Correct method found for drawing precise envelope of straight lines.
problem Widespread method fails to represent the precise shape of envelope.
method Recently discovered correct method for straight line families in the plane.
result Correct method precisely represents the envelope of straight lines.
A neural framework corrects bias in estimating individual treatment effects.
problem Estimating individual treatment effects from observational data.
method An anchored neural architecture and precision-corrected intersection-bound inference.
result Corrected bias and maintained nominal coverage in high-dimensional settings.
We present a general formalism for incorporating the string corrections in generalised geometry, which necessitates the extension of the generalised tangent bundle. Not only are such extensions obstructed, string symmetries and the existence of a well-defined effective action require a precise choice of the (generalise…
New invariant for prime alternating knots from error-correcting codes
problem Distinguishing prime alternating knots
method Alexander-Briggs code
result New invariant succeeds in separating knots that other invariants fail
Study finds a small correction to Asian option volatility.
problem Implied volatility of Asian options at short maturity.
method Large deviations property and asymptotic expansion for the Hartman-Watson distribution.
result Subleading correction to Asian option volatility is derived.
Boosted decision trees typically yield good accuracy, precision, and ROC area. However, because the outputs from boosting are not well calibrated posterior probabilities, boosting yields poor squared error and cross-entropy. We empirically demonstrate why AdaBoost predicts distorted probabilities and examine three cali…
SCaSML improves PDE solvers by correcting errors efficiently.
problem Reliable and error-free high-dimensional PDE solutions.
method Defect correction method to derive a Structural-preserving Law of Defect.
result SCaSML achieves faster convergence and reduced errors in high-dimensional PDEs.
Autonomy and adaptation of machines requires that they be able to measure their own errors. We consider the advantages and limitations of such an approach when a machine has to measure the error in a regression task. How can a machine measure the error of regression sub-components when it does not have the ground truth…
A method compares AI corrections to a base model for explaining predictions.
problem Creating explanations for AI predictions.
method Introduces a surrogate model to correct a simpler base model and provides criteria for accuracy and fidelity.
result Induces neighborhoods of instances with ideal accuracy and fidelity.
Anytime-valid confirmation of label-shift corrections
problem Small-batch scientific deployments with scarce labeled outcomes
method Conditional e-value and martingale-based rule
result Nonnegative martingale and anytime-valid confirmation rule
This paper explains how low-precision arithmetic causes loss spikes in deep learning models.
problem Loss spikes during long-term training of deep neural networks.
method Analyzes the impact of floating-point precision limits on gradient updates and feature means.
result Numerical Feature Inflation (NFI) explains loss spikes and rapid parameter norm growth.
Reweighting improves GAN accuracy without sacrificing statistical power.
problem Improving the fidelity of generative models.
method Post-hoc reweighting function applied to generated examples.
result Weighted GAN examples significantly improve accuracy.
A new method improves super learner validation efficiency.
problem Improving the efficiency of super learner validation.
method Bootstrap Bias Corrected Cross Validation applied to Super Learning.
result Bootstrap Bias Corrected Cross Validation proved efficient and cost-effective.
In the note we study Legendrian and transverse knots in rationally null-homologous knot types. In particular we generalize the standard definitions of self-linking number, Thurston-Bennequin invariant and rotation number. We then prove a version of Bennequin's inequality for these knots and classify precisely when the …
This paper presents an automated supervised method for Persian wordnet construction. Using a Persian corpus and a bi-lingual dictionary, the initial links between Persian words and Princeton WordNet synsets have been generated. These links will be discriminated later as correct or incorrect by employing seven features …
DisCor corrects reinforcement learning issues by re-weighting collected data.
problem Reinforcement learning algorithms struggle with instability and sensitivity to hyperparameters.
method DisCor reweights collected data to mitigate issues caused by the distribution of experience.
result DisCor improves reinforcement learning in challenging settings like multi-task learning and noisy reward signals.
Paper characterizes gradient descent in high-dimensional learning problems.
problem Understanding gradient descent dynamics in high-dimensional statistical learning.
method Non-asymptotic joint distributional characterization of gradient descent iterates and debiased statistics.
result Gradient descent iterates approximate normality after debiasing correction.
