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Sebastian Bordt

Publications and source records attributed to Sebastian Bordt.

At least 19 recordsLinked to original sources
arXiv2026

We Need Explanation Cards to Connect Explanation Algorithms to the Real World

Algorithmic explanations are intended to help stakeholders understand opaque algorithmic decisions, but in practice, they often fall short. First, the meaning of algorithmic explanations is often not what one might intuitively expect, so expert knowledge is required to interpret them correctly. Second, recent work has shown that popular explanation algorithms are uninformative about the behavior of complex decision functions. Together, these issues create a gap between what explanations appear to convey and what they actually provide. In this work, we propose Explanation Cards for Explanation Algorithms, which augment standard explanations with complementary information about robustness and validity, as well as clear instructions for interpretation. The complementary information can render otherwise uninformative explanations practically useful, while also helping to detect cases where they are not. Importantly, the interpretation instructions in explanation cards shift responsibility from users to providers: Rather than expecting users to recognize what can and cannot be concluded from an explanation, providers must make this explicit upfront. Using counterfactual explanations and SHAP as examples, we demonstrate how providers can construct explanation cards and that these cards provide users with the guidance needed for sound interpretation. We further argue that explanation cards offer a practical means of operationalising the explainability provisions of the EU AI Act. Overall, explanation cards are a significant step toward making explanation algorithms fit for real-world use cases.

cs.LG↗
arXiv2026

Validity Threats for Foundation Model Research

Controlled experiments are the backbone of machine learning research, but at the scale of modern foundation models, they have become prohibitively expensive. Instead, the community increasingly relies on research strategies that approximate the ideal experiment at a fraction of the cost: proxy experiments and scaling laws, observational studies with publicly available models, and single-run designs that leverage variation within individual training runs. In this work, we argue that there is no free lunch when approximating large-scale experiments on a compute budget. Specifically, savings in compute come at the cost of validity threats -- hidden and sometimes untestable assumptions that, when violated, can invalidate research claims. To help navigate such threats, we propose an evaluation framework that casts foundation model research as a causal inference problem. Within this framework, we evaluate different research strategies through four types of validity adapted from the empirical social sciences -- statistical, internal, external, and construct validity. We find that each strategy comes with a characteristic validity profile: proxy experiments trade external and construct validity for statistical and internal validity; observational studies face confounding and effect heterogeneity; and single-run designs are strained by interference between treated units. This analysis reveals several validity threats that have received insufficient attention in the literature. Overall, our evaluation framework provides researchers with a practical toolkit for scrutinizing validity threats in foundation model research~designs.

cs.LG↗
arXiv2026

How to Scale Mixture-of-Experts: From muP to the Maximally Scale-Stable Parameterization

Recent frontier large language models predominantly rely on Mixture-of-Experts (MoE) architectures. Despite empirical progress, there is still no principled understanding of how hyperparameters should scale with network width $N$, expert width $N_e$, number of experts $M$, sparsity $K$, and depth $L$ to ensure both stability and optimal performance at scale. We take a principled step toward resolving this gap by analyzing three different scaling regimes: (I) co-scaling $N\asymp N_e$, (II) co-scaling $N\asymp M\asymp K$, and (III) full proportional scaling of $N, N_e, M$, and $K$. For each regime, we develop a novel Dynamical Mean Field Theory (DMFT) description of the limiting training dynamics of MoEs that provides a formal foundation for our analysis. Within this framework, we derive the unique parameterization for SGD and Adam satisfying all maximal-update ($\mu$) desiderata. We then show that the resulting $\mu$P prescription does not reliably induce monotonic improvement with scale or robust learning-rate transfer. We trace these pathologies to scale-dependent observables in the aggregation dynamics, which motivates a refined set of desiderata that we term maximal scale stability. Guided by this principle, we derive a Maximally Scale-Stable Parameterization (MSSP) for both SGD and Adam in all three scaling regimes, and characterize the corresponding limiting dynamics - qualitatively distinct from the $\mu$P limit - through a separate DMFT analysis. Experiments verify that MSSP robustly recovers learning rate transfer and monotonic improvement with scale across regimes. Combined with existing depth-scaling theory, these results provide a complete scaling prescription for MoE architectures as a function of width, depth, expert width, and number of experts.

