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  1. Article ; Online: Neuromorphic quantum computing.

    Pehle, Christian / Wetterich, Christof

    Physical review. E

    2022  Volume 106, Issue 4-2, Page(s) 45311

    Abstract: Quantum computation builds on the use of correlations. Correlations could also play a central role for artificial intelligence, neuromorphic computing or "biological computing." As a step toward a systematic exploration of "correlated computing" we ... ...

    Abstract Quantum computation builds on the use of correlations. Correlations could also play a central role for artificial intelligence, neuromorphic computing or "biological computing." As a step toward a systematic exploration of "correlated computing" we demonstrate that neuromorphic computing can perform quantum operations. Spiking neurons in the active or silent states are connected to the two states of Ising spins. A quantum density matrix is constructed from the expectation values and correlations of the Ising spins. We show for a two qubit system that quantum gates can be learned as a change of parameters for neural network dynamics. These changes respect restrictions which ensure the quantum correlations. Our proposal for probabilistic computing goes beyond Markov chains and is not based on transition probabilities. Constraints on classical probability distributions relate changes made in one part of the system to other parts, similar to entangled quantum systems.
    Language English
    Publishing date 2022-10-11
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2844562-4
    ISSN 2470-0053 ; 2470-0045
    ISSN (online) 2470-0053
    ISSN 2470-0045
    DOI 10.1103/PhysRevE.106.045311
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  2. Article ; Online: Event-based backpropagation can compute exact gradients for spiking neural networks.

    Wunderlich, Timo C / Pehle, Christian

    Scientific reports

    2021  Volume 11, Issue 1, Page(s) 12829

    Abstract: Spiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation algorithm, ... ...

    Abstract Spiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation algorithm, applying this algorithm to spiking networks was previously hindered by the existence of discrete spike events and discontinuities. For the first time, this work derives the backpropagation algorithm for a continuous-time spiking neural network and a general loss function by applying the adjoint method together with the proper partial derivative jumps, allowing for backpropagation through discrete spike events without approximations. This algorithm, EventProp, backpropagates errors at spike times in order to compute the exact gradient in an event-based, temporally and spatially sparse fashion. We use gradients computed via EventProp to train networks on the Yin-Yang and MNIST datasets using either a spike time or voltage based loss function and report competitive performance. Our work supports the rigorous study of gradient-based learning algorithms in spiking neural networks and provides insights toward their implementation in novel brain-inspired hardware.
    Language English
    Publishing date 2021-06-18
    Publishing country England
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 2615211-3
    ISSN 2045-2322 ; 2045-2322
    ISSN (online) 2045-2322
    ISSN 2045-2322
    DOI 10.1038/s41598-021-91786-z
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  3. Book ; Online: jaxsnn

    Müller, Eric / Althaus, Moritz / Arnold, Elias / Spilger, Philipp / Pehle, Christian / Schemmel, Johannes

    Event-driven Gradient Estimation for Analog Neuromorphic Hardware

    2024  

    Abstract: Traditional neuromorphic hardware architectures rely on event-driven computation, where the asynchronous transmission of events, such as spikes, triggers local computations within synapses and neurons. While machine learning frameworks are commonly used ... ...

    Abstract Traditional neuromorphic hardware architectures rely on event-driven computation, where the asynchronous transmission of events, such as spikes, triggers local computations within synapses and neurons. While machine learning frameworks are commonly used for gradient-based training, their emphasis on dense data structures poses challenges for processing asynchronous data such as spike trains. This problem is particularly pronounced for typical tensor data structures. In this context, we present a novel library (jaxsnn) built on top of JAX, that departs from conventional machine learning frameworks by providing flexibility in the data structures used and the handling of time, while maintaining Autograd functionality and composability. Our library facilitates the simulation of spiking neural networks and gradient estimation, with a focus on compatibility with time-continuous neuromorphic backends, such as the BrainScaleS-2 system, during the forward pass. This approach opens avenues for more efficient and flexible training of spiking neural networks, bridging the gap between traditional neuromorphic architectures and contemporary machine learning frameworks.
    Keywords Computer Science - Neural and Evolutionary Computing
    Subject code 006
    Publishing date 2024-01-30
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Book ; Online: Event-based Backpropagation for Analog Neuromorphic Hardware

    Pehle, Christian / Blessing, Luca / Arnold, Elias / Müller, Eric / Schemmel, Johannes

    2023  

    Abstract: Neuromorphic computing aims to incorporate lessons from studying biological nervous systems in the design of computer architectures. While existing approaches have successfully implemented aspects of those computational principles, such as sparse spike- ... ...