A simplified tutorial on diffusion models for beginners.
problem Educating technical audiences on diffusion models.
method Simplified mathematical explanations and heuristic derivations.
result Accessible algorithms for diffusion models.
Noise-corrected Langevin algorithm improves sampling from noisy data.
problem Sampling from noisy data with biased score function.
method Noise-corrected Langevin algorithm using noisy score function.
result Bias due to noisy data is removed, improving sampling accuracy.
Quantum codes linked to abelian varieties, providing mathematical rigor.
problem Quantum error correction through complex abelian varieties.
method Mathematical formulation of Gottesman-Kitaev-Preskill codes using abelian varieties.
result Asymptotic isometry of encoding, precise gate realizations, and failure probability optimization.
Logarithmic corrections to Price's law near black hole event horizon.
problem Failure of smooth null infinity in black hole spacetimes.
method Analyzing linear wave equation on Schwarzschild background with specific initial conditions.
result Leading-order asymptotics of solutions near future null infinity and event horizon are logarithmically modified.
CONFINE enhances neural networks' interpretability without sacrificing accuracy.
problem Lack of interpretability in deep neural networks, especially in healthcare.
method CONFINE uses conformal prediction to generate prediction sets with robust uncertainty estimates.
result CONFINE achieves correct efficiency up to 3.3% higher than original accuracy.
New method corrects quantization errors in LLMs using low-rank matrices.
problem Correcting quantization errors in large language models.
method Introducing low-rank weight matrices to correct quantized activations in LLMs.
result Reduces accuracy gap with original model by more than 50% using low-rank matrices.
Unified framework for ranking-and-selection with multiple correct answers and non-answerable estimates
problem Fixed-precision ranking-and-selection in structured settings with non-unique answers and non-answerable estimates
method Unified framework based on answer-wise acceptance sets, restricted generalized likelihood ratio stopping, and answer-pitfall decomposition
result Unified recipe performs well across a broad range of pure-exploration problems
A common approach in positive-unlabeled learning is to train a classification model between labeled and unlabeled data. This strategy is in fact known to give an optimal classifier under mild conditions; however, it results in biased empirical estimates of the classifier performance. In this work, we show that the typi…
SCOPE estimator improves covariance and precision matrix estimation.
problem Estimating covariance and precision matrices accurately.
method Distributionally robust optimization with convex spectral divergence.
result SCOPE estimator reduces spectral bias and improves condition number.
We establish precise upper and lower bounds for the subelliptic heat kernel on nilpotent Lie groups G of H-type. Specifically, we show that there exist positive constants C1, C2 and a polynomial correction function Qt on G such that C1Qte−4td2≤pt≤C2Qte−4td2 wh…
Evaluation often aims to reduce the correctness or error characteristics of a system down to a single number, but that always involves trade-offs. Another way of dealing with this is to quote two numbers, such as Recall and Precision, or Sensitivity and Specificity. But it can also be useful to see more than this, and …
We introduce a technique to compute probably approximately correct (PAC) bounds on precision and recall for matching algorithms. The bounds require some verified matches, but those matches may be used to develop the algorithms. The bounds can be applied to network reconciliation or entity resolution algorithms, which i…
Quantum field theory connects deep neural networks to criticality.
problem Understanding the criticality and training dynamics of deep neural networks.
method Constructing quantum field theory for deep neural networks, computing corrections to correlation functions.
result Found precise analogy with O(N) vector model, providing corrections to correlation length. Boosting combines weak classifiers to form highly accurate predictors. Although the case of binary classification is well understood, in the multiclass setting, the "correct" requirements on the weak classifier, or the notion of the most efficient boosting algorithms are missing. In this paper, we create a broad and ge…
Study precise sample covariance error for Gaussian centered data.
problem Precise characterization of sample covariance error for Gaussian data.
method Developed a Random Duality Theory (RDT) framework to determine upper and lower bounds.
result Upper and lower bounds match in large-dimensional contexts, matching the spectral norm's limiting value.
Recently there has been significant interest in training machine-learning models at low precision: by reducing precision, one can reduce computation and communication by one order of magnitude. We examine training at reduced precision, both from a theoretical and practical perspective, and ask: is it possible to train …
Paper proposes efficient algorithms for bandit problems with costly sampling.
problem Maximizing expectation function over a finite set with high sampling cost.
method Proposes naive and adaptive stochastic bandit algorithms for PAC solution.
result Adaptive algorithm outperforms naive in terms of number of samples.