cs.LG↗
arXiv2026

Using predictive multiplicity to measure individual performance within the AI Act

When building AI systems for decision support, one often encounters the phenomenon of predictive multiplicity: a single best model does not exist; instead, one can construct many models with similar overall accuracy that differ in their predictions for individual cases. Especially when decisions have a direct impact on humans, this can be highly unsatisfactory. For a person subject to high disagreement between models, one could as well have chosen a different model of similar overall accuracy that would have decided the person's case differently. We argue that this arbitrariness conflicts with the EU AI Act, which requires providers of high-risk AI systems to report performance not only at the dataset level but also for specific persons. The goal of this paper is to put predictive multiplicity in context with the EU AI Act's provisions on accuracy and to subsequently derive concrete suggestions on how to evaluate and report predictive multiplicity in practice. Specifically: (1) We introduce the AI Act's accuracy provisions and argue that incorporating information about predictive multiplicity could serve compliance with specific provisions for providers. (2) Based on this legally rigorous analysis, we suggest individual conflict ratios and $\delta$-ambiguity as tools to quantify the disagreement between models on individual cases and to help detect individuals subject to conflicting predictions. (3) Based on computational insights, we derive easy-to-implement rules on how model providers could evaluate predictive multiplicity in practice. (4) Ultimately, we suggest that information about predictive multiplicity should be made available to deployers under the AI Act, enabling them to judge whether system outputs for specific individuals are reliable enough for their use case.

cs.LG↗
arXiv2026

Weight Decay Improves Language Model Plasticity

Large language models are typically trained in two broad phases: pretraining to produce a base model, followed by further training to improve downstream performance. However, hyperparameter optimization and scaling laws are studied primarily from the perspective of the base model's validation loss, overlooking a crucial model property: downstream adaptability. In this work, we study pretraining from the perspective of model plasticity, that is, the ability of the base model to successfully adapt to downstream tasks upon additional training. We focus on the role of weight decay, a key regularization parameter during pretraining, and show through systematic experiments that larger weight decay increases the plasticity of the pretrained model, resulting in greater performance gains downstream after fine-tuning. This effect can lead to counterintuitive trade-offs where base models that perform worse after pretraining can perform better after further training. Further investigation of weight decay's mechanistic effects on model behavior reveals that it encourages linearly separable representations, regularizes attention matrices, and reduces overfitting on the training data. Together, these findings highlight the importance of pretrained model plasticity, the limits of using cross-entropy loss as the sole metric for hyperparameter optimization, and the multifaceted role that a single optimization hyperparameter plays in shaping model behavior.

cs.LG↗
arXiv2025

Train Once, Answer All: Many Pretraining Experiments for the Cost of One

Recent work has demonstrated that controlled pretraining experiments are a powerful tool for studying the relationship between training data and large language model (LLM) behavior. However, the computational cost of pretraining presents a significant constraint. To overcome this constraint, we propose a new approach where multiple experiments are conducted simultaneously during a single training run. We validate our approach by performing ten experiments while training on 210B tokens, with models of up to 2.7B parameters. Although models are trained only once, we can replicate the results of multiple previous works on data contamination, poisoning, and memorization. We also conduct novel investigations into knowledge acquisition, mathematical reasoning, and watermarking. For example, we dynamically update the training data until a model acquires a particular piece of knowledge. Remarkably, the influence of the experiments on the model's training dynamics and overall performance is minimal. However, interactions between experiments may act as a confounder in our approach. We propose continual pretraining dependence testing (CPDT), a novel technique to test for interactions with continual pretraining experiments, finding them to be negligible in our setup. Overall, our results suggest that performing multiple pretraining experiments within a single training run can enable rigorous scientific experimentation with large models on a compute budget.

