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

The dominant paradigm for training large-scale vision and language models is He initialization and a single global learning rate (\textit{standard parameterization}, SP). Despite its practical success, standard parametrization remains poorly understood from a theoretical perspective: Existing infinite-width theory would predict instability under large learning rates and vanishing feature learning under stable learning rates. However, empirically optimal learning rates consistently decay much slower than theoretically predicted. By carefully studying neural network training dynamics, we demonstrate that this discrepancy is not fully explained by finite-width phenomena such as catapult effects or a lack of alignment between weights and incoming activations. We instead show that the apparent contradiction can be fundamentally resolved by taking the loss function into account: In contrast to Mean Squared Error (MSE) loss, we prove that under cross-entropy (CE) loss, an intermediate \textit{controlled divergence} regime emerges, where logits diverge but loss, gradients, and activations remain stable. Stable training under large learning rates enables persistent feature evolution at scale in all hidden layers, which is crucial for the practical success of SP. In experiments across optimizers (SGD, Adam), architectures (MLPs, GPT) and data modalities (vision, language), 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 optimal learning rate exponents. Finally, our analysis clarifies the effectiveness and limitations of recently proposed layerwise learning rate scalings for standard initialization.

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 use experimental evidence and theoretical estimates to 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). We find that 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. We then derive a simple theory of example forgetting via cumulative weight decay. It allows us to bound the number of gradient steps required to forget past data for any training run where we know the hyperparameters of AdamW. This indicates that many LLMs, including Llama 3, have forgotten the data seen at the beginning of training. Experimentally, we demonstrate that forgetting occurs faster than what is predicted by our bounds. Taken together, our results suggest that moderate amounts of contamination can be forgotten at the end of realistically scaled training runs.

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. Without fine-tuning, we find them to be limited. This suggests that much of the few-shot performance on novel 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 make the exposure tests we developed available as the tabmemcheck Python package at https://github.com/interpretml/LLM-Tabular-Memorization-Checker

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}.

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.

Statistics without Interpretation: A Sober Look at Explainable Machine Learning

In the rapidly growing literature on explanation algorithms, it often remains unclear what precisely these algorithms are for and how they should be used. We argue that this is because explanation algorithms are often mathematically complex but don't admit a clear interpretation. Unfortunately, complex statistical methods that don't have a clear interpretation are bound to lead to errors in interpretation, a fact that has become increasingly apparent in the literature. In order to move forward, papers on explanation algorithms should make clear how precisely the output of the algorithms should be interpreted. They should also clarify what questions about the function can and cannot be answered given the explanations. Our argument is based on the distinction between statistics and their interpretation. It also relies on parallels between explainable machine learning and applied statistics.

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.

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, noise augmentation, and randomized smoothing. 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.

ChatGPT Participates in a Computer Science Exam

We asked ChatGPT to participate in an undergraduate computer science exam on ''Algorithms and Data Structures''. We evaluated the program 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 tasks in our exam are structurally similar to those on other exams, solved homework problems, and teaching materials that can be found online. Therefore, it would be premature to conclude from this experiment that ChatGPT has any understanding of computer science. The transcript of our conversation with ChatGPT is available at \url{https://github.com/tml-tuebingen/chatgpt-algorithm-exam}, and the entire graded exam is in the appendix of this paper.

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. In this work, offer a novel perspective on Shapley Values, a prominent post-hoc explanation technique, and show that it is strongly connected with Glassbox-GAMs, a popular class of interpretable models. We introduce $n$-Shapley Values, a natural extension of Shapley Values that explain individual predictions with interaction terms up to order $n$. As $n$ increases, the $n$-Shapley Values converge towards the Shapley-GAM, a uniquely determined decomposition of the original function. From the Shapley-GAM, we can compute Shapley Values of arbitrary order, which gives precise insights into the limitations of these explanations. We then show that Shapley Values recover generalized additive models of order $n$, assuming that we allow for interaction terms up to order $n$ in the explanations. This implies that the original Shapley Values recover Glassbox-GAMs. At the technical end, we show that there is a one-to-one correspondence between different ways to choose the value function and different functional decompositions of the original function. This provides a novel perspective on the question of how to choose the value function. We also present an empirical analysis of the degree of variable interaction that is present in various standard classifiers, and discuss the implications of our results for algorithmic explanations. A python package to compute $n$-Shapley Values and replicate the results in this paper is available at \url{https://github.com/tml-tuebingen/nshap}.