New method creates vacuum data at minimal and borderline decay thresholds.
problem Creating vacuum initial data at specific decay thresholds.
method Conical solution-operator method applied to vacuum asymptotically flat initial data.
result Demonstrates global and exterior stability of Minkowski spacetime.
In this paper we continue our study of the Laplacian on manifolds with axial analytic asymptotically cylindrical ends initiated in~arXiv:1003.2538. By using the complex scaling method and the Phragmén-Lindelöf principle we prove exponential decay of the eigenfunctions corresponding to the non-threshold eigenvalues of t…
New method trains neural networks with threshold activation functions efficiently.
problem Training neural networks with threshold activation functions is challenging due to zero gradients.
method We study weight decay regularized training problems of deep neural networks with threshold activations, showing they can be formulated as convex optimization problems.
result Regularized deep threshold network training problems can be formulated as standard convex optimization problems, paralleling the LASSO method.
Weight decay stabilizes training dynamics by slowing progressive sharpening.
problem Understanding how weight decay affects training stability in deep learning models.
method Analyzing weight decay effects at the Edge of Stability, developing a mathematical framework.
result Weight decay dampens oscillations and stabilizes sharpness in CNNs, causing a phase transition in MLPs.
SAD-DPSGD improves model performance on imbalanced medical datasets like HAM10000.
problem Data leakage and imbalanced distribution in medical image classification datasets.
method SAD-DPSGD uses a linear decaying mechanism for noise and clipping thresholds to enhance performance.
result SAD-DPSGD outperforms Auto-DPSGD on HAM10000, improving accuracy by 2.15%.
Sparse Inverse Covariance Estimation (SICE) is useful in many practical data analyses. Recovering the connectivity, non-connectivity graph of covariates is classified amongst the most important data mining and learning problems. In this paper, we introduce a novel SICE approach using adaptive thresholding. Our method i…
Simplicial persistence measures financial market dynamics, revealing long-term structure evolution.
problem Understanding the long-term structure evolution of financial markets.
method Simplicial persistence, null models, TMFG filtering, thresholding, generative process analysis.
result More liquid markets exhibit slower persistence decay, suggesting higher fragility to systemic shocks.
Study on critical faces convergence in a Poisson point process.
problem Convergence of point processes associated with critical faces in a Čech filtration.
method Established convergence in M0-topology for critical faces above vanishing threshold. result Obtained limit theorems for positive and negative critical faces.
Survey on stability of Minkowski spacetime in relativity.
problem Nonlinear stability of Minkowski spacetime in general relativity.
method Decay assumptions, geometric foliations, energy identities, and gauge choices.
result Understanding of decay, dispersion, and geometry-analysis interplay.
New algorithm improves cache management with delayed feedback and decaying costs.
problem Improving cache replacement policies with delayed and decaying costs feedback.
method Proposed EXP4-DFDC adaptive reinforcement learning algorithm.
result Expected regret is a vanishing quantity as a function of time.
A class of heterogeneous agent models is investigated where investors switch trading position whenever their motivation to do so exceeds some critical threshold. These motivations can be psychological in nature or reflect behaviour suggested by the efficient market hypothesis (EMH). By introducing different propensitie…
We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected thre…
This paper describes the black hole threshold in a moduli space of spherically symmetric spacetimes.
problem Understanding the black hole threshold in a moduli space of spherically symmetric spacetimes.
method Complete description and analysis of the black hole threshold in the moduli space M. result The black hole threshold is the extremal leaf of a C1 foliation of the moduli space, separating black hole solutions from non-collapsing solutions. Study reveals phase transition in neural networks near interpolation.
problem Understanding generalization and learning transitions in neural networks.
method Effective theory for approximating Bayes-optimal generalisation error.
result Unveils a discontinuous phase transition between universal and specialisation phases.