cs.CL↗
arXiv2025

Informative Post-Hoc Explanations Only Exist for Simple Functions

Many researchers have suggested that local post-hoc explanation algorithms can be used to gain insights into the behavior of complex machine learning models. However, theoretical guarantees about such algorithms only exist for simple decision functions, and it is unclear whether and under which assumptions similar results might exist for complex models. In this paper, we introduce a general, learning-theory-based framework for what it means for an explanation to provide information about a decision function. We call an explanation informative if it serves to reduce the complexity of the space of plausible decision functions. With this approach, we show that many popular explanation algorithms are not informative when applied to complex decision functions, providing a rigorous mathematical rejection of the idea that it should be possible to explain any model. We then derive conditions under which different explanation algorithms become informative. These are often stronger than what one might expect. For example, gradient explanations and counterfactual explanations are non-informative with respect to the space of differentiable functions, and SHAP and anchor explanations are not informative with respect to the space of decision trees. Based on these results, we discuss how explanation algorithms can be modified to become informative. While the proposed analysis of explanation algorithms is mathematical, we argue that it holds strong implications for the practical applicability of these algorithms, particularly for auditing, regulation, and high-risk applications of AI.

cs.LG↗
arXiv2025

On the Surprising Effectiveness of Large Learning Rates under Standard Width Scaling

Scaling limits, such as infinite-width limits, serve as promising theoretical tools to study large-scale models. However, it is widely believed that existing infinite-width theory does not faithfully explain the behavior of practical networks, especially those trained in standard parameterization (SP) meaning He initialization with a global learning rate. For instance, existing theory for SP predicts instability at large learning rates and vanishing feature learning at stable ones. In practice, however, optimal learning rates decay slower than theoretically predicted and networks exhibit both stable training and non-trivial feature learning, even at very large widths. Here, we show that this discrepancy is not fully explained by finite-width phenomena. Instead, we find a resolution through a finer-grained analysis of the regime previously considered unstable and therefore uninteresting. In particular, we show that, under cross-entropy (CE) loss, the unstable regime comprises two distinct sub-regimes: a catastrophically unstable regime and a more benign controlled divergence regime, where logits diverge but gradients and activations remain stable. Moreover, under large learning rates at the edge of the controlled divergence regime, there exists a well-defined infinite width limit where features continue to evolve in all the hidden layers. In experiments across optimizers, architectures, and data modalities, we validate that neural networks operate in this controlled divergence regime under CE loss but not under MSE loss. Our empirical evidence suggests that width-scaling considerations are surprisingly useful for predicting empirically maximal stable learning rate exponents which provide useful guidance on optimal learning rate exponents. Finally, our analysis clarifies the effectiveness and limitations of recently proposed layerwise learning rate scaling for standard initialization.

cs.LG↗
arXiv2024

How Much Can We Forget about Data Contamination?

The leakage of benchmark data into the training data has emerged as a significant challenge for evaluating the capabilities of large language models (LLMs). In this work, we challenge the common assumption that small-scale contamination renders benchmark evaluations invalid. First, we experimentally quantify the magnitude of benchmark overfitting based on scaling along three dimensions: The number of model parameters (up to 1.6B), the number of times an example is seen (up to 144), and the number of training tokens (up to 40B). If model and data follow the Chinchilla scaling laws, minor contamination indeed leads to overfitting. At the same time, even 144 times of contamination can be forgotten if the training data is scaled beyond five times Chinchilla, a regime characteristic of many modern LLMs. Continual pre-training of OLMo-7B corroborates these results. Next, we study the impact of the weight decay parameter on example forgetting, showing that empirical forgetting occurs faster than the cumulative weight decay. This allows us to gauge the degree of example forgetting in large-scale training runs, indicating that many LLMs, including Lllama 3 405B, have forgotten the data seen at the beginning of training.

cs.LG↗
arXiv2024

The Manifold Hypothesis for Gradient-Based Explanations

When do gradient-based explanation algorithms provide perceptually-aligned explanations? We propose a criterion: the feature attributions need to be aligned with the tangent space of the data manifold. To provide evidence for this hypothesis, we introduce a framework based on variational autoencoders that allows to estimate and generate image manifolds. Through experiments across a range of different datasets -- MNIST, EMNIST, CIFAR10, X-ray pneumonia and Diabetic Retinopathy detection -- we demonstrate that the more a feature attribution is aligned with the tangent space of the data, the more perceptually-aligned it tends to be. We then show that the attributions provided by popular post-hoc methods such as Integrated Gradients and SmoothGrad are more strongly aligned with the data manifold than the raw gradient. Adversarial training also improves the alignment of model gradients with the data manifold. As a consequence, we suggest that explanation algorithms should actively strive to align their explanations with the data manifold. This is an extended version of a CVPR Workshop paper. Code is available at https://github.com/tml-tuebingen/explanations-manifold.

