arXiv subjects

Jakob Jordan

Publications and source records attributed to Jakob Jordan.

At least 19 recordsLinked to original sources

arXiv2026

Neuromorphic architectures as numerical solvers for computational neuroscience

Neuromorphic computing is closely associated with spiking neuronal networks. However, an alternative class of so-called "rate-based" models arising from computational neuroscience and machine learning forgoes spiking interactions and instead relies on continuous coupling between neurons. Existing neuromorphic implementations designed around spike-based interactions are not well-suited for emulating such models. Here view the distributed simulation of these models as message-passing algorithms on parallel hardware. Leveraging prior art in numerical algorithms and distributed simulation, we outline steps that enable the design of efficient digital neuromorphic accelerators for non-spiking neuronal models. In particular, we show that multi-bit packets, rather than spikes, are the most efficient communication strategy in packet-switched networks and that compared to basic numerical integration methods, higher-order differential equation solvers decrease both computation and communication costs while achieving lower numerical error, but that these benefits are ultimately limited by arithmetic precision. Using our proposed design principles, we convert an existing neuromorphic architecture into a distributed numerical solver - a spikeless neuromorphic system - for continuously-coupled neuronal models. We thereby demonstrate that our theoretical considerations indeed translate into practical advantages, namely reduced energy consumption and delay.

cs.AR↗

arXiv2026

Dendritic structure enables powerful plasticity

Over the past decades, it has become increasingly clear that the complex morphology of cortical neurons is more than just a quirk of evolution, and that dendritic compartments serve as computational elements in their own right, rather than just providing connections between nerve cell bodies. While most computational studies discuss the enhanced representational capabilities of multi-compartment models as compared to point neurons, we focus here on the implications of neuronal morphology for synaptic plasticity. We argue that the ability of single neurons to simultaneously encode multiple pieces of information gives synapses local access to more than just the classical Hebbian pre- and postsynaptic terms, and with much greater specificity and reaction speed than permitted by other globally modulated factors. Based on a comparative review of recent dendritic learning models, we show how such neuronal compartmentalization can provide synapses with the means for calculating various forms of error signals, which in turn give rise to powerful real-time and fully local instantiations of deep learning through gradient descent. Implemented within cortical microcircuits capable of propagating and manipulating these errors, compartmentalized neurons thus ultimately enable the learning of far more complex tasks than are achievable by globally modulated Hebbian plasticity alone.

q-bio.NC↗

arXiv2026

ILPU: Iterative Laplace-Based Phase Unwrapping via Bi-Level Optimization

Phase unwrapping is an essential preprocessing step for phase-based MRI applications, including susceptibility mapping, field mapping, thermometry, and MR elastography. We present Iterative Laplace-Based Phase Unwrapping (ILPU), a bi-level optimization algorithm. In this method, a lower-level solver recovers a continuous phase increment from an incremental Poisson equation using the discrete cosine transform (DCT), while an upper-level solver refines an integer offset map through quality-guided spatial regularization and a restricted local search. This coupling enables robust unwrapping in low-SNR regions through adaptive smoothness penalties and quality-weighted regularization. We evaluated ILPU on 2D and 3D brain MRI phase images against manually unwrapped reference data, using standard Laplace unwrapping, Flynn, and SEGUE as comparison methods. In 2D, ILPU achieves accuracy comparable to SEGUE. In 3D, ILPU attains a relative error of 2.12% compared with 67.59% for SEGUE and 81.02% for Laplace, demonstrating a clear advantage in volumetric unwrapping. The algorithm has O(N log N) complexity per iteration through DCT-based Laplacian estimation and is numerically faster than both Flynn and SEGUE while preserving superior accuracy. These results indicate that the bi-level optimization framework provides a robust and computationally efficient solution for phase unwrapping in MRI.

math.OC↗

arXiv2025

In Vivo Quantification of Glioma-Induced Solid Stress Using MR Elastography and Deformable Image Registration

