Lars Kai Hansen

Germans Savcisens, Tina Eliassi-Rad, Lars Kai Hansen et al.

Over the past decade, machine learning has revolutionized computers' ability to analyze text through flexible computational models. Due to their structural similarity to written language, transformer-based architectures have also shown promise as tools to make sense of a range of multi-variate sequences from protein-structures, music, electronic health records to weather-forecasts. We can also represent human lives in a way that shares this structural similarity to language. From one perspective, lives are simply sequences of events: People are born, visit the pediatrician, start school, move to a new location, get married, and so on. Here, we exploit this similarity to adapt innovations from natural language processing to examine the evolution and predictability of human lives based on detailed event sequences. We do this by drawing on arguably the most comprehensive registry data in existence, available for an entire nation of more than six million individuals across decades. Our data include information about life-events related to health, education, occupation, income, address, and working hours, recorded with day-to-day resolution. We create embeddings of life-events in a single vector space showing that this embedding space is robust and highly structured. Our models allow us to predict diverse outcomes ranging from early mortality to personality nuances, outperforming state-of-the-art models by a wide margin. Using methods for interpreting deep learning models, we probe the algorithm to understand the factors that enable our predictions. Our framework allows researchers to identify new potential mechanisms that impact life outcomes and associated possibilities for personalized interventions.

Sarthak Yadav, Sergios Theodoridis, Lars Kai Hansen et al.

In this work, we propose a Multi-Window Masked Autoencoder (MW-MAE) fitted with a novel Multi-Window Multi-Head Attention (MW-MHA) module that facilitates the modelling of local-global interactions in every decoder transformer block through attention heads of several distinct local and global windows. Empirical results on ten downstream audio tasks show that MW-MAEs consistently outperform standard MAEs in overall performance and learn better general-purpose audio representations, along with demonstrating considerably better scaling characteristics. Investigating attention distances and entropies reveals that MW-MAE encoders learn heads with broader local and global attention. Analyzing attention head feature representations through Projection Weighted Canonical Correlation Analysis (PWCCA) shows that attention heads with the same window sizes across the decoder layers of the MW-MAE learn correlated feature representations which enables each block to independently capture local and global information, leading to a decoupled decoder feature hierarchy. Code for feature extraction and downstream experiments along with pre-trained models will be released publically.

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.

Mikkel Godsk Jørgensen, Lars Kai Hansen

Sparse Autoencoders (SAEs) have been seen as a promising avenue for exploring the internals of Large Language Models (LLMs) and for steering model output generation. When AxBench - a model steering benchmark - was introduced in Wu et al. (2025), SAEs did not seem to live up to their original hype due to poor steering performance relative to a set of simple baselines. This work serves as a partial rebuttal for Sparse Autoencoders and suggests that the results of Wu et al. (2025) did not do them full justice. We find that Sparse Autoencoders can, in fact, perform close to on par with the reference LoRA performance on the AxBench benchmark, when features are selected and labelled with our supervised pipeline. We also find that our pipeline selects features that are surprisingly causal of their identified labels when using only its interpretability-based components. Lastly, we present evidence that high sparsity (low l0) may not be crucial for successful steering based on interpretability, which is in contrast to the earlier findings in Wang et al. (2025).

Jonathan Foldager, Mikkel Jordahn, Lars Kai Hansen et al.

Bayesian optimization (BO) is a popular method for black-box optimization, which relies on uncertainty as part of its decision-making process when deciding which experiment to perform next. However, not much work has addressed the effect of uncertainty on the performance of the BO algorithm and to what extent calibrated uncertainties improve the ability to find the global optimum. In this work, we provide an extensive study of the relationship between the BO performance (regret) and uncertainty calibration for popular surrogate models and compare them across both synthetic and real-world experiments. Our results confirm that Gaussian Processes are strong surrogate models and that they tend to outperform other popular models. Our results further show a positive association between calibration error and regret, but interestingly, this association disappears when we control for the type of model in the analysis. We also studied the effect of re-calibration and demonstrate that it generally does not lead to improved regret. Finally, we provide theoretical justification for why uncertainty calibration might be difficult to combine with BO due to the small sample sizes commonly used.

