Alexander Bauer

Alexander Bauer, Shinichi Nakajima, Klaus-Robert Müller

We focus on a specific use case in anomaly detection where the distribution of normal samples is supported by a lower-dimensional manifold. Here, regularized autoencoders provide a popular approach by learning the identity mapping on the set of normal examples, while trying to prevent good reconstruction on points outside of the manifold. Typically, this goal is implemented by controlling the capacity of the model, either directly by reducing the size of the bottleneck layer or implicitly by imposing some sparsity (or contraction) constraints on parts of the corresponding network. However, neither of these techniques does explicitly penalize the reconstruction of anomalous signals often resulting in poor detection. We tackle this problem by adapting a self-supervised learning regime that exploits discriminative information during training but focuses on the submanifold of normal examples. Informally, our training objective regularizes the model to produce locally consistent reconstructions, while replacing irregularities by acting as a filter that removes anomalous patterns. To support this intuition, we perform a rigorous formal analysis of the proposed method and provide a number of interesting insights. In particular, we show that the resulting model resembles a non-linear orthogonal projection of partially corrupted images onto the submanifold of uncorrupted samples. On the other hand, we identify the orthogonal projection as an optimal solution for a number of regularized autoencoders including the contractive and denoising variants. We support our theoretical analysis by empirical evaluation of the resulting detection and localization performance of the proposed method. In particular, we achieve a new state-of-the-art result on the MVTec AD dataset -- a challenging benchmark for visual anomaly detection in the manufacturing domain.

Santiago A. Cadena, Andrea Merlo, Emanuel Laude et al.

Stellarators are magnetic confinement devices under active development to deliver steady-state carbon-free fusion energy. Their design involves a high-dimensional, constrained optimization problem that requires expensive physics simulations and significant domain expertise. Recent advances in plasma physics and open-source tools have made stellarator optimization more accessible. However, broader community progress is currently bottlenecked by the lack of standardized optimization problems with strong baselines and datasets that enable data-driven approaches, particularly for quasi-isodynamic (QI) stellarator configurations, considered as a promising path to commercial fusion due to their inherent resilience to current-driven disruptions. Here, we release an open dataset of diverse QI-like stellarator plasma boundary shapes, paired with their ideal magnetohydrodynamic (MHD) equilibria and performance metrics. We generated this dataset by sampling a variety of QI fields and optimizing corresponding stellarator plasma boundaries. We introduce three optimization benchmarks of increasing complexity: (1) a single-objective geometric optimization problem, (2) a "simple-to-build" QI stellarator, and (3) a multi-objective ideal-MHD stable QI stellarator that investigates trade-offs between compactness and coil simplicity. For every benchmark, we provide reference code, evaluation scripts, and strong baselines based on classical optimization techniques. Finally, we show how learned models trained on our dataset can efficiently generate novel, feasible configurations without querying expensive physics oracles. By openly releasing the dataset along with benchmark problems and baselines, we aim to lower the entry barrier for optimization and machine learning researchers to engage in stellarator design and to accelerate cross-disciplinary progress toward bringing fusion energy to the grid.

Alexander Bauer, Klaus-Robert Müller

Anomaly detection plays a pivotal role in automated industrial inspection, aiming to identify subtle or rare defects in otherwise uniform visual patterns. As collecting representative examples of all possible anomalies is infeasible, we tackle structural anomaly detection using a self-supervised autoencoder that learns to repair corrupted inputs. To this end, we introduce a corruption model that injects artificial disruptions into training images to mimic structural defects. While reminiscent of denoising autoencoders, our approach differs in two key aspects. First, instead of unstructured i.i.d.\ noise, we apply structured, spatially coherent perturbations that make the task a hybrid of segmentation and inpainting. Second, and counterintuitively, we add and preserve Gaussian noise on top of the occlusions, which acts as a Tikhonov regularizer anchoring the Jacobian of the reconstruction function toward identity. This identity-anchored regularization stabilizes reconstruction and further improves both detection and segmentation accuracy. On the MVTec AD benchmark, our method achieves state-of-the-art results (I/P-AUROC: 99.9/99.4), supporting our theoretical framework and demonstrating its practical relevance for automatic inspection.

Alexander Bauer, Shinichi Nakajima

Considering the worst-case scenario, junction tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees. Unfortunately, its main tractability assumption requires the treewidth of a corresponding MRF to be bounded strongly limiting the range of admissible applications. In fact, many practical problems in the area of structured prediction require modelling of global dependencies by either directly introducing global factors or enforcing global constraints on the prediction variables. That, however, always results in a fully-connected graph making exact inference by means of this algorithm intractable. Previous work [1]-[4] focusing on the problem of loss-augmented inference has demonstrated how efficient inference can be performed on models with specific global factors representing non-decomposable loss functions within the training regime of SSVMs. In this paper, we extend the framework for an efficient exact inference proposed in in [3] by allowing much finer interactions between the energy of the core model and the sufficient statistics of the global terms with no additional computation costs. We demonstrate the usefulness of our method in several use cases, including one that cannot be handled by any of the previous approaches. Finally, we propose a new graph transformation technique via node cloning which ensures a polynomial run-time for solving our target problem independently of the form of a corresponding clique tree. This is important for the efficiency of the main algorithm and greatly improves upon the theoretical guarantees of the previous works.

Maximilian Kohlbrenner, Alexander Bauer, Shinichi Nakajima et al.

Within the last decade, neural network based predictors have demonstrated impressive - and at times super-human - capabilities. This performance is often paid for with an intransparent prediction process and thus has sparked numerous contributions in the novel field of explainable artificial intelligence (XAI). In this paper, we focus on a popular and widely used method of XAI, the Layer-wise Relevance Propagation (LRP). Since its initial proposition LRP has evolved as a method, and a best practice for applying the method has tacitly emerged, based however on humanly observed evidence alone. In this paper we investigate - and for the first time quantify - the effect of this current best practice on feedforward neural networks in a visual object detection setting. The results verify that the layer-dependent approach to LRP applied in recent literature better represents the model's reasoning, and at the same time increases the object localization and class discriminativity of LRP.

Alexander Bauer, Shinichi Nakajima, Nico Görnitz et al.

Many statistical learning problems in the area of natural language processing including sequence tagging, sequence segmentation and syntactic parsing has been successfully approached by means of structured prediction methods. An appealing property of the corresponding discriminative learning algorithms is their ability to integrate the loss function of interest directly into the optimization process, which potentially can increase the resulting performance accuracy. Here, we demonstrate on the example of constituency parsing how to optimize for F1-score in the max-margin framework of structural SVM. In particular, the optimization is with respect to the original (not binarized) trees.