arXiv subjects

Laurenz Wiskott

Publications and source records attributed to Laurenz Wiskott.

At least 19 recordsLinked to original sources

arXiv2026

Is Hierarchical Quantization Essential for Optimal Reconstruction?

Vector-quantized variational autoencoders (VQ-VAEs) are central to models that rely on high reconstruction fidelity, from neural compression to generative pipelines. Hierarchical extensions, such as VQ-VAE2, are often credited with superior reconstruction performance because they split global and local features across multiple levels. However, since higher levels derive all their information from lower levels, they should not carry additional reconstructive content beyond what the lower-level already encodes. Combined with recent advances in training objectives and quantization mechanisms, this leads us to ask whether a single-level VQ-VAE, with matched representational budget and no codebook collapse, can equal the reconstruction fidelity of its hierarchical counterpart. Although the multi-scale structure of hierarchical models may improve perceptual quality in downstream tasks, the effect of hierarchy on reconstruction accuracy, isolated from codebook utilization and overall representational capacity, remains empirically underexamined. We revisit this question by comparing a two-level VQ-VAE and a capacity-matched single-level model on high-resolution ImageNet images. Consistent with prior observations, we confirm that inadequate codebook utilization limits single-level VQ-VAEs and that overly high-dimensional embeddings destabilize quantization and increase codebook collapse. We show that lightweight interventions such as initialization from data, periodic reset of inactive codebook vectors, and systematic tuning of codebook hyperparameters significantly reduce collapse. Our results demonstrate that when representational budgets are matched, and codebook collapse is mitigated, single-level VQ-VAEs can match the reconstruction fidelity of hierarchical variants, challenging the assumption that hierarchical quantization is inherently superior for high-quality reconstructions.

cs.CV↗

arXiv2026

Probing Length Generalization in Mamba via Image Reconstruction

Mamba has attracted widespread interest as a general-purpose sequence model due to its low computational complexity and competitive performance relative to transformers. However, its performance can degrade when inference sequence lengths exceed those seen during training. We study this phenomenon using a controlled vision task in which Mamba reconstructs images from sequences of image patches. By analyzing reconstructions at different stages of sequence processing, we reveal that Mamba qualitatively adapts its behavior to the distribution of sequence lengths encountered during training, resulting in strategies that fail to generalize beyond this range. To support our analysis, we introduce a length-adaptive variant of Mamba that improves performance across training sequence lengths. Our results provide an intuitive perspective on length generalization in Mamba and suggest directions for improving the architecture.

cs.LG↗

arXiv2025

Effects of Distributional Biases on Gradient-Based Causal Discovery in the Bivariate Categorical Case

Gradient-based causal discovery shows great potential for deducing causal structure from data in an efficient and scalable way. Those approaches however can be susceptible to distributional biases in the data they are trained on. We identify two such biases: Marginal Distribution Asymmetry, where differences in entropy skew causal learning toward certain factorizations, and Marginal Distribution Shift Asymmetry, where repeated interventions cause faster shifts in some variables than in others. For the bivariate categorical setup with Dirichlet priors, we illustrate how these biases can occur even in controlled synthetic data. To examine their impact on gradient-based methods, we employ two simple models that derive causal factorizations by learning marginal or conditional data distributions - a common strategy in gradient-based causal discovery. We demonstrate how these models can be susceptible to both biases. We additionally show how the biases can be controlled. An empirical evaluation of two related, existing approaches indicates that eliminating competition between possible causal factorizations can make models robust to the presented biases.

cs.LG↗

arXiv2025

The Course Difficulty Analysis Cookbook

Curriculum analytics (CA) studies curriculum structure and student data to ensure the quality of educational programs. An essential aspect is studying course properties, which involves assigning each course a representative difficulty value. This is critical for several aspects of CA, such as quality control (e.g., monitoring variations over time), course comparisons (e.g., articulation), and course recommendation (e.g., advising). Measuring course difficulty requires careful consideration of multiple factors: First, when difficulty measures are sensitive to the performance level of enrolled students, it can bias interpretations by overlooking student diversity. By assessing difficulty independently of enrolled students' performances, we can reduce the risk of bias and enable fair, representative assessments of difficulty. Second, from a measurement theoretic perspective, the measurement must be reliable and valid to provide a robust basis for subsequent analyses. Third, difficulty measures should account for covariates, such as the characteristics of individual students within a diverse populations (e.g., transfer status). In recent years, various notions of difficulty have been proposed. This paper provides the first comprehensive review and comparison of existing approaches for assessing course difficulty based on grade point averages and latent trait modeling. It further offers a hands-on tutorial on model selection, assumption checking, and practical CA applications. These applications include monitoring course difficulty over time and detecting courses with disparate outcomes between distinct groups of students (e.g., dropouts vs. graduates), ultimately aiming to promote high-quality, fair, and equitable learning experiences. To support further research and application, we provide an open-source software package and artificial datasets, facilitating reproducibility and adoption.