Lenka Tětková, Lars Kai Hansen

As the use of deep neural networks continues to grow, understanding their behaviour has become more crucial than ever. Post-hoc explainability methods are a potential solution, but their reliability is being called into question. Our research investigates the response of post-hoc visual explanations to naturally occurring transformations, often referred to as augmentations. We anticipate explanations to be invariant under certain transformations, such as changes to the colour map while responding in an equivariant manner to transformations like translation, object scaling, and rotation. We have found remarkable differences in robustness depending on the type of transformation, with some explainability methods (such as LRP composites and Guided Backprop) being more stable than others. We also explore the role of training with data augmentation. We provide evidence that explanations are typically less robust to augmentation than classification performance, regardless of whether data augmentation is used in training or not.

Teresa Dorszewski, Lenka Tětková, Lorenz Linhardt et al.

Understanding how neural networks align with human cognitive processes is a crucial step toward developing more interpretable and reliable AI systems. Motivated by theories of human cognition, this study examines the relationship between \emph{convexity} in neural network representations and \emph{human-machine alignment} based on behavioral data. We identify a correlation between these two dimensions in pretrained and fine-tuned vision transformer models. Our findings suggest that the convex regions formed in latent spaces of neural networks to some extent align with human-defined categories and reflect the similarity relations humans use in cognitive tasks. While optimizing for alignment generally enhances convexity, increasing convexity through fine-tuning yields inconsistent effects on alignment, which suggests a complex relationship between the two. This study presents a first step toward understanding the relationship between the convexity of latent representations and human-machine alignment.

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.

William Lehn-Schiøler, Magnus Ruud Kjær, Rahul Thapa et al.

EEG foundation models achieve state-of-the-art clinical performance, yet the internal computations driving their predictions remain opaque: a barrier to clinical trust. We apply TopK Sparse Autoencoders (SAEs) across three architecturally distinct EEG transformers: SleepFM, REVE, and LaBraM to extract sparse feature dictionaries from their embeddings. By grounding these features in a clinical taxonomy (abnormality, age, sex, and medication), we benchmark monosemanticity and entanglement across architectures. A single hyperparameter procedure, driven by an intrinsic dictionary health audit, transfers robustly across all three architectures. Via concept steering, we introduce a "target vs. off-target" probe area metric to quantify steering selectivity and reveal three operational regimes: selectively steerable, encoded but entangled, and non-encoded. This framework exposes critical representational failures: "wrecking-ball" interventions that collapse global model performance, and clinical entanglements, such as age-pathology confounding, where it is impossible to suppress one concept without corrupting the other. Finally, a spectral decoder maps these interventions back to the amplitude spectrum, translating latent manipulations into physiologically interpretable frequency signatures, such as pathological slow-wave suppression and $α$-band restoration.

Teresa Dorszewski, Albert Kjøller Jacobsen, Lenka Tětková et al.

Self-supervised speech representation models, particularly those leveraging transformer architectures, have demonstrated remarkable performance across various tasks such as speech recognition, speaker identification, and emotion detection. Recent studies on transformer models revealed a high redundancy between layers and the potential for significant pruning, which we will investigate here for transformer-based speech representation models. We perform a detailed analysis of layer similarity in speech representation models using three similarity metrics: cosine similarity, centered kernel alignment, and mutual nearest-neighbor alignment. Our findings reveal a block-like structure of high similarity, suggesting two main processing steps and significant redundancy of layers. We demonstrate the effectiveness of pruning transformer-based speech representation models without the need for post-training, achieving up to 40% reduction in transformer layers while maintaining over 95% of the model's predictive capacity. Furthermore, we employ a knowledge distillation method to substitute the entire transformer stack with mimicking layers, reducing the network size 95-98% and the inference time by up to 94%. This substantial decrease in computational load occurs without considerable performance loss, suggesting that the transformer stack is almost completely redundant for downstream applications of speech representation models.

Beatrix M. G. Nielsen, Lars Kai Hansen

Semantic representations of text, i.e. representations of natural language which capture meaning by geometry, are essential for areas such as information retrieval and document grouping. High-dimensional trained dense vectors have received much attention in recent years as such representations. We investigate the structure of semantic spaces that arise from embeddings made with Sentence-BERT and find that the representations suffer from a well-known problem in high dimensions called hubness. Hubness results in asymmetric neighborhood relations, such that some texts (the hubs) are neighbours of many other texts while most texts (so-called anti-hubs), are neighbours of few or no other texts. We quantify the semantic quality of the embeddings using hubness scores and error rate of a neighbourhood based classifier. We find that when hubness is high, we can reduce error rate and hubness using hubness reduction methods. We identify a combination of two methods as resulting in the best reduction. For example, on one of the tested pretrained models, this combined method can reduce hubness by about 75% and error rate by about 9%. Thus, we argue that mitigating hubness in the embedding space provides better semantic representations of text.

