Modeling curvature-sensitive cells in visual cortex with geometric structures.
problem Understanding the functional architecture of curvature-sensitive cells in the visual cortex.
method Geometric model based on Engel structure and SIM(2) symmetry.
result Identified SIM(2) as the natural symmetry group for curvature-sensitive cells.
Modeling curvature-sensitive cells in visual cortex using manifold geometry.
problem Understanding how curvature influences cell function in the visual cortex.
method Developed a 4D manifold with canonical Engel structure to represent orientation, position, curvature, and scale.
result Characterized curvature-sensitive receptive profiles using left-invariant generators of the Engel structure.
Proposes a new model to identify unknown counterfactual outcomes for continuous variables.
problem Counterfactual inference for continuous outcomes with strong assumptions.
method Curvature Sensitivity Model to relax assumptions and provide informative bounds.
result Demonstrates effectiveness of the Curvature Sensitivity Model in identifying counterfactual outcomes.
The paper defines price sensitivity and liquidity in CFMMs and links it to curvature.
problem Understanding the relationship between CFMM curvature and market performance.
method Proposes a definition of price sensitivity and liquidity, and links it to CFMM curvature.
result Curvature of CFMMs affects market performance and liquidity provider incentives.
Revisits conformal metrics with finite Q-curvature, providing necessary and sufficient conditions.
problem Understanding conformal metrics with finite total Q-curvature.
method Introduces conformal mass and provides necessary and sufficient conditions for normality.
result Derives volume comparison theorems and proves a positive mass type theorem related to Q-curvature.
JORC-UMAP improves UMAP by incorporating geometric and topological priors.
problem UMAP's local Euclidean distance assumption fails to capture intrinsic manifold geometry, leading to topological tearing and structural collapse.
method JORC-UMAP introduces Ollivier-Ricci curvature as a geometric prior and Jaccard similarity as a topological prior to reinforce edges and reduce redundant links.
result JORC-UMAP reduces tearing and collapse more effectively than standard UMAP and other DR methods, as measured by SVM accuracy and triplet preservation scores.
New method uses Ricci curvature for hypergraph clustering, outperforming existing techniques.
problem Community detection in hypergraphs with large hyperedges.
method Extending Ricci flow to hypergraphs by defining edge probability measures and transporting them on the line expansion.
result Enhanced sensitivity to hypergraph structure, especially in large hyperedges.
We prove that a Ricci curvature based method of triangulation of compact Riemannian manifolds, due to Grove and Petersen, extends to the context of weighted Riemannian manifolds and more general metric measure spaces. In both cases the role of the lower bound on Ricci curvature is replaced by the curvature-dimension co…
HLRC offers a new curvature metric for hypergraphs that balances interpretability and efficiency.
problem Challenges in geometric characterization of hypergraphs with higher-order interactions.
method Hypergraph lower Ricci curvature (HLRC) defined in closed form.
result HLRC consistently reveals meaningful higher-order organization in diverse hypergraph datasets.
A new method for machine learning updates reduces complexity and improves robustness.
problem Stochastic gradient updates are inefficient and sensitive to feature scaling.
method Incremental Gauss-Newton Descent (IGND) reduces the need for matrix operations and improves robustness.
result IGND improves robustness to sensitivity scaling and can be competitive with common stochastic optimizers.
New Riemannian GNNs reduce over-squashing in graphs with negative curvature.
problem Over-squashing in Riemannian graph neural networks.
method Generalization of Hyperbolic GNNs to Riemannian manifolds of variable curvature.
result Bounds on sensitivity of node features in Riemannian GNNs as layers increase.
The study finds obstructions to certain Riemannian metrics using Lorentzian geometry.
problem Finding obstructions to curvature distinguished Riemannian metrics.
method Dual Lorentzian metrics and Penrose's plane wave limit.
result Necessary local conditions for certain Riemannian metrics.
Paper develops novel privacy mechanism for Riemannian manifold data using geometric analysis and heat diffusion.
problem Privacy-preserving estimation of generalized Frechet mean on Riemannian manifolds.
method Characterizes Renyi divergence via Harnack inequalities, introduces mechanisms based on heat diffusion and Langevin process.
result Proposes mechanisms for nonnegative and general Riemannian manifolds with detailed utility analyses.
Prevents sensitive data generation in diffusion models using labeled and unlabeled data.
problem Generating sensitive data in diffusion models using unlabeled data.
method Positive-Unlabeled Diffusion Models, approximating ELBO with labeled and unlabeled data.
result Prevents the generation of sensitive data without compromising image quality.
A framework for sensitivity measures using scoring functions.
problem Constructing sensitivity measures for any elicitable functional.
method Score-based sensitivities constructed via consistent scoring functions.
result Demonstrated intuitive and desirable properties of score-based sensitivities.
