Mirko Goldmann

Anas Skalli, Satoshi Sunada, Mirko Goldmann et al.

Artificial neural networks (ANNs), have become ubiquitous and revolutionized many applications ranging from computer vision to medical diagnoses. However, they offer a fundamentally connectionist and distributed approach to computing, in stark contrast to classical computers that use the von Neumann architecture. This distinction has sparked renewed interest in developing unconventional hardware to support more efficient implementations of ANNs, rather than merely emulating them on traditional systems. Photonics stands out as a particularly promising platform, providing scalability, high speed, energy efficiency, and the ability for parallel information processing. However, fully realized autonomous optical neural networks (ONNs) with in-situ learning capabilities are still rare. In this work, we demonstrate a fully autonomous and parallel ONN using a multimode vertical cavity surface emitting laser (VCSEL) using off-the-shelf components. Our ONN is highly efficient and is scalable both in network size and inference bandwidth towards the GHz range. High performance hardware-compatible optimization algorithms are necessary in order to minimize reliance on external von Neumann computers to fully exploit the potential of ONNs. As such we present and extensively study several algorithms which are broadly compatible with a wide range of systems. We then apply these algorithms to optimize our ONN, and benchmark them using the MNIST dataset. We show that our ONN can achieve high accuracy and convergence efficiency, even under limited hardware resources. Crucially, we compare these different algorithms in terms of scaling and optimization efficiency in term of convergence time which is crucial when working with limited external resources. Our work provides some guidance for the design of future ONNs as well as a simple and flexible way to train them.

Guillaume Pourcel, Mirko Goldmann, Ingo Fischer et al.

Recurrent Neural Networks excel at predicting and generating complex high-dimensional temporal patterns. Due to their inherent nonlinear dynamics and memory, they can learn unbounded temporal dependencies from data. In a Machine Learning setting, the network's parameters are adapted during a training phase to match the requirements of a given task/problem increasing its computational capabilities. After the training, the network parameters are kept fixed to exploit the learned computations. The static parameters thereby render the network unadaptive to changing conditions, such as external or internal perturbation. In this manuscript, we demonstrate how keeping parts of the network adaptive even after the training enhances its functionality and robustness. Here, we utilize the conceptor framework and conceptualize an adaptive control loop analyzing the network's behavior continuously and adjusting its time-varying internal representation to follow a desired target. We demonstrate how the added adaptivity of the network supports the computational functionality in three distinct tasks: interpolation of temporal patterns, stabilization against partial network degradation, and robustness against input distortion. Our results highlight the potential of adaptive networks in machine learning beyond training, enabling them to not only learn complex patterns but also dynamically adjust to changing environments, ultimately broadening their applicability.

Mirko Goldmann, Claudio R. Mirasso, Ingo Fischer et al.

We design scalable neural networks adapted to translational symmetries in dynamical systems, capable of inferring untrained high-dimensional dynamics for different system sizes. We train these networks to predict the dynamics of delay-dynamical and spatio-temporal systems for a single size. Then, we drive the networks by their own predictions. We demonstrate that by scaling the size of the trained network, we can predict the complex dynamics for larger or smaller system sizes. Thus, the network learns from a single example and, by exploiting symmetry properties, infers entire bifurcation diagrams.

Mirko Goldmann, Felix Köster, Kathy Lüdge et al.

The Deep Time-Delay Reservoir Computing concept utilizes unidirectionally connected systems with time-delays for supervised learning. We present how the dynamical properties of a deep Ikeda-based reservoir are related to its memory capacity (MC) and how that can be used for optimization. In particular, we analyze bifurcations of the corresponding autonomous system and compute conditional Lyapunov exponents, which measure the generalized synchronization between the input and the layer dynamics. We show how the MC is related to the systems distance to bifurcations or magnitude of the conditional Lyapunov exponent. The interplay of different dynamical regimes leads to a adjustable distribution between linear and nonlinear MC. Furthermore, numerical simulations show resonances between clock cycle and delays of the layers in all degrees of the MC. Contrary to MC losses in a single-layer reservoirs, these resonances can boost separate degrees of the MC and can be used, e.g., to design a system with maximum linear MC. Accordingly, we present two configurations that empower either high nonlinear MC or long time linear MC.