130 citations · 631 across the 25 of their papers we have counts for
20 papers · 1 filter
Reduction of interaction order in hard combinatorial optimization via conditionally independent degrees of freedom
Alexandru Ciobanu, David Dahmen, John Paul Strachan +1
Combinatorial optimization problems have a broad range of applications and map to physical systems with complex dynamics. Among them, the 3-SAT problem is prominent due to its NP-c…
Beyond-mean-field fluctuations for the solution of constraint satisfaction problems
Niklas Foos, Bastian Epping, Jannik Grundler +5
Constraint Satisfaction Problems (CSPs) lie at the heart of complexity theory and find application in a plethora of prominent tasks ranging from cryptography to genetics. Classical…
From Kernels to Features: A Multi-Scale Adaptive Theory of Feature Learning
Noa Rubin, Kirsten Fischer, Javed Lindner +5
Feature learning in neural networks is crucial for their expressive power and inductive biases, motivating various theoretical approaches. Some approaches describe network behavior…
Critical feature learning in deep neural networks
Kirsten Fischer, Javed Lindner, David Dahmen +3
A key property of neural networks driving their success is their ability to learn features from data. Understanding feature learning from a theoretical viewpoint is an emerging fie…
Effect of Synaptic Heterogeneity on Neuronal Coordination
Moritz Layer, Moritz Helias, David Dahmen
Recent advancements in measurement techniques have resulted in an increasing amount of data on neural activities recorded in parallel, revealing largely heterogeneous correlation p…
A theory of data variability in Neural Network Bayesian inference
Javed Lindner, David Dahmen, Michael Krämer +1
Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks…
Learning Interacting Theories from Data
Claudia Merger, Alexandre René, Kirsten Fischer +5
One challenge of physics is to explain how collective properties arise from microscopic interactions. Indeed, interactions form the building blocks of almost all physical theories…
Field theory for optimal signal propagation in ResNets
Kirsten Fischer, David Dahmen, Moritz Helias
Residual networks have significantly better trainability and thus performance than feed-forward networks at large depth. Introducing skip connections facilitates signal propagation…
Hidden connectivity structures control collective network dynamics
Lorenzo Tiberi, David Dahmen, Moritz Helias
Many observables of brain dynamics appear to be optimized for computation. Which connectivity structures underlie this fine-tuning? We propose that many of these structures are nat…
Decomposing neural networks as mappings of correlation functions
Kirsten Fischer, Alexandre René, Christian Keup +3
Understanding the functional principles of information processing in deep neural networks continues to be a challenge, in particular for networks with trained and thus non-random w…
Unified field theoretical approach to deep and recurrent neuronal networks
Kai Segadlo, Bastian Epping, Alexander van Meegen +3
Understanding capabilities and limitations of different network architectures is of fundamental importance to machine learning. Bayesian inference on Gaussian processes has proven…
Gell-Mann-Low criticality in neural networks
Lorenzo Tiberi, Jonas Stapmanns, Tobias Kühn +3
Criticality is deeply related to optimal computational capacity. The lack of a renormalized theory of critical brain dynamics, however, so far limits insights into this form of bio…
Unfolding recurrence by Green's functions for optimized reservoir computing
Sandra Nestler, Christian Keup, David Dahmen +3
Cortical networks are strongly recurrent, and neurons have intrinsic temporal dynamics. This sets them apart from deep feed-forward networks. Despite the tremendous progress in the…
Transient chaotic dimensionality expansion by recurrent networks
Christian Keup, Tobias Kühn, David Dahmen +1
Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog…
Capacity of the covariance perceptron
David Dahmen, Matthieu Gilson, Moritz Helias
The classical perceptron is a simple neural network that performs a binary classification by a linear mapping between static inputs and outputs and application of a threshold. For…
Statistical field theory for neural networks
Moritz Helias, David Dahmen
These notes attempt a self-contained introduction into statistical field theory applied to neural networks of rate units and binary spins. The presentation consists of three parts:…
Two types of criticality in the brain
David Dahmen, Sonja Grün, Markus Diesmann +1
Neural networks with equal excitatory and inhibitory feedback show high computational performance. They operate close to a critical point characterized by the joint activation of l…
Functional methods for disordered neural networks
Jannis Schuecker, Sven Goedeke, David Dahmen +1
Neural networks of the brain form one of the most complex systems we know. Many qualitative features of the emerging collective phenomena, such as correlated activity, stability, r…
Distributions of covariances as a window into the operational regime of neuronal networks
David Dahmen, Markus Diesmann, Moritz Helias
Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an expla…
Correlated fluctuations in strongly-coupled binary networks beyond equilibrium
David Dahmen, Hannah Bos, Moritz Helias
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, pr…