Geometric method improves uncertainty estimation in real-time.
problem Improving uncertainty estimation in machine learning models.
method Geometric distance from training inputs for uncertainty estimation, post-hoc calibration.
result Method yields better uncertainty estimations than existing approaches.
Develops geometric framework for uncertainty-aware multi-class classification.
problem Silent failure of AI models when uncertain, especially in multi-class settings.
method Geometric framework treating probability vectors as points on the (c−1)-dimensional probability simplex, using Fisher--Rao metric for calibration and uncertainty quantification. result Empirical validation shows 72.5% of errors captured while deferring 34.5% of ambiguous predictions, reducing automated decision error rates from 16.8% to 6.9%.
New conditions for calibrated submanifolds in Riemannian geometry.
problem Characterizing calibrated submanifolds with extrinsic geometry.
method Introducing compliancy condition and analyzing extrinsic geometry.
result Conditions for extrinsic geometry of calibrated submanifolds.
For product manifolds, cohomologically calibrated affine connections are geometrically irreducible.
problem Establishing geometric irreducibility of cohomologically calibrated affine connections on product manifolds.
method Proof relies on Hodge theory and integral arguments showing non-cancellation of off-diagonal components in the Riemann curvature tensor.
result Cohomologically calibrated affine connections on product manifolds are holonomically irreducible.
We shall obtain unobstructed deformations of four geometric structures: Calabi-Yau, HyperKähler, $\G$ and Spin(7) structures in terms of closed differential forms (calibrations). We develop a direct and unified construction of smooth moduli spaces of these four geometric structures and show that the local Torelli type …
Bayesian models for networks are often misspecified, leading to overconfident inference.
problem Real-world networks violate assumptions of geometry and link function in latent space models.
method Proposes a generalized posterior framework for random geometric graphs, using Link-Sequential R-SafeBayes to adaptively tune posterior regularization.
result Improved calibration and better link prediction performance demonstrated on synthetic and real-world networks.
Focal loss reduces model curvature for better calibration.
problem Improving model confidence in classification problems.
method Geometric interpretation of focal loss to reduce curvature.
result Focal loss reduces the curvature of the loss surface, enhancing model calibration.
Study quantifies geometric complexity of connections on product surfaces.
problem Understanding geometric complexity of connections on product manifolds.
method Establishes a topological lower bound on the holonomy of cohomologically calibrated connections.
result Proves a bound on the dimension of the holonomy that is a topological invariant.
We provide yet another proof of the existence of calibrated forecasters; it has two merits. First, it is valid for an arbitrary finite number of outcomes. Second, it is short and simple and it follows from a direct application of Blackwell's approachability theorem to carefully chosen vector-valued payoff function and …
Proposes a new calibration error estimator for deep neural networks.
problem Improves calibration of deep neural networks, especially for canonical calibration.
method Uses a Dirichlet kernel density estimate to create a low-bias, trainable calibration error estimator.
result Asymptotically converges to true Lp calibration error, enabling efficient estimation and mini-batch updates. We study statistical calibration, i.e., adjusting features of a computational model that are not observable or controllable in its associated physical system. We focus on functional calibration, which arises in many manufacturing processes where the unobservable features, called calibration variables, are a function of…
Weighted Monte Carlo prices exotic options calibrating the probabilities of previously generated paths by a regular Monte Carlo to fit a set of option premiums. When only vanilla call and put options and forward prices are considered, the Martingale condition might not be preserved. This paper shows that this is indeed…
New method calibrates deep models for both in-distribution and out-of-distribution samples.
problem Ensuring calibration for deep models in safety-critical applications, especially in OOD regions.
method Geodesic distance and Gaussian kernel to calibrate deep models.
result Proposed KDF and KDN methods achieve well-calibrated posteriors for both in-distribution and out-of-distribution samples.
