ. ModHiFi identifies critical components for model modification without gradients or loss function.
problem Modifying open weight models without access to training data or loss function.
method Theoretical analysis of Lipschitz-continuous networks, Subset Fidelity metric, and ModHiFi algorithm.
result ModHiFi-P and ModHiFi-U achieve significant performance improvements in model pruning and unlearning.
This work views neural networks as data generating systems and applies anomalous pattern detection techniques on that data in order to detect when a network is processing an anomalous input. Detecting anomalies is a critical component for multiple machine learning problems including detecting adversarial noise. More br…
Proves planar Lipschitz critical points of area functional are smooth.
problem Lawson-Osserman conjecture about smoothness of critical points.
method Outer variations to prove smoothness of critical points.
result Proves conjecture for planar case.
This paper uses Reinforcement Learning to select features from a large dataset.
problem Selecting the best features to minimize variance and bias in machine learning models.
method Formulated the feature selection problem as a Markov Decision Process (MDP) and used Temporal Difference (TD) algorithm.
result The approach using Reinforcement Learning outperformed other methods in selecting features.
The distance function to a generic submanifold behaves well under small perturbations.
problem The critical points of the distance function to a generic submanifold can be poorly behaved.
method Listed and proved regularity conditions on critical and μ-critical points of a submanifold, and showed they are generically satisfied and stable under small C2 perturbations. result The distance function to a submanifold satisfies Morse-like conditions when the regularity conditions are fulfilled.
The paper explores the shape of filling-systole subspace in surface moduli space and critical points of systole function.
problem Understanding the structure and critical points of the filling-systole subspace in surface moduli space.
method Analyzing Teichmüller and Weil-Petersson distances to determine the proximity of points to the subspace.
result Most points in Mg are within a specific Teichmüller distance from Xg and have a certain distance from the thick part of Mg. Study on CR curves in 3-sphere, focusing on critical curves integration and existence.
problem Addressing the integration and existence of critical curves in the CR 3-sphere.
method Provided a procedure for the explicit integration of general critical curves and characterized closed curves.
result Existence of infinite countably many closed critical curves.
New method characterizes minimal surfaces in 3D space.
problem Characterizing minimal surfaces in 3D space.
method Alexandrov Reflection Method
result Embedded minimal free boundary annuli in B3 are the critical catenoid. The tori Tr=rS1×sS1⊂S3, where r2+s2=1, are constrained Willmore surfaces, i.e. critical points of the Willmore functional among tori of the same conformal type. We compute which of the Tr are stable critical points.
Distance function to a finite set is a topological Morse function.
problem Characterizing the topological Morse function of a finite set.
method Analyzing the distance function to a finite set in \(\mathbb{R}^n\).
result Distance function is a topological Morse function, with precise critical points and indices.
We consider a variational problem for submanifolds Q ⊂ M with nonempty boundary ∂Q = K. We propose the definition that the boundary K of any critical point Q have constant mean curvature, which seems to be a new perspective when dim Q \textless{} dim M . We then construct small nearly-spherical solutio…
Given a parallel calibration φ∈Ωp(M) on a Riemannian manifold M, I prove that the φ--critical submanifolds with nonzero critical value are minimal submanifolds. I also show that the φ--critical submanifolds are precisely the integral manifolds of a C∞(M)--linear subspace $\sP \subset Ω^p(M…
We show that an embedded minimal annulus Σ2⊂B3 which intersects ∂B3 orthogonally and is invariant under reflection through the coordinate planes is the critical catenoid. The proof uses nodal domain arguments and a characterization, due to Fraser and Schoen, of the critical catenoid as the unique…
We prove that every continuous function on a separable infinite-dimensional Hilbert space X can be uniformly approximated by smooth functions with no critical points. This kind of result can be regarded as a sort of very strong approximate version of the Morse-Sard theorem. Some consequences of the main theorem are as …
ViTaX provides formal guarantees for targeted explanations in safety-critical systems.
problem Need trustworthy explanations for safety-critical deep neural networks.
method Formal reachability analysis for targeted, semifactual explanations.
result First method to provide formally guaranteed explanations of model resilience.
LLMs can be influenced by unseen dataset subtexts, revealing new ways to select data subsets.
problem Understanding how datasets subtly influence LLMs and their properties.
method Logit-Linear-Selection (LLS) method to select subsets of datasets.
result LLS reveals hidden effects in LLMs that persist across different models and architectures.
Study critical exponents in normal subgroups of higher rank Lie groups.
problem Understanding critical exponents in normal subgroups of higher rank Lie groups.
method Analyzing subgroups and their critical exponents in a higher rank semi-simple Lie group.
result Critical exponents of normal subgroups coincide under certain conditions.
We prove that every continuous mapping from a separable infinite-dimensional Hilbert space X into Rm can be uniformly approximated by C∞ smooth mappings {\em with no critical points}. This kind of result can be regarded as a sort of very strong approximate version of the Morse-Sard theorem. Some…
A new invariant captures geometric features of circle embeddings.
problem Capturing geometric features of circle embeddings invariantly.
method Chordal distance transform and persistent homology.
result Persistent homology of chordal distance transform is invariant.
XNB classifier improves model interpretability by selecting class-specific features.
problem Overfitting and poor model accuracy in high-dimensional datasets.
method XNB classifier uses Kernel Density Estimation and class-specific feature subsets.
result XNB classifier matches traditional Naive Bayes performance while improving interpretability.
