Christian Mayr

LG
h-index23
22papers
547citations
Novelty44%
AI Score46

22 Papers

LGJun 13, 2022Code
Efficient recurrent architectures through activity sparsity and sparse back-propagation through time

Anand Subramoney, Khaleelulla Khan Nazeer, Mark Schöne et al.

Recurrent neural networks (RNNs) are well suited for solving sequence tasks in resource-constrained systems due to their expressivity and low computational requirements. However, there is still a need to bridge the gap between what RNNs are capable of in terms of efficiency and performance and real-world application requirements. The memory and computational requirements arising from propagating the activations of all the neurons at every time step to every connected neuron, together with the sequential dependence of activations, contribute to the inefficiency of training and using RNNs. We propose a solution inspired by biological neuron dynamics that makes the communication between RNN units sparse and discrete. This makes the backward pass with backpropagation through time (BPTT) computationally sparse and efficient as well. We base our model on the gated recurrent unit (GRU), extending it with units that emit discrete events for communication triggered by a threshold so that no information is communicated to other units in the absence of events. We show theoretically that the communication between units, and hence the computation required for both the forward and backward passes, scales with the number of events in the network. Our model achieves efficiency without compromising task performance, demonstrating competitive performance compared to state-of-the-art recurrent network models in real-world tasks, including language modeling. The dynamic activity sparsity mechanism also makes our model well suited for novel energy-efficient neuromorphic hardware. Code is available at https://github.com/KhaleelKhan/EvNN/.

AIApr 10, 2023
NeuroBench: A Framework for Benchmarking Neuromorphic Computing Algorithms and Systems

Jason Yik, Korneel Van den Berghe, Douwe den Blanken et al. · eth-zurich

Neuromorphic computing shows promise for advancing computing efficiency and capabilities of AI applications using brain-inspired principles. However, the neuromorphic research field currently lacks standardized benchmarks, making it difficult to accurately measure technological advancements, compare performance with conventional methods, and identify promising future research directions. Prior neuromorphic computing benchmark efforts have not seen widespread adoption due to a lack of inclusive, actionable, and iterative benchmark design and guidelines. To address these shortcomings, we present NeuroBench: a benchmark framework for neuromorphic computing algorithms and systems. NeuroBench is a collaboratively-designed effort from an open community of researchers across industry and academia, aiming to provide a representative structure for standardizing the evaluation of neuromorphic approaches. The NeuroBench framework introduces a common set of tools and systematic methodology for inclusive benchmark measurement, delivering an objective reference framework for quantifying neuromorphic approaches in both hardware-independent (algorithm track) and hardware-dependent (system track) settings. In this article, we outline tasks and guidelines for benchmarks across multiple application domains, and present initial performance baselines across neuromorphic and conventional approaches for both benchmark tracks. NeuroBench is intended to continually expand its benchmarks and features to foster and track the progress made by the research community.

CVJun 8, 2022
Robust Environment Perception for Automated Driving: A Unified Learning Pipeline for Visual-Infrared Object Detection

Mohsen Vadidar, Ali Kariminezhad, Christian Mayr et al.

The RGB complementary metal-oxidesemiconductor (CMOS) sensor works within the visible light spectrum. Therefore it is very sensitive to environmental light conditions. On the contrary, a long-wave infrared (LWIR) sensor operating in 8-14 micro meter spectral band, functions independent of visible light. In this paper, we exploit both visual and thermal perception units for robust object detection purposes. After delicate synchronization and (cross-) labeling of the FLIR [1] dataset, this multi-modal perception data passes through a convolutional neural network (CNN) to detect three critical objects on the road, namely pedestrians, bicycles, and cars. After evaluation of RGB and infrared (thermal and infrared are often used interchangeably) sensors separately, various network structures are compared to fuse the data at the feature level effectively. Our RGB-thermal (RGBT) fusion network, which takes advantage of a novel entropy-block attention module (EBAM), outperforms the state-of-the-art network [2] by 10% with 82.9% mAP.

LGApr 10, 2023
Deploying Machine Learning Models to Ahead-of-Time Runtime on Edge Using MicroTVM

Chen Liu, Matthias Jobst, Liyuan Guo et al.