Solid stress is increasingly being recognized as a key driver of tumor progression and aggressiveness, yet it has not been directly measured in patients so far. Here, we combine multifrequency magnetic resonance elastography with 3D magnetic resonance imaging (MRI)-based diffeomorphic deformable image registration network analysis to noninvasively quantify glioma-induced solid stress. In both a mouse model and patients, we identified spatially heterogeneous deformation patterns extending well beyond tumor margins. While deformation magnitude was not found to correlate with tumor size or clinical outcome, excess solid stress - defined as the product of peritumoral volumetric strain and stiffness differential between unaffected brain and peritumoral tissue - was inversely associated with patient survival, highlighting its potential as a quantitative, imaging-derived biomarker. To our knowledge, this study provides the first direct quantification of mechanical stress in patients with glioma.

physics.med-ph↗

arXiv2024

Time-Harmonic Optical Flow with Applications in Elastography

In this paper, we propose mathematical models for reconstructing the optical flow in time-harmonic elastography. In this image acquisition technique, the object undergoes a special time-harmonic oscillation with known frequency so that only the spatially varying amplitude of the velocity field has to be determined. This allows for a simpler multi-frame optical flow analysis using Fourier analytic tools in time. We propose three variational optical flow models and show how their minimization can be tackled via Fourier transform in time. Numerical examples with synthetic as well as real-world data demonstrate the benefits of our approach. Keywords: optical flow, elastography, Fourier transform, iteratively reweighted least squares, Horn--Schunck method

math.NA↗

arXiv2024

Backpropagation through space, time, and the brain

How physical networks of neurons, bound by spatio-temporal locality constraints, can perform efficient credit assignment, remains, to a large extent, an open question. In machine learning, the answer is almost universally given by the error backpropagation algorithm, through both space and time. However, this algorithm is well-known to rely on biologically implausible assumptions, in particular with respect to spatio-temporal (non-)locality. Alternative forward-propagation models such as real-time recurrent learning only partially solve the locality problem, but only at the cost of scaling, due to prohibitive storage requirements. We introduce Generalized Latent Equilibrium (GLE), a computational framework for fully local spatio-temporal credit assignment in physical, dynamical networks of neurons. We start by defining an energy based on neuron-local mismatches, from which we derive both neuronal dynamics via stationarity and parameter dynamics via gradient descent. The resulting dynamics can be interpreted as a real-time, biologically plausible approximation of backpropagation through space and time in deep cortical networks with continuous-time neuronal dynamics and continuously active, local synaptic plasticity. In particular, GLE exploits the morphology of dendritic trees to enable more complex information storage and processing in single neurons, as well as the ability of biological neurons to phase-shift their output rate with respect to their membrane potential, which is essential in both directions of information propagation. For the forward computation, it enables the mapping of time-continuous inputs to neuronal space, effectively performing a spatio-temporal convolution. For the backward computation, it permits the temporal inversion of feedback signals, which consequently approximate the adjoint variables necessary for useful parameter updates.

q-bio.NC↗

arXiv2023

Optical time-harmonic elastography for multiscale stiffness mapping across the phylogenetic tree

Rapid mapping of the mechanical properties of soft biological tissues from light microscopy to macroscopic imaging could transform fundamental biophysical research by providing clinical biomarkers to complement in vivo elastography. We here introduce superfast optical time-harmonic elastography (OTHE) to remotely encode surface and subsurface shear wave fields for generating maps of tissue stiffness with unprecedented detail resolution. OTHE rigorously exploits the space-time propagation characteristics of time-harmonic waves to address current limitations of biomechanical imaging and elastography. Key solutions are presented for stimulation, encoding, and stiffness reconstruction of time-harmonic, multifrequency shear waves, all tuned to provide consistent stiffness values across resolutions from microns to millimeters. OTHE's versatility is demonstrated in Bacillus subtilis biofilms, zebrafish embryos, adult zebrafish, and human skeletal muscle, reflecting the diversity of the phylogenetic tree from a mechanics perspective. By zooming in on stiffness details from coarse to finer scales, OTHE advances developmental biology and offers a way to perform biomechanics-based tissue histology that consistently matches in vivo time-harmonic elastography in patients.