We prove a Chern-Lashof type formula computing the expected number of critical points of smooth function on a smooth manifold M randomly chosen from a finite dimensional subspace V⊂C∞(M) equipped with a Gaussian probability measure. We then use this formula this formula to find the asymptotics of the e…
The paper proves properties of curves in Riemannian manifolds.
problem Characterizing curves in Riemannian manifolds.
method Analyzing locally minimizing and weak geodesics.
result Locally minimizing curves are weak geodesics under certain conditions.
The paper proves that Gaussian field critical points have finite moments.
problem Proving the finiteness of moments for Gaussian field critical points.
method General approach not specific to critical points, using Taylor polynomial non-degeneracy.
result The finiteness of moments of the number of critical points of Gaussian fields.
Compression affects deep networks differently, impacting underrepresented data points.
problem Disparate impact of compression on different classes and images.
method Analysis of deep neural network pruning and quantization effects.
result Compression disproportionately impacts model performance on underrepresented data points.
We consider the estimation of the policy gradient in partially observable Markov decision processes (POMDP) with a special class of structured policies that are finite-state controllers. We show that the gradient estimation can be done in the Actor-Critic framework, by making the critic compute a "value" function that …
Tight isoparametric hypersurfaces in spheres have minimal critical points.
problem Finding minimal critical points on isoparametric hypersurfaces.
method Münzner's work on isoparametric hypersurfaces in spheres.
result Isoparametric hypersurfaces in spheres are tight.
We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Based on an idea of B. White, we prove an abstract genericity result that employs the infinite dimensional Sard--…
Develops an algorithm to find the best subset of points for maximizing the coefficient of determination.
problem Finding the optimal subset of points for maximizing the coefficient of determination in robust correlation analysis.
method The extit{quadratic sweep} method, which involves projecting points into \(\mathbb{R}^5\) and iterating over linearly separable \(k\)-subsets.
result The method optimally finds the best subset of points for maximizing the coefficient of determination without error over several million trials up to \(n=30\).
We propose definitions of fairness in machine learning and artificial intelligence systems that are informed by the framework of intersectionality, a critical lens arising from the Humanities literature which analyzes how interlocking systems of power and oppression affect individuals along overlapping dimensions inclu…
Flow of curves with curvature and forcing vector field exists.
problem Existence of a curve flow with curvature and forcing.
method Proved existence through Brakke motion law.
result Non-trivial flow of curves exists through singularities.
ELMV uses ensemble learning to handle missing values in EHR data.
problem Significant missing values in EHR data cause bias and unreliable conclusions.
method ELMV constructs multiple subsets with lower missing rates and uses a support set for ensemble learning.
result ELMV outperforms conventional methods in critical feature identification and outcome prediction.
The paper calculates critical points of systole function on Teichmüller space.
problem Critical points with pathological feature in surfaces of large genus.
method Integer linear programming with symmetry breaking technique.
result Found minimal filling sets of systoles in genus 5 with 8 geodesics.
Let K⊂S4 be a 2-knot, that is, a smoothly embedded 2-sphere in S4. The Morse-Novikov number MN(K) is the minimal possible number of critical points of a Morse map S4∖K→S1 belonging to the canonical class in H1(S4∖K). We prove that for a classical knot $K\sub…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also requires the storage of a large matrix in memory. These factors restrict the applicat…
Paper proposes a method to identify negative transfers in multitask learning using surrogate models.
problem Identifying subsets of source tasks that improve target task performance in multitask learning.
method Surrogate modeling to precompute multitask learning performances and approximate them with a linear regression model.
result The approach predicts negative transfers from multiple source tasks to target tasks more accurately than existing methods.
Estimates reliability of nuclear fuel using advanced modeling techniques.
problem Determining the reliability of TRISO-coated particle fuel, which has small failure probabilities and expensive computational models.
method Coupled active learning, multifidelity modeling, and subset simulation.
result Multifidelity modeling strategies consistently reduce the number of high-fidelity model calls.
The paper characterizes potential functions whose level sets are orbits in mechanical systems.
problem Characterizing smooth potential energy functions on the plane with specific level set properties.
method Analyzing inverse curvature flow and properties of level sets.
result Analytic or functions with totally path-disconnected critical sets must be radial, while every compact convex set is a critical set of a Levi potential.
AdOBEst-LDP improves privacy-preserving frequency estimation for categorical data.
problem Estimating categorical distributions online while preserving privacy.
method AdOBEst-LDP uses adaptive randomized response mechanism to enhance future data utility.
result AdOBEst-LDP selects optimal subset for LDP mechanism with high probability.
Let (X,0)⊂(Rn,0) be the germ of a closed subanalytic set and let f and g:(X,0)→(R,0) be two subanalytic functions. Under some conditions, we relate the critical points of g on the real Milnor fibre X∩f−1(δ)∩Bε, 0<∣δ∣≪ε≪1, to the topology of thi…
GraN-GAN normalizes gradients for better GAN performance.
problem Improving image generation in GANs with piecewise linear discriminators.
method Piecewise Gradient Normalization (GraN) for input-dependent normalization.
result Significant performance gains in image generation across various datasets.
Imputation-Powered Inference improves subpopulation efficiency in missing data settings.
problem Complex missing data patterns challenge standard inference methods.
method Imputation-Powered Inference (IPI) combines blackbox imputation with bias correction.
result IPI provides valid and efficient M-estimation under MCAR blockwise missingness.