Wolfgang Stammer

Nina Żukowska, Wolfgang Stammer, Bernt Schiele et al.

Transparency of neural networks' internal reasoning is at the heart of interpretability research, adding to trust, safety, and understanding of these models. The field of mechanistic interpretability has recently focused on studying task-specific computational graphs, defined by connections (edges) between model components. Such edge-based circuits have been defined in the context of large language models, yet vision-based approaches so far only consider neuron-based circuits. These tell which information is encoded, but not how it is routed through the complex wiring of a neural network. In this work, we investigate whether useful mechanistic circuits can be identified through computational graphs in vision transformers. We propose an effective method for Automatic Visual Circuit Discovery (Vi-CD) that recovers class-specific circuits for classification, identifies circuits underlying typographic attacks in CLIP, and discovers circuits that lend themselves for steering to correct harmful model behavior. Overall, we find that insightful and actionable edge-based circuits can be recovered from vision transformers, adding transparency to the internal computations of these models.

David Steinmann, Wolfgang Stammer, Felix Friedrich et al.

While deep learning models often lack interpretability, concept bottleneck models (CBMs) provide inherent explanations via their concept representations. Moreover, they allow users to perform interventional interactions on these concepts by updating the concept values and thus correcting the predictive output of the model. Up to this point, these interventions were typically applied to the model just once and then discarded. To rectify this, we present concept bottleneck memory models (CB2Ms), which keep a memory of past interventions. Specifically, CB2Ms leverage a two-fold memory to generalize interventions to appropriate novel situations, enabling the model to identify errors and reapply previous interventions. This way, a CB2M learns to automatically improve model performance from a few initially obtained interventions. If no prior human interventions are available, a CB2M can detect potential mistakes of the CBM bottleneck and request targeted interventions. Our experimental evaluations on challenging scenarios like handling distribution shifts and confounded data demonstrate that CB2Ms are able to successfully generalize interventions to unseen data and can indeed identify wrongly inferred concepts. Hence, CB2Ms are a valuable tool for users to provide interactive feedback on CBMs, by guiding a user's interaction and requiring fewer interventions.

Lukas Helff, Quentin Delfosse, David Steinmann et al.

As reinforcement Learning with Verifiable Rewards (RLVR) has become the dominant paradigm for scaling reasoning capabilities in LLMs, a new failure mode emerges: LLMs gaming verifiers. We study this phenomenon on inductive reasoning tasks, where models must induce and output logical rules. We find that RLVR-trained models systematically abandon rule induction. Instead of learning generalizable patterns (e.g., ``trains carrying red cars go east''), they enumerate instance-level labels, producing outputs that pass verifiers without capturing the relational patterns required by the task. We show that this behavior is not a failure of understanding but a form of reward hacking: imperfect verifiers that check only extensional correctness admit false positives. To detect such shortcuts, we introduce Isomorphic Perturbation Testing (IPT), which evaluates a single model output under both extensional and isomorphic verification, where the latter enforces invariance under logically isomorphic tasks. While genuine rule induction remains invariant, shortcut strategies fail. We find that shortcut behavior is specific to RLVR-trained reasoning models (e.g., GPT-5, Olmo3) and absent in non-RLVR models (e.g., GPT-4o, GPT-4.5, Ministral). Moreover, shortcut prevalence increases with task complexity and inference-time compute. In controlled training experiments, extensional verification directly induces shortcut strategies, while isomorphic verification eliminates them. These results show that RLVR can incentivize reward hacking not only through overt manipulation but also by exploiting what the verifier fails to enforce.

Quentin Delfosse, Wolfgang Stammer, Thomas Rothenbacher et al.