Jia Qian, Lars Kai Hansen, Xenofon Fafoutis et al.

Federated Learning is a framework that jointly trains a model \textit{with} complete knowledge on a remotely placed centralized server, but \textit{without} the requirement of accessing the data stored in distributed machines. Some work assumes that the data generated from edge devices are identically and independently sampled from a common population distribution. However, such ideal sampling may not be realistic in many contexts. Also, models based on intrinsic agency, such as active sampling schemes, may lead to highly biased sampling. So an imminent question is how robust Federated Learning is to biased sampling? In this work\footnote{\url{https://github.com/jiaqian/robustness_of_FL}}, we experimentally investigate two such scenarios. First, we study a centralized classifier aggregated from a collection of local classifiers trained with data having categorical heterogeneity. Second, we study a classifier aggregated from a collection of local classifiers trained by data through active sampling at the edge. We present evidence in both scenarios that Federated Learning is robust to data heterogeneity when local training iterations and communication frequency are appropriately chosen.

Radu Dragusin, Paula Petcu, Christina Lioma et al.

Background: The web has become a primary information resource about illnesses and treatments for both medical and non-medical users. Standard web search is by far the most common interface for such information. It is therefore of interest to find out how well web search engines work for diagnostic queries and what factors contribute to successes and failures. Among diseases, rare (or orphan) diseases represent an especially challenging and thus interesting class to diagnose as each is rare, diverse in symptoms and usually has scattered resources associated with it. Methods: We use an evaluation approach for web search engines for rare disease diagnosis which includes 56 real life diagnostic cases, state-of-the-art evaluation measures, and curated information resources. In addition, we introduce FindZebra, a specialized (vertical) rare disease search engine. FindZebra is powered by open source search technology and uses curated freely available online medical information. Results: FindZebra outperforms Google Search in both default setup and customised to the resources used by FindZebra. We extend FindZebra with specialized functionalities exploiting medical ontological information and UMLS medical concepts to demonstrate different ways of displaying the retrieved results to medical experts. Conclusions: Our results indicate that a specialized search engine can improve the diagnostic quality without compromising the ease of use of the currently widely popular web search engines. The proposed evaluation approach can be valuable for future development and benchmarking. The FindZebra search engine is available at http://www.findzebra.com/.

Teresa Dorszewski, Lenka Tětková, Lars Kai Hansen

Speech representation models based on the transformer architecture and trained by self-supervised learning have shown great promise for solving tasks such as speech and speaker recognition, keyword spotting, emotion detection, and more. Typically, it is found that larger models lead to better performance. However, the significant computational effort involved in such large transformer systems is a challenge for embedded and real-world applications. Recent work has shown that there is significant redundancy in the transformer models for NLP and massive layer pruning is feasible (Sajjad et al., 2023). Here, we investigate layer pruning in audio models. We base the pruning decision on a convexity criterion. Convexity of classification regions has recently been proposed as an indicator of subsequent fine-tuning performance in a range of application domains, including NLP and audio. In empirical investigations, we find a massive reduction in the computational effort with no loss of performance or even improvements in certain cases.

William Lehn-Schiøler, Magnus Ruud Kjær, Phillip Hempel et al.

Sleep foundation models have recently demonstrated strong performance on in-domain polysomnography tasks, including sleep staging, apnea detection, and disease risk prediction. In this work, we investigate whether sleep biosignals can serve as an effective pretraining distribution for learning representations that transfer beyond sleep to adjacent domains. Following sleep foundation models, we perform sleep-only multimodal contrastive pretraining (with a leave-one-out objective) and evaluate transfer to non-sleep EEG and ECG, two well-benchmarked biosignal modalities with heterogeneous datasets and clinically meaningful downstream tasks. Across eight downstream tasks spanning multiple EEG and ECG datasets, sleep pretraining consistently improves performance relative to training from scratch. Moreover, on several tasks, we achieve performance competitive with or surpassing prior specialized state-of-the-art and foundation models.

Teresa Dorszewski, Lenka Tětková, Robert Jenssen et al.

