arXiv subjects

Jonas von Berg

Publications and source records attributed to Jonas von Berg.

3 recordsLinked to original sources

arXiv2026

Scale Sensitivity in Low-Bit Post-Training Quantization: Curvature of the Quantization Error Landscape

Post-training quantization (PTQ) methods in the GPTQ family minimize a layer-wise reconstruction error on a uniform grid whose scale must be chosen; the common max-based choice degrades sharply at low bit-widths. We study how sensitive this objective is to the scale. For a layer with i.i.d. Gaussian weights and calibration activations of sufficiently large effective rank, we prove that, as the width grows, the normalized round-to-nearest loss converges with high probability, uniformly over all scales, to the mean-squared error of a uniform quantizer applied to a standard Gaussian; we verify the effective-rank condition for wide, randomly initialized MLPs with odd Lipschitz activations and isotropic Gaussian calibration data. The limiting objective has a unique nondegenerate minimizer, whose scale decreases strictly with the number of levels and whose curvature with respect to relative scale errors decays approximately exponentially with the bit-width. GPTQ experiments on five LLMs show the same trend: the scale rule changes perplexity substantially at 2--3 bits and negligibly from 6 bits on, and a local measure of GPTQ scale sensitivity decreases with bit-width in line with the Gaussian curvature. The Gaussian-optimal scale fails on raw weights; after Hadamard incoherence processing it matches the best searched rule at 3 bits and above without any search, but remains clearly worse at 2 bits.

cs.LG↗

arXiv2026

The Price of Robustness: Stable Classifiers Need Overparameterization

The relationship between overparameterization, stability, and generalization remains incompletely understood in the setting of discontinuous classifiers. We address this gap by establishing a generalization bound for finite function classes that improves inversely with class stability, defined as the expected distance to the decision boundary in the input domain (margin). Interpreting class stability as a quantifiable notion of robustness, we derive as a corollary a law of robustness for classification that extends the results of Bubeck and Sellke beyond smoothness assumptions to discontinuous functions. In particular, any interpolating model with $p \approx n$ parameters on $n$ data points must be unstable, implying that substantial overparameterization is necessary to achieve high stability. We obtain analogous results for parameterized infinite function classes by analyzing a stronger robustness measure derived from the margin in the codomain, which we refer to as the normalized co-stability. Experiments support our theory: stability increases with model size and correlates with test performance, while traditional norm-based measures remain largely uninformative.

cs.LG↗

arXiv2025

Graph Neural Networks for Enhancing Ensemble Forecasts of Extreme Rainfall

Climate change is increasing the occurrence of extreme precipitation events, threatening infrastructure, agriculture, and public safety. Ensemble prediction systems provide probabilistic forecasts but exhibit biases and difficulties in capturing extreme weather. While post-processing techniques aim to enhance forecast accuracy, they rarely focus on precipitation, which exhibits complex spatial dependencies and tail behavior. Our novel framework leverages graph neural networks to post-process ensemble forecasts, specifically modeling the extremes of the underlying distribution. This allows to capture spatial dependencies and improves forecast accuracy for extreme events, thus leading to more reliable forecasts and mitigating risks of extreme precipitation and flooding.

cs.LG↗