arXiv subjects

Karlheinz Meier

Publications and source records attributed to Karlheinz Meier.

At least 19 recordsLinked to original sources

arXiv2023

Emulating insect brains for neuromorphic navigation

Bees display the remarkable ability to return home in a straight line after meandering excursions to their environment. Neurobiological imaging studies have revealed that this capability emerges from a path integration mechanism implemented within the insect's brain. In the present work, we emulate this neural network on the neuromorphic mixed-signal processor BrainScaleS-2 to guide bees, virtually embodied on a digital co-processor, back to their home location after randomly exploring their environment. To realize the underlying neural integrators, we introduce single-neuron spike-based short-term memory cells with axo-axonic synapses. All entities, including environment, sensory organs, brain, actuators, and the virtual body, run autonomously on a single BrainScaleS-2 microchip. The functioning network is fine-tuned for better precision and reliability through an evolution strategy. As BrainScaleS-2 emulates neural processes 1000 times faster than biology, 4800 consecutive bee journeys distributed over 320 generations occur within only half an hour on a single neuromorphic core.

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arXiv2022

Versatile emulation of spiking neural networks on an accelerated neuromorphic substrate

We present first experimental results on the novel BrainScaleS-2 neuromorphic architecture based on an analog neuro-synaptic core and augmented by embedded microprocessors for complex plasticity and experiment control. The high acceleration factor of 1000 compared to biological dynamics enables the execution of computationally expensive tasks, by allowing the fast emulation of long-duration experiments or rapid iteration over many consecutive trials. The flexibility of our architecture is demonstrated in a suite of five distinct experiments, which emphasize different aspects of the BrainScaleS-2 system.

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arXiv2022

Cortical oscillations implement a backbone for sampling-based computation in spiking neural networks

Being permanently confronted with an uncertain world, brains have faced evolutionary pressure to represent this uncertainty in order to respond appropriately. Often, this requires visiting multiple interpretations of the available information or multiple solutions to an encountered problem. This gives rise to the so-called mixing problem: since all of these "valid" states represent powerful attractors, but between themselves can be very dissimilar, switching between such states can be difficult. We propose that cortical oscillations can be effectively used to overcome this challenge. By acting as an effective temperature, background spiking activity modulates exploration. Rhythmic changes induced by cortical oscillations can then be interpreted as a form of simulated tempering. We provide a rigorous mathematical discussion of this link and study some of its phenomenological implications in computer simulations. This identifies a new computational role of cortical oscillations and connects them to various phenomena in the brain, such as sampling-based probabilistic inference, memory replay, multisensory cue combination, and place cell flickering.

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arXiv2021

Fast and energy-efficient neuromorphic deep learning with first-spike times

For a biological agent operating under environmental pressure, energy consumption and reaction times are of critical importance. Similarly, engineered systems are optimized for short time-to-solution and low energy-to-solution characteristics. At the level of neuronal implementation, this implies achieving the desired results with as few and as early spikes as possible. With time-to-first-spike coding both of these goals are inherently emerging features of learning. Here, we describe a rigorous derivation of a learning rule for such first-spike times in networks of leaky integrate-and-fire neurons, relying solely on input and output spike times, and show how this mechanism can implement error backpropagation in hierarchical spiking networks. Furthermore, we emulate our framework on the BrainScaleS-2 neuromorphic system and demonstrate its capability of harnessing the system's speed and energy characteristics. Finally, we examine how our approach generalizes to other neuromorphic platforms by studying how its performance is affected by typical distortive effects induced by neuromorphic substrates.

