Are expansions and recessions more likely to end as their magnitude increases? In this paper we apply parametric hazard models to investigate this issue in a sample of 16 countries from 1881 to 2000. For the total sample we find evidence of positive magnitude dependence for recessions, while for expansions we are not a…
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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.
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48 results for “expansive ends”
The paper solves the Dirichlet problem at infinity for certain negatively curved 3-manifolds.
problem Solving the Dirichlet problem at infinity for negatively curved 3-manifolds with expansive ends.
method Based on a result that does not require explicit curvature assumptions, the paper presents an example of a metric on an end with indefinite curvature for which the Dirichlet Problem at Infinity is solvable.
result The Dirichlet problem at infinity is solvable for certain negatively curved 3-manifolds with expansive ends.
In this paper known results of symmetric orthogonality, as introduced by G. Birkhoff, and non-expansive nearest point projections are extended from the linear to the metric setting. If the space has non-positive curvature in the sense Busemann then it is shown that those concepts are actually equivalent. In the end it …
Hyperfitting improves LLM generation quality by enhancing diversity, contrary to simple temperature scaling.
problem Improving open-ended generation quality of LLMs with minimal fine-tuning effort.
method Demonstrates that hyperfitting, a phenomenon where LLMs are fine-tuned to near-zero training loss, enhances generation quality and mitigates repetition.
result Hyperfitting is distinct from temperature scaling and involves a dynamic, context-dependent rank reordering mechanism in the final transformer block.
We present a new conjectural symmetry of the colored Alexander polynomial, that is the specialization of the quantum invariant widely known as the colored HOMFLY-PT polynomial. We provide arguments in support of the existence of the symmetry by studying the loop expansion and the character expansion o…
Gradient oversmoothing and expansion hinder deep GNN training, solved with normalization.
problem Gradient oversmoothing and expansion prevent deep GNN training.
method Proposed normalization method to constrain the Lipschitz bound of each layer.
result Residual GNNs with hundreds of layers can be efficiently trained with the proposed normalization.
Develops AMITE for analyzing neural network nonlinearities.
problem Addressing difficulties in verification, explainability, and security in neural network analysis.
method Analytically modified integral transform expansion (AMITE) for neural network nonlinearities.
result First to provide six mutually exclusive desired expansion properties.
This paper is devoted to a third order study of the end-point map in sub-Riemannian geometry. We first prove third order open mapping results for maps from a Banach space into a finite dimensional manifold. In a second step, we compute the third order term in the Taylor expansion of the end-point map and we specialize …
Finite number of eigenvalues found in cylindrical surface.
problem Finding eigenvalues in manifolds with cylindrical ends.
method Constructing a surface with a cylindrical end attached to a hyperbolic torus.
result First example of a finite and nonzero number of embedded eigenvalues in a cylindrical manifold.
We consider a non-trapping -dimensional Lorentzian manifold endowed with an end structure modeled on the radial compactification of Minkowski space. We find a full asymptotic expansion for tempered forward solutions of the wave equation in all asymptotic regimes. The rates of decay seen in the asymptotic expansion a…
A new Fourier model improves ODE prediction.
problem Improving the accuracy of ODE solutions, especially for periodic functions.
method Constructing a Fourier state space model and a hybrid model combining Taylor and Fourier methods.
result The hybrid model can predict ODE solutions more accurately, especially for periodic functions.
Multilingual end-to-end (E2E) models have shown great promise in expansion of automatic speech recognition (ASR) coverage of the world's languages. They have shown improvement over monolingual systems, and have simplified training and serving by eliminating language-specific acoustic, pronunciation, and language models…
New algorithm finds corrupted vertices in graphs with few queries.
problem Adversarial tampering of graph edges and vertices.
method Active learning algorithm with polynomial query complexity.
result Efficiently recovers corrupted vertices with small query complexity.
Enhances polynomial chaos models with uncertainty intervals.
problem Uncertainty quantification in surrogate models.
method Jackknife-based conformal prediction integrated into polynomial chaos expansions.
result Produces accurate predictive intervals for low-accuracy models.
Paper improves CDO calibration using Magnus Expansion and Deep Learning.
problem Calibrating CDO to iTraxx market data.
method Large basket approximation, SPDE, Magnus expansion, Deep Learning.
result Highly accurate calibration to market data.
