Mattia Cerrato

Iman Peljto, Xenia Heilmann, Mattia Cerrato

Algorithm registers are public-facing databases that display basic information about algorithms employed in public administration. While several such registers exist across Europe and globally, their capacity to deliver meaningful transparency remains contested. In Germany, the landscape is notably fragmented: no federal-level register exists, yet at least five state- and federal-level initiatives publish information about AI systems with varying scopes and objectives. A recent conceptual proposal by Alina Lorenz (2025), outlines technical and governance requirements for a national AI transparency register in Germany. We repurpose this proposal as an audit instrument, extracting structured checklists from the transparency goals and subgoals it formulates. The resulting checklists, translated from German into English, is made publicly available to support practitioners auditing existing registers or designing new ones. We apply this framework to conduct an external audit of the two main existing German transparency initiatives, MaKI and Lernende Systeme, evaluating the extent to which they fulfill the proposed goals. Our audit reveals that several adaptations are likely needed for these registers to serve as an useful transparency instrument. We further propose a visualization of register transparency levels and derive concrete action items for improving existing German platforms.

Mattia Cerrato, Marius Köppel, Roberto Esposito et al.

Representation learning algorithms offer the opportunity to learn invariant representations of the input data with regard to nuisance factors. Many authors have leveraged such strategies to learn fair representations, i.e., vectors where information about sensitive attributes is removed. These methods are attractive as they may be interpreted as minimizing the mutual information between a neural layer's activations and a sensitive attribute. However, the theoretical grounding of such methods relies either on the computation of infinitely accurate adversaries or on minimizing a variational upper bound of a mutual information estimate. In this paper, we propose a methodology for direct computation of the mutual information between a neural layer and a sensitive attribute. We employ stochastically-activated binary neural networks, which lets us treat neurons as random variables. We are then able to compute (not bound) the mutual information between a layer and a sensitive attribute and use this information as a regularization factor during gradient descent. We show that this method compares favorably with the state of the art in fair representation learning and that the learned representations display a higher level of invariance compared to full-precision neural networks.

Mattia Cerrato, Marius Köppel, Philipp Wolf et al.

Fair Representation Learning (FRL) is a broad set of techniques, mostly based on neural networks, that seeks to learn new representations of data in which sensitive or undesired information has been removed. Methodologically, FRL was pioneered by Richard Zemel et al. about ten years ago. The basic concepts, objectives and evaluation strategies for FRL methodologies remain unchanged to this day. In this paper, we look back at the first ten years of FRL by i) revisiting its theoretical standing in light of recent work in deep learning theory that shows the hardness of removing information in neural network representations and ii) presenting the results of a massive experimentation (225.000 model fits and 110.000 AutoML fits) we conducted with the objective of improving on the common evaluation scenario for FRL. More specifically, we use automated machine learning (AutoML) to adversarially "mine" sensitive information from supposedly fair representations. Our theoretical and experimental analysis suggests that deterministic, unquantized FRL methodologies have serious issues in removing sensitive information, which is especially troubling as they might seem "fair" at first glance.

Xenia Heilmann, Luca Corbucci, Mattia Cerrato

The Rashomon set captures the collection of models that achieve near-identical empirical performance yet may differ substantially in their decision boundaries. Understanding the differences among these models, i.e., their multiplicity, is recognized as a crucial step toward model transparency, fairness, and robustness, as it reveals decision boundaries instabilities that standard metrics obscure. However, the existing definitions of Rashomon set and multiplicity metrics assume centralized learning and do not extend naturally to decentralized, multi-party settings like Federated Learning (FL). In FL, multiple clients collaboratively train models under a central server's coordination without sharing raw data, which preserves privacy but introduces challenges from heterogeneous client data distribution and communication constraints. In this setting, the choice of a single best model may homogenize predictive behavior across diverse clients, amplify biases, or undermine fairness guarantees. In this work, we provide the first formalization of Rashomon sets in FL.First, we adapt the Rashomon set definition to FL, distinguishing among three perspectives: (I) a global Rashomon set defined over aggregated statistics across all clients, (II) a t-agreement Rashomon set representing the intersection of local Rashomon sets across a fraction t of clients, and (III) individual Rashomon sets specific to each client's local distribution.Second, we show how standard multiplicity metrics can be estimated under FL's privacy constraints. Finally, we introduce a multiplicity-aware FL pipeline and conduct an empirical study on standard FL benchmark datasets. Our results demonstrate that all three proposed federated Rashomon set definitions offer valuable insights, enabling clients to deploy models that better align with their local data, fairness considerations, and practical requirements.

