Goto

Collaborating Authors

 checkpoint


Model Details

Neural Information Processing Systems

We decreased the confidence threshold to 0.1 to increase article and headline The following specifications were used: { resolution: 256, learning rate: 2e-3 }. This limit is binding for common words, e.g., "the". The recognizer is trained using the Supervised Contrastive ("SupCon") loss function [7], a gener-45 In particular, we work with the "outside" SupCon loss formulation We use a MobileNetV3 (Small) encoder pre-trained on ImageNet1k sourced from the timm [19] We use 0.1 as the temperature for Center Cropping, to avoid destroying too much information. C (Small) model that is developed in [2] for character recognition. If multiple article bounding boxes satisfy these rules for a given headline, then we take the highest.









A Scalable Measure of Loss Landscape Curvature for Analyzing the Training Dynamics of LLMs

Kalra, Dayal Singh, Gagnon-Audet, Jean-Christophe, Gromov, Andrey, Mediratta, Ishita, Niu, Kelvin, Miller, Alexander H, Shvartsman, Michael

arXiv.org Machine Learning

Understanding the curvature evolution of the loss landscape is fundamental to analyzing the training dynamics of neural networks. The most commonly studied measure, Hessian sharpness ($λ_{\max}^H$) -- the largest eigenvalue of the loss Hessian -- determines local training stability and interacts with the learning rate throughout training. Despite its significance in analyzing training dynamics, direct measurement of Hessian sharpness remains prohibitive for Large Language Models (LLMs) due to high computational cost. We analyze $\textit{critical sharpness}$ ($λ_c$), a computationally efficient measure requiring fewer than $10$ forward passes given the update direction $Δ\mathbfθ$. Critically, this measure captures well-documented Hessian sharpness phenomena, including progressive sharpening and Edge of Stability. Using this measure, we provide the first demonstration of these sharpness phenomena at scale, up to $7$B parameters, spanning both pre-training and mid-training of OLMo-2 models. We further introduce $\textit{relative critical sharpness}$ ($λ_c^{1\to 2}$), which quantifies the curvature of one loss landscape while optimizing another, to analyze the transition from pre-training to fine-tuning and guide data mixing strategies. Critical sharpness provides practitioners with a practical tool for diagnosing curvature dynamics and informing data composition choices at scale. More broadly, our work shows that scalable curvature measures can provide actionable insights for large-scale training.