Dutch Books for Language Models

People increasingly use language models to support life decisions. Many such decisions involve a probabilistic forecast: How likely is a major life event, a natural disaster, or an economic outcome? Users of language models may implicitly trust that these forecasts fall out of a coherent world model. In this paper, we evaluate the coherence of language model probabilistic forecasts through a procedure that builds on a theorem due to de Finetti. We elicit forecasts from language models across events generated from stock returns data. We then use linear programs to compute the largest Dutch-book profit - the profit an arbitrageur could guarantee by betting against model-generated probabilities - which we use as a measure of incoherence. Our procedure does not require outcome labels, so we can evaluate coherence even in settings where outcomes are not observed or have not yet resolved. We find substantial evidence of incoherence in language model forecasts. Such incoherence increases when there are richer logical relationships between events, and irrelevant contextual details can increase incoherence by an order of magnitude. We conclude by discussing how alternative training strategies may improve probabilistic coherence.

When Lexical Change Misleads: Rethinking Dynamic Topic Model Evaluation with Traditional and LLM-Based Metrics

Dynamic topic models capture evolving word distributions, but traditional coherence metrics may fail when vocabulary changes while semantic meaning persists. We evaluate 120 topics from CoNTM and DLDA across NYT, DBLP, and arXiv, using three human annotators and Low, Medium, and High lexical-change categories. Traditional temporal coherence shows highly variable agreement with human judgments ($ρ$=-0.256 to 0.614). In contrast, LLM-based semantic similarity agrees strongly with human semantic judgments for CoNTM on NYT ($ρ$=0.609), DBLP ($ρ$=0.721), and arXiv ($ρ$=0.502), but is less consistent for DLDA. Lexical-change stratification reveals variation hidden by aggregate evaluation. We therefore advocate lexical-change-aware evaluation, jointly reporting traditional coherence and LLM-based semantic measures as complementary rather than interchangeable signals.

Hölder++: Improving the Quality-Coherence Trade-off in Multimodal VAEs

Existing approaches for multimodal variational autoencoders (VAEs) face a trade-off between generative quality and coherence-i.e., they struggle to generate realistic and diverse samples that, at the same time, are semantically consistent across modalities. A recent work shows that using a simple approximation to Hölder pooling as an aggregation method improves coherence over the SOTA MMVAE+, despite assuming a single shared representation across all modalities. Yet, it slightly compromises sample diversity. Inspired by this insight, we propose Hölder++, a novel multimodal VAE that improves the generative quality-coherence trade-off through: (i) the first implementation of Hölder pooling without any approximation for multimodal VAEs; (ii) an extended architecture that models distinct shared and private (i.e., modality-specific) representations (Hölder+); and (iii) hierarchical inference that further enhances the disentanglement between the shared and private representations (Hölder++). Our experiments corroborate that Hölder++ consistently improves the generative quality-coherence trade-off, yields more structured latent spaces, and learns shared representations that are informative for downstream tasks.