Injectivity of ReLU networks is characterized for generative models and inverse problems.
problem Injectivity in ReLU networks for generative models and inverse problems.
method Layerwise analysis, worst-case Lipschitz constants, differential topology, random projections.
result Global injectivity of ReLU networks requires expansivity between 3.4 and 10.5 for Gaussian matrices.
Study asymptotic behavior of Weingarten surfaces at infinity.
problem Understanding the behavior of Weingarten surfaces at infinity.
method Derive asymptotic expansion and solve Dirichlet problem.
result Established maximum principle and solved Dirichlet problem.
Develops quantization for non-compact complex manifolds with spectral gap.
problem Quantization of non-compact complex manifolds with spectral gap.
method Berezin-Toeplitz quantization, spectral gap analysis, asymptotic expansion.
result Toeplitz operators form a closed algebra and satisfy a complete composition expansion.
Bayesian optimisation algorithm for unknown search spaces with sub-linear regret.
problem Efficient optimisation of expensive black-box functions in unknown search spaces.
method Expands search space over iterations based on a hyperharmonic series, scales to high dimensions.
result Sub-linear regret growth for both algorithms.
Diffeomorphism freedom induces a gauge dependence in the theory of spacetime perturbations. We derive a compact formula for gauge transformations of perturbations of arbitrary order. To this end, we develop the theory of Taylor expansions for one-parameter families (not necessarily groups) of diffeomorphisms. First, we…
Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been difficult to make formal claims about the basic properties of the learned systems. In …
Adaptive neural networks learn functional data bases for improved performance.
problem Applying deep learning to functional data is challenging due to high dimensionality.
method Proposes adaptive neural networks with Basis Layers that learn relevant basis functions.
result Empirically outperforms other neural network approaches across various tasks.
We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by Kordyukov, Mathai and Shubin (2005), with a more extended use of quadratic forms instead…
Paper approximates XVA for European contingent claims using BSDEs and polynomial expansions.
problem Computing Value Adjustment of European contingent claims with nonlinear features.
method Reduced-form approach, nonlinear Backward Stochastic Differential Equation (BSDE), change of numeraire, Taylor's polynomial expansion.
result Simple first-order approximation can be computationally efficient for CIR intensity model.
Quantum computing speeds up option pricing for multiple assets.
problem High-dimensional integration bottleneck in option pricing.
method Calibrated marginal distributions, Gaussian copula, QAMC with QAE.
result QAMC reduces integration queries by 10-100 times for similar precision.
This is a survey of recent results on zeta- and eta-function poles and values for realizations of Laplace- and Dirac-type operators defined by pseudodifferential projection boundary conditions (including the Atiyah-Patodi-Singer operator and its square). Section 1 recalls some useful results for ps.d.o.s on closed mani…
Proposes ContSup to boost local learning by supplying context between isolated modules.
problem Local learning's performance degrades with more isolated modules.
method Theoretical analysis and ContSup scheme to supply context between modules.
result Significant performance improvement with minimal overhead.
New equations simplify gauge-theoretic Khovanov homology solutions.
problem Solving the Haydys-Witten equations for Khovanov homology.
method Introduced decoupled version of Haydys-Witten equations; investigated asymptotic behavior.
result Decoupled equations simplify analysis of full equations on manifolds with ends and boundaries.
We develop a general regulated volume expansion for the volume of a manifold with boundary whose measure is suitably singular along a separating hypersurface. The expansion is shown to have a regulator independent anomaly term and a renormalized volume term given by the primitive of an associated anomaly operator. Thes…
Rescaling expansiveness proven for k*-expansive vector fields.
problem Proving rescaling expansiveness for k*-expansive vector fields.
method Introducing and exploring singular-expansive flows.
result Rescaling expansiveness established for k*-expansive vector fields.
The state price density of a basket, even under uncorrelated Black-Scholes dynamics, does not allow for a closed from density. (This may be rephrased as statement on the sum of lognormals and is especially annoying for such are used most frequently in Financial and Actuarial Mathematics.) In this note we discuss short …
Polynomial chaos expansions on Grassmannian submanifolds for high-dimensional stochastic systems.
problem Uncertainty quantification in high-dimensional stochastic systems.
method Principal Geodesic Analysis on the Grassmann manifold, adaptive algorithm for local submanifolds, polynomial chaos expansion.
result Efficient surrogate modeling of system behavior across different parameter spaces.