A2A metric evaluates bias correction methods, reducing ATE estimation errors.
problem Selection biases in non-randomized studies of medical treatments.
method Propensity score matching (PSM) with novel metric A2A.
result Reduces ATE estimation errors by up to 90% across synthetic and real-world datasets.
Let Omega^3(SU(n)) be the Lie group of based mappings from S^3 to SU(n). We construct a Lie group extension of Omega^3(SU(n)) for n>2 by the abelian group of the affine dual space of SU(n)-connections on S^3. In this article we give several improvement of J. Mickelsson's results in 1987, especially we give a precise de…
This paper introduces the first deep neural network-based estimation metric for the jigsaw puzzle problem. Given two puzzle piece edges, the neural network predicts whether or not they should be adjacent in the correct assembly of the puzzle, using nothing but the pixels of each piece. The proposed metric exhibits an e…
Confidence intervals improve evaluation of binary prediction rules in data mining.
problem Uncertainty in performance measures estimation from finite datasets.
method Asymptotic normal approximations for confidence intervals, with a blurring correction.
result Improved finite sample coverage probabilities and general performance measures inference.
This work identifies redundant tests in conditional-independence-based discovery that can improve graphical model accuracy.
problem Reliability and sensitivity of conditional-independence-based discovery algorithms.
method Analysis of redundant tests and their impact on error detection and correction.
result Redundant tests can improve graphical model accuracy but not all are beneficial.
Applicability of the concept of financial log-periodicity is discussed and encouragingly verified for various phases of the world stock markets development in the period 2000-2010. In particular, a speculative forecasting scenario designed in the end of 2004, that properly predicted the world stock market increases in …
Geometrically refines Cramér-Rao bound using extrinsic manifold curvature.
problem Improving estimator efficiency in non-asymptotic settings.
method Incorporates curvature-aware corrections based on extrinsic geometry of statistical model manifold.
result Meaningful tightening of estimator variance bounds.
Proposes a method to evaluate classifiers with missing labels using multiple imputation.
problem Missing labels during model evaluation can introduce bias, especially in Missing Not At Random (MNAR) data.
method Develops a multiple imputation technique to estimate and provide predictive distributions for metrics like precision, recall, and ROC-AUC.
result The predictive distribution's location and shape are generally correct, even in the MNAR regime.
The paper addresses the gap between theoretical and practical confidence set widths in universal inference.
problem Inference procedures can be overly conservative, leading to wider confidence sets than expected.
method The authors identify the source of asymptotic conservativeness and propose a remedy based on studentization and bias correction.
result The proposed method achieves exact asymptotic coverage at the nominal 1−α level, even under model misspecification. VAE global minima can learn correct manifold dimensions, even with conditioning variables.
problem Understanding VAE behavior on manifolds and adapting to varying dimensions.
method Proving VAE global minima can learn correct manifold dimensions and extending to CVAEs.
result Proven that VAE global minima can learn correct manifold dimensions and adapted to CVAEs.
We establish a Penrose-like inequality for general (not necessarily time-symmetric) initial data sets of the Einstein-Maxwell equations, which satisfy the dominant energy condition. More precisely, it is shown that the ADM energy is bounded below by an expression which is proportional to the sum of the square root of t…
Study shows AD for neural nets with machine-representable numbers can be incorrect.
problem Correctness of AD for neural nets with machine-representable numbers.
method Analyzed two sets of parameters: incorrect and non-differentiable. Proved bounds and conditions for AD correctness.
result AD can be incorrect for machine-representable numbers, but provides a Clarke subderivative on non-differentiable set.
Study on numerical reliability of AD for MaxPool in neural nets.
problem Reliability of automatic differentiation for nonsmooth operations like MaxPool.
method Investigation across precision levels and architectures on various datasets.
result Lower norms of nonsmooth Jacobians help maintain stable learning.
TIMELY improves consistency in labeling blood cell images.
problem Inconsistent labeling of blood cells in microscopy images leads to unreliable diagnoses.
method TIMELY combines pseudotime inference and hidden Markov trees to correct labeling mistakes.
result TIMELY outperforms baseline methods in identifying and correcting inconsistent labels.