The relaxation dynamics of aftershocks after large volatility shocks are investigated based on two high-frequency data sets of the Shanghai Stock Exchange Composite (SSEC) index. Compared with previous relevant work, we have defined main financial shocks based on large volatilities rather than large crashes. We find th…
In this paper, we describe a newly discovered statistical property of time series data for daily price changes. We conducted quantitative investigation of the {\it calm-time intervals} of price changes for 800 companies listed in the Tokyo Stock Exchange, and for the Nikkei 225 index over a 27-year period from January …
AI-driven investment strategies self-defeat at scale due to signal crowding and erosion.
problem Excess returns from AI-driven investment strategies diminish at scale due to signal crowding and erosion.
method Theoretical model and empirical validation using SEC Form 13F filings and hedge fund return dynamics.
result The alpha half-life of signals decreases significantly with AI adoption, leading to diminishing returns.
In a financial market, for agents with long investment horizons or at times of severe market stress, it is often changes in the asset price that act as the trigger for transactions or shifts in investment position. This suggests the use of price thresholds to simulate agent behavior over much longer timescales than are…
It will be discussed the statistics of the extreme values in time series characterized by finite-term correlations with non-exponential decay. Precisely, it will be considered the results of numerical analyses concerning the return intervals of extreme values of the fluctuations of resistance and defect-fraction displa…
WBCP improves conformal prediction for distribution shifts using weighted Dirichlet posteriors.
problem Handling distribution shifts in conformal prediction.
method Generalizes Bayesian Quadrature Conformal Prediction (BQ-CP) to arbitrary importance-weighted settings.
result WBCP maintains coverage guarantees while providing richer uncertainty information.
Hybrid regularization avoids double descent in random feature models.
problem Avoiding the double descent phenomenon in random feature models.
method Combines early stopping and weight decay, using GCV for hyperparameter selection.
result Hybrid method successfully avoids double descent and achieves comparable generalization.
In this paper, we propose a communication- and computation-efficient algorithm to solve a convex consensus optimization problem defined over a decentralized network. A remarkable existing algorithm to solve this problem is the alternating direction method of multipliers (ADMM), in which at every iteration every node up…
New method proves non-contrastive self-supervised learning learns useful features.
problem Understanding how non-contrastive self-supervised learning (NS-SL) learns useful features.
method Proved in a linear network, NS-SL learns a desirable projection matrix and reduces sample complexity. Suggested weight decay acts as an implicit threshold.
result DirectCopy, a simpler and more efficient algorithm, outperforms DirectPred on various datasets.
The three-state agent-based 2D model of financial markets in the version proposed by Giulia Iori in 2002 has been herein extended. We have introduced the increase of herding behaviour by modelling the altering trust of an agent in his nearest neighbours. The trust increases if the neighbour has foreseen the price chang…
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.
Continuous phase transitions identified in Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
problem Phase transitions in multimodal models and their properties.
method Sharp coercivity estimate and constrained Lebedev--Milin inequality.
result Continuous phase transitions at critical coupling strengths for Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
We study approximations of the partition function of dense graphical models. Partition functions of graphical models play a fundamental role is statistical physics, in statistics and in machine learning. Two of the main methods for approximating the partition function are Markov Chain Monte Carlo and Variational Method…
Look-Ahead-Bench evaluates financial LLMs for lookahead bias, revealing significant differences in model performance.
problem Measuring and mitigating lookahead bias in financial LLMs.
method Standardized benchmark evaluating model behavior in practical financial scenarios, analyzing performance decay across market regimes.
result Standard LLMs exhibit significant lookahead bias, while Pitinf models show improved generalization and reasoning abilities.
Deep networks generalize well even when they fit training data perfectly, thanks to overparametrization.
problem Understanding generalization in overparametrized deep networks.
method Random features regression, asymptotic analysis, ensemble averaging.
result Bias remains constant beyond the interpolation threshold, while variance components decay with overparametrization.
The paper models market dynamics using a limit order book system to explain slippage and inefficiency.
problem Inefficiency in matching markets due to structural liquidity constraints and slippage.
method Introduces a market microstructure framework with a latent preference state matrix and a dynamic discrete choice execution model.
result Persistent slippage and regional invariance of preference orderings are explained by liquidity thresholds.
A hierarchical model shows how scaling laws emerge from sequential feature recovery.
problem Emergence of scaling laws from feature learning in multi-layer networks.
method Layer-wise spectral algorithm adapted to compositional structure, sequential feature detection.
result Sequential detection of latent features, leading to explicit power-law decay of prediction error.