Minh Duc Bui, Xenia Heilmann, Mattia Cerrato et al.

Prior work evaluates code generation bias primarily through simple conditional statements, which represent only a narrow slice of real-world programming and reveal solely overt, explicitly encoded bias. We demonstrate that this approach dramatically underestimates bias in practice by examining a more realistic task: generating machine learning (ML) pipelines. Testing both code-specialized and general-instruction large language models, we find that generated pipelines exhibit significant bias during feature selection. Sensitive attributes appear in 87.7% of cases on average, despite models demonstrably excluding irrelevant features (e.g., including "race" while dropping "favorite color" for credit scoring). This bias is substantially more prevalent than that captured by conditional statements, where sensitive attributes appear in only 59.2% of cases. These findings are robust across prompt mitigation strategies, varying numbers of attributes, and different pipeline difficulty levels. Our results challenge simple conditionals as valid proxies for bias evaluation and suggest current benchmarks underestimate bias risk in practical deployments.

Marius Köppel, Niklas Witzig, Tim Klausmann et al.

The global Biochar Industry has witnessed a surge in biochar production, with a total of 350k mt/year production in 2023. With the pressing climate goals set and the potential of Biochar Carbon Removal (BCR) as a climate-relevant technology, scaling up the number of new plants to over 1000 facilities per year by 2030 becomes imperative. However, such a massive scale-up presents not only technical challenges but also control and regulation issues, ensuring maximal output of plants while conforming to regulatory requirements. In this paper, we present a novel method of optimizing the process of a biochar plant based on machine learning methods. We show how a standard Random Forest Regressor can be used to model the states of the pyrolysis machine, the physics of which remains highly complex. This model then serves as a surrogate of the machine -- reproducing several key outcomes of the machine -- in a numerical optimization. This, in turn, could enable us to reduce NOx emissions -- a key regulatory goal in that industry -- while achieving maximal output still. In a preliminary test our approach shows remarkable results, proves to be applicable on two different machines from different manufacturers, and can be implemented on standard Internet of Things (IoT) devices more generally.

Xenia Heilmann, Ernst Althaus, Mattia Cerrato et al.

A sum-product network (SPN) is a graphical model that allows several types of probabilistic inference to be performed efficiently. In this paper, we propose a privacy-preserving protocol which tackles structure generation and parameter learning of SPNs. Additionally, we provide a protocol for private inference on SPNs, subsequent to training. To preserve the privacy of the participants, we derive our protocol based on secret sharing, which guarantees privacy in the honest-but-curious setting even when at most half of the parties cooperate to disclose the data. The protocol makes use of a forest of randomly generated SPNs, which is trained and weighted privately and can then be used for private inference on data points. Our experiments indicate that preserving the privacy of all participants does not decrease log-likelihood performance on both homogeneously and heterogeneously partitioned data. We furthermore show that our protocol's performance is comparable to current state-of-the-art SPN learners in homogeneously partitioned data settings. In terms of runtime and memory usage, we demonstrate that our implementation scales well when increasing the number of parties, comparing favorably to protocols for neural networks, when they are trained to reproduce the input-output behavior of SPNs.

