Finite-precision learning of anh networks is limited by the Monte Carlo rate.
problem Learning anh neural networks under finite precision method Using iterated anh activations to construct localized bump functions result No adaptive randomized algorithm can achieve higher convergence rate than Monte Carlo rate in finite precision
HierLPR ranks labels hierarchically for multi-label classification, optimizing a new eAUC metric.
problem Hierarchical multi-label classification with emphasis on first call accuracy.
method Introduces HierLPR algorithm optimizing eAUC metric under tree constraint.
result HierLPR outperforms other methods in early precision-recall curve stages.
We study statistical risk minimization problems under a privacy model in which the data is kept confidential even from the learner. In this local privacy framework, we establish sharp upper and lower bounds on the convergence rates of statistical estimation procedures. As a consequence, we exhibit a precise tradeoff be…
We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold for model prices and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a chan…
Study problem-dependent rates in statistical learning theory, achieving optimal generalization error bounds.
problem Generalization error in statistical learning theory.
method Uniform localized convergence framework.
result Optimal generalization error bounds for various learning problems.
A networked learning method for correlated data outperforms federated learning in precision.
problem Estimating models from correlated data distributed across a network.
method Local linear model estimation with network regularization and information exchange.
result The weighted ensemble average estimate converges faster and more precisely than federated learning.
In this paper, we study the price of Variable Annuity Guarantees, especially of Guaranteed Annuity Options (GAO) and Guaranteed Minimum Income Benefit (GMIB), and this in the settings of a derivative pricing model where the underlying spot (the fund) is locally governed by a geometric Brownian motion with local volatil…
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study of pointwise power decay rates almost everywhere of the quadratic tilt-excess is completed by establishing the precise decay rate for two-di…
Local minimax analysis for Poisson deconvolution of discrete signals.
problem Estimating a discrete uniform signal from Poisson convolutions.
method Local minimax risk analysis of a broad class of kernels.
result Sharp estimation rates as a function of signal clustering.
We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we consider goodness-of-fit testing when the null distribution has a possibly growing or…
New bounds on learning shared representations improve model performance and efficiency.
problem Improving model performance and efficiency through shared representations across clients.
method Established new upper and lower bounds on statistical error, designed a spectral estimator for non-convex least-squares solutions.
result Optimal statistical rate achieved when shared representation is well covered across clients.
Study optimizes linear regression analysis for high-dimensional settings.
problem Understanding high-dimensional linear regression with interpolation and regularization.
method Localized uniform convergence analysis of optimistic rates for linear regression.
result Recover guarantees for ridge and LASSO regression under random designs.
Study reveals strong co-jumping behavior in U.S. yield curves compared to Europe.
problem Understanding co-jumps in interest rate futures markets.
method Localized co-jumps through wavelet coefficients, identified statistically significant ones, and analyzed using high frequency data.
result Stronger co-jumping behavior in U.S. yield curves compared to European ones.
Decentralized detection avoids sharing data, controls false discoveries.
problem Global false discovery rate control in decentralized novelty detection.
method Quantized surrogate models for low-precision sharing, preserving exchangeability.
result Quantized composite scores maintain competitive statistical power with reduced communication.
We provide novel theoretical results regarding local optima of regularized M-estimators, allowing for nonconvexity in both loss and penalty functions. Under restricted strong convexity on the loss and suitable regularity conditions on the penalty, we prove that \emph{any stationary point} of the composite objective f…
Paper discusses binary classification with metric space predictors, privacy constraints, and convergence rates.
problem Binary classification with metric space predictors under privacy constraints.
method Derives convergence rates for Proto-NN classifier with and without privacy constraints.
result Proto-NN classifier is universally consistent under privacy constraints.
Study precise asymptotics of noncompact Type-IIb solutions to mean curvature flow.
problem Understanding the behavior of noncompact Type-IIb solutions to mean curvature flow as time approaches infinity.
method Constructed rotationally symmetric solutions with specific asymptotic behavior and analyzed their properties.
result The highest curvature concentrates at the tip of the hypersurface and blows up at the Type-IIb rate (2t+1)(γ−1)/2. The AAA credit rating may have been overly precise given available data.
problem The feasibility of achieving high reliability targets for structured credit products.
method Bayes' theorem and historical data analysis.
result High reliability targets for structured products require substantial statistical discrimination, which was not achievable with available data.