physics.bio-ph↗

arXiv2023

Learning beyond sensations: how dreams organize neuronal representations

Semantic representations in higher sensory cortices form the basis for robust, yet flexible behavior. These representations are acquired over the course of development in an unsupervised fashion and continuously maintained over an organism's lifespan. Predictive learning theories propose that these representations emerge from predicting or reconstructing sensory inputs. However, brains are known to generate virtual experiences, such as during imagination and dreaming, that go beyond previously experienced inputs. Here, we suggest that virtual experiences may be just as relevant as actual sensory inputs in shaping cortical representations. In particular, we discuss two complementary learning principles that organize representations through the generation of virtual experiences. First, "adversarial dreaming" proposes that creative dreams support a cortical implementation of adversarial learning in which feedback and feedforward pathways engage in a productive game of trying to fool each other. Second, "contrastive dreaming" proposes that the invariance of neuronal representations to irrelevant factors of variation is acquired by trying to map similar virtual experiences together via a contrastive learning process. These principles are compatible with known cortical structure and dynamics and the phenomenology of sleep thus providing promising directions to explain cortical learning beyond the classical predictive learning paradigm.

q-bio.NC↗

arXiv2023

Conductance-based dendrites perform Bayes-optimal cue integration

A fundamental function of cortical circuits is the integration of information from different sources to form a reliable basis for behavior. While animals behave as if they optimally integrate information according to Bayesian probability theory, the implementation of the required computations in the biological substrate remains unclear. We propose a novel, Bayesian view on the dynamics of conductance-based neurons and synapses which suggests that they are naturally equipped to optimally perform information integration. In our approach apical dendrites represent prior expectations over somatic potentials, while basal dendrites represent likelihoods of somatic potentials. These are parametrized by local quantities, the effective reversal potentials and membrane conductances. We formally demonstrate that under these assumptions the somatic compartment naturally computes the corresponding posterior. We derive a gradient-based plasticity rule, allowing neurons to learn desired target distributions and weight synaptic inputs by their relative reliabilities. Our theory explains various experimental findings on the system and single-cell level related to multi-sensory integration, which we illustrate with simulations. Furthermore, we make experimentally testable predictions on Bayesian dendritic integration and synaptic plasticity.

q-bio.NC↗

arXiv2023

Melting, bubble-like expansion and explosion of superheated plasmonic nanoparticles

We report on time-resolved coherent diffraction imaging of gas-phase silver nanoparticles, strongly heated via their plasmon resonance. The x-ray diffraction images reveal a broad range of phenomena for different excitation strengths, from simple melting over strong cavitation to explosive disintegration. Molecular dynamics simulations fully reproduce this behavior and show that the heating induces rather similar trajectories through the phase diagram in all cases, with the very different outcomes being due only to whether and where the stability limit of the metastable superheated liquid is crossed.

physics.atm-clus↗

arXiv2022

Three-Dimensional Coherent Diffractive Imaging of Isolated Faceted Nanostructures

The structure and dynamics of isolated nanosamples in free flight can be directly visualized via single-shot coherent diffractive imaging using the intense and short pulses of X-ray free-electron lasers. Wide-angle scattering images even encode three-dimensional morphological information of the samples, but the retrieval of this information remains a challenge. Up to now, effective three-dimensional morphology reconstructions from single shots were only achieved via fitting with highly constrained models, requiring a priori knowledge about possible geometrical shapes. Here we present a much more generic imaging approach. Relying on a model that allows for any sample morphology described by a convex polyhedron, we reconstruct wide-angle diffraction patterns from individual silver nanoparticles. In addition to known structural motives with high symmetries, we retrieve imperfect shapes and agglomerates which were not accessible previously. Our results open new routes towards true 3D structure determination of single nanoparticles and, ultimately, 3D movies of ultrafast nanoscale dynamics.