Vision Transformers (ViTs) are increasingly utilized in various computer vision tasks due to their powerful representation capabilities. However, it remains understudied how ViTs process information layer by layer. Numerous studies have shown that convolutional neural networks (CNNs) extract features of increasing complexity throughout their layers, which is crucial for tasks like domain adaptation and transfer learning. ViTs, lacking the same inductive biases as CNNs, can potentially learn global dependencies from the first layers due to their attention mechanisms. Given the increasing importance of ViTs in computer vision, there is a need to improve the layer-wise understanding of ViTs. In this work, we present a novel, layer-wise analysis of concepts encoded in state-of-the-art ViTs using neuron labeling. Our findings reveal that ViTs encode concepts with increasing complexity throughout the network. Early layers primarily encode basic features such as colors and textures, while later layers represent more specific classes, including objects and animals. As the complexity of encoded concepts increases, the number of concepts represented in each layer also rises, reflecting a more diverse and specific set of features. Additionally, different pretraining strategies influence the quantity and category of encoded concepts, with finetuning to specific downstream tasks generally reducing the number of encoded concepts and shifting the concepts to more relevant categories.

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.

Lenka Tětková, Teresa Karen Scheidt, Maria Mandrup Fogh et al.

Concept-based explainable AI is promising as a tool to improve the understanding of complex models at the premises of a given user, viz.\ as a tool for personalized explainability. An important class of concept-based explainability methods is constructed with empirically defined concepts, indirectly defined through a set of positive and negative examples, as in the TCAV approach (Kim et al., 2018). While it is appealing to the user to avoid formal definitions of concepts and their operationalization, it can be challenging to establish relevant concept datasets. Here, we address this challenge using general knowledge graphs (such as, e.g., Wikidata or WordNet) for comprehensive concept definition and present a workflow for user-driven data collection in both text and image domains. The concepts derived from knowledge graphs are defined interactively, providing an opportunity for personalization and ensuring that the concepts reflect the user's intentions. We test the retrieved concept datasets on two concept-based explainability methods, namely concept activation vectors (CAVs) and concept activation regions (CARs) (Crabbe and van der Schaar, 2022). We show that CAVs and CARs based on these empirical concept datasets provide robust and accurate explanations. Importantly, we also find good alignment between the models' representations of concepts and the structure of knowledge graphs, i.e., human representations. This supports our conclusion that knowledge graph-based concepts are relevant for XAI.

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.

Søren Vejlgaard Holm, Lars Kai Hansen, Martin Carsten Nielsen

The language technology moonshot moment of Generative Large Language Models (GLLMs) was not limited to English: These models brought a surge of technological applications, investments, and hype to low-resource languages as well. However, the capabilities of these models in languages such as Danish were, until recently, difficult to verify beyond qualitative demonstrations due to a lack of applicable evaluation corpora. We present a GLLM benchmark to evaluate \emph{Danoliteracy}, a measure of Danish language and cultural competency across eight diverse scenarios such as Danish citizenship tests and abstractive social media question answering. This limited-size benchmark was found to produce a robust ranking that correlates to human feedback at $ρ\sim 0.8$ with GPT-4 and Claude Opus models achieving the highest rankings. Analyzing these model results across scenarios, we find one strong underlying factor explaining $95\%$ of scenario performance variance for GLLMs in Danish, suggesting a $g$ factor of model consistency in language adaptation.

Lenka Tětková, Erik Schou Dreier, Robin Malm et al.

Much machine learning research progress is based on developing models and evaluating them on a benchmark dataset (e.g., ImageNet for images). However, applying such benchmark-successful methods to real-world data often does not work as expected. This is particularly the case for biological data where we expect variability at multiple time and spatial scales. In this work, we are using grain data and the goal is to detect diseases and damages. Pink fusarium, skinned grains, and other diseases and damages are key factors in setting the price of grains or excluding dangerous grains from food production. Apart from challenges stemming from differences of the data from the standard toy datasets, we also present challenges that need to be overcome when explaining deep learning models. For example, explainability methods have many hyperparameters that can give different results, and the ones published in the papers do not work on dissimilar images. Other challenges are more general: problems with visualization of the explanations and their comparison since the magnitudes of their values differ from method to method. An open fundamental question also is: How to evaluate explanations? It is a non-trivial task because the "ground truth" is usually missing or ill-defined. Also, human annotators may create what they think is an explanation of the task at hand, yet the machine learning model might solve it in a different and perhaps counter-intuitive way. We discuss several of these challenges and evaluate various post-hoc explainability methods on grain data. We focus on robustness, quality of explanations, and similarity to particular "ground truth" annotations made by experts. The goal is to find the methods that overall perform well and could be used in this challenging task. We hope the proposed pipeline will be used as a framework for evaluating explainability methods in specific use cases.

Lenka Tětková, Thea Brüsch, Teresa Karen Scheidt et al.

