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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.
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Affiliation(s)
- Christian Pehle
- Kirchhoff-Institute for Physics, Heidelberg University, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Christof Wetterich
- Institute for Theoretical Physics, Heidelberg University, Philosophenweg 16, 69120 Heidelberg, Germany
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2
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Müller E, Arnold E, Breitwieser O, Czierlinski M, Emmel A, Kaiser J, Mauch C, Schmitt S, Spilger P, Stock R, Stradmann Y, Weis J, Baumbach A, Billaudelle S, Cramer B, Ebert F, Göltz J, Ilmberger J, Karasenko V, Kleider M, Leibfried A, Pehle C, Schemmel J. A Scalable Approach to Modeling on Accelerated Neuromorphic Hardware. Front Neurosci 2022; 16:884128. [PMID: 35663548 PMCID: PMC9157770 DOI: 10.3389/fnins.2022.884128] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2022] [Accepted: 04/20/2022] [Indexed: 11/29/2022] Open
Abstract
Neuromorphic systems open up opportunities to enlarge the explorative space for computational research. However, it is often challenging to unite efficiency and usability. This work presents the software aspects of this endeavor for the BrainScaleS-2 system, a hybrid accelerated neuromorphic hardware architecture based on physical modeling. We introduce key aspects of the BrainScaleS-2 Operating System: experiment workflow, API layering, software design, and platform operation. We present use cases to discuss and derive requirements for the software and showcase the implementation. The focus lies on novel system and software features such as multi-compartmental neurons, fast re-configuration for hardware-in-the-loop training, applications for the embedded processors, the non-spiking operation mode, interactive platform access, and sustainable hardware/software co-development. Finally, we discuss further developments in terms of hardware scale-up, system usability, and efficiency.
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Affiliation(s)
- Eric Müller
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Elias Arnold
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Oliver Breitwieser
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Milena Czierlinski
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Arne Emmel
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Jakob Kaiser
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Christian Mauch
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Sebastian Schmitt
- Third Institute of Physics, University of Göttingen, Göttingen, Germany
| | - Philipp Spilger
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Raphael Stock
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Yannik Stradmann
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Johannes Weis
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Andreas Baumbach
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
- Department of Physiology, University of Bern, Bern, Switzerland
| | | | - Benjamin Cramer
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Falk Ebert
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Julian Göltz
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
- Department of Physiology, University of Bern, Bern, Switzerland
| | - Joscha Ilmberger
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Vitali Karasenko
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Mitja Kleider
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Aron Leibfried
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Christian Pehle
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Johannes Schemmel
- Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
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3
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Pehle C, Billaudelle S, Cramer B, Kaiser J, Schreiber K, Stradmann Y, Weis J, Leibfried A, Müller E, Schemmel J. The BrainScaleS-2 Accelerated Neuromorphic System With Hybrid Plasticity. Front Neurosci 2022; 16:795876. [PMID: 35281488 PMCID: PMC8907969 DOI: 10.3389/fnins.2022.795876] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Accepted: 01/27/2022] [Indexed: 12/30/2022] Open
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.
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Affiliation(s)
| | | | | | | | | | | | | | | | | | - Johannes Schemmel
- Electronic Visions, Kirchhoff-Institute for Physics, Heidelberg University, Heidelberg, Germany
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4
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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.
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Affiliation(s)
- Timo C Wunderlich
- Kirchhoff-Institute for Physics, Heidelberg University, 69120, Heidelberg, Germany.
- Berlin Institute of Health, Charité-Universitätsmedizin, 10117, Berlin, Germany.
| | - Christian Pehle
- Kirchhoff-Institute for Physics, Heidelberg University, 69120, Heidelberg, Germany.
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5
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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.
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Affiliation(s)
- Thomas Bohnstingl
- Institute for Theoretical Computer Science, Graz University of Technology, Graz, Austria
| | - Franz Scherr
- Institute for Theoretical Computer Science, Graz University of Technology, Graz, Austria
| | - Christian Pehle
- Kirchhoff-Institute for Physics, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
| | - Karlheinz Meier
- Kirchhoff-Institute for Physics, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
| | - Wolfgang Maass
- Institute for Theoretical Computer Science, Graz University of Technology, Graz, Austria
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6
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Wunderlich T, Kungl AF, Müller E, Hartel A, Stradmann Y, Aamir SA, Grübl A, Heimbrecht A, Schreiber K, Stöckel D, Pehle C, Billaudelle S, Kiene G, Mauch C, Schemmel J, Meier K, Petrovici MA. Demonstrating Advantages of Neuromorphic Computation: A Pilot Study. Front Neurosci 2019; 13:260. [PMID: 30971881 PMCID: PMC6444279 DOI: 10.3389/fnins.2019.00260] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2018] [Accepted: 03/05/2019] [Indexed: 11/26/2022] Open
Abstract
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 a simplified version of 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 57 mW. 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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Affiliation(s)
- Timo Wunderlich
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Akos F Kungl
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Eric Müller
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Andreas Hartel
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Yannik Stradmann
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Syed Ahmed Aamir
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Andreas Grübl
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Arthur Heimbrecht
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Korbinian Schreiber
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - David Stöckel
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Christian Pehle
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Sebastian Billaudelle
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Gerd Kiene
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Christian Mauch
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Johannes Schemmel
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Karlheinz Meier
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany
| | - Mihai A Petrovici
- Department of Physics, Kirchhoff Institute for Physics, Heidelberg University, Heidelberg, Germany.,Department of Physiology, University of Bern, Bern, Switzerland
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