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Christian Hardmeier

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Computation and Language Machine Learning Artificial Intelligence

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preprint2026arXiv

Tracing Uncertainty in Language Model "Reasoning"

Language model (LM) "reasoning", commonly described as Chain-of-Thought or test-time scaling, often improves benchmark performance, but the dynamics underlying this process remain poorly understood. We study these dynamics through the lens of uncertainty quantification by treating the "reasoning" traces, the intermediate token sequences generated by LMs, as evolving model states. We summarize each trace by an uncertainty trace profile: a small set of features describing the shape of the uncertainty signal over its trace, such as its slope and linearity. We find that across five LMs evaluated on GSM8K and ProntoQA, these profiles predict whether a trace yields a correct final answer with AUROC up to 0.807, improving markedly on recent related work. We reach AUROC 0.801 using only the first few hundred tokens of full traces, suggesting that errors can be detected early in the generation. A detailed comparison of correct and incorrect traces further reveals qualitatively distinct uncertainty profiles, with correct traces showing a steeper and less linear decline in uncertainty. Together, the results suggest that our method, grounded in decision-making under uncertainty, provides a principled lens for studying the generative process underlying LM "reasoning".

preprint2022arXiv

deep-significance - Easy and Meaningful Statistical Significance Testing in the Age of Neural Networks

A lot of Machine Learning (ML) and Deep Learning (DL) research is of an empirical nature. Nevertheless, statistical significance testing (SST) is still not widely used. This endangers true progress, as seeming improvements over a baseline might be statistical flukes, leading follow-up research astray while wasting human and computational resources. Here, we provide an easy-to-use package containing different significance tests and utility functions specifically tailored towards research needs and usability.

preprint2020arXiv

Principal Word Vectors

We generalize principal component analysis for embedding words into a vector space. The generalization is made in two major levels. The first is to generalize the concept of the corpus as a counting process which is defined by three key elements vocabulary set, feature (annotation) set, and context. This generalization enables the principal word embedding method to generate word vectors with regard to different types of contexts and different types of annotations provided for a corpus. The second is to generalize the transformation step used in most of the word embedding methods. To this end, we define two levels of transformations. The first is a quadratic transformation, which accounts for different types of weighting over the vocabulary units and contextual features. Second is an adaptive non-linear transformation, which reshapes the data distribution to be meaningful to principal component analysis. The effect of these generalizations on the word vectors is intrinsically studied with regard to the spread and the discriminability of the word vectors. We also provide an extrinsic evaluation of the contribution of the principal word vectors on a word similarity benchmark and the task of dependency parsing. Our experiments are finalized by a comparison between the principal word vectors and other sets of word vectors generated with popular word embedding methods. The results obtained from our intrinsic evaluation metrics show that the spread and the discriminability of the principal word vectors are higher than that of other word embedding methods. The results obtained from the extrinsic evaluation metrics show that the principal word vectors are better than some of the word embedding methods and on par with popular methods of word embedding.

preprint2015arXiv

Learning Structural Kernels for Natural Language Processing

Structural kernels are a flexible learning paradigm that has been widely used in Natural Language Processing. However, the problem of model selection in kernel-based methods is usually overlooked. Previous approaches mostly rely on setting default values for kernel hyperparameters or using grid search, which is slow and coarse-grained. In contrast, Bayesian methods allow efficient model selection by maximizing the evidence on the training data through gradient-based methods. In this paper we show how to perform this in the context of structural kernels by using Gaussian Processes. Experimental results on tree kernels show that this procedure results in better prediction performance compared to hyperparameter optimization via grid search. The framework proposed in this paper can be adapted to other structures besides trees, e.g., strings and graphs, thereby extending the utility of kernel-based methods.