12 papers
Towards Digital Halftoning on Closed Manifolds--An Error Diffusion Scheme for the Torus based on Sigma-Delta Quantization along the Rank-one Lattice
Felix Krahmer, Alessandro Lupoli
Digital halftoning aims to represent continuous-tone images by binary patterns while preserving their visually relevant low-frequency content. Among the many available approaches,…
KV Cache Compression Through the Lens of Transform Coding
Hannah Laus, Claudio Mayrink Verdun, Hao Wang +2
The key-value (KV) cache stores information from past tokens and is a major memory bottleneck in long-context inference. Existing quantization methods address this bottleneck by re…
Plug-in Losses for Evidential Deep Learning: A Simplified Framework for Uncertainty Estimation that Includes the Softmax Classifier
Berk Hayta, Hannah Laus, Simon Mittermaier +1
Real-world sensor-based learning systems require uncertainty estimation that is both reliable and computationally efficient. Evidential Deep Learning (EDL) provides single-pass unc…
On Trajectory-Based Stability Analysis for -bit Sigma-Delta Quantization and its Application to the Second-Order Case
Rohan Joy, Felix Krahmer, Alessandro Lupoli
A state-of-the-art strategy for digitally representing a bandlimited signal is quantization. quantization schemes choose a bit sequence representing the sampl…
Low-Bit Quantization of Bandlimited Graph Signals via Iterative Methods
Felix Krahmer, He Lyu, Rayan Saab +3
We study the quantization of real-valued bandlimited signals on graphs, focusing on low-bit representations. We propose iterative noise-shaping algorithms for quantization, includi…
Phasebook: A Survey of Selected Open Problems in Phase Retrieval
Marc Allain, Selin Aslan, Wim Coene +13
Phase retrieval is an inverse problem that, on one hand, is crucial in many applications across imaging and physics, and, on the other hand, leads to deep research questions in the…
Spectral method for low-dose Poisson and Bernoulli phase retrieval
Sjoerd Dirksen, Felix Krahmer, Patricia Römer +1
We consider the problem of phaseless reconstruction from measurements with Poisson or Bernoulli distributed noise. This is of particular interest in biological imaging experiments…
Solving Inverse Problems with Deep Linear Neural Networks: Global Convergence Guarantees for Gradient Descent with Weight Decay
Hannah Laus, Suzanna Parkinson, Vasileios Charisopoulos +2
Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition p…
Implicit Regularization for Tubal Tensor Factorizations via Gradient Descent
Santhosh Karnik, Anna Veselovska, Mark Iwen +1
We provide a rigorous analysis of implicit regularization in an overparametrized tensor factorization problem beyond the lazy training regime. For matrix factorization problems, th…
Non-Asymptotic Uncertainty Quantification in High-Dimensional Learning
Frederik Hoppe, Claudio Mayrink Verdun, Hannah Laus +2
Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We devel…
With or Without Replacement? Improving Confidence in Fourier Imaging
Frederik Hoppe, Claudio Mayrink Verdun, Felix Krahmer +2
Over the last few years, debiased estimators have been proposed in order to establish rigorous confidence intervals for high-dimensional problems in machine learning and data scien…
The Mathematics of Dots and Pixels: On the Theoretical Foundations of Image Halftoning
Felix Krahmer, Anna Veselovska
The evolution of image halftoning, from its analog roots to contemporary digital methodologies, encapsulates a fascinating journey marked by technological advancements and creative…