physics.atm-clus↗

arXiv2022

Routing brain traffic through the von Neumann bottleneck: Efficient cache usage in spiking neural network simulation code on general purpose computers

Simulation is a third pillar next to experiment and theory in the study of complex dynamic systems such as biological neural networks. Contemporary brain-scale networks correspond to directed graphs of a few million nodes, each with an in-degree and out-degree of several thousands of edges, where nodes and edges correspond to the fundamental biological units, neurons and synapses, respectively. When considering a random graph, each node's edges are distributed across thousands of parallel processes. The activity in neuronal networks is also sparse. Each neuron occasionally transmits a brief signal, called spike, via its outgoing synapses to the corresponding target neurons. This spatial and temporal sparsity represents an inherent bottleneck for simulations on conventional computers: Fundamentally irregular memory-access patterns cause poor cache utilization. Using an established neuronal network simulation code as a reference implementation, we investigate how common techniques to recover cache performance such as software-induced prefetching and software pipelining can benefit a real-world application. The algorithmic changes reduce simulation time by up to 50%. The study exemplifies that many-core systems assigned with an intrinsically parallel computational problem can overcome the von Neumann bottleneck of conventional computer architectures.

cs.DC↗

arXiv2022

Routing brain traffic through the von Neumann bottleneck: Parallel sorting and refactoring

Generic simulation code for spiking neuronal networks spends the major part of time in the phase where spikes have arrived at a compute node and need to be delivered to their target neurons. These spikes were emitted over the last interval between communication steps by source neurons distributed across many compute nodes and are inherently irregular with respect to their targets. For finding the targets, the spikes need to be dispatched to a three-dimensional data structure with decisions on target thread and synapse type to be made on the way. With growing network size a compute node receives spikes from an increasing number of different source neurons until in the limit each synapse on the compute node has a unique source. Here we show analytically how this sparsity emerges over the practically relevant range of network sizes from a hundred thousand to a billion neurons. By profiling a production code we investigate opportunities for algorithmic changes to avoid indirections and branching. Every thread hosts an equal share of the neurons on a compute node. In the original algorithm all threads search through all spikes to pick out the relevant ones. With increasing network size the fraction of hits remains invariant but the absolute number of rejections grows. An alternative algorithm equally divides the spikes among the threads and sorts them in parallel according to target thread and synapse type. After this every thread completes delivery solely of the section of spikes for its own neurons. The new algorithm halves the number of instructions in spike delivery which leads to a reduction of simulation time of up to 40 %. Thus, spike delivery is a fully parallelizable process with a single synchronization point and thereby well suited for many-core systems. Our analysis indicates that further progress requires a reduction of the latency instructions experience in accessing memory.

q-bio.NC↗

arXiv2022

Learning cortical representations through perturbed and adversarial dreaming

Humans and other animals learn to extract general concepts from sensory experience without extensive teaching. This ability is thought to be facilitated by offline states like sleep where previous experiences are systemically replayed. However, the characteristic creative nature of dreams suggests that learning semantic representations may go beyond merely replaying previous experiences. We support this hypothesis by implementing a cortical architecture inspired by generative adversarial networks (GANs). Learning in our model is organized across three different global brain states mimicking wakefulness, NREM and REM sleep, optimizing different, but complementary objective functions. We train the model on standard datasets of natural images and evaluate the quality of the learned representations. Our results suggest that generating new, virtual sensory inputs via adversarial dreaming during REM sleep is essential for extracting semantic concepts, while replaying episodic memories via perturbed dreaming during NREM sleep improves the robustness of latent representations. The model provides a new computational perspective on sleep states, memory replay and dreams and suggests a cortical implementation of GANs.

q-bio.NC↗

arXiv2022

DELAUNAY: a dataset of abstract art for psychophysical and machine learning research