cs.CY↗

arXiv2025

Understanding Transformer-based Vision Models through Inversion

Understanding the mechanisms underlying deep neural networks remains a fundamental challenge in machine learning and computer vision. One promising, yet only preliminarily explored approach, is feature inversion, which attempts to reconstruct images from intermediate representations using trained inverse neural networks. In this study, we revisit feature inversion, introducing a novel, modular variation that enables significantly more efficient application of the technique. We demonstrate how our method can be systematically applied to the large-scale transformer-based vision models, Detection Transformer and Vision Transformer, and how reconstructed images can be qualitatively interpreted in a meaningful way. We further quantitatively evaluate our method, thereby uncovering underlying mechanisms of representing image features that emerge in the two transformer architectures. Our analysis reveals key insights into how these models encode contextual shape and image details, how their layers correlate, and their robustness against color perturbations. These findings contribute to a deeper understanding of transformer-based vision models and their internal representations. The code for reproducing our experiments is available at github.com/wiskott-lab/inverse-tvm.

cs.CV↗

arXiv2025

Object-centric Denoising Diffusion Models for Physical Reasoning

Reasoning about the trajectories of multiple, interacting objects is integral to physical reasoning tasks in machine learning. This involves conditions imposed on the objects at different time steps, for instance initial states or desired goal states. Existing approaches in physical reasoning generally rely on autoregressive modeling, which can only be conditioned on initial states, but not on later states. In fields such as planning for reinforcement learning, similar challenges are being addressed with denoising diffusion models. In this work, we propose an object-centric denoising diffusion model architecture for physical reasoning that is translation equivariant over time, permutation equivariant over objects, and can be conditioned on arbitrary time steps for arbitrary objects. We demonstrate how this model can solve tasks with multiple conditions and examine its performance when changing object numbers and trajectory lengths during inference.

cs.LG↗

arXiv2025

Slow Feature Analysis on Markov Chains from Goal-Directed Behavior

Slow Feature Analysis is a unsupervised representation learning method that extracts slowly varying features from temporal data and can be used as a basis for subsequent reinforcement learning. Often, the behavior that generates the data on which the representation is learned is assumed to be a uniform random walk. Less research has focused on using samples generated by goal-directed behavior, as commonly the case in a reinforcement learning setting, to learn a representation. In a spatial setting, goal-directed behavior typically leads to significant differences in state occupancy between states that are close to a reward location and far from a reward location. Through the perspective of optimal slow features on ergodic Markov chains, this work investigates the effects of these differences on value-function approximation in an idealized setting. Furthermore, three correction routes, which can potentially alleviate detrimental scaling effects, are evaluated and discussed. In addition, the special case of goal-averse behavior is considered.

cs.LG↗

arXiv2025

Slow Feature Analysis as Variational Inference Objective

This work presents a novel probabilistic interpretation of Slow Feature Analysis (SFA) through the lens of variational inference. Unlike prior formulations that recover linear SFA from Gaussian state-space models with linear emissions, this approach relaxes the key constraint of linearity. While it does not lead to full equivalence to non-linear SFA, it recasts the classical slowness objective in a variational framework. Specifically, it allows the slowness objective to be interpreted as a regularizer to a reconstruction loss. Furthermore, we provide arguments, why -- from the perspective of slowness optimization -- the reconstruction loss takes on the role of the constraints that ensure informativeness in SFA. We conclude with a discussion of potential new research directions.

cs.LG↗

arXiv2025

What is the relation between Slow Feature Analysis and the Successor Representation?

Slow feature analysis (SFA) is an unsupervised method for extracting representations from time series data. The successor representation (SR) is a method for representing states in a Markov decision process (MDP) based on transition statistics. While SFA and SR stem from distinct areas of machine learning, they share important properties, both in terms of their mathematics and the types of information they are sensitive to. This work studies their connection along these two axes. In particular, both SFA and SR are explored analytically, and in the setting of a one-hot encoded MDP, a formal equivalence is demonstrated in terms of the grid-like representations that occur as solutions/eigenvectors. Moreover, it is shown that the columns of the matrices involved in SFA contain place-like representations, which are formally distinct from place-cell models that have already been defined using SFA.

cs.LG↗

arXiv2024

Putting the Iterative Training of Decision Trees to the Test on a Real-World Robotic Task