Proves estimates for Calabi-Yau metrics as Kahler classes shrink.
problem Estimates for Calabi-Yau metrics under shrinking Kahler classes.
method Proves asymptotic expansion in terms of powers of fiber diameter with uniform C^k-estimates.
result Uniform estimates for all orders of derivatives of Calabi-Yau metrics.
The most common stochastic volatility models such as the Ornstein-Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull-White models define volatility as a Markovian process. In this work we check of the applicability of the Markovian approximation at separate times scales and will try to answer the question …
The paper derives expansions for Green's operators and resolvents using Hadamard methods.
problem Analyzing normally hyperbolic operators and their Green's functions.
method Hadamard expansions for powers of Green's operators and resolvents.
result Derives expansions involving Hadamard coefficients for advanced/retarded Green's operators.
Study irrational rotations and construct 2-filling rays on infinite type surfaces.
problem Understanding dense orbits in skew product transformations.
method Skew product transformation with continued fraction analysis.
result Existence of infinite cliques of 2-filling rays on infinite type surfaces.
Neural plasticity is an important functionality of human brain, in which number of neurons and synapses can shrink or expand in response to stimuli throughout the span of life. We model this dynamic learning process as an -norm regularized binary optimization problem, in which each unit of a neural network (e.g., …
Heterotic string compactifications on integrable structure manifolds with instanton bundles yield supersymmetric three-dimensional vacua that are of interest in physics. In this paper, we define a covariant exterior derivative and show that it is equivalent to a heterotic …
Develops a martingale expansion for stochastic volatility models.
problem Approximating marginal distributions of stochastic volatility models.
method Martingale expansion framework for continuous stochastic volatility models.
result First-order perturbation expansions for small volatility-of-volatility and fast mean-reversion models.
Proposes a label propagation framework for domain adaptation.
problem Subpopulation shift in machine learning domains.
method Label propagation based on a teacher classifier trained on source domain.
result End-to-end finite-sample guarantees on domain adaptation algorithm.
Taylor expansions improve reinforcement learning policies.
problem Improving reinforcement learning policy optimization.
method Taylor expansion policy optimization.
result Taylor expansions enhance performance of distributed algorithms.
Analytic torsion expansions for symmetric and complex homogeneous spaces.
problem Calculating the full asymptotic expansion of analytic torsion for various spaces.
method Explicit calculation and comparison with existing results.
result Explicit full asymptotic expansions for symmetric and complex homogeneous spaces.
Proved cyclotomic expansion for double twist knots' HOMFLY-PT invariants.
problem Proving cyclotomic expansion for colored HOMFLY-PT invariants of double twist knots.
method Cyclotomic expansion formula for double twist knots.
result Confirmed cyclotomic expansion conjecture for SU(N)-invariants.
Study of hypersurfaces with specific expansion properties.
problem Existence and properties of hypersurfaces with prescribed null expansion.
method Adapted Eichmair's Perron approach for existence.
result Topology theorem for hypersurfaces with prescribed null expansion.
A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.
problem Information loss in hypergraph expansions on either vertex or hyperedge level.
method Proposes a new hypergraph formulation named line expansion (LE) that treats vertices and hyperedges symmetrically.
result The proposed line expansion method outperforms state-of-the-art baselines on five hypergraph datasets.
The paper calculates asymptotic expansions for specific types of oscillatory integrals.
problem Analyzing oscillatory integrals with complex phase functions.
method Using asymptotic expansions of simpler phase functions to derive results for more complex cases.
result Explicit computation of coefficients in asymptotic expansions for certain integrals.
Dropout increases the generalization of neural networks by expanding the weight space.
problem Understanding and improving the generalization of neural networks.
method Introducing weight expansion and showing that dropout leads to it.
result Dropout increases the generalization of neural networks by expanding the weight space.
We propose two conjectures about Ricci-flat metrics: Conjecture 1: A Ricci-flat projectively induced metric is flat. Conjecture 2: A Ricci-flat metric on an -dimensional complex manifold such that the coefficient of the TYZ expansion vanishes is flat. We verify Conjecture 1 (see Theorem 1.1) under the assu…