This work forecasts electricity prices using Bayesian regime detection and conditional neural processes.
problem Forecasting electricity prices with optimal operational outcomes.
method Bayesian regime detection with conditional neural processes, integrating multi-criteria decision support.
result R-NP model outperformed other models in comprehensive operational utility assessments.
Neural operators achieve fast convergence rates for solving PDEs.
problem Solving partial differential equations (PDEs) efficiently.
method Two-layer neural operators with gradient descent analysis in RKHS.
result Fast convergence rates are minimax optimal for early-stopped GD.
Study of Dirac-like operators on spin manifolds with large mass parameters.
problem Understanding spectra of Dirac-like operators with piecewise constant mass terms.
method Analysis of asymptotic regimes to derive effective operators.
result Extension of MIT Bag operator concept to spin geometry.
DOODL learns shared spectral dynamics across related dynamical systems.
problem Learning independent dynamical operators for each system limits discovery of shared structure.
method DOODL learns a dictionary of characteristic spectral dynamics on a manifold of related systems.
result DOODL achieves errors one to two orders of magnitude lower than independent operator estimation methods.
Foundation models outperform supervised methods in time series forecasting across various operational regimes.
problem Lack of domain-specific training and ongoing maintenance in supervised learning for time series forecasting.
method Evaluation of foundation models against standard supervised approaches across four operational regimes: periodic, physically constrained, stochastic, and demand forecasting.
result Foundation models are optimal for cold-start or long-tail scenarios and perform well in domains with transferable periodic structures.
Neural networks parameterize time-varying Markov dynamics in financial time series.
problem Estimating Markov transition matrices in high-resolution, high-noise financial data.
method Introduces a neural network framework to generate explicit, time-varying Markov transition matrices, constraining neural outputs to formal stochastic operators.
result Learned operators capture regime shifts, with high-volatility regimes homogenizing transition dynamics.
In this work we analyse a stochastic control problem for the valuation of a natural gas power station while taking into account operating characteristics. Both electricity and gas spot price processes exhibit mean-reverting spikes and Markov regime-switches. The Levy regime-switching model incorporates the effects of d…
We analyze operational risk in terms of a spin glass model. Several regimes are investigated, as a functions of the parameters that characterize the dynamics. The system is found to be robust against variations of these parameters. We unveil the presence of limit cycles and scrutinize the features of the asymptotic sta…
New findings on kernel regression in the quadratic regime, improving understanding of machine learning models.
problem Understanding kernel ridge regression in the quadratic asymptotic regime.
method Extended study of kernel regression to the quadratic regime, establishing approximation bounds and spectral distributions.
result Broad class of inner-product kernels exhibit behavior similar to a quadratic kernel, with precise asymptotic training and test errors characterized.
A fast method learns plasma collision kernels from simulations, improving kinetic models.
problem Improving kinetic models for plasma dynamics beyond the weakly coupled regime.
method Data-driven collisional operator, fast spectral separation method.
result Accurately captures plasma dynamics in moderately coupled regime.
Study compares adaptive vs fixed query learning methods.
problem Comparing adaptive and fixed query learning methods for task approximation.
method Examined in-context and agentic learning in two settings: unrestricted and realizable.
result Adaptivity does not hinder performance in unrestricted setting but can in realizable setting.
Mixture model-based clustering, usually applied to multidimensional data, has become a popular approach in many data analysis problems, both for its good statistical properties and for the simplicity of implementation of the Expectation-Maximization (EM) algorithm. Within the context of a railway application, this pape…
Embedded ensembles improve neural network performance efficiently.
problem Improving neural network performance with fewer resources.
method Analyzing the wide network limit of gradient descent dynamics using Neural-Tangent-Kernel.
result Embedded ensembles exhibit two regimes: independent and collective, affecting performance.
New findings support a new community recovery threshold for Stochastic Block Model with many communities.
problem Recovering communities in Stochastic Block Model with more than sqrt(n) communities.
method Counting specific motifs to achieve polynomial-time community recovery above a new threshold.
result LDP fails below the new threshold, but polynomial-time recovery is possible above it.
New theory predicts deep neural networks can operate in an extended critical regime without fine-tuning.
problem Understanding the dynamics and computational principles of deep neural networks.
method Combining theories of heavy-tailed random matrices and non-equilibrium statistical physics.
result Deep neural networks can operate in an extended critical regime without fine-tuning parameters.