We analyze the memory in volatility by studying volatility return intervals, defined as the time between two consecutive fluctuations larger than a given threshold, in time periods following stock market crashes. Such an aftercrash period is characterized by the Omori law, which describes the decay in the rate of after…
In this paper we investigate the computational complexity of learning the graph structure underlying a discrete undirected graphical model from i.i.d. samples. We first observe that the notoriously difficult problem of learning parities with noise can be captured as a special case of learning graphical models. This lea…
Extends Minkowski stability proof to minimal decay assumptions.
problem Global stability of Minkowski spacetime with minimal decay.
method Extends Christodoulou-Klainerman's proof to minimal decay assumptions.
result Exterior stability of Minkowski holds with borderline decay.
The problem of learning forest-structured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu tree through adaptive thresholding is proposed. It is shown that this algorithm is both structurally consistent and risk consistent and the error probability of structure …
Unique solutions found for wave-like decaying null infinity equations.
problem Wave-like decaying null infinity equations with spherically symmetric Einstein-scalar-field.
method Local and global unique solutions for small initial data.
result Sharp decaying condition for unique solutions.
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with longer memory than those considered in the current literature. We show that severa…
The paper examines how heavy-tailed risks behave under Gaussian copula models.
problem Understanding tail risk probabilities with heavy-tailed marginal risks and Gaussian dependence.
method Modeling heavy-tailed risks using regular variation and analyzing tail probabilities under Gaussian copula.
result The rate of decay of tail set probabilities varies with the type of tail sets and Gaussian correlation matrix.
New findings on flatness of certain metrics with fast decay.
problem Rigidity of positive mass theorem under fast metric decay.
method Considered metrics with nonnegative scalar curvature and rapid decay at infinity.
result Any such metric is necessarily flat in dimensions 4 and higher if decay rate exceeds Schwarzschild metric.
We study quantitatively the level of false multifractal signal one may encounter while analyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis (MF-DFA). The investigated effect appears as a result of finite length of used data series and is additionally amplified by the long-t…
Study on curvature decay in steady Ricci solitons, proving dichotomy.
problem Curvature decay in steady Ricci solitons.
method Established a dichotomy for curvature decay in specific types of solitons.
result Proved a dichotomy on curvature decay for certain steady Ricci solitons.
Cautious Weight Decay modifies weight decay for better optimization.
problem Improving optimization in deep learning models.
method Applies weight decay selectively based on parameter sign alignment.
result Consistently improves model performance across various tasks and scales.
New method identifies network structure without regularization for sparse teacher couplings.
problem Identifying network structure in inverse Ising problems with model mismatch.
method Ridge linear regression with two-stage estimator.
result Perfect identification of network structure possible without regularization for sparse teacher couplings.
Study on scalar curvature decay on non-compact manifolds linked at infinity.
problem Understanding scalar curvature decay on non-compact manifolds with topological linking at infinity.
method Analyzing polynomial decay, developing obstruction theory, using μ--bubble exhaustions, and index theory. result Topological linking at infinity forces polynomial decay of scalar curvature on manifolds of weakly bounded geometry.
Study on massless Vlasov equation on Reissner-Nordström spacetimes, showing decay rates and non-decay phenomena.
problem Analyzing decay and non-decay rates of solutions to the massless Vlasov equation on Reissner-Nordström spacetimes.
method Quantitative analysis of geodesic flow and comparison to wave equation instability results.
result Exponential decay rates in subextremal cases and polynomial rates in extremal cases, with non-decay of transversal derivatives in extremal cases.
The study shows that the visible range from a point on harmonic manifolds follows an exponential distribution.
problem Understanding the visible range from a point on harmonic manifolds.
method Analyzing Poisson Boolean models on harmonic manifolds, focusing on the geometric mechanism of tube volumes around geodesic segments.
result The visible range from a point on harmonic manifolds follows an exponential distribution.
Model captures asymmetric extreme events in financial returns.
problem Capturing asymmetric extreme events in financial returns.
method Two-tailed peak-over-threshold Hawkes model.
result Extreme losses contribute twice as much as gains but decay more quickly.
We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods to get algorithms for calculating partition functions in these families. These …