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arXiv2020

Structural plasticity on an accelerated analog neuromorphic hardware system

In computational neuroscience, as well as in machine learning, neuromorphic devices promise an accelerated and scalable alternative to neural network simulations. Their neural connectivity and synaptic capacity depends on their specific design choices, but is always intrinsically limited. Here, we present a strategy to achieve structural plasticity that optimizes resource allocation under these constraints by constantly rewiring the pre- and gpostsynaptic partners while keeping the neuronal fan-in constant and the connectome sparse. In particular, we implemented this algorithm on the analog neuromorphic system BrainScaleS-2. It was executed on a custom embedded digital processor located on chip, accompanying the mixed-signal substrate of spiking neurons and synapse circuits. We evaluated our implementation in a simple supervised learning scenario, showing its ability to optimize the network topology with respect to the nature of its training data, as well as its overall computational efficiency.

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arXiv2020

Accelerated physical emulation of Bayesian inference in spiking neural networks

The massively parallel nature of biological information processing plays an important role for its superiority to human-engineered computing devices. In particular, it may hold the key to overcoming the von Neumann bottleneck that limits contemporary computer architectures. Physical-model neuromorphic devices seek to replicate not only this inherent parallelism, but also aspects of its microscopic dynamics in analog circuits emulating neurons and synapses. However, these machines require network models that are not only adept at solving particular tasks, but that can also cope with the inherent imperfections of analog substrates. We present a spiking network model that performs Bayesian inference through sampling on the BrainScaleS neuromorphic platform, where we use it for generative and discriminative computations on visual data. By illustrating its functionality on this platform, we implicitly demonstrate its robustness to various substrate-specific distortive effects, as well as its accelerated capability for computation. These results showcase the advantages of brain-inspired physical computation and provide important building blocks for large-scale neuromorphic applications.

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arXiv2020

Control of criticality and computation in spiking neuromorphic networks with plasticity

The critical state is assumed to be optimal for any computation in recurrent neural networks, because criticality maximizes a number of abstract computational properties. We challenge this assumption by evaluating the performance of a spiking recurrent neural network on a set of tasks of varying complexity at - and away from critical network dynamics. To that end, we developed a spiking network with synaptic plasticity on a neuromorphic chip. We show that the distance to criticality can be easily adapted by changing the input strength, and then demonstrate a clear relation between criticality, task-performance and information-theoretic fingerprint. Whereas the information-theoretic measures all show that network capacity is maximal at criticality, this is not the case for performance on specific tasks: Only the complex, memory-intensive tasks profit from criticality, whereas the simple tasks suffer from it. Thereby, we challenge the general assumption that criticality would be beneficial for any task, and provide instead an understanding of how the collective network state should be tuned to task requirement to achieve optimal performance.

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arXiv2020

Criticality or Supersymmetry Breaking ?

In many stochastic dynamical systems, ordinary chaotic behavior is preceded by a full-dimensional phase that exhibits 1/f-type power-spectra and/or scale-free statistics of (anti)instantons such as neuroavalanches, earthquakes, etc. In contrast with the phenomenological concept of self-organized criticality, the recently developed approximation-free supersymmetric theory of stochastic differential equations, or stochastics, (STS) identifies this phase as the noise-induced chaos (N-phase), i.e., the phase where the topological supersymmetry pertaining to all stochastic dynamical systems is broken spontaneously by the condensation of the noise-induced (anti-)instantons. Here, we support this picture in the context of neurodynamics. We study a 1D chain of neuron-like elements and find that the dynamics in the N-phase is indeed featured by positive stochastic Lyapunov exponents and dominated by (anti)instantonic processes of (creation)annihilation of kinks and antikinks, which can be viewed as predecessors of boundaries of neuroavalanches. We also construct the phase diagram of emulated stochastic neurodynamics on Spikey neuromorphic hardware and demonstrate that the width of the N-phase vanishes in the deterministic limit in accordance with STS. As a first result of the application of STS to neurodynamics comes the conclusion that a conscious brain can reside only in the N-phase.

