Anders Gjølbye

Anders Gjølbye, William Lehn-Schiøler, Áshildur Jónsdóttir et al.

Deep learning models are complex due to their size, structure, and inherent randomness in training procedures. Additional complexity arises from the selection of datasets and inductive biases. Addressing these challenges for explainability, Kim et al. (2018) introduced Concept Activation Vectors (CAVs), which aim to understand deep models' internal states in terms of human-aligned concepts. These concepts correspond to directions in latent space, identified using linear discriminants. Although this method was first applied to image classification, it was later adapted to other domains, including natural language processing. In this work, we attempt to apply the method to electroencephalogram (EEG) data for explainability in Kostas et al.'s BENDR (2021), a large-scale transformer model. A crucial part of this endeavor involves defining the explanatory concepts and selecting relevant datasets to ground concepts in the latent space. Our focus is on two mechanisms for EEG concept formation: the use of externally labeled EEG datasets, and the application of anatomically defined concepts. The former approach is a straightforward generalization of methods used in image classification, while the latter is novel and specific to EEG. We present evidence that both approaches to concept formation yield valuable insights into the representations learned by deep EEG models.

Anders Gjølbye, Lars Kai Hansen, Sanmi Koyejo

Reasoning-trained language models often spend more tokens on harder problems, but longer chains of thought do not show whether a model is merely computing for more steps or following a different internal trajectory. We study this distinction through hidden-state trajectories during chain-of-thought generation across competitive programming, mathematics, and Boolean satisfiability. Raw trajectory geometry is strongly shaped by generation length: longer generations mechanically alter path statistics, so difficulty-dependent comparisons are misleading without adjustment. After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines. Corrected difficulty-geometry coupling is weaker, but still present, in mathematics and Boolean satisfiability. Prompt-stage linear probes do not mirror the code-domain separation, and behavioral annotations show that stronger corrected coupling co-occurs with strategy shifts and uncertainty monitoring. Together, these findings establish length correction as a prerequisite for generation-time trajectory analysis and show that reasoning training can be associated with distinct corrected trajectory geometry, with the strength of the effect depending on the domain.

Anders Gjølbye, Lina Skerath, William Lehn-Schiøler et al.

Electroencephalography (EEG) research typically focuses on tasks with narrowly defined objectives, but recent studies are expanding into the use of unlabeled data within larger models, aiming for a broader range of applications. This addresses a critical challenge in EEG research. For example, Kostas et al. (2021) show that self-supervised learning (SSL) outperforms traditional supervised methods. Given the high noise levels in EEG data, we argue that further improvements are possible with additional preprocessing. Current preprocessing methods often fail to efficiently manage the large data volumes required for SSL, due to their lack of optimization, reliance on subjective manual corrections, and validation processes or inflexible protocols that limit SSL. We propose a Python-based EEG preprocessing pipeline optimized for self-supervised learning, designed to efficiently process large-scale data. This optimization not only stabilizes self-supervised training but also enhances performance on downstream tasks compared to training with raw data.

Anders Gjølbye, Ida Kargaard, Emma Kargaard et al.

Partial Least Squares (PLS) learns shared structure from paired data via the top singular vectors of the empirical cross-covariance (PLS-SVD), but multimodal datasets often have missing entries in both views. We study PLS-SVD under independent entry-wise missing-completely-at-random masking in a proportional high-dimensional spiked model. After appropriate normalization, the masked cross-covariance behaves like a spiked rectangular random matrix whose effective signal strength is attenuated by $\sqrtρ$, where $ρ$ is the joint entry retention probability. As a result, PLS-SVD exhibits a sharp BBP-type phase transition: below a critical signal-to-noise threshold the leading singular vectors are asymptotically uninformative, while above it they achieve nontrivial alignment with the latent shared directions, with closed-form asymptotic overlap formulas. Simulations and semi-synthetic multimodal experiments corroborate the predicted phase diagram and recovery curves across aspect ratios, signal strengths, and missingness levels.

Sebastian Ray Mason, Anders Gjølbye, Phillip Chavarria Højbjerg et al.

Mental rotation is a key test of spatial reasoning in humans and has been central to understanding how perception supports cognition. Despite the success of modern vision transformers, it is still unclear how well these models develop similar abilities. In this work, we present a systematic evaluation of ViT, CLIP, DINOv2, and DINOv3 across a range of mental-rotation tasks, from simple block structures similar to those used by Shepard and Metzler to study human cognition, to more complex block figures, three types of text, and photo-realistic objects. By probing model representations layer by layer, we examine where and how these networks succeed. We find that i) self-supervised ViTs capture geometric structure better than supervised ViTs; ii) intermediate layers perform better than final layers; iii) task difficulty increases with rotation complexity and occlusion, mirroring human reaction times and suggesting similar constraints in embedding space representations.