Recent unsupervised multi-object detection models have shown impressive performance improvements, largely attributed to novel architectural inductive biases. Unfortunately, they may produce suboptimal object encodings for downstream tasks. To overcome this, we propose to exploit object motion and continuity, i.e., objects do not pop in and out of existence. This is accomplished through two mechanisms: (i) providing priors on the location of objects through integration of optical flow, and (ii) a contrastive object continuity loss across consecutive image frames. Rather than developing an explicit deep architecture, the resulting Motion and Object Continuity (MOC) scheme can be instantiated using any baseline object detection model. Our results show large improvements in the performances of a SOTA model in terms of object discovery, convergence speed and overall latent object representations, particularly for playing Atari games. Overall, we show clear benefits of integrating motion and object continuity for downstream tasks, moving beyond object representation learning based only on reconstruction.

Wolfgang Stammer, Felix Friedrich, David Steinmann et al.

Much of explainable AI research treats explanations as a means for model inspection. Yet, this neglects findings from human psychology that describe the benefit of self-explanations in an agent's learning process. Motivated by this, we introduce a novel workflow in the context of image classification, termed Learning by Self-Explaining (LSX). LSX utilizes aspects of self-refining AI and human-guided explanatory machine learning. The underlying idea is that a learner model, in addition to optimizing for the original predictive task, is further optimized based on explanatory feedback from an internal critic model. Intuitively, a learner's explanations are considered "useful" if the internal critic can perform the same task given these explanations. We provide an overview of important components of LSX and, based on this, perform extensive experimental evaluations via three different example instantiations. Our results indicate improvements via Learning by Self-Explaining on several levels: in terms of model generalization, reducing the influence of confounding factors, and providing more task-relevant and faithful model explanations. Overall, our work provides evidence for the potential of self-explaining within the learning phase of an AI model.

Felix Friedrich, Wolfgang Stammer, Patrick Schramowski et al.

Current transformer language models (LM) are large-scale models with billions of parameters. They have been shown to provide high performances on a variety of tasks but are also prone to shortcut learning and bias. Addressing such incorrect model behavior via parameter adjustments is very costly. This is particularly problematic for updating dynamic concepts, such as moral values, which vary culturally or interpersonally. In this work, we question the current common practice of storing all information in the model parameters and propose the Revision Transformer (RiT) to facilitate easy model updating. The specific combination of a large-scale pre-trained LM that inherently but also diffusely encodes world knowledge with a clear-structured revision engine makes it possible to update the model's knowledge with little effort and the help of user interaction. We exemplify RiT on a moral dataset and simulate user feedback demonstrating strong performance in model revision even with small data. This way, users can easily design a model regarding their preferences, paving the way for more transparent AI models.

Felix Friedrich, Wolfgang Stammer, Patrick Schramowski et al.

As machine learning models become increasingly larger, trained weakly supervised on large, possibly uncurated data sets, it becomes increasingly important to establish mechanisms for inspecting, interacting, and revising models to mitigate learning shortcuts and guarantee their learned knowledge is aligned with human knowledge. The recently proposed XIL framework was developed for this purpose, and several such methods have been introduced, each with individual motivations and methodological details. In this work, we provide a unification of various XIL methods into a single typology by establishing a common set of basic modules. In doing so, we pave the way for a principled comparison of existing, but, importantly, also future XIL approaches. In addition, we discuss existing and introduce novel measures and benchmarks for evaluating the overall abilities of a XIL method. Given this extensive toolbox, including our typology, measures, and benchmarks, we finally compare several recent XIL methods methodologically and quantitatively. In our evaluations, all methods prove to revise a model successfully. However, we found remarkable differences in individual benchmark tasks, revealing valuable application-relevant aspects for integrating these benchmarks in developing future methods.

Lukas Helff, Wolfgang Stammer, Hikaru Shindo et al.