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arXiv2019

Stochasticity from function -- why the Bayesian brain may need no noise

An increasing body of evidence suggests that the trial-to-trial variability of spiking activity in the brain is not mere noise, but rather the reflection of a sampling-based encoding scheme for probabilistic computing. Since the precise statistical properties of neural activity are important in this context, many models assume an ad-hoc source of well-behaved, explicit noise, either on the input or on the output side of single neuron dynamics, most often assuming an independent Poisson process in either case. However, these assumptions are somewhat problematic: neighboring neurons tend to share receptive fields, rendering both their input and their output correlated; at the same time, neurons are known to behave largely deterministically, as a function of their membrane potential and conductance. We suggest that spiking neural networks may, in fact, have no need for noise to perform sampling-based Bayesian inference. We study analytically the effect of auto- and cross-correlations in functionally Bayesian spiking networks and demonstrate how their effect translates to synaptic interaction strengths, rendering them controllable through synaptic plasticity. This allows even small ensembles of interconnected deterministic spiking networks to simultaneously and co-dependently shape their output activity through learning, enabling them to perform complex Bayesian computation without any need for noise, which we demonstrate in silico, both in classical simulation and in neuromorphic emulation. These results close a gap between the abstract models and the biology of functionally Bayesian spiking networks, effectively reducing the architectural constraints imposed on physical neural substrates required to perform probabilistic computing, be they biological or artificial.

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arXiv2019

Neuromorphic Hardware learns to learn

Hyperparameters and learning algorithms for neuromorphic hardware are usually chosen by hand. In contrast, the hyperparameters and learning algorithms of networks of neurons in the brain, which they aim to emulate, have been optimized through extensive evolutionary and developmental processes for specific ranges of computing and learning tasks. Occasionally this process has been emulated through genetic algorithms, but these require themselves hand-design of their details and tend to provide a limited range of improvements. We employ instead other powerful gradient-free optimization tools, such as cross-entropy methods and evolutionary strategies, in order to port the function of biological optimization processes to neuromorphic hardware. As an example, we show that this method produces neuromorphic agents that learn very efficiently from rewards. In particular, meta-plasticity, i.e., the optimization of the learning rule which they use, substantially enhances reward-based learning capability of the hardware. In addition, we demonstrate for the first time Learning-to-Learn benefits from such hardware, in particular, the capability to extract abstract knowledge from prior learning experiences that speeds up the learning of new but related tasks. Learning-to-Learn is especially suited for accelerated neuromorphic hardware, since it makes it feasible to carry out the required very large number of network computations.

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arXiv2019

Demonstrating Advantages of Neuromorphic Computation: A Pilot Study

Neuromorphic devices represent an attempt to mimic aspects of the brain's architecture and dynamics with the aim of replicating its hallmark functional capabilities in terms of computational power, robust learning and energy efficiency. We employ a single-chip prototype of the BrainScaleS 2 neuromorphic system to implement a proof-of-concept demonstration of reward-modulated spike-timing-dependent plasticity in a spiking network that learns to play the Pong video game by smooth pursuit. This system combines an electronic mixed-signal substrate for emulating neuron and synapse dynamics with an embedded digital processor for on-chip learning, which in this work also serves to simulate the virtual environment and learning agent. The analog emulation of neuronal membrane dynamics enables a 1000-fold acceleration with respect to biological real-time, with the entire chip operating on a power budget of 57mW. Compared to an equivalent simulation using state-of-the-art software, the on-chip emulation is at least one order of magnitude faster and three orders of magnitude more energy-efficient. We demonstrate how on-chip learning can mitigate the effects of fixed-pattern noise, which is unavoidable in analog substrates, while making use of temporal variability for action exploration. Learning compensates imperfections of the physical substrate, as manifested in neuronal parameter variability, by adapting synaptic weights to match respective excitability of individual neurons.

