Beyond the Loss Curve: Scaling Laws, Active Learning, and the Limits of Learning from Exact Posteriors

• URL: http://arxiv.org/abs/2602.00315v1
• Date: Fri, 30 Jan 2026 21:08:55 GMT
• Title: Beyond the Loss Curve: Scaling Laws, Active Learning, and the Limits of Learning from Exact Posteriors
• Authors: Arian Khorasani, Nathaniel Chen, Yug D Oswal, Akshat Santhana Gopalan, Egemen Kolemen, Ravid Shwartz-Ziv,
• Abstract summary: We use class-conditional normalizing flows as oracles that make exact posteriors tractable on realistic images.<n>Our framework reveals that standard metrics hide ongoing learning, mask architectural differences, and cannot diagnose the nature of distribution shift.
• Score: 8.410613979416203
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: How close are neural networks to the best they could possibly do? Standard benchmarks cannot answer this because they lack access to the true posterior p(y|x). We use class-conditional normalizing flows as oracles that make exact posteriors tractable on realistic images (AFHQ, ImageNet). This enables five lines of investigation. Scaling laws: Prediction error decomposes into irreducible aleatoric uncertainty and reducible epistemic error; the epistemic component follows a power law in dataset size, continuing to shrink even when total loss plateaus. Limits of learning: The aleatoric floor is exactly measurable, and architectures differ markedly in how they approach it: ResNets exhibit clean power-law scaling while Vision Transformers stall in low-data regimes. Soft labels: Oracle posteriors contain learnable structure beyond class labels: training with exact posteriors outperforms hard labels and yields near-perfect calibration. Distribution shift: The oracle computes exact KL divergence of controlled perturbations, revealing that shift type matters more than shift magnitude: class imbalance barely affects accuracy at divergence values where input noise causes catastrophic degradation. Active learning: Exact epistemic uncertainty distinguishes genuinely informative samples from inherently ambiguous ones, improving sample efficiency. Our framework reveals that standard metrics hide ongoing learning, mask architectural differences, and cannot diagnose the nature of distribution shift.

Related papers

• A Model of Artificial Jagged Intelligence [0.0]
  Generative AI systems often display highly uneven performance across tasks that appear nearby''<n>We call this phenomenon Artificial Jagged Intelligence (AJI)<n>This paper develops a tractable economic model of AJI that treats adoption as an information problem.
  arXiv  Detail & Related papers  (2026-01-12T14:27:30Z)
• Relative Scaling Laws for LLMs [91.73497548097775]
  Scaling laws describe how language models improve with additional data, parameters, and compute.<n>We introduce relative scaling laws, which track how performance gaps between test distributions evolve with scale.<n>These results show that although scaling improves overall performance, it is not a universal equalizer.
  arXiv  Detail & Related papers  (2025-10-28T16:55:22Z)
• Reliable Active Learning from Unreliable Labels via Neural Collapse Geometry [5.1511135538176]
  Active Learning (AL) promises to reduce annotation cost by prioritizing informative samples, yet its reliability is undermined when labels are noisy or when the data distribution shifts.<n>We propose Active Learning via Neural Collapse Geometry (NCAL-R), a framework that leverages the emergent geometric regularities of deep networks to counteract unreliable supervision.
  arXiv  Detail & Related papers  (2025-10-10T17:50:31Z)
• Guess-and-Learn (G&L): Measuring the Cumulative Error Cost of Cold-Start Adaptation [0.11102988539107704]
  Evaluation of machine learning models typically emphasizes final accuracy, overlooking the cost of adaptation cumulative errors incurred while learning from scratch.<n>Guess-and- Learn (G&L) v1.0 addresses this gap by measuring cold-start adaptability - the total mistakes a model makes while sequentially labeling an unlabeled dataset.
  arXiv  Detail & Related papers  (2025-08-29T00:13:02Z)
• Practical estimation of the optimal classification error with soft labels and calibration [47.001801756596926]
  We extend a previous work that utilizes soft labels for estimating the Bayes error, the optimal error rate.<n>We tackle a more challenging problem setting: estimation with corrupted soft labels.<n>Our method is instance-free, i.e., we do not assume access to any input instances.
  arXiv  Detail & Related papers  (2025-05-27T06:04:57Z)
• Dirichlet-Based Prediction Calibration for Learning with Noisy Labels [40.78497779769083]
  Learning with noisy labels can significantly hinder the generalization performance of deep neural networks (DNNs) Existing approaches address this issue through loss correction or example selection methods. We propose the textitDirichlet-based Prediction (DPC) method as a solution.
  arXiv  Detail & Related papers  (2024-01-13T12:33:04Z)
• Deep Imbalanced Regression via Hierarchical Classification Adjustment [50.19438850112964]
  Regression tasks in computer vision are often formulated into classification by quantizing the target space into classes. The majority of training samples lie in a head range of target values, while a minority of samples span a usually larger tail range. We propose to construct hierarchical classifiers for solving imbalanced regression tasks. Our novel hierarchical classification adjustment (HCA) for imbalanced regression shows superior results on three diverse tasks.
  arXiv  Detail & Related papers  (2023-10-26T04:54:39Z)
• Do We Really Need a Learnable Classifier at the End of Deep Neural Network? [118.18554882199676]
  We study the potential of learning a neural network for classification with the classifier randomly as an ETF and fixed during training. Our experimental results show that our method is able to achieve similar performances on image classification for balanced datasets.
  arXiv  Detail & Related papers  (2022-03-17T04:34:28Z)
• Understanding Square Loss in Training Overparametrized Neural Network Classifiers [31.319145959402462]
  We contribute to the theoretical understanding of square loss in classification by systematically investigating how it performs for overparametrized neural networks. We consider two cases, according to whether classes are separable or not. In the general non-separable case, fast convergence rate is established for both misclassification rate and calibration error. The resulting margin is proven to be lower bounded away from zero, providing theoretical guarantees for robustness.
  arXiv  Detail & Related papers  (2021-12-07T12:12:30Z)
• SLA$^2$P: Self-supervised Anomaly Detection with Adversarial Perturbation [77.71161225100927]
  Anomaly detection is a fundamental yet challenging problem in machine learning. We propose a novel and powerful framework, dubbed as SLA$2$P, for unsupervised anomaly detection.
  arXiv  Detail & Related papers  (2021-11-25T03:53:43Z)
• Distribution Mismatch Correction for Improved Robustness in Deep Neural Networks [86.42889611784855]
  normalization methods increase the vulnerability with respect to noise and input corruptions. We propose an unsupervised non-parametric distribution correction method that adapts the activation distribution of each layer. In our experiments, we empirically show that the proposed method effectively reduces the impact of intense image corruptions.
  arXiv  Detail & Related papers  (2021-10-05T11:36:25Z)
• Evaluating Prediction-Time Batch Normalization for Robustness under Covariate Shift [81.74795324629712]
  We call prediction-time batch normalization, which significantly improves model accuracy and calibration under covariate shift. We show that prediction-time batch normalization provides complementary benefits to existing state-of-the-art approaches for improving robustness. The method has mixed results when used alongside pre-training, and does not seem to perform as well under more natural types of dataset shift.
  arXiv  Detail & Related papers  (2020-06-19T05:08:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.