Image datasets are commonly used in psychophysical experiments and in machine learning research. Most publicly available datasets are comprised of images of realistic and natural objects. However, while typical machine learning models lack any domain specific knowledge about natural objects, humans can leverage prior experience for such data, making comparisons between artificial and natural learning challenging. Here, we introduce DELAUNAY, a dataset of abstract paintings and non-figurative art objects labelled by the artists' names. This dataset provides a middle ground between natural images and artificial patterns and can thus be used in a variety of contexts, for example to investigate the sample efficiency of humans and artificial neural networks. Finally, we train an off-the-shelf convolutional neural network on DELAUNAY, highlighting several of its intriguing features.

cs.LG↗

arXiv2021

A Modular Workflow for Performance Benchmarking of Neuronal Network Simulations

Modern computational neuroscience strives to develop complex network models to explain dynamics and function of brains in health and disease. This process goes hand in hand with advancements in the theory of neuronal networks and increasing availability of detailed anatomical data on brain connectivity. Large-scale models that study interactions between multiple brain areas with intricate connectivity and investigate phenomena on long time scales such as system-level learning require progress in simulation speed. The corresponding development of state-of-the-art simulation engines relies on information provided by benchmark simulations which assess the time-to-solution for scientifically relevant, complementary network models using various combinations of hardware and software revisions. However, maintaining comparability of benchmark results is difficult due to a lack of standardized specifications for measuring the scaling performance of simulators on high-performance computing (HPC) systems. Motivated by the challenging complexity of benchmarking, we define a generic workflow that decomposes the endeavor into unique segments consisting of separate modules. As a reference implementation for the conceptual workflow, we develop beNNch: an open-source software framework for the configuration, execution, and analysis of benchmarks for neuronal network simulations. The framework records benchmarking data and metadata in a unified way to foster reproducibility. For illustration, we measure the performance of various versions of the NEST simulator across network models with different levels of complexity on a contemporary HPC system, demonstrating how performance bottlenecks can be identified, ultimately guiding the development toward more efficient simulation technology.

q-bio.NC↗

arXiv2021

Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neurons

The response time of physical computational elements is finite, and neurons are no exception. In hierarchical models of cortical networks each layer thus introduces a response lag. This inherent property of physical dynamical systems results in delayed processing of stimuli and causes a timing mismatch between network output and instructive signals, thus afflicting not only inference, but also learning. We introduce Latent Equilibrium, a new framework for inference and learning in networks of slow components which avoids these issues by harnessing the ability of biological neurons to phase-advance their output with respect to their membrane potential. This principle enables quasi-instantaneous inference independent of network depth and avoids the need for phased plasticity or computationally expensive network relaxation phases. We jointly derive disentangled neuron and synapse dynamics from a prospective energy function that depends on a network's generalized position and momentum. The resulting model can be interpreted as a biologically plausible approximation of error backpropagation in deep cortical networks with continuous-time, leaky neuronal dynamics and continuously active, local plasticity. We demonstrate successful learning of standard benchmark datasets, achieving competitive performance using both fully-connected and convolutional architectures, and show how our principle can be applied to detailed models of cortical microcircuitry. Furthermore, we study the robustness of our model to spatio-temporal substrate imperfections to demonstrate its feasibility for physical realization, be it in vivo or in silico.

q-bio.NC↗

arXiv2021

Evolving Neuronal Plasticity Rules using Cartesian Genetic Programming

We formulate the search for phenomenological models of synaptic plasticity as an optimization problem. We employ Cartesian genetic programming to evolve biologically plausible human-interpretable plasticity rules that allow a given network to successfully solve tasks from specific task families. While our evolving-to-learn approach can be applied to various learning paradigms, here we illustrate its power by evolving plasticity rules that allow a network to efficiently determine the first principal component of its input distribution. We demonstrate that the evolved rules perform competitively with known hand-designed solutions. We explore how the statistical properties of the datasets used during the evolutionary search influences the form of the plasticity rules and discover new rules which are adapted to the structure of the corresponding datasets.

cs.NE↗