In the past few years, more and more AI applications have been applied to edge devices. However, models trained by data scientists with machine learning frameworks, such as PyTorch or TensorFlow, can not be seamlessly executed on edge. In this paper, we develop an end-to-end code generator parsing a pre-trained model to C source libraries for the backend using MicroTVM, a machine learning compiler framework extension addressing inference on bare metal devices. An analysis shows that specific compute-intensive operators can be easily offloaded to the dedicated accelerator with a Universal Modular Accelerator (UMA) interface, while others are processed in the CPU cores. By using the automatically generated ahead-of-time C runtime, we conduct a hand gesture recognition experiment on an ARM Cortex M4F core.

36.2ETMar 25
Characterization of Off-wafer Pulse Communication in BrainScaleS Neuromorphic System

Bernhard Vogginger, Vasilis Thanasoulis, Johannes Partzsch et al.

Neuromorphic VLSI systems take inspiration from biology to enable efficient emulation of large-scale spiking neural networks and to explore new computational paradigms. To establish large neuromorphic systems, a sophisticated routing infrastructure is needed to communicate spikes between chips and to/from the host computer. For the BrainScaleS wafer-scale neuromorphic system considered in this work, especially the stimulation with input spikes and the recording of spikes is demanding, requiring high bandwidth and temporal resolution due to the accelerated emulation of neural dynamics 10.000 faster than biological real time. Here, we present a systematic characterization of the BrainScaleS off-wafer communication infrastructure implemented around Kintex7 FPGAs. The communication flow is characterized in terms of throughput, transmission delay, jitter and pulse loss. Further, we analyze the effect of the communication distortions (like pulse loss and jitter) on a neural benchmark model with highly varying spike activity. The presented methods and techniques for communication evaluation are general applicable and provide useful insights for the mapping of network models to the hardware such as the distribution of input spikes across communication channels.

LGNov 13, 2023
Activity Sparsity Complements Weight Sparsity for Efficient RNN Inference

Rishav Mukherji, Mark Schöne, Khaleelulla Khan Nazeer et al.

Artificial neural networks open up unprecedented machine learning capabilities at the cost of ever growing computational requirements. Sparsifying the parameters, often achieved through weight pruning, has been identified as a powerful technique to compress the number of model parameters and reduce the computational operations of neural networks. Yet, sparse activations, while omnipresent in both biological neural networks and deep learning systems, have not been fully utilized as a compression technique in deep learning. Moreover, the interaction between sparse activations and weight pruning is not fully understood. In this work, we demonstrate that activity sparsity can compose multiplicatively with parameter sparsity in a recurrent neural network model based on the GRU that is designed to be activity sparse. We achieve up to $20\times$ reduction of computation while maintaining perplexities below $60$ on the Penn Treebank language modeling task. This magnitude of reduction has not been achieved previously with solely sparsely connected LSTMs, and the language modeling performance of our model has not been achieved previously with any sparsely activated recurrent neural networks or spiking neural networks. Neuromorphic computing devices are especially good at taking advantage of the dynamic activity sparsity, and our results provide strong evidence that making deep learning models activity sparse and porting them to neuromorphic devices can be a viable strategy that does not compromise on task performance. Our results also drive further convergence of methods from deep learning and neuromorphic computing for efficient machine learning.

ETJan 9, 2024
SpiNNaker2: A Large-Scale Neuromorphic System for Event-Based and Asynchronous Machine Learning

Hector A. Gonzalez, Jiaxin Huang, Florian Kelber et al.

The joint progress of artificial neural networks (ANNs) and domain specific hardware accelerators such as GPUs and TPUs took over many domains of machine learning research. This development is accompanied by a rapid growth of the required computational demands for larger models and more data. Concurrently, emerging properties of foundation models such as in-context learning drive new opportunities for machine learning applications. However, the computational cost of such applications is a limiting factor of the technology in data centers, and more importantly in mobile devices and edge systems. To mediate the energy footprint and non-trivial latency of contemporary systems, neuromorphic computing systems deeply integrate computational principles of neurobiological systems by leveraging low-power analog and digital technologies. SpiNNaker2 is a digital neuromorphic chip developed for scalable machine learning. The event-based and asynchronous design of SpiNNaker2 allows the composition of large-scale systems involving thousands of chips. This work features the operating principles of SpiNNaker2 systems, outlining the prototype of novel machine learning applications. These applications range from ANNs over bio-inspired spiking neural networks to generalized event-based neural networks. With the successful development and deployment of SpiNNaker2, we aim to facilitate the advancement of event-based and asynchronous algorithms for future generations of machine learning systems.