Kiara Stempel, Mattia Cerrato, Stefan Kramer

Decision trees have been studied extensively in the context of fairness, aiming to maximize prediction performance while ensuring non-discrimination against different groups. Techniques in this space usually focus on imposing constraints at training time, constraining the search space so that solutions which display unacceptable values of relevant metrics are not considered, discarded, or discouraged. If we assume one target variable y and one sensitive attribute s, the design space of tree learning algorithms can be spanned as follows: (i) One can have one tree T that is built using an objective function that is a function of y, s, and T. For instance, one can build a tree based on the weighted information gain regarding y (maximizing) and s (minimizing). (ii) The second option is to have one tree model T that uses an objective function in y and T and a constraint on s and T. Here, s is no longer part of the objective, but part of a constraint. This can be achieved greedily by aborting a further split as soon as the condition that optimizes the objective in y fails to satisfy the constraint on s. A simple way to explore other splits is to backtrack during tree construction once a fairness constraint is violated. (iii) The third option is to have two trees T_y and T_s, one for y and one for s, such that the tree structure for y and s does not have to be shared. In this way, information regarding y and regarding s can be used independently, without having to constrain the choices in tree construction by the mutual information between the two variables. Quite surprisingly, of the three options, only the first one and the greedy variant of the second have been studied in the literature so far. In this paper, we introduce the above two additional options from that design space and characterize them experimentally on multiple datasets.

Xenia Heilmann, Luca Corbucci, Mattia Cerrato et al.

Federated Learning (FL) enables collaborative model training across multiple clients without sharing clients' private data. However, the diverse and often conflicting biases present across clients pose significant challenges to model fairness. Current fairness-enhancing FL solutions often fall short, as they typically mitigate biases for a single, usually binary, sensitive attribute, while ignoring the heterogeneous fairness needs that exist in real-world settings. Moreover, these solutions often evaluate unfairness reduction only on the server side, hiding persistent unfairness at the individual client level. To support more robust and reproducible fairness research in FL, we introduce a comprehensive benchmarking framework for fairness-aware FL at both the global and client levels. Our contributions are three-fold: (1) We introduce \fairdataset, a library to create tabular datasets tailored to evaluating fair FL methods under heterogeneous client bias; (2) we release four bias-heterogeneous datasets and corresponding benchmarks to compare fairness mitigation methods in a controlled environment; (3) we provide ready-to-use functions for evaluating fairness outcomes for these datasets.

Jannis Brugger, Mattia Cerrato, David Richter et al.

Deep learning approaches are becoming increasingly attractive for equation discovery. We show the advantages and disadvantages of using neural-guided equation discovery by giving an overview of recent papers and the results of experiments using our modular equation discovery system MGMT ($\textbf{M}$ulti-Task $\textbf{G}$rammar-Guided $\textbf{M}$onte-Carlo $\textbf{T}$ree Search for Equation Discovery). The system uses neural-guided Monte-Carlo Tree Search (MCTS) and supports both supervised and reinforcement learning, with a search space defined by a context-free grammar. We summarize seven desirable properties of equation discovery systems, emphasizing the importance of embedding tabular data sets for such learning approaches. Using the modular structure of MGMT, we compare seven architectures (among them, RNNs, CNNs, and Transformers) for embedding tabular datasets on the auxiliary task of contrastive learning for tabular data sets on an equation discovery task. For almost all combinations of modules, supervised learning outperforms reinforcement learning. Moreover, our experiments indicate an advantage of using grammar rules as action space instead of tokens. Two adaptations of MCTS -- risk-seeking MCTS and AmEx-MCTS -- can improve equation discovery with that kind of search.

Cedric Derstroff, Mattia Cerrato, Jannis Brugger et al.

Peer learning is a novel high-level reinforcement learning framework for agents learning in groups. While standard reinforcement learning trains an individual agent in trial-and-error fashion, all on its own, peer learning addresses a related setting in which a group of agents, i.e., peers, learns to master a task simultaneously together from scratch. Peers are allowed to communicate only about their own states and actions recommended by others: "What would you do in my situation?". Our motivation is to study the learning behavior of these agents. We formalize the teacher selection process in the action advice setting as a multi-armed bandit problem and therefore highlight the need for exploration. Eventually, we analyze the learning behavior of the peers and observe their ability to rank the agents' performance within the study group and understand which agents give reliable advice. Further, we compare peer learning with single agent learning and a state-of-the-art action advice baseline. We show that peer learning is able to outperform single-agent learning and the baseline in several challenging discrete and continuous OpenAI Gym domains. Doing so, we also show that within such a framework complex policies from action recommendations beyond discrete action spaces can evolve.