In this paper, we determine the optimal convergence rates for strongly convex and smooth distributed optimization in two settings: centralized and decentralized communications over a network. For centralized (i.e. master/slave) algorithms, we show that distributing Nesterov's accelerated gradient descent is optimal and…
SGHMC improves sampling and optimization under local conditions.
problem Nonconvex optimization and sampling under local conditions.
method Nonasymptotic analysis of SGHMC convergence.
result SGHMC provides high-precision results uniformly in iterations.
The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to estimate low-dimensional parameters at parametric square-root rate in a large Gau…
SWALP averages SGD iterates for low-precision training, improving scalability and performance.
problem Improving scalability and performance in low-precision training.
method Averages low-precision SGD iterates with a modified learning rate schedule.
result SWALP matches full-precision SGD performance with 8-bit quantization and converges to optimal solutions.
We propose communication-efficient distributed estimation and inference methods for the transelliptical graphical model, a semiparametric extension of the elliptical distribution in the high dimensional regime. In detail, the proposed method distributes the d-dimensional data of size N generated from a transellipti…
Paper addresses FL over MAC with DP constraints, proposing a novel consensus scheme.
problem Federated learning over a multiple access channel with differential privacy constraints.
method Proposes a novel consensus scheme using digital distributed stochastic gradient descent (D-DSGD) with artificial noise to preserve DP.
result Demonstrates improved convergence rate and DP level for a given MAC capacity.
Defines a new short rate model and convexity adjustment formulae.
problem Interest rate convexity in a Gaussian framework.
method Defines a short rate model driven by a Gaussian Volterra process and derives convexity adjustment formulae.
result Explicit formulae for convexity adjustment derived.
Study precise rates of horizontal gap shrinkage on generic translation surfaces.
problem Understanding precise decay rates of horizontal gaps in translation surfaces.
method Analyzing saddle connections and their angles on translation surfaces.
result Obtained precise decay rates for the difference in angle between almost horizontal saddle connections.
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the nonconvex estimator, and it attains a linear rate of convergence to the true regres…
The study examines how class imbalance affects precision-recall curves.
problem Understanding how precision changes with class imbalance ratios.
method Analyzes the relationship between precision, class imbalance ratio, and true/false positive rates.
result Predicts changes in precision-recall curves and other measures with class imbalance ratios.
SQWA improves low-precision DNNs with model averaging and quantization.
problem Designing good generalization DNNs with quantized weights.
method Floating-point model training, direct quantization, multiple low-precision models, weight averaging, re-quantization, fine-tuning, loss visualization.
result State-of-the-art results for 2-bit QDNNs on CIFAR-100 and ImageNet datasets.
We prove that any minimal (maximal) strongly regular surface in the three-dimensional Minkowski space locally admits canonical principal parameters. Using this result, we find a canonical representation of minimal strongly regular time-like surfaces, which makes more precise the Weierstrass representation and shows mor…
Study on curvature blow-up rates in black hole interiors from gravitational collapse.
problem Understanding curvature blow-up rates in black hole interiors during gravitational collapse.
method Investigation of spherically symmetric Einstein-scalar field spacetimes, focusing on blow-up rates of curvature and mass.
result Kretschmann scalar blows up faster than in Schwarzschild setting, indicating a new blow-up phenomenon.
This paper establishes lower bounds for SGD's error, matching upper bounds.
problem Proving lower error bounds for SGD optimization algorithm.
method Analysis of mean square error for SGD with specific learning rates.
result Essentially matching lower and upper bounds for SGD's mean square error.
Study reveals how Fisher information changes with network depth, finding it grows linearly.
problem Understanding the trainability of deep neural networks (DNNs).
method Investigates the spectral distribution of the conditional Fisher information matrix (FIM) for fully-connected networks achieving dynamical isometry.
result The conditional FIM's spectrum concentrates around the maximum and grows linearly with depth.