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 twist construction is a method to build new interesting examples of geometric structures with torus symmetry from well-known ones. In fact it can be used to construct arbitrary nilmanifolds from tori. In our previous paper, we presented a generalization of the twist, a shear construction of rank one, which allowed …
The study analyzes Dirac operators twisted by specific bundles, revealing their geometric and regularity properties.
problem Analyzing Dirac operators twisted by ramified Euclidean line bundles.
method Describes closed extensions of Dirac operators in terms of Gelfand-Robbin quotient, constructs geometric realizations, and develops an L2 regularity theory. result Geometric realizations of the Gelfand-Robbin quotient and an L2 regularity theory are constructed. We show that the properties of Lagrangian mean curvature flow are a special case of a more general phenomenon, concerning couplings between geometric flows of the ambient space and of totally real submanifolds. Both flows are driven by ambient Ricci curvature or, in the non-Kähler case, by its analogues. To this end we…
We shall develop a new deformation theory of geometric structures in terms of closed differential forms. This theory is a generalization of Kodaira -Spencer theory and further we obtain a criterion of unobstructed deformations. We apply this theory to certain geometric structures: Calabi-Yau, HyperKähler, $\G$ and $\Sp…
New forms calibrate minimal graphs in arbitrary dimensions.
problem Calibrating minimal graphs in arbitrary codimension.
method Constructing closed forms from minimal graphs and estimating their comass.
result Conditions ensuring minimal graphs are calibrated and area-minimizing.
A novel approach models rating transitions using Lie groups and Deep Learning.
problem Modeling rating transitions with geometric properties and stochastic processes.
method Introducing Itô-SDEs on Lie groups, using TimeGAN for calibration, and examining rating matrix properties.
result The geometric approach using Lie groups and Deep Learning generates a good fit for rating transitions.
Solves Plateau's Problem in Heisenberg group for graphs.
problem Plateau's Problem in the Heisenberg group for intrinsic graphs.
method Geometric construction and calibration argument.
result Solves Plateau's Problem under smallness conditions.
These notes are based on lectures given at the Clay School on Geometry and String Theory, Isaac Newton Institute, Cambridge, 25 March - 19 April 2002. They attempt to provide an elementary and somewhat self contained discussion of the construction of supergravity solutions describing branes wrapping calibrated cycles, …
Develop a decision-calibrated conformal framework for pacing decisions in streaming advertising.
problem Pacing decisions in streaming advertising
method Develop a decision-calibrated conformal framework
result The proposed score is the smallest valid uncertainty measure that uniformly protects all deployable pacing policies.
The paper introduces a new concept of frame vorticity and uses it to find optimal sections in specific geometric settings.
problem Finding optimal sections in geometric settings using frame vorticity.
method Defining frame vorticity, relating it to split pseudo-Riemannian metrics, and using split special Lagrangian calibrations.
result Explicit homologically volume maximizing sections and optimal sections for specific manifolds.
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.
This study uses DRL to hedge American put options, outperforming traditional methods.
problem Hedging American put options with high accuracy and low transaction costs.
method Deep Deterministic Policy Gradient (DDPG) method, trained on stochastic volatility models.
result DRL agents outperform traditional methods in both simulated and real-world scenarios.
Let H be the hyperbolic space of dimension n+1. A geodesic foliation of H is given by a smooth unit vector field on H all of whose integral curves are geodesics. Each geodesic foliation of H determines an n-dimensional submanifold M of the 2n-dimensional manifold L of all the oriented geodesics of H (up to orientation …
No policy can simultaneously be fully autonomous, optimally calibrated, and helpful, proving a trilemma.
problem Proving impossibility of a policy achieving maximum helpfulness, optimal calibration, and full autonomy.
method Geometric proof showing that adding any non-affine autonomy incentive to a strictly proper scoring rule destroys strict properness.
result The Behavioral Credibility Trilemma: no policy can achieve all three goals simultaneously.
OrthoGrad improves neural calibration by constraining gradient updates orthogonally.
problem Overconfidence in neural networks, leading to poor uncertainty estimates.
method Orthogonal gradient updates to optimize for decision boundaries and reduce overconfidence.
result Significant improvements in test loss, predictive entropy, and confidence measures.
Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide variety of geometric situations, including, for example, Lagrangian plurisubhamon…
In this paper we study several issues related to the generation of superpotential induced by background Ramond-Ramond fluxes in compactification of Type IIA string theory on Calabi-Yau four-folds. Identifying BPS solitons with D-branes wrapped over calibrated submanifolds in a Calabi-Yau space, we propose a general for…
We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1-flat, but seems full of other possibilities. We start by the study of the most basic properties of our construction. The structure is co-ca…
Study shows TAP free energy minimization provides better posterior inference in high-dimensional linear models.
problem Deviation from true posterior mean and underestimation of posterior uncertainty in variational inference.
method Minimization of TAP free energy in a high-dimensional asymptotic framework, showing geometric and statistical properties.
result Local minimizer of TAP free energy provides consistent estimate of posterior marginals and correctly calibrated posterior inference.