This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the probability of misclassification to zero in the low-noise regime, both for rando…
We study the structure of the Kauffman algebra of a surface with parameter equal to sqrt(-1). We obtain an interpretation of this algebra as an algebra of parallel transport operators acting on sections of a line bundle over the moduli space of flat connections in a trivial SU(2)-bundle over the surface. We analyse the…
Gradient descent on neural nets often operates at the Edge of Stability, where loss behavior is complex but loss decreases over time.
problem Understanding the optimization dynamics of neural networks at the Edge of Stability.
method Empirical demonstration of gradient descent behavior in neural network training.
result Gradient descent on neural networks typically occurs at the Edge of Stability, where loss behavior is non-monotonic but loss decreases over time.
We consider a compact Riemannian manifold with a Hermitian line bundle whose curvature is non-degenerate. The Laplacian acting on high tensor powers (the semiclassical regime) of the bundle exhibits a cluster of low-energy states. We demonstrate that the orthogonal projectors onto these states are the Fourier component…
NO approximates non-Markovian BSDEs with polynomial scaling in 1/ε.
problem Complexity of NO approximations for structured families of BSDEs.
method Identifying structured families of non-Markovian BSDEs, informing NO's inductive bias.
result Polynomial scaling in 1/ε for NO approximations of BSDE solution operators.
Study shows how to learn optimal policies quickly in stochastic control problems.
problem Learning optimal policies in large, continuous state and action spaces with limited data.
method Analyzes three geometric exponents to quantify fast policy regret convergence.
result Shows that fast policy regret convergence is induced by specific geometric structures.
LSCI provides locally adaptive prediction sets for operator models with tighter coverage.
problem Generating robust, calibrated uncertainty quantification for operator models.
method Local Sliced Conformal Inference (LSCI) for operator models.
result LSCI yields tighter prediction sets with stronger adaptivity compared to conformal baselines.
Study reveals three limiting regimes for neural network functionals.
problem Understanding the behavior of functionals of random neural networks.
method Central and non-central limit theorems, Hermite expansions, Diagram Formula, Stein-Malliavin techniques.
result Three distinct limiting regimes based on fixed points of covariance function.
We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of…
This note is devoted to Keller-Lieb-Thirring spectral estimates for Schrödinger operators on infinite cylinders: the absolute value of the ground state level is bounded by a function of a norm of the potential. Optimal potentials with small norms are shown to depend on a single variable. The proof is a perturbation arg…
Study on stock trading model with uncertain market status, proving free boundaries and optimal strategies.
problem Optimal trading strategies in a stock market with uncertain market status.
method Free boundary problem, variational inequality system, degenerate operator, C^∞-smoothness.
result All four switching free boundaries are no-overlapping, monotonic, and C^∞-smooth, and their relative localities are completely determined.
The study establishes minimax bounds for estimating operators from noisy samples.
problem Estimating unknown operators between Hilbert spaces from noisy data.
method Developed a minimax theory for uniformly bounded Lipschitz operators, proving lower and upper bounds.
result Sharp characterizations of minimax risk for generic Lipschitz operators, showing a curse of sample complexity.
Large learning rates work surprisingly well in standard parameterization, contrary to theory.
problem Theoretical limits of large learning rates do not match practical network behavior.
method Fine-grained analysis of learning rates and network behavior under cross-entropy loss.
result There are two distinct sub-regimes of unstable learning rates, with a controlled divergence regime where features continue to evolve.
Neurons and networks in the cerebral cortex must operate reliably despite multiple sources of noise. To evaluate the impact of both input and output noise, we determine the robustness of single-neuron stimulus selective responses, as well as the robustness of attractor states of networks of neurons performing memory ta…
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
Study of integral flows on Riemannian manifolds with focus on blow-up profiles and concentration-compactness.
problem Analyzing nonlinear integral flows on Riemannian manifolds with specific focus on blow-up profiles and concentration-compactness.
method Investigation of a family of nonlinear integral flows involving Riesz potentials, focusing on the Hardy-Littlewood-Sobolev (HLS) subcritical and critical regimes.
result Established convergence on unit spheres and certain locally conformally flat manifolds for the dual Yamabe flow.
Gradient descent learns useful features even in the NTK regime.
problem The ability of neural networks to learn useful features.
method Local convergence analysis of gradient descent with regularization.
result Gradient descent can capture ground-truth directions for feature learning even after the loss threshold is reached.
Paper introduces a new power-dominance axis in estimator design.
problem Estimator design trade-off between bias and variance.
method Introduces a third power regime, `power-dominant', with an unavoidable error penalty.
result Any estimator in the `power-dominant' regime is structurally sub-optimal.