cs.LG↗
arXiv2024

Elephants Never Forget: Memorization and Learning of Tabular Data in Large Language Models

While many have shown how Large Language Models (LLMs) can be applied to a diverse set of tasks, the critical issues of data contamination and memorization are often glossed over. In this work, we address this concern for tabular data. Specifically, we introduce a variety of different techniques to assess whether a language model has seen a tabular dataset during training. This investigation reveals that LLMs have memorized many popular tabular datasets verbatim. We then compare the few-shot learning performance of LLMs on datasets that were seen during training to the performance on datasets released after training. We find that LLMs perform better on datasets seen during training, indicating that memorization leads to overfitting. At the same time, LLMs show non-trivial performance on novel datasets and are surprisingly robust to data transformations. We then investigate the in-context statistical learning abilities of LLMs. While LLMs are significantly better than random at solving statistical classification problems, the sample efficiency of few-shot learning lags behind traditional statistical learning algorithms, especially as the dimension of the problem increases. This suggests that much of the observed few-shot performance on novel real-world datasets is due to the LLM's world knowledge. Overall, our results highlight the importance of testing whether an LLM has seen an evaluation dataset during pre-training. We release the https://github.com/interpretml/LLM-Tabular-Memorization-Checker Python package to test LLMs for memorization of tabular datasets.

cs.LG↗
arXiv2024

Which Models have Perceptually-Aligned Gradients? An Explanation via Off-Manifold Robustness

One of the remarkable properties of robust computer vision models is that their input-gradients are often aligned with human perception, referred to in the literature as perceptually-aligned gradients (PAGs). Despite only being trained for classification, PAGs cause robust models to have rudimentary generative capabilities, including image generation, denoising, and in-painting. However, the underlying mechanisms behind these phenomena remain unknown. In this work, we provide a first explanation of PAGs via \emph{off-manifold robustness}, which states that models must be more robust off- the data manifold than they are on-manifold. We first demonstrate theoretically that off-manifold robustness leads input gradients to lie approximately on the data manifold, explaining their perceptual alignment. We then show that Bayes optimal models satisfy off-manifold robustness, and confirm the same empirically for robust models trained via gradient norm regularization, randomized smoothing, and adversarial training with projected gradient descent. Quantifying the perceptual alignment of model gradients via their similarity with the gradients of generative models, we show that off-manifold robustness correlates well with perceptual alignment. Finally, based on the levels of on- and off-manifold robustness, we identify three different regimes of robustness that affect both perceptual alignment and model accuracy: weak robustness, bayes-aligned robustness, and excessive robustness. Code is available at \url{https://github.com/tml-tuebingen/pags}.

cs.LG↗
arXiv2024

Elephants Never Forget: Testing Language Models for Memorization of Tabular Data

While many have shown how Large Language Models (LLMs) can be applied to a diverse set of tasks, the critical issues of data contamination and memorization are often glossed over. In this work, we address this concern for tabular data. Starting with simple qualitative tests for whether an LLM knows the names and values of features, we introduce a variety of different techniques to assess the degrees of contamination, including statistical tests for conditional distribution modeling and four tests that identify memorization. Our investigation reveals that LLMs are pre-trained on many popular tabular datasets. This exposure can lead to invalid performance evaluation on downstream tasks because the LLMs have, in effect, been fit to the test set. Interestingly, we also identify a regime where the language model reproduces important statistics of the data, but fails to reproduce the dataset verbatim. On these datasets, although seen during training, good performance on downstream tasks might not be due to overfitting. Our findings underscore the need for ensuring data integrity in machine learning tasks with LLMs. To facilitate future research, we release an open-source tool that can perform various tests for memorization \url{https://github.com/interpretml/LLM-Tabular-Memorization-Checker}.

cs.LG↗
arXiv2024

Data Science with LLMs and Interpretable Models

Recent years have seen important advances in the building of interpretable models, machine learning models that are designed to be easily understood by humans. In this work, we show that large language models (LLMs) are remarkably good at working with interpretable models, too. In particular, we show that LLMs can describe, interpret, and debug Generalized Additive Models (GAMs). Combining the flexibility of LLMs with the breadth of statistical patterns accurately described by GAMs enables dataset summarization, question answering, and model critique. LLMs can also improve the interaction between domain experts and interpretable models, and generate hypotheses about the underlying phenomenon. We release \url{https://github.com/interpretml/TalkToEBM} as an open-source LLM-GAM interface.