In previous research, we developed methods to train decision trees (DT) as agents for reinforcement learning tasks, based on deep reinforcement learning (DRL) networks. The samples from which the DTs are built, use the environment's state as features and the corresponding action as label. To solve the nontrivial task of selecting samples, which on one hand reflect the DRL agent's capabilities of choosing the right action but on the other hand also cover enough state space to generalize well, we developed an algorithm to iteratively train DTs. In this short paper, we apply this algorithm to a real-world implementation of a robotic task for the first time. Real-world tasks pose additional challenges compared to simulations, such as noise and delays. The task consists of a physical pendulum attached to a cart, which moves on a linear track. By movements to the left and to the right, the pendulum is to be swung in the upright position and balanced in the unstable equilibrium. Our results demonstrate the applicability of the algorithm to real-world tasks by generating a DT whose performance matches the performance of the DRL agent, while consisting of fewer parameters. This research could be a starting point for distilling DTs from DRL agents to obtain transparent, lightweight models for real-world reinforcement learning tasks.

cs.LG↗

arXiv2024

Exploring the limits of Hierarchical World Models in Reinforcement Learning

Hierarchical model-based reinforcement learning (HMBRL) aims to combine the benefits of better sample efficiency of model based reinforcement learning (MBRL) with the abstraction capability of hierarchical reinforcement learning (HRL) to solve complex tasks efficiently. While HMBRL has great potential, it still lacks wide adoption. In this work we describe a novel HMBRL framework and evaluate it thoroughly. To complement the multi-layered decision making idiom characteristic for HRL, we construct hierarchical world models that simulate environment dynamics at various levels of temporal abstraction. These models are used to train a stack of agents that communicate in a top-down manner by proposing goals to their subordinate agents. A significant focus of this study is the exploration of a static and environment agnostic temporal abstraction, which allows concurrent training of models and agents throughout the hierarchy. Unlike most goal-conditioned H(MB)RL approaches, it also leads to comparatively low dimensional abstract actions. Although our HMBRL approach did not outperform traditional methods in terms of final episode returns, it successfully facilitated decision making across two levels of abstraction using compact, low dimensional abstract actions. A central challenge in enhancing our method's performance, as uncovered through comprehensive experimentation, is model exploitation on the abstract level of our world model stack. We provide an in depth examination of this issue, discussing its implications for the field and suggesting directions for future research to overcome this challenge. By sharing these findings, we aim to contribute to the broader discourse on refining HMBRL methodologies and to assist in the development of more effective autonomous learning systems for complex decision-making environments.

cs.LG↗

arXiv2024

Gaining Insights into Group-Level Course Difficulty via Differential Course Functioning

Curriculum Analytics (CA) studies curriculum structure and student data to ensure the quality of educational programs. One desirable property of courses within curricula is that they are not unexpectedly more difficult for students of different backgrounds. While prior work points to likely variations in course difficulty across student groups, robust methodologies for capturing such variations are scarce, and existing approaches do not adequately decouple course-specific difficulty from students' general performance levels. The present study introduces Differential Course Functioning (DCF) as an Item Response Theory (IRT)-based CA methodology. DCF controls for student performance levels and examines whether significant differences exist in how distinct student groups succeed in a given course. Leveraging data from over 20,000 students at a large public university, we demonstrate DCF's ability to detect inequities in undergraduate course difficulty across student groups described by grade achievement. We compare major pairs with high co-enrollment and transfer students to their non-transfer peers. For the former, our findings suggest a link between DCF effect sizes and the alignment of course content to student home department motivating interventions targeted towards improving course preparedness. For the latter, results suggest minor variations in course-specific difficulty between transfer and non-transfer students. While this is desirable, it also suggests that interventions targeted toward mitigating grade achievement gaps in transfer students should encompass comprehensive support beyond enhancing preparedness for individual courses. By providing more nuanced and equitable assessments of academic performance and difficulties experienced by diverse student populations, DCF could support policymakers, course articulation officers, and student advisors.

cs.CY↗

arXiv2024

ProtoP-OD: Explainable Object Detection with Prototypical Parts

Interpretation and visualization of the behavior of detection transformers tends to highlight the locations in the image that the model attends to, but it provides limited insight into the \emph{semantics} that the model is focusing on. This paper introduces an extension to detection transformers that constructs prototypical local features and uses them in object detection. These custom features, which we call prototypical parts, are designed to be mutually exclusive and align with the classifications of the model. The proposed extension consists of a bottleneck module, the prototype neck, that computes a discretized representation of prototype activations and a new loss term that matches prototypes to object classes. This setup leads to interpretable representations in the prototype neck, allowing visual inspection of the image content perceived by the model and a better understanding of the model's reliability. We show experimentally that our method incurs only a limited performance penalty, and we provide examples that demonstrate the quality of the explanations provided by our method, which we argue outweighs the performance penalty.

cs.CV↗

arXiv2024

Interpretable Brain-Inspired Representations Improve RL Performance on Visual Navigation Tasks

Visual navigation requires a whole range of capabilities. A crucial one of these is the ability of an agent to determine its own location and heading in an environment. Prior works commonly assume this information as given, or use methods which lack a suitable inductive bias and accumulate error over time. In this work, we show how the method of slow feature analysis (SFA), inspired by neuroscience research, overcomes both limitations by generating interpretable representations of visual data that encode location and heading of an agent. We employ SFA in a modern reinforcement learning context, analyse and compare representations and illustrate where hierarchical SFA can outperform other feature extractors on navigation tasks.

cs.LG↗

arXiv2024

Classification and Reconstruction Processes in Deep Predictive Coding Networks: Antagonists or Allies?