Current work on human-machine alignment aims at understanding machine-learned latent spaces and their correspondence to human representations. G{ä}rdenfors' conceptual spaces is a prominent framework for understanding human representations. Convexity of object regions in conceptual spaces is argued to promote generalizability, few-shot learning, and interpersonal alignment. Based on these insights, we investigate the notion of convexity of concept regions in machine-learned latent spaces. We develop a set of tools for measuring convexity in sampled data and evaluate emergent convexity in layered representations of state-of-the-art deep networks. We show that convexity is robust to basic re-parametrization and, hence, meaningful as a quality of machine-learned latent spaces. We find that approximate convexity is pervasive in neural representations in multiple application domains, including models of images, audio, human activity, text, and medical images. Generally, we observe that fine-tuning increases the convexity of label regions. We find evidence that pretraining convexity of class label regions predicts subsequent fine-tuning performance.

Raluca Alexandra Fetic, Mikkel Jordahn, Lucas Chaves Lima et al.

For a multilingual podcast streaming service, it is critical to be able to deliver relevant content to all users independent of language. Podcast content relevance is conventionally determined using various metadata sources. However, with the increasing quality of speech recognition in many languages, utilizing automatic transcriptions to provide better content recommendations becomes possible. In this work, we explore the robustness of a Latent Dirichlet Allocation topic model when applied to transcripts created by an automatic speech recognition engine. Specifically, we explore how increasing transcription noise influences topics obtained from transcriptions in Danish; a low resource language. First, we observe a baseline of cosine similarity scores between topic embeddings from automatic transcriptions and the descriptions of the podcasts written by the podcast creators. We then observe how the cosine similarities decrease as transcription noise increases and conclude that even when automatic speech recognition transcripts are erroneous, it is still possible to obtain high-quality topic embeddings from the transcriptions.

Petr Taborsky, Lars Kai Hansen

We take a geometrical viewpoint and present a unifying view on supervised deep learning with the Bregman divergence loss function - this entails frequent classification and prediction tasks. Motivated by simulations we suggest that there is principally no implicit bias of vanilla stochastic gradient descent training of deep models towards "simpler" functions. Instead, we show that good generalization may be instigated by bounded spectral products over layers leading to a novel geometric regularizer. It is revealed that in deep enough models such a regularizer enables both, extreme accuracy and generalization, to be reached. We associate popular regularization techniques like weight decay, drop out, batch normalization, and early stopping with this perspective. Backed up by theory we further demonstrate that "generalization by design" is practically possible and that good generalization may be encoded into the structure of the network. We design two such easy-to-use structural regularizers that insert an additional \textit{generalization layer} into a model architecture, one with a skip connection and another one with drop-out. We verify our theoretical results in experiments on various feedforward and convolutional architectures, including ResNets, and datasets (MNIST, CIFAR10, synthetic data). We believe this work opens up new avenues of research towards better generalizing architectures.

Jia Qian, Hiba Nassar, Lars Kai Hansen

\ac{fl} proposed a distributed \ac{ml} framework where every distributed worker owns a complete copy of global model and their own data. The training is occurred locally, which assures no direct transmission of training data. However, the recent work \citep{zhu2019deep} demonstrated that input data from a neural network may be reconstructed only using knowledge of gradients of that network, which completely breached the promise of \ac{fl} and sabotaged the user privacy. In this work, we aim to further explore the theoretical limits of reconstruction, speedup and stabilize the reconstruction procedure. We show that a single input may be reconstructed with the analytical form, regardless of network depth using a fully-connected neural network with one hidden node. Then we generalize this result to a gradient averaged over batches of size $B$. In this case, the full batch can be reconstructed if the number of hidden units exceeds $B$. For a \ac{cnn}, the number of required kernels in convolutional layers is decided by multiple factors, e.g., padding, kernel and stride size, etc. We require the number of kernels $h\geq (\frac{d}{d^{\prime}})^2C$, where we define $d$ as input width, $d^{\prime}$ as output width after convolutional layer, and $C$ as channel number of input. We validate our observation and demonstrate the improvements using bio-medical (fMRI, \ac{wbc}) and benchmark data (MNIST, Kuzushiji-MNIST, CIFAR100, ImageNet and face images).

Laura Rieger, Lars Kai Hansen

With machine learning models being used for more sensitive applications, we rely on interpretability methods to prove that no discriminating attributes were used for classification. A potential concern is the so-called "fair-washing" - manipulating a model such that the features used in reality are hidden and more innocuous features are shown to be important instead. In our work we present an effective defence against such adversarial attacks on neural networks. By a simple aggregation of multiple explanation methods, the network becomes robust against manipulation. This holds even when the attacker has exact knowledge of the model weights and the explanation methods used.