Scalable Gaussian Process Operator tackles high-dimensional PDEs.
problem Scaling Gaussian Process Operators to high-dimensional, data-intensive regimes.
method Nearest-neighbor-based local kernel approximations, sparse kernel approximation, structured Kronecker factorizations, operator-aware kernel structures, task-informed mean functions.
result Consistently achieves high accuracy across varying discretization scales.
New findings show mini-batch SGD operates in a 'Edge of Stochastic Stability' regime.
problem Understanding the stability and convergence of mini-batch SGD.
method Analyzing the mini-batch Hessian and its directional curvature.
result Mini-batch SGD operates in a different stability regime (Edge of Stochastic Stability) compared to full-batch GD.
The market efficiency hypothesis has been proposed to explain the behavior of time series of stock markets. The Black-Scholes model (B-S) for example, is based on the assumption that markets are efficient. As a consequence, it is impossible, at least in principle, to "predict" how a market behaves, whatever the circums…
The paper analyzes Adam and SGD in nonstationary optimization, revealing tradeoffs between noise and drift.
problem Analyzing Adam and SGD in nonstationary optimization problems.
method Theoretical analysis of Adam and SGD under non-stationary stochastic objectives, separating two regimes.
result Characterizes the tradeoff between noise and drift in Adam and SGD, revealing when adaptive step-sizing is beneficial or harmful.
The present paper aims at locating the breakings of the integration process of an international system observed during about 50 years in the 19th century. A historical study could link them to special events, which operated as exogenous shocks on this process. The indicator of integration used is the spread between the…
Study on-chain peak shaving to reduce Ethereum transaction costs.
problem Reducing transaction costs in blockchain networks, especially during congested periods.
method Analyzing transaction-level data from multiple firms across various industries to understand scheduling responses and cost management strategies.
result Firms' scheduling responses to congestion vary, leading to different fee savings and residual costs.
Formula for index in Lorentzian spacetimes.
problem Developing an index formula for spacetimes with boundary.
method Reduction from equivariant to non-equivariant, Lorentzian spectral flow.
result Equivalence of equivariant index and spectral flow in Lorentzian spacetimes.
Efficiently predicts long-time dynamics of quantum spin models using MLP regression.
problem Challenges in calculating long-time expectation values for quantum spin models.
method Utilized a multi-layer perceptron (MLP) model for regression on matrix product states (MPS) expectation values.
result Significantly reduced computational cost for generating long-time dynamics while maintaining high accuracy.
This paper improves adversarial robustness of deep learning models.
problem Vulnerability of machine learning models to adversarial perturbations.
method Analyzes adversarial training for linear regression and neural networks, incorporating L1 penalty.
result Incorporating L1 penalty leads to consistent adversarially robust estimation in high-dimensional settings.
DeepSVM learns SVMs without PDE solving, achieving high pricing accuracy.
problem Computational bottleneck in real-time calibration of stochastic volatility models.
method Physics-informed Deep Operator Network (PI-DeepONet) that enforces terminal payoffs and no-arbitrage conditions.
result DeepSVM achieves high pricing accuracy across various market dynamics.
Momentum affects optimization differently at small vs large batch sizes near instability.
problem Understanding how momentum impacts optimization near the edge of stability.
method Demonstrated through batch-size dependent behavior of SGD with momentum.
result Momentum operates in two distinct regimes: amplifying stochastic fluctuations at small batch sizes and stabilizing at large batch sizes.
The paper studies PCA of probability measures with varying sample sizes and finds optimal convergence rates.
problem PCA of multiple probability measures with varying sample sizes.
method Double asymptotic regime analysis with convergence rates n−1/2+m−α for empirical covariance and PCA risk. result Optimal convergence rates for empirical covariance and PCA risk in the dense regime are proven.
SGD works well with large learning rates at the edge of stability.
problem Stochasticity at the edge of stability in deep learning.
method Sharp convergence guarantees for SGD with multiclass cross-entropy loss.
result SGD self-stabilizes, ensuring convergence with large learning rates.
The aim of this paper is to propose a realistic and operational model to quantify the systematic risk of mortality included in an engagement of retirement. The model presented is built on the basis of model of Lee-Carter. The stochastic prospective tables thus built make it possible to project the evolution of the rand…
Deep ReLU networks approximate as well as shallow ones in kernel regimes.
problem Understanding the limitations of kernel methods for deep ReLU networks.
method Characterizing eigenvalue decays of kernels derived from deep ReLU networks.
result Deep ReLU networks and shallow two-layer networks have equivalent approximation properties in kernel regimes.