Despite the successes of recent developments in visual AI, different shortcomings still exist; from missing exact logical reasoning, to abstract generalization abilities, to understanding complex and noisy scenes. Unfortunately, existing benchmarks, were not designed to capture more than a few of these aspects. Whereas deep learning datasets focus on visually complex data but simple visual reasoning tasks, inductive logic datasets involve complex logical learning tasks, however, lack the visual component. To address this, we propose the diagnostic visual logical learning dataset, V-LoL, that seamlessly combines visual and logical challenges. Notably, we introduce the first instantiation of V-LoL, V-LoL-Train, - a visual rendition of a classic benchmark in symbolic AI, the Michalski train problem. By incorporating intricate visual scenes and flexible logical reasoning tasks within a versatile framework, V-LoL-Train provides a platform for investigating a wide range of visual logical learning challenges. We evaluate a variety of AI systems including traditional symbolic AI, neural AI, as well as neuro-symbolic AI. Our evaluations demonstrate that even SOTA AI faces difficulties in dealing with visual logical learning challenges, highlighting unique advantages and limitations of each methodology. Overall, V-LoL opens up new avenues for understanding and enhancing current abilities in visual logical learning for AI systems.

Quentin Delfosse, Sebastian Sztwiertnia, Mark Rothermel et al.

Goal misalignment, reward sparsity and difficult credit assignment are only a few of the many issues that make it difficult for deep reinforcement learning (RL) agents to learn optimal policies. Unfortunately, the black-box nature of deep neural networks impedes the inclusion of domain experts for inspecting the model and revising suboptimal policies. To this end, we introduce *Successive Concept Bottleneck Agents* (SCoBots), that integrate consecutive concept bottleneck (CB) layers. In contrast to current CB models, SCoBots do not just represent concepts as properties of individual objects, but also as relations between objects which is crucial for many RL tasks. Our experimental results provide evidence of SCoBots' competitive performances, but also of their potential for domain experts to understand and regularize their behavior. Among other things, SCoBots enabled us to identify a previously unknown misalignment problem in the iconic video game, Pong, and resolve it. Overall, SCoBots thus result in more human-aligned RL agents. Our code is available at https://github.com/k4ntz/SCoBots .

Antonia Wüst, Wolfgang Stammer, Quentin Delfosse et al.

The challenge in learning abstract concepts from images in an unsupervised fashion lies in the required integration of visual perception and generalizable relational reasoning. Moreover, the unsupervised nature of this task makes it necessary for human users to be able to understand a model's learnt concepts and potentially revise false behaviours. To tackle both the generalizability and interpretability constraints of visual concept learning, we propose Pix2Code, a framework that extends program synthesis to visual relational reasoning by utilizing the abilities of both explicit, compositional symbolic and implicit neural representations. This is achieved by retrieving object representations from images and synthesizing relational concepts as lambda-calculus programs. We evaluate the diverse properties of Pix2Code on the challenging reasoning domains, Kandinsky Patterns and CURI, thereby testing its ability to identify compositional visual concepts that generalize to novel data and concept configurations. Particularly, in stark contrast to neural approaches, we show that Pix2Code's representations remain human interpretable and can be easily revised for improved performance.

Antonia Wüst, Tim Woydt, Lukas Helff et al.

Recently, newly developed Vision-Language Models (VLMs), such as OpenAI's o1, have emerged, seemingly demonstrating advanced reasoning capabilities across text and image modalities. However, the depth of these advances in language-guided perception and abstract reasoning remains underexplored, and it is unclear whether these models can truly live up to their ambitious promises. To assess the progress and identify shortcomings, we enter the wonderland of Bongard problems, a set of classic visual reasoning puzzles that require human-like abilities of pattern recognition and abstract reasoning. With our extensive evaluation setup, we show that while VLMs occasionally succeed in identifying discriminative concepts and solving some of the problems, they frequently falter. Surprisingly, even elementary concepts that may seem trivial to humans, such as simple spirals, pose significant challenges. Moreover, when explicitly asked to recognize ground truth concepts, they continue to falter, suggesting not only a lack of understanding of these elementary visual concepts but also an inability to generalize to unseen concepts. We compare the results of VLMs to human performance and observe that a significant gap remains between human visual reasoning capabilities and machine cognition.