Predictive coding-inspired deep networks for visual computing integrate classification and reconstruction processes in shared intermediate layers. Although synergy between these processes is commonly assumed, it has yet to be convincingly demonstrated. In this study, we take a critical look at how classifying and reconstructing interact in deep learning architectures. Our approach utilizes a purposefully designed family of model architectures reminiscent of autoencoders, each equipped with an encoder, a decoder, and a classification head featuring varying modules and complexities. We meticulously analyze the extent to which classification- and reconstruction-driven information can seamlessly coexist within the shared latent layer of the model architectures. Our findings underscore a significant challenge: Classification-driven information diminishes reconstruction-driven information in intermediate layers' shared representations and vice versa. While expanding the shared representation's dimensions or increasing the network's complexity can alleviate this trade-off effect, our results challenge prevailing assumptions in predictive coding and offer guidance for future iterations of predictive coding concepts in deep networks.

cs.LG↗

arXiv2023

Improving Reinforcement Learning Efficiency with Auxiliary Tasks in Non-Visual Environments: A Comparison

Real-world reinforcement learning (RL) environments, whether in robotics or industrial settings, often involve non-visual observations and require not only efficient but also reliable and thus interpretable and flexible RL approaches. To improve efficiency, agents that perform state representation learning with auxiliary tasks have been widely studied in visual observation contexts. However, for real-world problems, dedicated representation learning modules that are decoupled from RL agents are more suited to meet requirements. This study compares common auxiliary tasks based on, to the best of our knowledge, the only decoupled representation learning method for low-dimensional non-visual observations. We evaluate potential improvements in sample efficiency and returns for environments ranging from a simple pendulum to a complex simulated robotics task. Our findings show that representation learning with auxiliary tasks only provides performance gains in sufficiently complex environments and that learning environment dynamics is preferable to predicting rewards. These insights can inform future development of interpretable representation learning approaches for non-visual observations and advance the use of RL solutions in real-world scenarios.

cs.LG↗

arXiv2022

A Tutorial on the Spectral Theory of Markov Chains

Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically. This tutorial provides an in-depth introduction to Markov chains, and explores their connection to graphs and random walks. We utilize tools from linear algebra and graph theory to describe the transition matrices of different types of Markov chains, with a particular focus on exploring properties of the eigenvalues and eigenvectors corresponding to these matrices. The results presented are relevant to a number of methods in machine learning and data mining, which we describe at various stages. Rather than being a novel academic study in its own right, this text presents a collection of known results, together with some new concepts. Moreover, the tutorial focuses on offering intuition to readers rather than formal understanding, and only assumes basic exposure to concepts from linear algebra and probability theory. It is therefore accessible to students and researchers from a wide variety of disciplines.

cs.LG↗

arXiv2021

A model of semantic completion in generative episodic memory

Many different studies have suggested that episodic memory is a generative process, but most computational models adopt a storage view. In this work, we propose a computational model for generative episodic memory. It is based on the central hypothesis that the hippocampus stores and retrieves selected aspects of an episode as a memory trace, which is necessarily incomplete. At recall, the neocortex reasonably fills in the missing information based on general semantic information in a process we call semantic completion. As episodes we use images of digits (MNIST) augmented by different backgrounds representing context. Our model is based on a VQ-VAE which generates a compressed latent representation in form of an index matrix, which still has some spatial resolution. We assume that attention selects some part of the index matrix while others are discarded, this then represents the gist of the episode and is stored as a memory trace. At recall the missing parts are filled in by a PixelCNN, modeling semantic completion, and the completed index matrix is then decoded into a full image by the VQ-VAE. The model is able to complete missing parts of a memory trace in a semantically plausible way up to the point where it can generate plausible images from scratch. Due to the combinatorics in the index matrix, the model generalizes well to images not trained on. Compression as well as semantic completion contribute to a strong reduction in memory requirements and robustness to noise. Finally we also model an episodic memory experiment and can reproduce that semantically congruent contexts are always recalled better than incongruent ones, high attention levels improve memory accuracy in both cases, and contexts that are not remembered correctly are more often remembered semantically congruently than completely wrong.

q-bio.NC↗