Stefan Kramer, Mattia Cerrato, Jannis Brugger et al.

The paper surveys automated scientific discovery, from equation discovery and symbolic regression to autonomous discovery systems and agents. It discusses the individual approaches from a "big picture" perspective and in context, but also discusses open issues and recent topics like the various roles of deep neural networks in this area, aiding in the discovery of human-interpretable knowledge. Further, we will present closed-loop scientific discovery systems, starting with the pioneering work on the Adam system up to current efforts in fields from material science to astronomy. Finally, we will elaborate on autonomy from a machine learning perspective, but also in analogy to the autonomy levels in autonomous driving. The maximal level, level five, is defined to require no human intervention at all in the production of scientific knowledge. Achieving this is one step towards solving the Nobel Turing Grand Challenge to develop AI Scientists: AI systems capable of making Nobel-quality scientific discoveries highly autonomously at a level comparable, and possibly superior, to the best human scientists by 2050.

Mattia Cerrato, Alesia Vallenas Coronel, Marius Köppel et al.

Neural network architectures have been extensively employed in the fair representation learning setting, where the objective is to learn a new representation for a given vector which is independent of sensitive information. Various representation debiasing techniques have been proposed in the literature. However, as neural networks are inherently opaque, these methods are hard to comprehend, which limits their usefulness. We propose a new framework for fair representation learning that is centered around the learning of "correction vectors", which have the same dimensionality as the given data vectors. Correction vectors may be computed either explicitly via architectural constraints or implicitly by training an invertible model based on Normalizing Flows. We show experimentally that several fair representation learning models constrained in such a way do not exhibit losses in ranking or classification performance. Furthermore, we demonstrate that state-of-the-art results can be achieved by the invertible model. Finally, we discuss the law standing of our methodology in light of recent legislation in the European Union.

Mattia Cerrato, Marius Köppel, Alexander Segner et al.

Neural network architectures have been extensively employed in the fair representation learning setting, where the objective is to learn a new representation for a given vector which is independent of sensitive information. Various "representation debiasing" techniques have been proposed in the literature. However, as neural networks are inherently opaque, these methods are hard to comprehend, which limits their usefulness. We propose a new framework for fair representation learning which is centered around the learning of "correction vectors", which have the same dimensionality as the given data vectors. The corrections are then simply summed up to the original features, and can therefore be analyzed as an explicit penalty or bonus to each feature. We show experimentally that a fair representation learning problem constrained in such a way does not impact performance.

Mattia Cerrato, Marius Köppel, Alexander Segner et al.

The issue of fairness in machine learning stems from the fact that historical data often displays biases against specific groups of people which have been underprivileged in the recent past, or still are. In this context, one of the possible approaches is to employ fair representation learning algorithms which are able to remove biases from data, making groups statistically indistinguishable. In this paper, we instead develop a fair representation learning algorithm which is able to map individuals belonging to different groups in a single group. This is made possible by training a pair of Normalizing Flow models and constraining them to not remove information about the ground truth by training a ranking or classification model on top of them. The overall, ``chained'' model is invertible and has a tractable Jacobian, which allows to relate together the probability densities for different groups and ``translate'' individuals from one group to another. We show experimentally that our methodology is competitive with other fair representation learning algorithms. Furthermore, our algorithm achieves stronger invariance w.r.t. the sensitive attribute.

Roberto Esposito, Mattia Cerrato, Marco Locatelli

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows practitioners to assess the importance of each group and of each variable in the group. We formally show that the new formulation is not convex and provide two alternative methods to deal with the problem: one non-exact method based on an alternating least squares approach; and one exact method based on a reformulation of the problem using an exponential number of sub-problems whose minimum is guaranteed to be the optimal solution. We formally show the correctness of the exact method and also compare the two solutions showing that the exact solution provides better results in a fraction of the time required by the alternating least squares solution (assuming that the number of partitions is small). For the sake of completeness, we also provide an alternative branch and bound algorithm that can be used in place of the exact method when the number of partitions is too large, and a proof of NP-completeness of the optimization problem introduced in this paper.