LGApr 29, 2024
Scalable Event-by-event Processing of Neuromorphic Sensory Signals With Deep State-Space Models

Mark Schöne, Neeraj Mohan Sushma, Jingyue Zhuge et al.

Event-based sensors are well suited for real-time processing due to their fast response times and encoding of the sensory data as successive temporal differences. These and other valuable properties, such as a high dynamic range, are suppressed when the data is converted to a frame-based format. However, most current methods either collapse events into frames or cannot scale up when processing the event data directly event-by-event. In this work, we address the key challenges of scaling up event-by-event modeling of the long event streams emitted by such sensors, which is a particularly relevant problem for neuromorphic computing. While prior methods can process up to a few thousand time steps, our model, based on modern recurrent deep state-space models, scales to event streams of millions of events for both training and inference. We leverage their stable parameterization for learning long-range dependencies, parallelizability along the sequence dimension, and their ability to integrate asynchronous events effectively to scale them up to long event streams. We further augment these with novel event-centric techniques enabling our model to match or beat the state-of-the-art performance on several event stream benchmarks. In the Spiking Speech Commands task, we improve state-of-the-art by a large margin of 7.7% to 88.4%. On the DVS128-Gestures dataset, we achieve competitive results without using frames or convolutional neural networks. Our work demonstrates, for the first time, that it is possible to use fully event-based processing with purely recurrent networks to achieve state-of-the-art task performance in several event-based benchmarks.

NEDec 14, 2023
Language Modeling on a SpiNNaker 2 Neuromorphic Chip

Khaleelulla Khan Nazeer, Mark Schöne, Rishav Mukherji et al.

As large language models continue to scale in size rapidly, so too does the computational power required to run them. Event-based networks on neuromorphic devices offer a potential way to reduce energy consumption for inference significantly. However, to date, most event-based networks that can run on neuromorphic hardware, including spiking neural networks (SNNs), have not achieved task performance even on par with LSTM models for language modeling. As a result, language modeling on neuromorphic devices has seemed a distant prospect. In this work, we demonstrate the first-ever implementation of a language model on a neuromorphic device - specifically the SpiNNaker 2 chip - based on a recently published event-based architecture called the EGRU. SpiNNaker 2 is a many-core neuromorphic chip designed for large-scale asynchronous processing, while the EGRU is architected to leverage such hardware efficiently while maintaining competitive task performance. This implementation marks the first time a neuromorphic language model matches LSTMs, setting the stage for taking task performance to the level of large language models. We also demonstrate results on a gesture recognition task based on inputs from a DVS camera. Overall, our results showcase the feasibility of this neuro-inspired neural network in hardware, highlighting significant gains versus conventional hardware in energy efficiency for the common use case of single batch inference.

LGMay 1, 2024
Weight Sparsity Complements Activity Sparsity in Neuromorphic Language Models

Rishav Mukherji, Mark Schöne, Khaleelulla Khan Nazeer et al.

Activity and parameter sparsity are two standard methods of making neural networks computationally more efficient. Event-based architectures such as spiking neural networks (SNNs) naturally exhibit activity sparsity, and many methods exist to sparsify their connectivity by pruning weights. While the effect of weight pruning on feed-forward SNNs has been previously studied for computer vision tasks, the effects of pruning for complex sequence tasks like language modeling are less well studied since SNNs have traditionally struggled to achieve meaningful performance on these tasks. Using a recently published SNN-like architecture that works well on small-scale language modeling, we study the effects of weight pruning when combined with activity sparsity. Specifically, we study the trade-off between the multiplicative efficiency gains the combination affords and its effect on task performance for language modeling. To dissect the effects of the two sparsities, we conduct a comparative analysis between densely activated models and sparsely activated event-based models across varying degrees of connectivity sparsity. We demonstrate that sparse activity and sparse connectivity complement each other without a proportional drop in task performance for an event-based neural network trained on the Penn Treebank and WikiText-2 language modeling datasets. Our results suggest sparsely connected event-based neural networks are promising candidates for effective and efficient sequence modeling.

LGApr 9, 2025
Efficient Deployment of Spiking Neural Networks on SpiNNaker2 for DVS Gesture Recognition Using Neuromorphic Intermediate Representation

Sirine Arfa, Bernhard Vogginger, Chen Liu et al.

