The Geometry of Alignment Collapse: When Fine-Tuning Breaks Safety

Fine-tuning aligned language models on benign tasks unpredictably degrades safety guardrails, even when training data contains no harmful content and developers have no adversarial intent. We show that the prevailing explanation, that fine-tuning updates should be orthogonal to safety-critical directions in high-dimensional parameter space, offers false reassurance: we show this orthogonality is structurally unstable and collapses under the dynamics of gradient descent. We then resolve this through a novel geometric analysis, proving that alignment concentrates in low-dimensional subspaces with sharp curvature, creating a brittle structure that first-order methods cannot detect or defend. While initial fine-tuning updates may indeed avoid these subspaces, the curvature of the fine-tuning loss generates second-order acceleration that systematically steers trajectories into alignment-sensitive regions. We formalize this mechanism through the Alignment Instability Condition, three geometric properties that, when jointly satisfied, lead to safety degradation. Our main result establishes a quartic scaling law: alignment loss grows with the fourth power of training time, governed by the sharpness of alignment geometry and the strength of curvature coupling between the fine-tuning task and safety-critical parameters. These results expose a structural blind spot in the current safety paradigm. The dominant approaches to safe fine-tuning address only the initial snapshot of a fundamentally dynamic problem. Alignment fragility is not a bug to be patched; it is an intrinsic geometric property of gradient descent on curved manifolds. Our results motivate the development of curvature-aware methods, and we hope will further enable a shift in alignment safety analysis from reactive red-teaming to predictive diagnostics for open-weight model deployment.

How do data owners say no? A case study of data consent mechanisms in web-scraped vision-language AI training datasets

The internet has become the main source of data to train modern text-to-image or vision-language models, yet it is increasingly unclear whether web-scale data collection practices for training AI systems adequately respect data owners' wishes. Ignoring the owner's indication of consent around data usage not only raises ethical concerns but also has recently been elevated into lawsuits around copyright infringement cases. In this work, we aim to reveal information about data owners' consent to AI scraping and training, and study how it's expressed in DataComp, a popular dataset of 12.8 billion text-image pairs. We examine both the sample-level information, including the copyright notice, watermarking, and metadata, and the web-domain-level information, such as a site's Terms of Service (ToS) and Robots Exclusion Protocol. We estimate at least 122M of samples exhibit some indication of copyright notice in CommonPool, and find that 60\% of the samples in the top 50 domains come from websites with ToS that prohibit scraping. Furthermore, we estimate 9-13\% with 95\% confidence interval of samples from CommonPool to contain watermarks, where existing watermark detection methods fail to capture them in high fidelity. Our holistic methods and findings show that data owners rely on various channels to convey data consent, of which current AI data collection pipelines do not entirely respect. These findings highlight the limitations of the current dataset curation/release practice and the need for a unified data consent framework taking AI purposes into consideration.