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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,742 papers · 148 categories

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3875113150 · May 202619922001200920172026
48 results for cohomological calibration

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.

The paper constructs non-Riemannian Einstein solutions on S2imesT2S^2 imes T^2 using cohomologically calibrated affine connections.

problem Constructing non-Riemannian Einstein manifolds on S2imesT2S^2 imes T^2.
method Using cohomologically calibrated affine connections and analyzing the torsion tensor within the family Tω\mathcal{T}_ω.
result Explicit non-Riemannian Einstein solutions are constructed using a torsion tensor associated with the purelly harmonic 3-form.

The paper constructs a lamination related to minimal hypersurfaces calibrated by a cohomology class.

problem Understanding the geometry of stable norm balls constrained by manifold topology.
method Constructing a lamination λρλ_ρ of minimal hypersurfaces calibrated by ρρ.
result Establishes a close analogy between stable norm and earthquake norms.

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.

In this paper, we prove various results on the topology of the Grassmannian of oriented 3-planes in Euclidean 6-space and compute its cohomology ring. We give self-contained proofs. These spaces come up when studying submanifolds of manifolds with calibrated geometries. We collect these results here for the sake of com…

2019-04-08abs ↗pdf ↗

This paper finds a metric on \(S^2 imes T^2\) with strictly positive biorthogonal curvature using an affine connection with antisymmetric torsion.

problem Existence of a Riemannian metric on \(S^2 imes T^2\) with strictly positive biorthogonal curvature.
method Introducing an affine connection with antisymmetric torsion calibrated via non-trivial cohomology classes, which allows overcoming topological constraints.
result Demonstrates the construction of a metric on \(S^2 imes T^2\) with strictly positive biorthogonal curvature.

In this paper we will investigate torus actions on complete manifolds with calibrations. For Calabi-Yau manifolds M^2n with a Hamiltonian structure-preserving k-torus action we show that any symplectic reduction has a natural holomorphic volume form. Moreover Special Lagrangian (SLag) submanifolds of the reduction lift…

2000-02-14abs ↗pdf ↗

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.

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.

Certified calibration methods protect model confidence from adversarial attacks.

problem Adversarial attacks degrade model calibration, reducing confidence in predictions.
method Developed certified calibration methods to provide worst-case bounds on calibration under adversarial perturbations.
result Certified calibration methods produce analytic and approximate bounds for the Brier score and expected calibration error.

Meta-Cal improves post-hoc calibration of neural networks.

problem Improving the accuracy of uncalibrated neural network predictions.
method Meta-Cal uses a base calibrator and a ranking model with constraints to provide high-probability bounds.
result Meta-Cal significantly outperforms existing methods in post-hoc multi-class classification calibration.

Post-processing predictors reduces calibration errors for decision-making.

problem Predictors with low calibration error for machine learning may have high error for decision-making.
method Post-processing with ε distance to calibration adds noise to make predictions differentially private.
result Post-processing achieves O(√ε) ECE and CDL, asymptotically optimal.

A new method for multiclass calibration using vector quantization.

problem Challenges in multiclass calibration, especially in high-stakes settings.
method Compositional approach via Vector Quantization (VQ) to learn region-specific calibration maps.
result Significant improvements in local calibration with competitive global calibration and predictive performance.

This post introduces model calibration and evaluation measures, highlighting issues with a common measure.

problem Ensuring model confidence accurately reflects true outcomes.
method Explains common calibration definition, ECE, and its drawbacks.
result New evaluation measures needed for comprehensive model calibration.

Unified calibration metrics improve forecast sharpness and accuracy.

problem Improving the sharpness of probabilistic forecasts while maintaining calibration.
method Kernel-based calibration metrics that unify and generalize existing methods for classification and regression.
result Enhanced calibration, sharpness, and decision-making across various tasks.

Smooth calibration improves forecast reliability even with leaked information.

problem Improving forecast reliability with leaked information.
method Combining nearby forecasts to ensure smooth calibration, which can be guaranteed by deterministic procedures.
result Smooth calibration can be guaranteed by deterministic procedures even with leaked forecasts, and it yields uncoupled finite-memory dynamics in games.

We describe a family of calibrations arising naturally on a hyperkähler manifold MM. These calibrations calibrate the holomorphic Lagrangian, holomorphic isotropic and holomorphic coisotropic subvarieties. When MM is an HKT (hyperkaehler with torsion) manifold with holonomy SL(n,H)SL(n, {\Bbb H}), we construct another fam…

2010-09-06abs ↗pdf ↗

This paper rethinks confidence calibration under covariate shifts.

problem Calibration methods struggle with covariate shifts and unstable importance weighting.
method Derives Expectation consistency condition and proposes Expectation consistency loss (ECL).
result ECL loss is compatible with various types of calibration and has the same sample complexity as ECE.

New method calibrates neural network predictions for better reliability.

problem Improper probability estimates from deep networks leading to unreliable predictions.
method Proposes a constrained optimization approach for a monotonic calibration map.
result Achieves state-of-the-art performance across various datasets and models.

Develops confidence intervals for ECE, a measure of model calibration.

problem Ensuring the calibration of probabilistic predictions in machine learning models.
method Develops confidence intervals for the 2\ell_2 Expected Calibration Error (ECE), considering top-1-to-kk calibration.
result Shows asymptotic normality and different convergence rates for calibrated and miscalibrated models, developing methods to construct valid confidence intervals.

The paper addresses poor calibration in fine-tuned LLMs after preference alignment.

problem Poor calibration in fine-tuned Large Language Models (LLMs) after preference alignment.
method Proposes a calibration-aware fine-tuning approach to restore calibration without compromising model performance.
result Demonstrates the effectiveness of the proposed methods through extensive experiments.

New calibration bands for various distributions improve testing for auto-calibration.

problem Testing for auto-calibration in finite samples is challenging.
method Construct calibration bands for the exponential dispersion family using finite sample properties.
result Calibration bands allow for various tests for calibration and auto-calibration.

This paper improves multi-class calibration methods using mutual information maximization-based binning.

problem Calibration of deep neural network predictions, especially for small prior classes.
method I-Max concept for binning, shared class-wise calibration strategy.
result Improves multi-class ranking and calibration performance using a small calibration set.

Response calibration is the process of inferring how much the measured data depend on the signal one is interested in. It is essential for any quantitative signal estimation on the basis of the data. Here, we investigate self-calibration methods for linear signal measurements and linear dependence of the response on th…

2013-12-04abs ↗pdf ↗

T-Cal tests model calibration with a minimax optimal test.

problem Detecting mis-calibration of predictive models using a finite validation dataset.
method T-Cal is a minimax optimal test for calibration based on a debiased plug-in estimator of the 2\ell_2-Expected Calibration Error (ECE).
result T-Cal is a practical tool for testing the calibration of probabilistic classification methods.

Optimizes calibration error estimators for better classifier trustworthiness.

problem Lack of guidance on selecting and tuning calibration error estimators.
method Reformulates calibration estimation as a regression problem with i.i.d. input pairs.
result Demonstrates the effectiveness of optimized calibration estimators on image classification tasks.

Improves calibration of regression models without requiring additional data.

problem Poor calibration of regression models leading to unreliable predictions.
method Quantile regularizer based on cumulative KL divergence.
result Significantly improves calibration for regression models trained with Dropout VI and Deep Ensembles.