Spiking Neural Networks (SNNs) are highly energy-efficient during inference, making them particularly suitable for deployment on neuromorphic hardware. Their ability to process event-driven inputs, such as data from dynamic vision sensors (DVS), further enhances their applicability to edge computing tasks. However, the resource constraints of edge hardware necessitate techniques like weight quantization, which reduce the memory footprint of SNNs while preserving accuracy. Despite its importance, existing quantization methods typically focus on synaptic weights quantization without taking account of other critical parameters, such as scaling neuron firing thresholds. To address this limitation, we present the first benchmark for the DVS gesture recognition task using SNNs optimized for the many-core neuromorphic chip SpiNNaker2. Our study evaluates two quantization pipelines for fixed-point computations. The first approach employs post training quantization (PTQ) with percentile-based threshold scaling, while the second uses quantization aware training (QAT) with adaptive threshold scaling. Both methods achieve accurate 8-bit on-chip inference, closely approximating 32-bit floating-point performance. Additionally, our baseline SNNs perform competitively against previously reported results without specialized techniques. These models are deployed on SpiNNaker2 using the neuromorphic intermediate representation (NIR). Ultimately, we achieve 94.13% classification accuracy on-chip, demonstrating the SpiNNaker2's potential for efficient, low-energy neuromorphic computing.

CVNov 19, 2024
STREAM: A Universal State-Space Model for Sparse Geometric Data

Mark Schöne, Yash Bhisikar, Karan Bania et al. · cmu

Handling sparse and unstructured geometric data, such as point clouds or event-based vision, is a pressing challenge in the field of machine vision. Recently, sequence models such as Transformers and state-space models entered the domain of geometric data. These methods require specialized preprocessing to create a sequential view of a set of points. Furthermore, prior works involving sequence models iterate geometric data with either uniform or learned step sizes, implicitly relying on the model to infer the underlying geometric structure. In this work, we propose to encode geometric structure explicitly into the parameterization of a state-space model. State-space models are based on linear dynamics governed by a one-dimensional variable such as time or a spatial coordinate. We exploit this dynamic variable to inject relative differences of coordinates into the step size of the state-space model. The resulting geometric operation computes interactions between all pairs of N points in O(N) steps. Our model deploys the Mamba selective state-space model with a modified CUDA kernel to efficiently map sparse geometric data to modern hardware. The resulting sequence model, which we call STREAM, achieves competitive results on a range of benchmarks from point-cloud classification to event-based vision and audio classification. STREAM demonstrates a powerful inductive bias for sparse geometric data by improving the PointMamba baseline when trained from scratch on the ModelNet40 and ScanObjectNN point cloud analysis datasets. It further achieves, for the first time, 100% test accuracy on all 11 classes of the DVS128 Gestures dataset.

LGJul 31, 2025
Hardware-Aware Fine-Tuning of Spiking Q-Networks on the SpiNNaker2 Neuromorphic Platform

Sirine Arfa, Bernhard Vogginger, Christian Mayr

Spiking Neural Networks (SNNs) promise orders-of-magnitude lower power consumption and low-latency inference on neuromorphic hardware for a wide range of robotic tasks. In this work, we present an energy-efficient implementation of a reinforcement learning (RL) algorithm using quantized SNNs to solve two classical control tasks. The network is trained using the Q-learning algorithm, then fine-tuned and quantized to low-bit (8-bit) precision for embedded deployment on the SpiNNaker2 neuromorphic chip. To evaluate the comparative advantage of SpiNNaker2 over conventional computing platforms, we analyze inference latency, dynamic power consumption, and energy cost per inference for our SNN models, comparing performance against a GTX 1650 GPU baseline. Our results demonstrate SpiNNaker2's strong potential for scalable, low-energy neuromorphic computing, achieving up to 32x reduction in energy consumption. Inference latency remains on par with GPU-based execution, with improvements observed in certain task settings, reinforcing SpiNNaker2's viability for real-time neuromorphic control and making the neuromorphic approach a compelling direction for efficient deep Q-learning.

LGJul 18, 2025
An End-to-End DNN Inference Framework for the SpiNNaker2 Neuromorphic MPSoC

Matthias Jobst, Tim Langer, Chen Liu et al.

This work presents a multi-layer DNN scheduling framework as an extension of OctopuScheduler, providing an end-to-end flow from PyTorch models to inference on a single SpiNNaker2 chip. Together with a front-end comprised of quantization and lowering steps, the proposed framework enables the edge-based execution of large and complex DNNs up to transformer scale using the neuromorphic platform SpiNNaker2.