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arXiv2018

Emulating quantum computation with artificial neural networks

We demonstrate, that artificial neural networks (ANN) can be trained to emulate single or multiple basic quantum operations. In order to realize a quantum state, we implement a novel "quantumness gate" that maps an arbitrary matrix to the real representation of a positive hermitean normalized density matrix. We train the CNOT gate, the Hadamard gate and a rotation in Hilbert space as basic building blocks for processing the quantum density matrices of two entangled qubits. During the training process the neural networks learn to represent the complex structure, the hermiticity, the normalization and the positivity of the output matrix. The requirement of successful training allows us to find a critical bottleneck dimension which reflects the relevant quantum information. Chains of individually trained neural quantum gates can be constructed to realize any unitary transformation. For scaling to larger quantum systems, we propose to use correlations of stochastic macroscopic two-level observables or classical bits. This novel concept provides a path for a classical implementation of computationally relevant quantum information processing on classical neural networks, in particular on neuromorphic computing machines featuring stochastic operations.

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arXiv2018

A Mixed-Signal Structured AdEx Neuron for Accelerated Neuromorphic Cores

Here we describe a multi-compartment neuron circuit based on the Adaptive-Exponential I&F (AdEx) model, developed for the second-generation BrainScaleS hardware. Based on an existing modular Leaky Integrate-and-Fire (LIF) architecture designed in 65 nm CMOS, the circuit features exponential spike generation, neuronal adaptation, inter-compartmental connections as well as a conductance-based reset. The design reproduces a diverse set of firing patterns observed in cortical pyramidal neurons. Further, it enables the emulation of sodium and calcium spikes, as well as N-Methyl-D-Aspartate (NMDA) plateau potentials known from apical and thin dendrites. We characterize the AdEx circuit extensions and exemplify how the interplay between passive and non-linear active signal processing enhances the computational capabilities of single (but structured) on-chip neurons.

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arXiv2018

An Accelerated LIF Neuronal Network Array for a Large Scale Mixed-Signal Neuromorphic Architecture

We present an array of leaky integrate-and-fire (LIF) neuron circuits designed for the second-generation BrainScaleS mixed-signal 65-nm CMOS neuromorphic hardware. The neuronal array is embedded in the analog network core of a scaled-down prototype HICANN-DLS chip. Designed as continuous-time circuits, the neurons are highly tunable and reconfigurable elements with accelerated dynamics. Each neuron integrates input current from a multitude of incoming synapses and evokes a digital spike event output. The circuit offers a wide tuning range for synaptic and membrane time constants, as well as for refractory periods to cover a number of computational models. We elucidate our design methodology, underlying circuit design, calibration and measurement results from individual sub-circuits across multiple dies. The circuit dynamics match with the behavior of the LIF mathematical model. We further demonstrate a winner-take-all network on the prototype chip as a typical element of cortical processing.

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arXiv2018

Full Wafer Redistribution and Wafer Embedding as Key Technologies for a Multi-Scale Neuromorphic Hardware Cluster

Together with the Kirchhoff-Institute for Physics(KIP) the Fraunhofer IZM has developed a full wafer redistribution and embedding technology as base for a large-scale neuromorphic hardware system. The paper will give an overview of the neuromorphic computing platform at the KIP and the associated hardware requirements which drove the described technological developments. In the first phase of the project standard redistribution technologies from wafer level packaging were adapted to enable a high density reticle-to-reticle routing on 200mm CMOS wafers. Neighboring reticles were interconnected across the scribe lines with an 8μm pitch routing based on semi-additive copper metallization. Passivation by photo sensitive benzocyclobutene was used to enable a second intra-reticle routing layer. Final IO pads with flash gold were generated on top of each reticle. With that concept neuromorphic systems based on full wafers could be assembled and tested. The fabricated high density inter-reticle routing revealed a very high yield of larger than 99.9%. In order to allow an upscaling of the system size to a large number of wafers with feasible effort a full wafer embedding concept for printed circuit boards was developed and proven in the second phase of the project. The wafers were thinned to 250μm and laminated with additional prepreg layers and copper foils into a core material. After lamination of the PCB panel the reticle IOs of the embedded wafer were accessed by micro via drilling, copper electroplating, lithography and subtractive etching of the PCB wiring structure. The created wiring with 50um line width enabled an access of the reticle IOs on the embedded wafer as well as a board level routing. The panels with the embedded wafers were subsequently stressed with up to 1000 thermal cycles between 0C and 100C and have shown no severe failure formation over the cycle time.