Florian Peter Busch, Roshni Kamath, Rupert Mitchell et al.

A dataset is confounded if it is most easily solved via a spurious correlation, which fails to generalize to new data. In this work, we show that, in a continual learning setting where confounders may vary in time across tasks, the challenge of mitigating the effect of confounders far exceeds the standard forgetting problem normally considered. In particular, we provide a formal description of such continual confounders and identify that, in general, spurious correlations are easily ignored when training for all tasks jointly, but it is harder to avoid confounding when they are considered sequentially. These descriptions serve as a basis for constructing a novel CLEVR-based continually confounded dataset, which we term the ConCon dataset. Our evaluations demonstrate that standard continual learning methods fail to ignore the dataset's confounders. Overall, our work highlights the challenges of confounding factors, particularly in continual learning settings, and demonstrates the need for developing continual learning methods to robustly tackle these.

Tim Woydt, Moritz Willig, Antonia Wüst et al.

Strong meta-learning capabilities for systematic compositionality are emerging as an important skill for navigating the complex and changing tasks of today's world. However, in presenting models for robust adaptation to novel environments, it is important to refrain from making unsupported claims about the performance of meta-learning systems that ultimately do not stand up to scrutiny. While Fodor and Pylyshyn famously posited that neural networks inherently lack this capacity as they are unable to model compositional representations or structure-sensitive operations, and thus are not a viable model of the human mind, Lake and Baroni recently presented meta-learning as a pathway to compositionality. In this position paper, we critically revisit this claim and highlight limitations in the proposed meta-learning framework for compositionality. Our analysis shows that modern neural meta-learning systems can only perform such tasks, if at all, under a very narrow and restricted definition of a meta-learning setup. We therefore claim that `Fodor and Pylyshyn's legacy' persists, and to date, there is no human-like systematic compositionality learned in neural networks.

Lukas Helff, Ahmad Omar, Felix Friedrich et al.

We introduce SLR, an end-to-end framework for systematic evaluation and training of Large Language Models (LLMs) via Scalable Logical Reasoning. Given a user's task specification, SLR automatically synthesizes (i) an instruction prompt for an inductive reasoning task, (ii) a validation program, executable on model outputs to provide verifiable rewards, and (iii) the latent ground-truth rule. This process is fully automated, scalable, requires no human annotations, and offers precise control over task difficulty. Using SLR, we create SLR-Bench, a benchmark comprising 19k prompts organized into 20 curriculum levels that progressively increase in relational, arithmetic, and recursive complexity. Large-scale evaluation reveals that contemporary LLMs readily produce syntactically valid rules, yet often fail at correct logical inference. Recent reasoning LLMs demonstrate improved performance but incur very high test-time computation, with costs exceeding $300 for just 1,000 prompts. Finally, curriculum learning via SLR doubles Llama-3-8B accuracy on SLR-Bench, achieving parity with Gemini-Flash-Thinking at a fraction of computational cost. Moreover, these reasoning capabilities generalize to a wide range of established benchmarks, underscoring the effectiveness of SLR for downstream reasoning.

Antonia Wüst, Wolfgang Stammer, Hikaru Shindo et al.

Vision-Language models (VLMs) achieve strong performance on multimodal tasks but often fail at systematic visual reasoning tasks, leading to inconsistent or illogical outputs. Neuro-symbolic methods promise to address this by inducing interpretable logical rules, though they exploit rigid, domain-specific perception modules. We propose Vision-Language Programs (VLP), which combine the perceptual flexibility of VLMs with systematic reasoning of program synthesis. Rather than embedding reasoning inside the VLM, VLP leverages the model to produce structured visual descriptions that are compiled into neuro-symbolic programs. The resulting programs execute directly on images, remain consistent with task constraints, and provide human-interpretable explanations that enable easy shortcut mitigation. Experiments on synthetic and real-world datasets demonstrate that VLPs outperform direct and structured prompting, particularly on tasks requiring complex logical reasoning.

