arXiv subjects

Dirk Ostwald

Publications and source records attributed to Dirk Ostwald.

4 recordsLinked to original sources

arXiv2026

On Agentic Behavioral Modeling

Integrating theoretical neuroscience, decision theory, and probabilistic inference offers a promising route to understanding human cognition, yet concrete methodological bridges between agentic AI models and behavioral data analysis remain formally underdeveloped. We advance this synthesis under the framework of agentic behavioral modeling (ABM), which treats artificial agents as latent, generative hypotheses about cognitive mechanisms and evaluates them by their statistical adequacy in explaining human behavior. After outlining its conceptual foundations, we apply the framework to two minimal laboratory paradigms: a binary perceptual contrast-discrimination task and a symmetric two-armed bandit learning task. We formalize each task-agent-data system as a joint probability model, derive explicit conditional log-likelihoods for behavioral inference, validate different model variants using model and parameter recovery simulations, and evaluate them in light of empirical data. Using these minimal examples, we provide an agent-centric interpretation of the psychometric function, derive optimal policies for both tasks, and show the equivalence between Rescorla-Wagner learning and Bayesian inference in symmetric bandits. More broadly, this work may serve as a conceptual and practical foundation for applying ABM to cognitive behavioral science.

q-bio.NC↗

arXiv2021

Random field theory-based p-values: A review of the SPM implementation

P-values and null-hypothesis significance testing are popular data-analytical tools in functional neuroimaging. Sparked by the analysis of resting-state fMRI data, there has been a resurgence of interest in the validity of some of the p-values evaluated with the widely used software SPM in recent years. The default parametric p-values reported in SPM are based on the application of results from random field theory to statistical parametric maps, a framework commonly referred to as RFT. While RFT was established two decades ago and has since been applied in a plethora of fMRI studies, there does not exist a unified documentation of the mathematical and computational underpinnings of RFT as implemented in current versions of SPM. Here, we provide such a documentation with the aim of contributing to contemporary efforts towards higher levels of computational transparency in functional neuroimaging.

q-bio.QM↗

arXiv2021

An induction proof of the backpropagation algorithm in matrix notation

Backpropagation (BP) is a core component of the contemporary deep learning incarnation of neural networks. Briefly, BP is an algorithm that exploits the computational architecture of neural networks to efficiently evaluate the gradient of a cost function during neural network parameter optimization. The validity of BP rests on the application of a multivariate chain rule to the computational architecture of neural networks and their associated objective functions. Introductions to deep learning theory commonly present the computational architecture of neural networks in matrix form, but eschew a parallel formulation and justification of BP in the framework of matrix differential calculus. This entails several drawbacks for the theory and didactics of deep learning. In this work, we overcome these limitations by providing a full induction proof of the BP algorithm in matrix notation. Specifically, we situate the BP algorithm in the framework of matrix differential calculus, encompass affine-linear potential functions, prove the validity of the BP algorithm in inductive form, and exemplify the implementation of the matrix form BP algorithm in computer code.

stat.ML↗

arXiv2017

Computing Integrated Information

Integrated information theory (IIT) has established itself as one of the leading theories for the study of consciousness. IIT essentially proposes that quantitative consciousness is identical to maximally integrated conceptual information, quantified by a measure called $Φ^{max}$, and that phenomenological experience corresponds to the associated set of maximally irreducible cause-effect repertoires of a physical system being in a certain state. However, in order to ultimately apply the theory to experimental data, a sufficiently general formulation is needed. With the current work, we provide this general formulation, which comprehensively and parsimoniously expresses $Φ^{max}$ in the language of probabilistic models. Here, the stochastic process describing a system under scrutiny corresponds to a first-order time-invariant Markov process, and all necessary mathematical operations for the definition of $Φ^{max}$ are fully specified by a system's joint probability distribution over two adjacent points in discrete time. We present a detailed constructive rule for the decomposition of a system into two disjoint subsystems based on flexible marginalization and factorization of this joint distribution. Furthermore, we suspend the approach of interventional calculus based on system perturbations, which allows us to omit undefined conditional distributions and virtualization. We validate our formulation in a previously established discrete example system, in which we furthermore address the previously unexplored theoretical issue of quale underdetermination due to non-uniqueness of maximally irreducible cause-effect repertoires, which in turn also entails the sensitivity of $Φ^{max}$ to the shape of the conceptual structure in qualia space. In constructive spirit, we propose several modifications of the framework in order to address some of these issues.

q-bio.NC↗