LGMay 24, 2023
Block-local learning with probabilistic latent representations

David Kappel, Khaleelulla Khan Nazeer, Cabrel Teguemne Fokam et al.

The ubiquitous backpropagation algorithm requires sequential updates through the network introducing a locking problem. In addition, back-propagation relies on the transpose of forward weight matrices to compute updates, introducing a weight transport problem across the network. Locking and weight transport are problems because they prevent efficient parallelization and horizontal scaling of the training process. We propose a new method to address both these problems and scale up the training of large models. Our method works by dividing a deep neural network into blocks and introduces a feedback network that propagates the information from the targets backwards to provide auxiliary local losses. Forward and backward propagation can operate in parallel and with different sets of weights, addressing the problems of locking and weight transport. Our approach derives from a statistical interpretation of training that treats output activations of network blocks as parameters of probability distributions. The resulting learning framework uses these parameters to evaluate the agreement between forward and backward information. Error backpropagation is then performed locally within each block, leading to "block-local" learning. Several previously proposed alternatives to error backpropagation emerge as special cases of our model. We present results on a variety of tasks and architectures, demonstrating state-of-the-art performance using block-local learning. These results provide a new principled framework for training networks in a distributed setting.

NEFeb 25, 2022
Time-coded Spiking Fourier Transform in Neuromorphic Hardware

Javier López-Randulfe, Nico Reeb, Negin Karimi et al.

After several decades of continuously optimizing computing systems, the Moore's law is reaching itsend. However, there is an increasing demand for fast and efficient processing systems that can handlelarge streams of data while decreasing system footprints. Neuromorphic computing answers thisneed by creating decentralized architectures that communicate with binary events over time. Despiteits rapid growth in the last few years, novel algorithms are needed that can leverage the potential ofthis emerging computing paradigm and can stimulate the design of advanced neuromorphic chips.In this work, we propose a time-based spiking neural network that is mathematically equivalent tothe Fourier transform. We implemented the network in the neuromorphic chip Loihi and conductedexperiments on five different real scenarios with an automotive frequency modulated continuouswave radar. Experimental results validate the algorithm, and we hope they prompt the design of adhoc neuromorphic chips that can improve the efficiency of state-of-the-art digital signal processorsand encourage research on neuromorphic computing for signal processing.

NESep 18, 2020
Low-Power Low-Latency Keyword Spotting and Adaptive Control with a SpiNNaker 2 Prototype and Comparison with Loihi

Yexin Yan, Terrence C. Stewart, Xuan Choo et al.

We implemented two neural network based benchmark tasks on a prototype chip of the second-generation SpiNNaker (SpiNNaker 2) neuromorphic system: keyword spotting and adaptive robotic control. Keyword spotting is commonly used in smart speakers to listen for wake words, and adaptive control is used in robotic applications to adapt to unknown dynamics in an online fashion. We highlight the benefit of a multiply accumulate (MAC) array in the SpiNNaker 2 prototype which is ordinarily used in rate-based machine learning networks when employed in a neuromorphic, spiking context. In addition, the same benchmark tasks have been implemented on the Loihi neuromorphic chip, giving a side-by-side comparison regarding power consumption and computation time. While Loihi shows better efficiency when less complicated vector-matrix multiplication is involved, with the MAC array, the SpiNNaker 2 prototype shows better efficiency when high dimensional vector-matrix multiplication is involved.

NEMar 30, 2020
The Operating System of the Neuromorphic BrainScaleS-1 System

Eric Müller, Sebastian Schmitt, Christian Mauch et al.

BrainScaleS-1 is a wafer-scale mixed-signal accelerated neuromorphic system targeted for research in the fields of computational neuroscience and beyond-von-Neumann computing. The BrainScaleS Operating System (BrainScaleS OS) is a software stack giving users the possibility to emulate networks described in the high-level network description language PyNN with minimal knowledge of the system. At the same time, expert usage is facilitated by allowing to hook into the system at any depth of the stack. We present operation and development methodologies implemented for the BrainScaleS-1 neuromorphic architecture and walk through the individual components of BrainScaleS OS constituting the software stack for BrainScaleS-1 platform operation.

NEMar 21, 2019
Dynamic Power Management for Neuromorphic Many-Core Systems

Sebastian Hoeppner, Bernhard Vogginger, Yexin Yan et al.