Lukas Helff, Ruben Härle, Wolfgang Stammer et al.

Large language models (LLMs) excel at generating fluent text, but their internal reasoning remains opaque and difficult to control. Sparse autoencoders (SAEs) make hidden activations more interpretable by exposing latent features that often align with human concepts. Yet, these features are fragile and passive, offering no mechanism for systematic reasoning or model control. To address this, we introduce ActivationReasoning (AR), a framework that embeds explicit logical reasoning into the latent space of LLMs. It proceeds in three stages: (1) Finding latent representations, first latent concept representations are identified (e.g., via SAEs) and organized into a dictionary; (2) Activating propositions, at inference time AR detects activating concepts and maps them to logical propositions; and (3)Logical reasoning, applying logical rules over these propositions to infer higher-order structures, compose new concepts, and steer model behavior. We evaluate AR on multi-hop reasoning (PrOntoQA), abstraction and robustness to indirect concept cues (Rail2Country), reasoning over natural and diverse language (ProverQA), and context-sensitive safety (BeaverTails). Across all tasks, AR scales robustly with reasoning complexity, generalizes to abstract and context-sensitive tasks, and transfers across model backbones. These results demonstrate that grounding logical structure in latent activations not only improves transparency but also enables structured reasoning, reliable control, and alignment with desired behaviors, providing a path toward more reliable and auditable AI.

Berkant Turan, Suhrab Asadulla, David Steinmann et al.

While Prover-Verifier Games (PVGs) offer a promising path toward verifiability in nonlinear classification models, they have not yet been applied to complex inputs such as high-dimensional images. Conversely, Concept Bottleneck Models (CBMs) effectively translate such data into interpretable concepts but are limited by their reliance on low-capacity linear predictors. In this work, we introduce the Neural Concept Verifier (NCV), a unified framework combining PVGs with concept encodings for interpretable, nonlinear classification in high-dimensional settings. NCV achieves this by utilizing recent minimally supervised concept discovery models to extract structured concept encodings from raw inputs. A prover then selects a subset of these encodings, which a verifier -- implemented as a nonlinear predictor -- uses exclusively for decision-making. Our evaluations show that NCV outperforms CBM and pixel-based PVG classifier baselines on high-dimensional, logically complex datasets and also helps mitigate shortcut behavior. Overall, we demonstrate NCV as a promising step toward performative, verifiable AI.

David Steinmann, Wolfgang Stammer, Antonia Wüst et al.

Developing high-performing, yet interpretable models remains a critical challenge in modern AI. Concept-based models (CBMs) attempt to address this by extracting human-understandable concepts from a global encoding (e.g., image encoding) and then applying a linear classifier on the resulting concept activations, enabling transparent decision-making. However, their reliance on holistic image encodings limits their expressiveness in object-centric real-world settings and thus hinders their ability to solve complex vision tasks beyond single-label classification. To tackle these challenges, we introduce Object-Centric Concept Bottlenecks (OCB), a framework that combines the strengths of CBMs and pre-trained object-centric foundation models, boosting performance and interpretability. We evaluate OCB on complex image datasets and conduct a comprehensive ablation study to analyze key components of the framework, such as strategies for aggregating object-concept encodings. The results show that OCB outperforms traditional CBMs and allows one to make interpretable decisions for complex visual tasks.

Wolfgang Stammer, Antonia Wüst, David Steinmann et al.