Jeppe Nørregaard, Lars Kai Hansen

In this paper we develop a principled, probabilistic, unified approach to non-standard classification tasks, such as semi-supervised, positive-unlabelled, multi-positive-unlabelled and noisy-label learning. We train a classifier on the given labels to predict the label-distribution. We then infer the underlying class-distributions by variationally optimizing a model of label-class transitions.

Christoffer Riis, Damian Konrad Kowalczyk, Lars Kai Hansen

Our global population contributes visual content on platforms like Instagram, attempting to express themselves and engage their audiences, at an unprecedented and increasing rate. In this paper, we revisit the popularity prediction on Instagram. We present a robust, efficient, and explainable baseline for population-based popularity prediction, achieving strong ranking performance. We employ the latest methods in computer vision to maximize the information extracted from the visual modality. We use transfer learning to extract visual semantics such as concepts, scenes, and objects, allowing a new level of scrutiny in an extensive, explainable ablation study. We inform feature selection towards a robust and scalable model, but also illustrate feature interactions, offering new directions for further inquiry in computational social science. Our strongest models inform a lower limit to population-based predictability of popularity on Instagram. The models are immediately applicable to social media monitoring and influencer identification.

Laura Rieger, Lars Kai Hansen

The adoption of machine learning in health care hinges on the transparency of the used algorithms, necessitating the need for explanation methods. However, despite a growing literature on explaining neural networks, no consensus has been reached on how to evaluate those explanation methods. We propose IROF, a new approach to evaluating explanation methods that circumvents the need for manual evaluation. Compared to other recent work, our approach requires several orders of magnitude less computational resources and no human input, making it accessible to lower resource groups and robust to human bias.

Jia Qian, Sayantan Sengupta, Lars Kai Hansen

Industry 4.0 becomes possible through the convergence between Operational and Information Technologies. All the requirements to realize the convergence is integrated on the Fog Platform. Fog Platform is introduced between the cloud server and edge devices when the unprecedented generation of data causes the burden of the cloud server, leading the ineligible latency. In this new paradigm, we divide the computation tasks and push it down to edge devices. Furthermore, local computing (at edge side) may improve privacy and trust. To address these problems, we present a new method, in which we decompose the data aggregation and processing, by dividing them between edge devices and fog nodes intelligently. We apply active learning on edge devices; and federated learning on the fog node which significantly reduces the data samples to train the model as well as the communication cost. To show the effectiveness of the proposed method, we implemented and evaluated its performance for an image classification task. In addition, we consider two settings: massively distributed and non-massively distributed and offer the corresponding solutions.

Jeppe Nørregaard, Lars Kai Hansen

We investigate probabilistic decoupling of labels supplied for training, from the underlying classes for prediction. Decoupling enables an inference scheme general enough to implement many classification problems, including supervised, semi-supervised, positive-unlabelled, noisy-label and suggests a general solution to the multi-positive-unlabelled learning problem. We test the method on the Fashion MNIST and 20 News Groups datasets for performance benchmarks, where we simulate noise, partial labelling etc.

Niels Bruun Ipsen, Lars Kai Hansen

How does missing data affect our ability to learn signal structures? It has been shown that learning signal structure in terms of principal components is dependent on the ratio of sample size and dimensionality and that a critical number of observations is needed before learning starts (Biehl and Mietzner, 1993). Here we generalize this analysis to include missing data. Probabilistic principal component analysis is regularly used for estimating signal structures in datasets with missing data. Our analytic result suggests that the effect of missing data is to effectively reduce signal-to-noise ratio rather than - as generally believed - to reduce sample size. The theory predicts a phase transition in the learning curves and this is indeed found both in simulation data and in real datasets.

Laura Rieger, Lars Kai Hansen

Despite a growing literature on explaining neural networks, no consensus has been reached on how to explain a neural network decision or how to evaluate an explanation. Our contributions in this paper are twofold. First, we investigate schemes to combine explanation methods and reduce model uncertainty to obtain a single aggregated explanation. We provide evidence that the aggregation is better at identifying important features, than on individual methods. Adversarial attacks on explanations is a recent active research topic. As our second contribution, we present evidence that aggregate explanations are much more robust to attacks than individual explanation methods.