    Abstract Neuromorphic computing aims to incorporate lessons from studying biological nervous systems in the design of computer architectures. While existing approaches have successfully implemented aspects of those computational principles, such as sparse spike-based computation, event-based scalable learning has remained an elusive goal in large-scale systems. However, only then the potential energy-efficiency advantages of neuromorphic systems relative to other hardware architectures can be realized during learning. We present our progress implementing the EventProp algorithm using the example of the BrainScaleS-2 analog neuromorphic hardware. Previous gradient-based approaches to learning used "surrogate gradients" and dense sampling of observables or were limited by assumptions on the underlying dynamics and loss functions. In contrast, our approach only needs spike time observations from the system while being able to incorporate other system observables, such as membrane voltage measurements, in a principled way. This leads to a one-order-of-magnitude improvement in the information efficiency of the gradient estimate, which would directly translate to corresponding energy efficiency improvements in an optimized hardware implementation. We present the theoretical framework for estimating gradients and results verifying the correctness of the estimation, as well as results on a low-dimensional classification task using the BrainScaleS-2 system. Building on this work has the potential to enable scalable gradient estimation in large-scale neuromorphic hardware as a continuous measurement of the system state would be prohibitive and energy-inefficient in such instances. It also suggests the feasibility of a full on-device implementation of the algorithm that would enable scalable, energy-efficient, event-based learning in large-scale analog neuromorphic hardware.
    Keywords Quantitative Biology - Neurons and Cognition ; Computer Science - Neural and Evolutionary Computing
    Subject code 006
    Publishing date 2023-02-13
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Book ; Online: EventProp

    Wunderlich, Timo C. / Pehle, Christian

    Backpropagation for Exact Gradients in Spiking Neural Networks

    2020  

    Abstract: We derive the backpropagation algorithm for spiking neural networks composed of leaky integrate-and-fire neurons operating in continuous time. This algorithm, EventProp, computes the exact gradient of an arbitrary loss function of spike times and ... ...

    Abstract We derive the backpropagation algorithm for spiking neural networks composed of leaky integrate-and-fire neurons operating in continuous time. This algorithm, EventProp, computes the exact gradient of an arbitrary loss function of spike times and membrane potentials by backpropagating errors in time. For the first time, by leveraging methods from optimal control theory, we are able to backpropagate errors through spike discontinuities and avoid approximations or smoothing operations. EventProp can be applied to spiking networks with arbitrary connectivity, including recurrent, convolutional and deep feed-forward architectures. While we consider the leaky integrate-and-fire neuron model in this work, our methodology to derive the gradient can be applied to other spiking neuron models. As errors are backpropagated in an event-based manner (at spike times), EventProp requires the storage of state variables only at these times, providing favorable memory requirements. We demonstrate learning using gradients computed via EventProp in a deep spiking network using an event-based simulator and a non-linearly separable dataset encoded using spike time latencies. Our work supports the rigorous study of gradient-based methods to train spiking neural networks while providing insights toward the development of learning algorithms in neuromorphic hardware.

    Comment: 14 pages, 3 figures
    Keywords Quantitative Biology - Neurons and Cognition ; Computer Science - Neural and Evolutionary Computing
    Subject code 612
    Publishing date 2020-09-17
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  6. Article: The BrainScaleS-2 Accelerated Neuromorphic System With Hybrid Plasticity.

    Pehle, Christian / Billaudelle, Sebastian / Cramer, Benjamin / Kaiser, Jakob / Schreiber, Korbinian / Stradmann, Yannik / Weis, Johannes / Leibfried, Aron / Müller, Eric / Schemmel, Johannes

    Frontiers in neuroscience

    2022  Volume 16, Page(s) 795876

    Abstract: Since the beginning of information processing by electronic components, the nervous system has served as a metaphor for the organization of computational primitives. Brain-inspired computing today encompasses a class of approaches ranging from using ... ...

    Abstract Since the beginning of information processing by electronic components, the nervous system has served as a metaphor for the organization of computational primitives. Brain-inspired computing today encompasses a class of approaches ranging from using novel nano-devices for computation to research into large-scale neuromorphic architectures, such as TrueNorth, SpiNNaker, BrainScaleS, Tianjic, and Loihi. While implementation details differ, spiking neural networks-sometimes referred to as the third generation of neural networks-are the common abstraction used to model computation with such systems. Here we describe the second generation of the BrainScaleS neuromorphic architecture, emphasizing applications enabled by this architecture. It combines a custom analog accelerator core supporting the accelerated physical emulation of bio-inspired spiking neural network primitives with a tightly coupled digital processor and a digital event-routing network.
    Language English
    Publishing date 2022-02-24
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2411902-7
    ISSN 1662-453X ; 1662-4548
    ISSN (online) 1662-453X
    ISSN 1662-4548
    DOI 10.3389/fnins.2022.795876
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  7. Article: Neuromorphic Hardware Learns to Learn.