The challenge in object-based visual reasoning lies in generating concept representations that are both descriptive and distinct. Achieving this in an unsupervised manner requires human users to understand the model's learned concepts and, if necessary, revise incorrect ones. To address this challenge, we introduce the Neural Concept Binder (NCB), a novel framework for deriving both discrete and continuous concept representations, which we refer to as "concept-slot encodings". NCB employs two types of binding: "soft binding", which leverages the recent SysBinder mechanism to obtain object-factor encodings, and subsequent "hard binding", achieved through hierarchical clustering and retrieval-based inference. This enables obtaining expressive, discrete representations from unlabeled images. Moreover, the structured nature of NCB's concept representations allows for intuitive inspection and the straightforward integration of external knowledge, such as human input or insights from other AI models like GPT-4. Additionally, we demonstrate that incorporating the hard binding mechanism preserves model performance while enabling seamless integration into both neural and symbolic modules for complex reasoning tasks. We validate the effectiveness of NCB through evaluations on our newly introduced CLEVR-Sudoku dataset.

Wolfgang Stammer, Marius Memmel, Patrick Schramowski et al.

Learning visual concepts from raw images without strong supervision is a challenging task. In this work, we show the advantages of prototype representations for understanding and revising the latent space of neural concept learners. For this purpose, we introduce interactive Concept Swapping Networks (iCSNs), a novel framework for learning concept-grounded representations via weak supervision and implicit prototype representations. iCSNs learn to bind conceptual information to specific prototype slots by swapping the latent representations of paired images. This semantically grounded and discrete latent space facilitates human understanding and human-machine interaction. We support this claim by conducting experiments on our novel data set "Elementary Concept Reasoning" (ECR), focusing on visual concepts shared by geometric objects.

Arseny Skryagin, Wolfgang Stammer, Daniel Ochs et al.

The goal of combining the robustness of neural networks and the expressivity of symbolic methods has rekindled the interest in neuro-symbolic AI. Recent advancements in neuro-symbolic AI often consider specifically-tailored architectures consisting of disjoint neural and symbolic components, and thus do not exhibit desired gains that can be achieved by integrating them into a unifying framework. We introduce SLASH -- a novel deep probabilistic programming language (DPPL). At its core, SLASH consists of Neural-Probabilistic Predicates (NPPs) and logical programs which are united via answer set programming. The probability estimates resulting from NPPs act as the binding element between the logical program and raw input data, thereby allowing SLASH to answer task-dependent logical queries. This allows SLASH to elegantly integrate the symbolic and neural components in a unified framework. We evaluate SLASH on the benchmark data of MNIST addition as well as novel tasks for DPPLs such as missing data prediction and set prediction with state-of-the-art performance, thereby showing the effectiveness and generality of our method.

Wolfgang Stammer, Patrick Schramowski, Kristian Kersting

Most explanation methods in deep learning map importance estimates for a model's prediction back to the original input space. These "visual" explanations are often insufficient, as the model's actual concept remains elusive. Moreover, without insights into the model's semantic concept, it is difficult -- if not impossible -- to intervene on the model's behavior via its explanations, called Explanatory Interactive Learning. Consequently, we propose to intervene on a Neuro-Symbolic scene representation, which allows one to revise the model on the semantic level, e.g. "never focus on the color to make your decision". We compiled a novel confounded visual scene data set, the CLEVR-Hans data set, capturing complex compositions of different objects. The results of our experiments on CLEVR-Hans demonstrate that our semantic explanations, i.e. compositional explanations at a per-object level, can identify confounders that are not identifiable using "visual" explanations only. More importantly, feedback on this semantic level makes it possible to revise the model from focusing on these factors.

Patrick Schramowski, Wolfgang Stammer, Stefano Teso et al.

Deep neural networks have shown excellent performances in many real-world applications. Unfortunately, they may show "Clever Hans"-like behavior -- making use of confounding factors within datasets -- to achieve high performance. In this work, we introduce the novel learning setting of "explanatory interactive learning" (XIL) and illustrate its benefits on a plant phenotyping research task. XIL adds the scientist into the training loop such that she interactively revises the original model via providing feedback on its explanations. Our experimental results demonstrate that XIL can help avoiding Clever Hans moments in machine learning and encourages (or discourages, if appropriate) trust into the underlying model.