David Mildenberger

Georgios Kaissis, David Mildenberger, Juan Felipe Gomez et al.

We study how individual training examples shape the internal computation of looped transformers, where a shared block is applied for $τ$ recurrent iterations to enable latent reasoning. Existing training-data influence estimators such as TracIn yield a single scalar score that aggregates over all loop iterations, obscuring when during the recurrent computation a training example matters. We introduce \textit{Step-Decomposed Influence (SDI)}, which decomposes TracIn into a length-$τ$ influence trajectory by unrolling the recurrent computation graph and attributing influence to specific loop iterations. To make SDI practical at transformer scale, we propose a TensorSketch implementation that never materialises per-example gradients. Experiments on looped GPT-style models and algorithmic reasoning tasks show that SDI scales excellently, matches full-gradient baselines with low error and supports a broad range of data attribution and interpretability tasks with per-step insights into the latent reasoning process.

David Mildenberger, Paul Hager, Daniel Rueckert et al.

Supervised contrastive learning (SupCon) has proven to be a powerful alternative to the standard cross-entropy loss for classification of multi-class balanced datasets. However, it struggles to learn well-conditioned representations of datasets with long-tailed class distributions. This problem is potentially exacerbated for binary imbalanced distributions, which are commonly encountered during many real-world problems such as medical diagnosis. In experiments on seven binary datasets of natural and medical images, we show that the performance of SupCon decreases with increasing class imbalance. To substantiate these findings, we introduce two novel metrics that evaluate the quality of the learned representation space. By measuring the class distribution in local neighborhoods, we are able to uncover structural deficiencies of the representation space that classical metrics cannot detect. Informed by these insights, we propose two new supervised contrastive learning strategies tailored to binary imbalanced datasets that improve the structure of the representation space and increase downstream classification accuracy over standard SupCon by up to 35%. We make our code available.