Simon Kamronn, Andreas Trier Poulsen, Lars Kai Hansen

Correlated component analysis as proposed by Dmochowski et al. (2012) is a tool for investigating brain process similarity in the responses to multiple views of a given stimulus. Correlated components are identified under the assumption that the involved spatial networks are identical. Here we propose a hierarchical probabilistic model that can infer the level of universality in such multi-view data, from completely unrelated representations, corresponding to canonical correlation analysis, to identical representations as in correlated component analysis. This new model, which we denote Bayesian correlated component analysis, evaluates favourably against three relevant algorithms in simulated data. A well-established benchmark EEG dataset is used to further validate the new model and infer the variability of spatial representations across multiple subjects.

Georgios Arvanitidis, Lars Kai Hansen, Søren Hauberg

Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator imply that the latent space gives a distorted view of the input space. Under mild conditions, we show that this distortion can be characterized by a stochastic Riemannian metric, and demonstrate that distances and interpolants are significantly improved under this metric. This in turn improves probability distributions, sampling algorithms and clustering in the latent space. Our geometric analysis further reveals that current generators provide poor variance estimates and we propose a new generator architecture with vastly improved variance estimates. Results are demonstrated on convolutional and fully connected variational autoencoders, but the formalism easily generalize to other deep generative models.

Albert Vilamala, Kristoffer Hougaard Madsen, Lars Kai Hansen

Functional Magnetic Resonance Imaging (fMRI) relies on multi-step data processing pipelines to accurately determine brain activity; among them, the crucial step of spatial smoothing. These pipelines are commonly suboptimal, given the local optimisation strategy they use, treating each step in isolation. With the advent of new tools for deep learning, recent work has proposed to turn these pipelines into end-to-end learning networks. This change of paradigm offers new avenues to improvement as it allows for a global optimisation. The current work aims at benefitting from this paradigm shift by defining a smoothing step as a layer in these networks able to adaptively modulate the degree of smoothing required by each brain volume to better accomplish a given data analysis task. The viability is evaluated on real fMRI data where subjects did alternate between left and right finger tapping tasks.

Albert Vilamala, Kristoffer Hougaard Madsen, Lars Kai Hansen

The study of neurocognitive tasks requiring accurate localisation of activity often rely on functional Magnetic Resonance Imaging, a widely adopted technique that makes use of a pipeline of data processing modules, each involving a variety of parameters. These parameters are frequently set according to the local goal of each specific module, not accounting for the rest of the pipeline. Given recent success of neural network research in many different domains, we propose to convert the whole data pipeline into a deep neural network, where the parameters involved are jointly optimised by the network to best serve a common global goal. As a proof of concept, we develop a module able to adaptively apply the most suitable spatial smoothing to every brain volume for each specific neuroimaging task, and we validate its results in a standard brain decoding experiment.

Georgios Arvanitidis, Lars Kai Hansen, Søren Hauberg

The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing (Riemannian) metric that favors regions of high local density. The resulting locally adaptive normal distribution (LAND) is a generalization of the normal distribution to the "manifold" setting, where data is assumed to lie near a potentially low-dimensional manifold embedded in $\mathbb{R}^D$. The LAND is parametric, depending only on a mean and a covariance, and is the maximum entropy distribution under the given metric. The underlying metric is, however, non-parametric. We develop a maximum likelihood algorithm to infer the distribution parameters that relies on a combination of gradient descent and Monte Carlo integration. We further extend the LAND to mixture models, and provide the corresponding EM algorithm. We demonstrate the efficiency of the LAND to fit non-trivial probability distributions over both synthetic data, and EEG measurements of human sleep.

Andreas Trier Poulsen, Simon Kamronn, Jacek Dmochowski et al.

We performed simultaneous recordings of electroencephalography (EEG) from multiple students in a classroom, and measured the inter-subject correlation (ISC) of activity evoked by a common video stimulus. The neural reliability, as quantified by ISC, has been linked to engagement and attentional modulation in earlier studies that used high-grade equipment in laboratory settings. Here we reproduce many of the results from these studies using portable low-cost equipment, focusing on the robustness of using ISC for subjects experiencing naturalistic stimuli. The present data shows that stimulus-evoked neural responses, known to be modulated by attention, can be tracked in for groups of students with synchronized EEG acquisition. This is a step towards real-time inference of engagement in the classroom.

Søren Hauberg, Oren Freifeld, Anders Boesen Lindbo Larsen et al.

