Jakob Paul Zimmermann

I am a master's student in Computer Science at TU Berlin, a researcher in the Discrete Geometry Group at Freie Universität Berlin, and a working student at Fraunhofer HHI in Berlin.

Contact: jakob.paul.zimmermann@campus.tu-berlin.de

Research

Current

FU Berlin – Discrete Geometry Group

With professor Georg Loho, I work on the mathematical foundations of Deep Learning. We investigate the geometry of the Newton Polytopes of Neural Networks and develop new Explainable AI (XAI) methods using the Difference-of-Convex decomposition of Neural Networks.

Current

Fraunhofer HHI – Berlin

With professor Wojciech Samek I am working on new backpropagation based XAI methods for the Transformer Architecture.

Previously

Fraunhofer IOSB – Karlsruhe

I have worked on runtime monitoring of image recognition models and representation learning. I developed a monitoring approach that is knowledge-guided and works on internal representations of image recognition models and embedding models such as DINO.

Goals

I want machine learning models to be:

Safe and Reliable – especially in critical applications and under distribution shifts
Interpretable – transparent decision-making that humans can understand and verify
Aligned – reasoning that mirrors human intuition and values

I investigate how geometric and mathematical structures in Neural Networks can help achieve these properties, and how to explain the decision-making of Neural Networks in a way understandable to humans.

Publications

Induced Turán problem in bipartite graphs

Maria Axenovich and Jakob Zimmermann

Discrete Applied Mathematics, Volume 360, Pages 497–505, January 2025

Preprints

Hidden Monotonicity: Explaining Deep Neural Networks via their DC Decomposition

Jakob Paul Zimmermann and Georg Loho

arXiv:2601.07700, January 2026

To appear in CVPR 2026

DC decomposition of a ReLU network into positive and negative monotone components

We propose an algorithm to decompose any ReLU Neural Network (CNN, MLP, ResNet) into a difference of two monotone and convex Maxout networks and to stabilize the forward and backward pass through this decomposition. This provides a principled approach for Explainable AI, enabling separate analysis of positive and negative contributions to the network output. Our proposed saliency methods – SplitCAM and SplitLRP – improve on SOTA results on both VGG16 and ResNet18 on ImageNet-S across all Quantus saliency metric categories.

Bipartite Turán problem on cographs

Jakob Zimmermann

arXiv:2601.07406, January 2025

Preprint

K_2,3-free extremal cograph on 18 vertices — drag to explore

We investigate the bipartite Turán problem on cographs and fully classify the edge-maximal cographs with respect to not containing certain bicliques. These extremal cographs turn out to be star-shaped, highly symmetrical and beautiful. Explore more extremal cographs →

Mathematical Interests

Stochastics Statistical Learning Discrete Geometry Extremal Combinatorics Turán-type Problems

Education

I completed my bachelor's degrees in Mathematics and Computer Science at KIT (Karlsruhe Institute of Technology) in Karlsruhe.

My bachelor thesis “Induced Turán problems” was supervised by Maria Axenovich and Thorsten Ueckerdt. The thesis studies extremal problems for induced and biinduced subgraphs, connections to Vapnik–Chervonenkis dimension, and includes a simplified proof of the Erdős–Hajnal conjecture for graphs with bounded VC dimension.