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Can Adaptive Gradient Methods Converge under Heavy-Tailed Noise? A Case Study of AdaGrad Shallow ReLU$^s$ Networks in $L^p$-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization On Stability and Decomposition of Sample Quantiles under Heavy-Tailed Distributions Improved Baselines with Representation Autoencoders Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent A Two-Parameter Weibull Framework for Diagnosing Transformer Weight Distributions Calibeating for general proper losses: A Bregman divergence approach Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space Sample-efficient inductive matrix completion with noise and inexact side-information Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safety XAI and Statistical Analysis for Reliable Intrusion Detection in the UAVIDS-2025 Dataset: From Tree to Hybrid and Tabular DNN Ensembles Reasoning Models Don't Just Think Longer, They Move Differently TabPFN-3: Technical Report Reframing preprocessing selection as model-internal calibration in near-infrared spectroscopy: A large-scale benchmark of operator-adaptive PLS and Ridge models Towards a holistic understanding of Selection Bias for Causal Effect Identification Adaptive Kernel Density Estimation with Pre-training Coreset-Induced Conditional Velocity Flow Matching RISED: A Pre-Deployment Evaluation Framework for High-Stakes AI Decision-Support Systems, with Application to Healthcare ISOMORPH: A Supply Chain Digital Twin for Simulation, Dataset Generation, and Forecasting Benchmarks Yield Curves Dynamics Using Variational Autoencoders Under No-arbitrage Model-based Bootstrap of Controlled Markov Chains Online Learning-to-Defer with Varying Experts Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantification Keeping Score: Efficiency Improvements in Neural Likelihood Surrogate Training via Score-Augmented Loss Functions One-Step Generative Modeling via Wasserstein Gradient Flows Exact Stiefel Optimization for Probabilistic PLS: Closed-Form Updates, Error Bounds, and Calibrated Uncertainty A Composite Activation Function for Learning Stable Binary Representations Adaptive Calibration in Non-Stationary Environments Real vs. Semi-Simulated: Rethinking Evaluation for Treatment Effect Estimation Federated Language Models Under Bandwidth Budgets: Distillation Rates and Conformal Coverage On Variance Reduction in Learning Mean Flows When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? 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The frame problem in quantitative practice: ontological uncertainty and epistemic humility in an age of automated inference
William Faur · 2026-05-25 · via stat updates on arXiv.org

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Abstract:Quantitative practice across statistics, engineering, and machine learning has been transformed by the automation of inference. Predictions are produced, validated, and deployed at scale and speed that human-mediated reasoning could not match. This shift intersects with a structural limit of reasoning that no methodological refinement dissolves: every inference rests on a finite specification of conditions, and what falls outside the specification does not appear as a widened uncertainty band -it does not appear at all. The choice of specification -the frame -is upstream of the inference and cannot be audited from inside the system that uses it. This paper offers a synthetic, application-oriented review. We argue that three categories of uncertainty operate in quantitative practice -aleatory, epistemic, and frame (or ontological) -and that the third, the residue of finite specification, is structurally invisible to formal analysis within the chosen frame and is the locus of most consequential failures. We trace why the limit applies equally to deductive and inductive reasoning, why no meta-level procedure dissolves the regress, and why current conditions of automated inference make epistemic humility -the practical disposition this argument supports -more, not less, important. We articulate the argument's specific resonances for five typical figures of contemporary quantitative work -the engineer, the statistician, the mathematician, the machine-learning practitioner, and the non-specialist recipient of expert claims -showing how the structural argument bears on each practice's natural defenses. The argument is not against rigor or against quantification; it is for distinguishing rigor earned within a frame from rigor with respect to the frame.
Subjects: Methodology (stat.ME)
Cite as: arXiv:2605.23614 [stat.ME]
  (or arXiv:2605.23614v1 [stat.ME] for this version)
  https://doi.org/10.48550/arXiv.2605.23614

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: William FAURIAT [view email] [via CCSD proxy]
[v1] Fri, 22 May 2026 13:21:05 UTC (29 KB)