    Bohnstingl, Thomas / Scherr, Franz / Pehle, Christian / Meier, Karlheinz / Maass, Wolfgang

    Frontiers in neuroscience

    2019  Volume 13, Page(s) 483

    Abstract: Hyperparameters and learning algorithms for neuromorphic hardware are usually chosen by hand to suit a particular task. In contrast, networks of neurons in the brain were optimized through extensive evolutionary and developmental processes to work well ... ...

    Abstract Hyperparameters and learning algorithms for neuromorphic hardware are usually chosen by hand to suit a particular task. In contrast, networks of neurons in the brain were optimized through extensive evolutionary and developmental processes to work well on a range 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 these optimization algorithms enable neuromorphic agents to 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.
    Language English
    Publishing date 2019-05-21
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2411902-7
    ISSN 1662-453X ; 1662-4548
    ISSN (online) 1662-453X
    ISSN 1662-4548
    DOI 10.3389/fnins.2019.00483
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  8. Book ; Online: hxtorch.snn

    Spilger, Philipp / Arnold, Elias / Blessing, Luca / Mauch, Christian / Pehle, Christian / Müller, Eric / Schemmel, Johannes

    Machine-learning-inspired Spiking Neural Network Modeling on BrainScaleS-2

    2022  

    Abstract: Neuromorphic systems require user-friendly software to support the design and optimization of experiments. In this work, we address this need by presenting our development of a machine learning-based modeling framework for the BrainScaleS-2 neuromorphic ... ...

    Abstract Neuromorphic systems require user-friendly software to support the design and optimization of experiments. In this work, we address this need by presenting our development of a machine learning-based modeling framework for the BrainScaleS-2 neuromorphic system. This work represents an improvement over previous efforts, which either focused on the matrix-multiplication mode of BrainScaleS-2 or lacked full automation. Our framework, called hxtorch.snn, enables the hardware-in-the-loop training of spiking neural networks within PyTorch, including support for auto differentiation in a fully-automated hardware experiment workflow. In addition, hxtorch.snn facilitates seamless transitions between emulating on hardware and simulating in software. We demonstrate the capabilities of hxtorch.snn on a classification task using the Yin-Yang dataset employing a gradient-based approach with surrogate gradients and densely sampled membrane observations from the BrainScaleS-2 hardware system.
    Keywords Computer Science - Neural and Evolutionary Computing
    Subject code 006
    Publishing date 2022-12-23
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  9. Article ; Online: Surrogate gradients for analog neuromorphic computing.

    Cramer, Benjamin / Billaudelle, Sebastian / Kanya, Simeon / Leibfried, Aron / Grübl, Andreas / Karasenko, Vitali / Pehle, Christian / Schreiber, Korbinian / Stradmann, Yannik / Weis, Johannes / Schemmel, Johannes / Zenke, Friedemann

    Proceedings of the National Academy of Sciences of the United States of America

    2022  Volume 119, Issue 4

    Abstract: To rapidly process temporal information at a low metabolic cost, biological neurons integrate inputs as an analog sum, but communicate with spikes, binary events in time. Analog neuromorphic hardware uses the same principles to emulate spiking neural ... ...

    Abstract To rapidly process temporal information at a low metabolic cost, biological neurons integrate inputs as an analog sum, but communicate with spikes, binary events in time. Analog neuromorphic hardware uses the same principles to emulate spiking neural networks with exceptional energy efficiency. However, instantiating high-performing spiking networks on such hardware remains a significant challenge due to device mismatch and the lack of efficient training algorithms. Surrogate gradient learning has emerged as a promising training strategy for spiking networks, but its applicability for analog neuromorphic systems has not been demonstrated. Here, we demonstrate surrogate gradient learning on the BrainScaleS-2 analog neuromorphic system using an in-the-loop approach. We show that learning self-corrects for device mismatch, resulting in competitive spiking network performance on both vision and speech benchmarks. Our networks display sparse spiking activity with, on average, less than one spike per hidden neuron and input, perform inference at rates of up to 85,000 frames per second, and consume less than 200 mW. In summary, our work sets several benchmarks for low-energy spiking network processing on analog neuromorphic hardware and paves the way for future on-chip learning algorithms.
    MeSH term(s) Action Potentials/physiology ; Algorithms ; Brain/physiology ; Computers ; Models, Biological ; Models, Neurological ; Models, Theoretical ; Neural Networks, Computer ; Neurons/physiology
    Language English
    Publishing date 2022-01-18
    Publishing country United States
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 209104-5
    ISSN 1091-6490 ; 0027-8424
    ISSN (online) 1091-6490
    ISSN 0027-8424
    DOI 10.1073/pnas.2109194119
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  10. Book ; Online: Neuromorphic Hardware learns to learn

    Bohnstingl, Thomas / Scherr, Franz / Pehle, Christian / Meier, Karlheinz / Maass, Wolfgang

    2019  

    Abstract: 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 ... ...

    Abstract 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.
    Keywords Computer Science - Neural and Evolutionary Computing
    Subject code 006
    Publishing date 2019-03-15
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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