This work presents a dynamic power management architecture for neuromorphic many core systems such as SpiNNaker. A fast dynamic voltage and frequency scaling (DVFS) technique is presented which allows the processing elements (PE) to change their supply voltage and clock frequency individually and autonomously within less than 100 ns. This is employed by the neuromorphic simulation software flow, which defines the performance level (PL) of the PE based on the actual workload within each simulation cycle. A test chip in 28 nm SLP CMOS technology has been implemented. It includes 4 PEs which can be scaled from 0.7 V to 1.0 V with frequencies from 125 MHz to 500 MHz at three distinct PLs. By measurement of three neuromorphic benchmarks it is shown that the total PE power consumption can be reduced by 75%, with 80% baseline power reduction and a 50% reduction of energy per neuron and synapse computation, all while maintaining temporary peak system performance to achieve biological real-time operation of the system. A numerical model of this power management model is derived which allows DVFS architecture exploration for neuromorphics. The proposed technique is to be used for the second generation SpiNNaker neuromorphic many core system.

NEMar 20, 2019
Efficient Reward-Based Structural Plasticity on a SpiNNaker 2 Prototype

Yexin Yan, David Kappel, Felix Neumaerker et al.

Advances in neuroscience uncover the mechanisms employed by the brain to efficiently solve complex learning tasks with very limited resources. However, the efficiency is often lost when one tries to port these findings to a silicon substrate, since brain-inspired algorithms often make extensive use of complex functions such as random number generators, that are expensive to compute on standard general purpose hardware. The prototype chip of the 2nd generation SpiNNaker system is designed to overcome this problem. Low-power ARM processors equipped with a random number generator and an exponential function accelerator enable the efficient execution of brain-inspired algorithms. We implement the recently introduced reward-based synaptic sampling model that employs structural plasticity to learn a function or task. The numerical simulation of the model requires to update the synapse variables in each time step including an explorative random term. To the best of our knowledge, this is the most complex synapse model implemented so far on the SpiNNaker system. By making efficient use of the hardware accelerators and numerical optimizations the computation time of one plasticity update is reduced by a factor of 2. This, combined with fitting the model into to the local SRAM, leads to 62% energy reduction compared to the case without accelerators and the use of external DRAM. The model implementation is integrated into the SpiNNaker software framework allowing for scalability onto larger systems. The hardware-software system presented in this work paves the way for power-efficient mobile and biomedical applications with biologically plausible brain-inspired algorithms.

NCMar 17, 2017
Pattern representation and recognition with accelerated analog neuromorphic systems

Mihai A. Petrovici, Sebastian Schmitt, Johann Klähn et al.

Despite being originally inspired by the central nervous system, artificial neural networks have diverged from their biological archetypes as they have been remodeled to fit particular tasks. In this paper, we review several possibilites to reverse map these architectures to biologically more realistic spiking networks with the aim of emulating them on fast, low-power neuromorphic hardware. Since many of these devices employ analog components, which cannot be perfectly controlled, finding ways to compensate for the resulting effects represents a key challenge. Here, we discuss three different strategies to address this problem: the addition of auxiliary network components for stabilizing activity, the utilization of inherently robust architectures and a training method for hardware-emulated networks that functions without perfect knowledge of the system's dynamics and parameters. For all three scenarios, we corroborate our theoretical considerations with experimental results on accelerated analog neuromorphic platforms.

NEMar 6, 2017
Neuromorphic Hardware In The Loop: Training a Deep Spiking Network on the BrainScaleS Wafer-Scale System

Sebastian Schmitt, Johann Klaehn, Guillaume Bellec et al.

Emulating spiking neural networks on analog neuromorphic hardware offers several advantages over simulating them on conventional computers, particularly in terms of speed and energy consumption. However, this usually comes at the cost of reduced control over the dynamics of the emulated networks. In this paper, we demonstrate how iterative training of a hardware-emulated network can compensate for anomalies induced by the analog substrate. We first convert a deep neural network trained in software to a spiking network on the BrainScaleS wafer-scale neuromorphic system, thereby enabling an acceleration factor of 10 000 compared to the biological time domain. This mapping is followed by the in-the-loop training, where in each training step, the network activity is first recorded in hardware and then used to compute the parameter updates in software via backpropagation. An essential finding is that the parameter updates do not have to be precise, but only need to approximately follow the correct gradient, which simplifies the computation of updates. Using this approach, after only several tens of iterations, the spiking network shows an accuracy close to the ideal software-emulated prototype. The presented techniques show that deep spiking networks emulated on analog neuromorphic devices can attain good computational performance despite the inherent variations of the analog substrate.