Proposes new Monte Carlo methods for calibrating local volatility models with stochastic components.
problem Calibrating local volatility models with stochastic drift and diffusion.
method Developed Monte Carlo algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and stochastic local volatility with stochastic interest rates.
result Conditions for the existence of local volatility given European option prices, stochastic interest rate model parameters, and correlations.
The study analyzes convergence of adaptive optimizers under low-precision training.
problem Understanding why low-precision training remains effective for large models.
method Developed a theoretical framework for analyzing convergence of adaptive optimizers under floating-point quantization.
result Adaptive optimizers retain convergence rates close to full-precision methods under logarithmic mantissa scaling.
We study the Morse-Novikov cohomology and its almost-symplectic counterpart on manifolds admitting locally conformally symplectic structures. More precisely, we introduce lcs cohomologies and we study elliptic Hodge theory, dualities, Hard Lefschetz Condition. We consider solvmanifolds and Oeljeklaus-Toma manifolds. In…
A new method for optimizing non-decomposable metrics with constraints.
problem Optimizing complex machine learning objectives with thresholded constraints.
method Formulate rate-constrained optimization using the Implicit Function theorem and solve with gradient-based methods.
result Demonstrated effectiveness over existing methods on benchmark datasets.
The paper tests semantic importance in opaque models using betting.
problem Precise statistical guarantees for semantic concepts in black-box models.
method Formalizes global and local statistical importance via conditional independence and SKIT.
result Shows effectiveness and flexibility of the framework on various models.
Local update methods' performance depends on learning rates, affecting convergence rates and alignment with true loss.
problem The performance of local update methods in federated learning and meta-learning is sensitive to learning rates.
method Proved that local update methods perform SGD on a surrogate loss function, characterized the surrogate loss, and derived convergence rates.
result Proper learning rate tuning is crucial for near-optimal behavior in communication-limited settings.
Method calibrates local volatility and stochastic short rate models for equity-rate dynamics.
problem Joint calibration of local volatility and stochastic short rate models.
method Iterative approach using semimartingale optimal transport.
result Demonstrated performance on market data using European SPX options and cap interest rate options.
Crochet creates precise 2D shapes from 1D material.
problem Creating precise 2D shapes from 1D material.
method Using crochet to generate constant flat, spherical, or hyperbolic shapes.
result Crochet is the most flexible and precise method for building dynamical systems with high curvature precision.
Paper provides an explicit formula for local volatility in Cheyette models.
problem Approximating local volatility in Cheyette interest rate models.
method Extended Dupire framework, perturbation methods, probabilistic techniques.
result Explicit analytical formula for local volatility in Cheyette models.
Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local non-stationarity or the presence of an external perturbation to the system. In this paper we propose a novel procedure for the detection…
In many applications, data come with a natural ordering. This ordering can often induce local dependence among nearby variables. However, in complex data, the width of this dependence may vary, making simple assumptions such as a constant neighborhood size unrealistic. We propose a framework for learning this local dep…
Study finds no significant short-term impact on liquidity supply after protocol fees were reduced.
problem Liquidity provider welfare is affected by protocol fees, but the impact on liquidity supply is unclear.
method Used a matched-overlap event-study difference-in-differences design to estimate the liquidity-supply response to take-rate cuts.
result No significant short-term impact on active liquidity or local depth; no change in LP participation or composition.
New insights into optimizing Local SGD's outer optimizer for faster convergence.
problem Understanding the impact of outer optimizer and its hyperparameters in Local SGD.
method Analyzing convergence guarantees with new outer learning rates and momentum.
result Tuning the outer learning rate can improve convergence and handle inner learning rate ill-tuning.
A new method reduces training time and improves accuracy in machine learning models.
problem The tradeoff between training accuracy and precision in low-precision machine learning.
method A low-precision stochastic gradient descent variant called HALP, using SVRG to reduce gradient variance and bit centering to reduce quantization error.
result HALP converges at the same theoretical rate as full-precision algorithms despite quantization noise.
Enhances KWS in vehicles with multi-source fusion.
problem Improving precision and recall rates in vehicle keyword spotting.
method Integrates vehicle information into a DNN for speech classification and selects optimal sensitivity parameters.
result Significantly improved performance metrics (precision, recall, MSE) compared to baseline.