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.
Minimal volume vector fields on surfaces via calibrations.
The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calib…
We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in abundance whereas the corresponding pluriharmonics are generally quite scarce. A…
We provide an introduction to the theory of calibrated submanifolds through the key examples related with special holonomy. We focus on calibrated geometry in Calabi-Yau, G and Spin(7) manifolds, and describe fundamental results and techniques in the field.
We show that any semi-calibration of degree 2 is locally induced by a smooth almost complex structure. We provide some applications of this result in the regularity theory for semi-calibrated 2-currents
New framework ensures valid uncertainty estimates for any data stream changes.
Study of interactions between functions on manifolds via submersions.
New loss improves DNN calibration without sacrificing accuracy.
New decision-theoretic calibration error metric improves prediction reliability.
New method calibrates models under covariate shifts.
We review some results concerning the deformations of calibrated minimal submanifolds which occur in Riemannian manifolds with special holonomy. The calibrated submanifolds are assumed compact with a non-empty boundary which is constrained to move in a particular fixed submanifold. The results extend McLean's deformati…
We introduce a version of Aubry-Mather theory for the length functional of causal curves in compact Lorentzian manifolds. Results include the existence of maximal invariant measures, calibrations and calibrated curves. We prove two versions of the Mather's graph theorem. A class of examples, the Lorentzian Hedlund exam…
For Hitchin's generalised geometries we introduce and analyse the concept of a structured submanifold which encapsulates the classical notion of a calibrated submanifold. Under a suitable integrability condition on the ambient geometry, these generalised calibrated cycles minimise a functional occurring as D-brane ener…
New method improves decision-making accuracy without complex calculations.
New framework allows selective removal of stale data in option calibration.
We construct a deep portfolio theory. By building on Markowitz's classic risk-return trade-off, we develop a self-contained four-step routine of encode, calibrate, validate and verify to formulate an automated and general portfolio selection process. At the heart of our algorithm are deep hierarchical compositions of p…
This paper argues against using calibration metrics for assessing posterior probabilities and proposes expected proper scoring rules instead.
Algorithm constructs confidence sets for deep neural networks with PAC guarantees.
Unique solutions found for Plateau problems in smooth and continuous calibrations.
For product manifolds, cohomologically calibrated affine connections are geometrically irreducible.
New truthful calibration errors improve model ranking in multiclass prediction.
Study adiabatic limits of calibrated submanifolds in Riemannian geometry.
This work proves -regularized ERM controls smCE without post-hoc correction.
The paper improves methods for generating prediction intervals in regression.
In this paper we introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy many of their important properties. Moreover, they exist in abundance whereas the corresponding pluriharmonics are gen…
The paper studies -harmonic functions and their conjugates, showing they converge to calibrations of laminations.
LLMs show surprising confidence in their answers, beyond just tokens.
Post-hoc calibration of neural networks using g-Layers proves theoretical justification.
The paper extends minimal network theory to the sphere, proving local minimality.
MCP extends conformal prediction to vector-valued score functions without data splitting.
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, …
New proof of minimal vector fields on spheres using calibrations.
The paper uses optimal transport to calibrate stochastic simulations.
We present a method for constructing the log-optimal portfolio using the well-calibrated forecasts of market values. Dawid's notion of calibration and the Blackwell approachability theorem are used for computing well-calibrated forecasts. We select a portfolio using this "artificial" probability distribution of market …
The subject of these Notes is the new proof, proposed in [F. H{é}lein, In{é}galit{é} isop{é}rim{é}trique et calibrations, Annales de l'Institut Fourier 44, 4 (1994), 1211-1218] of the classical isoperimetric inequality in the plane. This proof is far from being the first one, but its interest is that it uses essentiall…
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…
TS improves class coverage but reduces CP set size, offering a trade-off.
New method calibrates machine learning models with theoretical guarantees.
New method achieves faster calibration without randomization.
We systematically analyse the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form R^{1,9-d} \times M_d, in the common NS-NS sector of type II string theory and also type I/heterotic string theory. The results are phrased in terms of the intrinsic torsion of G-str…
Survey of algorithms to correct past mistakes in prediction.
Recently the authors showed that there is a robust potential theory attached to any calibrated manifold (X,φ). In particular, on X there exist φ-plurisubharmonic functions, φ-convex domains, φ-convex boundaries, etc., all inter-related and having a number of good properties. In this paper we show that, in a strong sens…
The study analyzes Dirac operators twisted by specific bundles, revealing their geometric and regularity properties.
This work tackles uncertainty quantification in language models, proposing a principled approach.
Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their ability to represent uncertainty about predictions. In safety-critical applicatio…
We present surrogate regret bounds for arbitrary surrogate losses in the context of binary classification with label-dependent costs. Such bounds relate a classifier's risk, assessed with respect to a surrogate loss, to its cost-sensitive classification risk. Two approaches to surrogate regret bounds are developed. The…
We present a universal algorithm for online trading in Stock Market which performs asymptotically at least as good as any stationary trading strategy that computes the investment at each step using a fixed function of the side information that belongs to a given RKHS (Reproducing Kernel Hilbert Space). Using a universa…
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…