FRESH combines patient-level and aggregate-level data for better clinical decision making.
problem Combining patient-level and aggregate-level data for clinical decision making.
method FRESH method that re-calibrates a patient-level model to match specified aggregate statistics.
result Unified data-efficient model for clinical decision making.
Hasse principle applied to area-minimizing submanifolds across different homology types.
problem Understanding the behavior of area-minimizing submanifolds in various homology contexts.
method Extending the Hasse principle from number theory to geometric variational problems.
result Recovering information about area-minimizing submanifolds in integral homology from those in real and mod n homology. The paper extends minimal network theory to the sphere, proving local minimality.
problem Finding networks of minimal length on the sphere.
method Adapted spherical geometry, calibration method, and local metric perturbation estimates.
result Spherical minimal networks composed of great-circle arcs are locally length-minimizing within small geodesic balls.
Decision trees and shallow neural networks have different geometric complexities, impacting their interpretability and accuracy.
problem The geometric simplicity of decision boundaries in decision trees conflicts with the approximation capabilities of shallow neural networks.
method Analysis of the Radon total variation (RTV) seminorm to compare geometric complexity of decision regions and neural network approximations.
result Smooth barrier scores can approximate decision regions with finite RTV, but their performance depends on the tube-mass condition near the decision boundary.
Proposes new method for calibrating treatment effect predictors.
problem Calibrating predictors of heterogeneous treatment effects.
method Causal isotonic calibration and cross-calibration.
result Achieves fast calibration rates under weak conditions.
Paper proposes a probabilistic alignment method for domain adaptation.
problem Latent distribution mismatch and miscalibrated uncertainty in adapting large-scale models.
method Bayesian latent transport framework with PAC-Bayesian regularization.
result Reduction in latent manifold discrepancy and improved uncertainty calibration.
The paper studies multi-curve interest rate models and their consistency and finite-dimensional realizations.
problem Consistency and existence of finite-dimensional realizations for multi-curve interest rate models.
method Geometric approach, characterizing consistency and existence of finite-dimensional realizations for multi-curve models.
result Characterization of consistency and existence of finite-dimensional realizations for multi-curve models.
Proposes top-label calibration and M2B framework for multiclass to binary calibration.
problem Multiclass calibration and interpretation issues.
method Top-label calibration and M2B reduction framework.
result M2B + HB achieves lower calibration error than other methods.
The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.
problem Approximating functionals of non-geometric rough paths.
method Extending rough paths with time and quadratic variation terms, proving uniform approximation.
result Linear functionals of extended signatures uniformly approximate continuous functionals.
Study explores calibration properties in neural architectures.
problem Calibration issues in deep neural networks despite improved accuracy.
method Leverages Neural Architecture Search (NAS) to evaluate 117,702 neural networks.
result Identifies key architectural designs beneficial for calibration.
A new perfectly truthful calibration measure improves prediction reliability.
problem Improving the reliability of predictions by ensuring they are conditionally unbiased.
method Designing a simple, perfectly truthful calibration measure called ATB.
result ATB is the first perfectly truthful calibration measure in the batch setting.
Temperature scaling improves model uncertainty but not diversity in LLMs.
problem Improving the calibration and stochasticity of probabilistic models.
method Investigates theoretical properties of temperature scaling in classification and LLMs.
result Temperature scaling increases model uncertainty but not diversity in LLMs.
New truthful calibration errors improve model ranking in multiclass prediction.
problem Non-truthful calibration errors can mislead model comparisons.
method Introduced perfectly truthful calibration errors for multiclass predictions.
result Truthful calibration errors preserve decision-theoretic dominance and stabilize model rankings.
New framework for evaluating multiclass classifier calibration.
problem Ensuring classifiers are well-calibrated for trustworthy predictions.
method Utility Calibration framework that measures calibration error relative to a utility function.
result Unified and robust interpretation of existing calibration metrics.
We propose a new framework to improve the calibration of neural networks.
problem Improving the accuracy of model confidence predictions.
method Introducing a differentiable surrogate for expected calibration error (DECE) and a meta-learning framework to optimise model hyper-parameters for validation set calibration.
result Achieved competitive performance with existing calibration approaches.