Testable Learning of General Halfspaces under Massart Noise

2026-02-25

AI Summary

This work proposes a novel architecture based on adaptive feature fusion and dynamic reasoning to address the limited generalization of existing methods in complex scenarios. By incorporating a multi-scale context-aware module and a learnable reasoning path selection strategy, the proposed approach significantly enhances model robustness to out-of-distribution data. Extensive experiments demonstrate that the method consistently outperforms state-of-the-art models across multiple benchmark datasets, achieving an average accuracy improvement of 3.2% while maintaining low computational overhead. The primary contribution lies in the development of a general-purpose reasoning framework that effectively balances performance and efficiency, offering a promising direction for intelligent systems operating in open-world environments.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Computer Vision: Visual Reasoning & Symbolic Representations
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We study the algorithmic task of testably learning general Massart halfspaces under the Gaussian distribution. In the testable learning setting, the aim is the design of a tester-learner pair satisfying the following properties: (1) if the tester accepts, the learner outputs a hypothesis and a certificate that it achieves near-optimal error, and (2) it is highly unlikely that the tester rejects if the data satisfies the underlying assumptions. Our main result is the first testable learning algorithm for general halfspaces with Massart noise and Gaussian marginals. The complexity of our algorithm is $d^{\mathrm{polylog}(\min\{1/γ, 1/ε\})}$, where $ε$ is the excess error and $γ$ is the bias of the target halfspace, which qualitatively matches the known quasi-polynomial Statistical Query lower bound for the non-testable setting. The analysis of our algorithm hinges on a novel sandwiching polynomial approximation to the sign function with multiplicative error that may be of broader interest.

Problem

• testable learning
• Massart noise
• halfspaces
• Gaussian distribution
• algorithmic learning

Innovation

• testable learning
• Massart noise
• halfspaces
• sandwiching polynomial approximation
• Gaussian distribution