Data augmentation is a key element in training high-dimensional models. In this approach, one synthesizes new observations by applying pre-specified transformations to the original training data; e.g.~new images are formed by rotating old ones. Current augmentation schemes, however, rely on manual specification of the applied transformations, making data augmentation an implicit form of feature engineering. With an eye towards true end-to-end learning, we suggest learning the applied transformations on a per-class basis. Particularly, we align image pairs within each class under the assumption that the spatial transformation between images belongs to a large class of diffeomorphisms. We then learn a class-specific probabilistic generative models of the transformations in a Riemannian submanifold of the Lie group of diffeomorphisms. We demonstrate significant performance improvements in training deep neural nets over manually-specified augmentation schemes. Our code and augmented datasets are available online.

Michael Riis Andersen, Aki Vehtari, Ole Winther et al.

In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the solution in both space and time by imposing a transformed Gaussian process on the spike-and-slab probabilities. An expectation propagation (EP) algorithm for posterior inference under the proposed model is derived. For large scale problems, the standard EP algorithm can be prohibitively slow. We therefore introduce three different approximation schemes to reduce the computational complexity. Finally, we demonstrate the proposed model using numerical experiments based on both synthetic and real data sets.

Michael Riis Andersen, Ole Winther, Lars Kai Hansen

We are interested in solving the multiple measurement vector (MMV) problem for instances, where the underlying sparsity pattern exhibit spatio-temporal structure motivated by the electroencephalogram (EEG) source localization problem. We propose a probabilistic model that takes this structure into account by generalizing the structured spike and slab prior and the associated Expectation Propagation inference scheme. Based on numerical experiments, we demonstrate the viability of the model and the approximate inference scheme.

Rasmus Troelsgård, Bjørn Sand Jensen, Lars Kai Hansen

Calculating similarities between objects defined by many heterogeneous data modalities is an important challenge in many multimedia applications. We use a multi-modal topic model as a basis for defining such a similarity between objects. We propose to compare the resulting similarities from different model realizations using the non-parametric Mantel test. The approach is evaluated on a music dataset.

Bjarne Ørum Fruergaard, Toke Jansen Hansen, Lars Kai Hansen

In online advertising, display ads are increasingly being placed based on real-time auctions where the advertiser who wins gets to serve the ad. This is called real-time bidding (RTB). In RTB, auctions have very tight time constraints on the order of 100ms. Therefore mechanisms for bidding intelligently such as clickthrough rate prediction need to be sufficiently fast. In this work, we propose to use dimensionality reduction of the user-website interaction graph in order to produce simplified features of users and websites that can be used as predictors of clickthrough rate. We demonstrate that the Infinite Relational Model (IRM) as a dimensionality reduction offers comparable predictive performance to conventional dimensionality reduction schemes, while achieving the most economical usage of features and fastest computations at run-time. For applications such as real-time bidding, where fast database I/O and few computations are key to success, we thus recommend using IRM based features as predictors to exploit the recommender effects from bipartite graphs.

Jerónimo Arenas-García, Kaare Brandt Petersen, Gustavo Camps-Valls et al.

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever higher resolution, and problems involving multimodal data sources become more common. A plethora of feature extraction methods are available in the literature collectively grouped under the field of Multivariate Analysis (MVA). This paper provides a uniform treatment of several methods: Principal Component Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis (CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions derived by means of the theory of reproducing kernel Hilbert spaces. We also review their connections to other methods for classification and statistical dependence estimation, and introduce some recent developments to deal with the extreme cases of large-scale and low-sized problems. To illustrate the wide applicability of these methods in both classification and regression problems, we analyze their performance in a benchmark of publicly available data sets, and pay special attention to specific real applications involving audio processing for music genre prediction and hyperspectral satellite images for Earth and climate monitoring.

Arkadiusz Stopczynski, Carsten Stahlhut, Jakob Eg Larsen et al.

Combining low cost wireless EEG sensors with smartphones offers novel opportunities for mobile brain imaging in an everyday context. We present a framework for building multi-platform, portable EEG applications with real-time 3D source reconstruction. The system - Smartphone Brain Scanner - combines an off-the-shelf neuroheadset or EEG cap with a smartphone or tablet, and as such represents the first fully mobile system for real-time 3D EEG imaging. We discuss the benefits and challenges of a fully portable system, including technical limitations as well as real-time reconstruction of 3D images of brain activity. We present examples of the brain activity captured in a simple experiment involving imagined finger tapping, showing that the acquired signal in a relevant brain region is similar to that obtained with standard EEG lab equipment. Although the quality of the signal in a mobile solution using a off-the-shelf consumer neuroheadset is lower compared to that obtained using high density standard EEG equipment, we propose that mobile application development may offset the disadvantages and provide completely new opportunities for neuroimaging in natural settings.