Jakob Paul Zimmermann

Research

Goals

I want to understand neural networks at the level where their computations become mathematically inspectable: as piecewise-linear and geometric objects. My goal is to turn this structure into methods that make modern models more transparent, more monitorable, and more reliable in deployment.

Concretely, I work on three connected questions:

• What structure is hidden inside a trained network? I study decompositions of networks into monotone and convex parts, and reformulations of the backward pass as two-player games on an extended network graph — both expose how positive and negative evidence propagate through a model.
• When can explanations be trusted? I develop attribution methods whose behaviour is tied to the network’s actual computation rather than only to visual plausibility.
• How can models recognise their own failures? I investigate monitoring methods that detect safety-critical perception failures by comparing internal model representations with foundation-model embeddings.

This puts my work at the interface of discrete geometry, explainable AI, and safety: I use Newton polytopes, difference-of-convex decompositions, and two-player games on computational graphs to derive explanations, certificates, and failure signals from the mathematical structure neural networks already have.

Publications

Hidden Monotonicity: Explaining Deep Neural Networks via their DC Decomposition

Jakob Paul Zimmermann and Georg Loho

CVPR 2026 Highlight Award Candidate

Paper Poster Video arXiv

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.

Knowledge-Guided Failure Prediction: Detecting When Object Detectors Miss Safety-Critical Objects

Jakob Paul Zimmermann, Gerrit Holzbach, and David Lerch

SAIAD Workshop at CVPR 2026

arXiv

We introduce KGFP, a representation-based monitoring framework for detecting when an object detector is likely to miss safety-critical objects. KGFP measures semantic misalignment between YOLOv8 internal features and DINO foundation-model embeddings using a dual-encoder architecture with an angular distance metric. On COCO person detection, KGFP improves person recall from 64.3% to 84.5% at 5% False Positive Rate.

Preprints

Playing the Network Backward: A Game Theoretic Attribution Framework

Jakob Paul Zimmermann, Jim Berend, Georg Loho, Sebastian Lapuschkin, and Wojciech Samek

arXiv:2605.06212, May 2026

Preprint

Backward attribution methods — gradients, LRP, and transformer-specific rules — are usually presented as a zoo of recipes with method-specific stabilisers and no common comparison framework. Building on the ReLU Net Game of Gaubert and Vlassopoulos, we lift the backward pass through a network into a two-player game on an extended computational graph. The game relates to a novel Stopping Decomposition that splits weights by sign into W = W⁺ − W⁻ — a sign-based weight decomposition related to the DC decomposition used directly for attribution in our Hidden Monotonicity work — and unravels excitatory and inhibitory contributions throughout the network. At each state the two players answer (1) stop or go? and (2) where to route?; their optimal policies induce a trajectory distribution, and a weighted trajectory integral recovers the attribution. Game-theoretic ideas — risk aversion, action-space augmentation, policy regularisation — map back to principled adaptations of classical backpropagation rules and boost their performance: one such adaptation outperforms all prior transformer-specific backward methods on ViT-B/16 across localisation metrics.

Talks & Conferences

Mathematical Interests

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.