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arXiv2017

Deterministic networks for probabilistic computing

Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own private source of randomness, often in the form of uncorrelated external noise. However, both in vivo and in silico, the number of noise sources is limited due to space and bandwidth constraints. Hence, neurons in large networks usually need to share noise sources. Here, we show that the resulting shared-noise correlations can significantly impair the performance of stochastic network models. We demonstrate that this problem can be overcome by using deterministic recurrent neural networks as sources of uncorrelated noise, exploiting the decorrelating effect of inhibitory feedback. Consequently, even a single recurrent network of a few hundred neurons can serve as a natural noise source for large ensembles of functional networks, each comprising thousands of units. We successfully apply the proposed framework to a diverse set of binary-unit networks with different dimensionalities and entropies, as well as to a network reproducing handwritten digits with distinct predefined frequencies. Finally, we show that the same design transfers to functional networks of spiking neurons.

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arXiv2017

Spiking neurons with short-term synaptic plasticity form superior generative networks

Spiking networks that perform probabilistic inference have been proposed both as models of cortical computation and as candidates for solving problems in machine learning. However, the evidence for spike-based computation being in any way superior to non-spiking alternatives remains scarce. We propose that short-term plasticity can provide spiking networks with distinct computational advantages compared to their classical counterparts. In this work, we use networks of leaky integrate-and-fire neurons that are trained to perform both discriminative and generative tasks in their forward and backward information processing paths, respectively. During training, the energy landscape associated with their dynamics becomes highly diverse, with deep attractor basins separated by high barriers. Classical algorithms solve this problem by employing various tempering techniques, which are both computationally demanding and require global state updates. We demonstrate how similar results can be achieved in spiking networks endowed with local short-term synaptic plasticity. Additionally, we discuss how these networks can even outperform tempering-based approaches when the training data is imbalanced. We thereby show how biologically inspired, local, spike-triggered synaptic dynamics based simply on a limited pool of synaptic resources can allow spiking networks to outperform their non-spiking relatives.

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arXiv2017

Spike-based probabilistic inference with correlated noise

A steadily increasing body of evidence suggests that the brain performs probabilistic inference to interpret and respond to sensory input and that trial-to-trial variability in neural activity plays an important role. The neural sampling hypothesis interprets stochastic neural activity as sampling from an underlying probability distribution and has been shown to be compatible with biologically observed firing patterns. In many studies, uncorrelated noise is used as a source of stochasticity, discounting the fact that cortical neurons may share a significant portion of their presynaptic partners, which impacts their computation. This is relevant in biology and for implementations of neural networks where bandwidth constraints limit the amount of independent noise. When receiving correlated noise, the resulting correlations cannot be directly countered by changes in synaptic weights $W$. We show that this is contingent on the chosen coding: when changing the state space from $z\in\{0,1\}$ to $z'\in\{-1,1\}$, correlated noise has the exact same effect as changes in $W'$. The translation of the problem to the $\{-1,1\}$ space allows to find a weight configuration that compensates for the induced correlations. For an artificial embedding of sampling networks, this allows a straightforward transfer between platforms with different bandwidth constraints. The existence of the mapping is important for learning. Since in the $\{-1,1\}$-coding the correlated noise can be compensated by parameter changes and the probability distribution can be kept invariant when changing the coding, the distribution will be found in the $\{0,1\}$-coding as well during learning, as demonstrated in simulations. Conclusively, sampling spiking networks are impervious to noise correlations when trained. If such computation happens in cortex, network plasticity does not need to take account of shared noise inputs.

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