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Maximilian Nickel

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Machine Learning Artificial Intelligence Social and Information Networks

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preprint2026arXiv

SCRuB: Social Concept Reasoning under Rubric-Based Evaluation

While many studies of Large Language Model (LLM) reasoning capabilities emphasize mathematical or technical tasks, few address reasoning about social concepts: the abstract ideas shaping social norms, culture, and institutions. This understudied capability is essential for modern models acting as social agents, yet no systematic evaluation methodology targets it. We introduce SCRuB (Social Concept Reasoning under Rubric-Based Evaluation), a framework designed for this setting of task indeterminacy. Our goal is to measure the degree to which a model reasons about social concepts with the depth and critical rigor of a human expert. SCRuB proceeds in three phases: prompt construction from established sources, response generation by experts and models, and comparative evaluation using a five-dimensional critical thinking rubric. To enable generalization of the pipeline, we introduce a Panel of Disciplinary Perspectives ensemble validated against independent expert judges. We release SCRuBEval (n=4,711 evaluation prompts) and SCRuBAnnotations (300 expert-authored responses and 150 expert comparative judgments from 45 PhD-level scholars). Our results show that frontier models consistently outperform human experts across all five rubric dimensions. Across 1,170 pairwise comparisons, expert judges ranked a model response first in 80.8% of judgments and preferred model responses overall 74.4% of the time. Ultimately, this study provides the first expert-grounded demonstration of evaluation saturation for social concept reasoning: the single-turn exam-style format has reached its ceiling for models and humans alike.

preprint2022arXiv

Matching Normalizing Flows and Probability Paths on Manifolds

Continuous Normalizing Flows (CNFs) are a class of generative models that transform a prior distribution to a model distribution by solving an ordinary differential equation (ODE). We propose to train CNFs on manifolds by minimizing probability path divergence (PPD), a novel family of divergences between the probability density path generated by the CNF and a target probability density path. PPD is formulated using a logarithmic mass conservation formula which is a linear first order partial differential equation relating the log target probabilities and the CNF's defining vector field. PPD has several key benefits over existing methods: it sidesteps the need to solve an ODE per iteration, readily applies to manifold data, scales to high dimensions, and is compatible with a large family of target paths interpolating pure noise and data in finite time. Theoretically, PPD is shown to bound classical probability divergences. Empirically, we show that CNFs learned by minimizing PPD achieve state-of-the-art results in likelihoods and sample quality on existing low-dimensional manifold benchmarks, and is the first example of a generative model to scale to moderately high dimensional manifolds.

preprint2020arXiv

Learning Multivariate Hawkes Processes at Scale

Multivariate Hawkes Processes (MHPs) are an important class of temporal point processes that have enabled key advances in understanding and predicting social information systems. However, due to their complex modeling of temporal dependencies, MHPs have proven to be notoriously difficult to scale, what has limited their applications to relatively small domains. In this work, we propose a novel model and computational approach to overcome this important limitation. By exploiting a characteristic sparsity pattern in real-world diffusion processes, we show that our approach allows to compute the exact likelihood and gradients of an MHP -- independently of the ambient dimensions of the underlying network. We show on synthetic and real-world datasets that our model does not only achieve state-of-the-art predictive results, but also improves runtime performance by multiple orders of magnitude compared to standard methods on sparse event sequences. In combination with easily interpretable latent variables and influence structures, this allows us to analyze diffusion processes at previously unattainable scale.

preprint2016arXiv

Relational Models

We provide a survey on relational models. Relational models describe complete networked {domains by taking into account global dependencies in the data}. Relational models can lead to more accurate predictions if compared to non-relational machine learning approaches. Relational models typically are based on probabilistic graphical models, e.g., Bayesian networks, Markov networks, or latent variable models. Relational models have applications in social networks analysis, the modeling of knowledge graphs, bioinformatics, recommendation systems, natural language processing, medical decision support, and linked data.

preprint2015arXiv

A Review of Relational Machine Learning for Knowledge Graphs

Relational machine learning studies methods for the statistical analysis of relational, or graph-structured, data. In this paper, we provide a review of how such statistical models can be "trained" on large knowledge graphs, and then used to predict new facts about the world (which is equivalent to predicting new edges in the graph). In particular, we discuss two fundamentally different kinds of statistical relational models, both of which can scale to massive datasets. The first is based on latent feature models such as tensor factorization and multiway neural networks. The second is based on mining observable patterns in the graph. We also show how to combine these latent and observable models to get improved modeling power at decreased computational cost. Finally, we discuss how such statistical models of graphs can be combined with text-based information extraction methods for automatically constructing knowledge graphs from the Web. To this end, we also discuss Google's Knowledge Vault project as an example of such combination.

preprint2015arXiv

Holographic Embeddings of Knowledge Graphs

Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HolE) to learn compositional vector space representations of entire knowledge graphs. The proposed method is related to holographic models of associative memory in that it employs circular correlation to create compositional representations. By using correlation as the compositional operator HolE can capture rich interactions but simultaneously remains efficient to compute, easy to train, and scalable to very large datasets. In extensive experiments we show that holographic embeddings are able to outperform state-of-the-art methods for link prediction in knowledge graphs and relational learning benchmark datasets.

preprint2013arXiv

Logistic Tensor Factorization for Multi-Relational Data

Tensor factorizations have become increasingly popular approaches for various learning tasks on structured data. In this work, we extend the RESCAL tensor factorization, which has shown state-of-the-art results for multi-relational learning, to account for the binary nature of adjacency tensors. We study the improvements that can be gained via this approach on various benchmark datasets and show that the logistic extension can improve the prediction results significantly.