This work provides efficient algorithms for approximating ℓ_p sensitivities and related statistics.
problem Estimating the importance of datapoints in high-dimensional datasets.
method Efficient algorithms for computing α-approximation of ℓ_1 sensitivities and total sensitivity using importance sampling and sensitivity computations.
result Real-world datasets have significantly lower intrinsic effective dimensionality than theoretical predictions.
Unified framework for CVA sensitivities, hedging, and risk assessment.
problem Computing and managing Credit Value Adjustment (CVA) sensitivities and risks.
method Probabilistic machine learning and refined regression on simulated data, validated by Monte Carlo methods.
result Identification of optimal sensitivities for practical tasks like hedging and risk assessment.
New method speeds up causal sensitivity analysis.
problem Bounding causal effects in unobserved confounding.
method Amortized approach using prior-data fitted networks.
result Orders of magnitude faster computation.
A new approach to sensitivity analysis without the Sobol decomposition.
problem Traditional sensitivity indices like Sobol indices have limitations.
method Introducing sensitivity measures that generalize existing indices and define interaction effects.
result Sensitivity measures can create new indices and define interaction effects.
Differentially private geodesic regression for non-Euclidean data.
problem Protecting sensitive data on non-linear spaces like manifolds.
method K-Norm Gradient (KNG) mechanism for Riemannian manifolds.
result Theoretical bounds for sensitivity of geodesic regression parameters.
Worst-Case Sensitivity measures model sensitivity to uncertainty set size.
problem Model sensitivity to uncertainty set size in Distributionally Robust Optimization.
method Introducing Worst-Case Sensitivity as a measure of model sensitivity, and deriving closed-form expressions for various uncertainty sets.
result DRO solutions can be sensitive to the family and size of the uncertainty set, and worst-case sensitivity reflects these properties.
Simplified equation predicts model sensitivity to data.
problem Understanding model sensitivity to training data is challenging and costly.
method Derived using Bayesian principles, the Memory-Perturbation Equation (MPE) unifies and generalizes existing sensitivity measures.
result Empirical results show sensitivity estimates during training can predict generalization on unseen test data.
Paper introduces AIF for anomaly detection with variable feature sensitivity.
problem Lack of variable sensitivity in anomaly detection methods.
method Extended Isolation Forest with feature sensitivities (Anisotropic Isolation Forest).
result AIF enables anomaly detection with controllable sensitivity to different features.
Geometric modeling for human food and chemical sensitivities.
problem Modeling biochemical processes in humans with sensitivities.
method Geometric approach to biochemical modeling.
result Geometric models improve understanding of sensitivities.
New approach detects sensitive info in text, outperforming previous methods.
problem Detecting sensitive information in unstructured text documents.
method Developed novel recursive neural network approaches for sensitive info detection, assuming only labeled examples.
result Our approaches significantly outperform previous keyword-based methods on real-world data.
SeReNe prunes neurons with low sensitivity to reduce network size.
problem Large neural networks consume too many resources on resource-constrained devices.
method Exploits neural sensitivity as a regularizer to prune neurons with low sensitivity.
result Pruning neurons with low sensitivity achieves competitive compression ratios.
A new procedure for learning cost-sensitive SVM(CS-SVM) classifiers is proposed. The SVM hinge loss is extended to the cost sensitive setting, and the CS-SVM is derived as the minimizer of the associated risk. The extension of the hinge loss draws on recent connections between risk minimization and probability elicitat…
Proposes a new adaptive gradient method based on gradient differences.
problem Manual tuning of stepsize in vanilla gradient methods.
method Adaptation driven by cumulative squared norms of gradient differences.
result More robust than AdaGrad in various settings.
Paper uses Chebyshev Tensors for accurate dynamic sensitivities and ISDA SIMM computation.
problem Computing dynamic sensitivities and initial margin for financial instruments.
method Uses Chebyshev Tensors in Monte Carlo simulations to compute dynamic sensitivities and ISDA SIMM.
result High accuracy and computational gains for FX swaps and Spread Options.
New method calculates sensitivity of system failure probability.
problem Difficulty in computing sensitivity of failure probability.
method Monte Carlo strategy using response gradient and kernel smoothing.
result Single Monte Carlo run for sensitivity estimates.
Paper introduces RCaI, a risk-sensitive control method using Rényi divergence.
problem Risk-sensitive control in reinforcement learning.
method RCaI extends CaI using Rényi divergence variational inference.
result Risk-sensitive optimal policy can be obtained by solving a soft Bellman equation.
The paper analyzes robustness and sensitivity of rough Volterra stochastic volatility models.
problem Analyzing the robustness and sensitivity of stochastic volatility models.
method Statistical tests and empirical analysis on Apple Inc. equity options.
result Comparison of different models' robustness and sensitivity to option data structure.