cs.LG↗
arXiv2024

Rethinking Explainable Machine Learning as Applied Statistics

In the rapidly growing literature on explanation algorithms, it often remains unclear what precisely these algorithms are for and how they should be used. In this position paper, we argue for a novel and pragmatic perspective: Explainable machine learning needs to recognize its parallels with applied statistics. Concretely, explanations are statistics of high-dimensional functions, and we should think about them analogously to traditional statistical quantities. Among others, this implies that we must think carefully about the matter of interpretation, or how the explanations relate to intuitive questions that humans have about the world. The fact that this is scarcely being discussed in research papers is one of the main drawbacks of the current literature. Moving forward, the analogy between explainable machine learning and applied statistics suggests fruitful ways for how research practices can be improved.

cs.LG↗
arXiv2023

LLMs Understand Glass-Box Models, Discover Surprises, and Suggest Repairs

We show that large language models (LLMs) are remarkably good at working with interpretable models that decompose complex outcomes into univariate graph-represented components. By adopting a hierarchical approach to reasoning, LLMs can provide comprehensive model-level summaries without ever requiring the entire model to fit in context. This approach enables LLMs to apply their extensive background knowledge to automate common tasks in data science such as detecting anomalies that contradict prior knowledge, describing potential reasons for the anomalies, and suggesting repairs that would remove the anomalies. We use multiple examples in healthcare to demonstrate the utility of these new capabilities of LLMs, with particular emphasis on Generalized Additive Models (GAMs). Finally, we present the package $\texttt{TalkToEBM}$ as an open-source LLM-GAM interface.

stat.ML↗
arXiv2023

ChatGPT Participates in a Computer Science Exam

We asked ChatGPT to participate in an undergraduate computer science exam on ''Algorithms and Data Structures''. The program was evaluated on the entire exam as posed to the students. We hand-copied its answers onto an exam sheet, which was subsequently graded in a blind setup alongside those of 200 participating students. We find that ChatGPT narrowly passed the exam, obtaining 20.5 out of 40 points. This impressive performance indicates that ChatGPT can indeed succeed in challenging tasks like university exams. At the same time, the questions in our exam are structurally similar to those of other exams, solved homework problems, and teaching materials that can be found online and might have been part of ChatGPT's training data. Therefore, it would be inadequate to conclude from this experiment that ChatGPT has any understanding of computer science. We also assess the improvements brought by GPT-4. We find that GPT-4 would have obtained about 17\% more exam points than GPT-3.5, reaching the performance of the average student. The transcripts of our conversations with ChatGPT are available at \url{https://github.com/tml-tuebingen/chatgpt-algorithm-exam}, and the entire graded exam is in the appendix of this paper.

cs.CL↗
arXiv2023

From Shapley Values to Generalized Additive Models and back

In explainable machine learning, local post-hoc explanation algorithms and inherently interpretable models are often seen as competing approaches. This work offers a partial reconciliation between the two by establishing a correspondence between Shapley Values and Generalized Additive Models (GAMs). We introduce $n$-Shapley Values, a parametric family of local post-hoc explanation algorithms that explain individual predictions with interaction terms up to order $n$. By varying the parameter $n$, we obtain a sequence of explanations that covers the entire range from Shapley Values up to a uniquely determined decomposition of the function we want to explain. The relationship between $n$-Shapley Values and this decomposition offers a functionally-grounded characterization of Shapley Values, which highlights their limitations. We then show that $n$-Shapley Values, as well as the Shapley Taylor- and Faith-Shap interaction indices, recover GAMs with interaction terms up to order $n$. This implies that the original Shapely Values recover GAMs without variable interactions. Taken together, our results provide a precise characterization of Shapley Values as they are being used in explainable machine learning. They also offer a principled interpretation of partial dependence plots of Shapley Values in terms of the underlying functional decomposition. A package for the estimation of different interaction indices is available at \url{https://github.com/tml-tuebingen/nshap}.

cs.LG↗