Optimizes portfolios using neural network approximations of asset sensitivities to common drivers.
problem Optimizing portfolios with complex asset dynamics and common drivers.
method Model asset dynamics with PDEs, approximate sensitivities with neural networks, and use hierarchical clustering on sensitivity matrix for optimization.
result Achieves over-performance in portfolio optimization across various markets and datasets.
Refines geometric center of mass analysis for Einstein field equations.
problem Analyzing the geometric center of mass of Willmore surfaces in initial data for Einstein field equations.
method Refined Lyapunov-Schmidt analysis to study geometric center of mass of area-constrained Willmore surfaces.
result The geometric center of mass agrees with the Hamiltonian center of mass under specific conditions.
The paper shows how to use proxy attributes for fairness in machine learning models with missing sensitive group data.
problem Measuring and enforcing fairness in machine learning models with incomplete sensitive group data.
method Using proxy-sensitive attributes to derive upper bounds on multiaccuracy and multicalibration violations and adjust models to satisfy these fairness notions.
result Provable upper bounds on multiaccuracy and multicalibration violations can be derived using proxy-sensitive attributes in the absence of sensitive group data.
Linking output sensitivity to deep learning generalization.
problem Understanding and comparing the generalization properties of deep neural networks.
method Linking the loss function to output sensitivity and analyzing its relation to bias-variance decomposition.
result Output sensitivity is a strong metric for comparing generalization performance of deep networks.
Transformers are less sensitive to input perturbations compared to other models.
problem Understanding the inductive biases of transformers and distinguishing them from other architectures.
method Identified token-wise sensitivity as a metric to explain transformers' inductive biases across different data modalities.
result Transformers have lower sensitivity than MLPs, CNNs, ConvMixers, and LSTMs, across vision and language tasks.
Paper introduces a new method for risk-sensitive investment management using RL.
problem Risk-sensitive portfolio management with unknown model parameters.
method Combines RL and risk-sensitive stochastic control with Gaussian perturbations for exploration.
result Endogenous relative-entropy regularization and optimal investment strategy derived.
The paper proves a new discrete Laplacian for 3D meshes and shows its superiority over primal construction.
problem Developing a more accurate discrete Laplacian for 3D meshes.
method Proves the Euler-Lagrange equation for the Dirichlet energy using the associated discrete Laplacian of the dual construction.
result The associated discrete Laplacian is optimal in R3 compared to the primal construction. Proposes efficient sensitivity analysis for complex Bayesian models.
problem Inefficiency of sensitivity analyses in complex Bayesian models.
method SA-ABI: weight sharing and neural network rapid inference.
result Efficiently integrates sensitivity analyses into Bayesian inference.
This paper proposes CSADA to make DNNs cost-sensitive.
problem Over-parameterization challenges cost-sensitive classification in DNNs.
method CSADA framework using adversarial data augmentation.
result CSADA effectively minimizes overall cost and reduces critical errors.
New CRB derived for curved models using extrinsic geometry.
problem Estimate curved statistical families accurately.
method Vector generalization of CRB with curvature correction using SDP and SOS relaxations.
result Directional curvature correction provides more accurate estimation.
Recent work has explored how to train machine learning models which do not discriminate against any subgroup of the population as determined by sensitive attributes such as gender or race. To avoid disparate treatment, sensitive attributes should not be considered. On the other hand, in order to avoid disparate impact,…
NeuralCSA uses neural networks to analyze causal effects under unobserved confounding.
problem Challenges in causal inference from observational data due to unobserved confounding.
method Proposes a neural framework (NeuralCSA) for generalized causal sensitivity analysis.
result Demonstrates theoretical and empirical validity of NeuralCSA for causal inference.
Proposes an angle-based framework for multicategory cost-sensitive classification.
problem Cost-sensitive multicategory classification challenges.
method Angle-based cost-sensitive classification framework without sum-to-zero constraint.
result Proposed boosting algorithms yield competitive classification performances.
Popular approaches to differential privacy, such as the Laplace and exponential mechanisms, calibrate randomised smoothing through global sensitivity of the target non-private function. Bounding such sensitivity is often a prohibitively complex analytic calculation. As an alternative, we propose a straightforward sampl…
Deep learning predicts market sensitivities for cost-effective index tracking.
problem Costly and impractical replication of index funds.
method Learning to predict market sensitivities using deep learning models.
result Significant reduction in prediction errors compared to historical methods.
Improved bounds for ℓp sensitivity sampling reducing the sample complexity for structured matrices.
problem Improving the sample complexity for structured matrices using ℓp sensitivity sampling. method Developed new bounds for ℓp sensitivity sampling, achieving a bound of roughly S2−2/p for 2<p<∞. result Achieved improved bounds for ℓp sensitivity sampling, reducing the sample complexity for structured matrices.