David Kappel

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/.

Reza Sedghi, Robin Schiewer, Anand Subramoney et al.

At typical context lengths, the feed-forward MLP block accounts for a large share of a transformer's compute budget, motivating sparse alternatives to dense MLP blocks. We study sparse, tree-structured feed-forward layers as drop-in replacements for MLP blocks in deep transformer architectures, enabling conditional computation via hard hierarchical routing without a separate router network. We demonstrate for the first time that this form of tree-structured conditional sparsity can be applied for autoregressive language modeling and downstream question answering, including zero- and few-shot settings, and its scalability beyond 1B parameters. Despite activating fewer than 5% of the feed-forward block's units per token, our models match dense baselines under controlled training and fine-tuning protocols. We further analyze training dynamics and identify an emergent auto-pruning effect: the interaction of hard routing with asymmetric nonlinearities progressively deactivates unused paths, yielding partial conversion of dynamic routing into static structural sparsity. We show that simple architectural choices can modulate this behavior and recover balanced trees without auxiliary losses. Overall, our work demonstrates that tree-structured feed-forward layers provide a scalable and controllable mechanism for sparsifying large transformer models.

Jan Rathjens, Shirin Reyhanian, David Kappel et al.

Understanding the mechanisms underlying deep neural networks remains a fundamental challenge in machine learning and computer vision. One promising, yet only preliminarily explored approach, is feature inversion, which attempts to reconstruct images from intermediate representations using trained inverse neural networks. In this study, we revisit feature inversion, introducing a novel, modular variation that enables significantly more efficient application of the technique. We demonstrate how our method can be systematically applied to the large-scale transformer-based vision models, Detection Transformer and Vision Transformer, and how reconstructed images can be qualitatively interpreted in a meaningful way. We further quantitatively evaluate our method, thereby uncovering underlying mechanisms of representing image features that emerge in the two transformer architectures. Our analysis reveals key insights into how these models encode contextual shape and image details, how their layers correlate, and their robustness against color perturbations. These findings contribute to a deeper understanding of transformer-based vision models and their internal representations. The code for reproducing our experiments is available at github.com/wiskott-lab/inverse-tvm.

Lukas König, Manuel Kuhn, David Kappel et al.

Existing frameworks for gradient-based training of spiking neural networks face a trade-off: discrete-time methods using surrogate gradients support arbitrary neuron models but introduce gradient bias and constrain spike-time resolution, while continuous-time methods that compute exact gradients require analytical expressions for spike times and state evolution, restricting them to simple neuron types such as Leaky Integrate and Fire (LIF). We introduce the Eventax framework, which resolves this trade-off by combining differentiable numerical ODE solvers with event-based spike handling. Built in JAX, our frame-work uses Diffrax ODE-solvers to compute gradients that are exact with respect to the forward simulation for any neuron model defined by ODEs . It also provides a simple API where users can specify just the neuron dynamics, spike conditions, and reset rules. Eventax prioritises modelling flexibility, supporting a wide range of neuron models, loss functions, and network architectures, which can be easily extended. We demonstrate Eventax on multiple benchmarks, including Yin-Yang and MNIST, using diverse neuron models such as Leaky Integrate-and-fire (LIF), Quadratic Integrate-and-fire (QIF), Exponential integrate-and-fire (EIF), Izhikevich and Event-based Gated Recurrent Unit (EGRU) with both time-to-first-spike and state-based loss functions, demonstrating its utility for prototyping and testing event-based architectures trained with exact gradients. We also demonstrate the application of this framework for more complex neuron types by implementing a multi-compartment neuron that uses a model of dendritic spikes in human layer 2/3 cortical Pyramidal neurons for computation. Code available at https://github.com/efficient-scalable-machine-learning/eventax.

Jacques Kaiser, Michael Hoff, Andreas Konle et al.

The endeavor to understand the brain involves multiple collaborating research fields. Classically, synaptic plasticity rules derived by theoretical neuroscientists are evaluated in isolation on pattern classification tasks. This contrasts with the biological brain which purpose is to control a body in closed-loop. This paper contributes to bringing the fields of computational neuroscience and robotics closer together by integrating open-source software components from these two fields. The resulting framework allows to evaluate the validity of biologically-plausibe plasticity models in closed-loop robotics environments. We demonstrate this framework to evaluate Synaptic Plasticity with Online REinforcement learning (SPORE), a reward-learning rule based on synaptic sampling, on two visuomotor tasks: reaching and lane following. We show that SPORE is capable of learning to perform policies within the course of simulated hours for both tasks. Provisional parameter explorations indicate that the learning rate and the temperature driving the stochastic processes that govern synaptic learning dynamics need to be regulated for performance improvements to be retained. We conclude by discussing the recent deep reinforcement learning techniques which would be beneficial to increase the functionality of SPORE on visuomotor tasks.

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.

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.

Neeraj Mohan Sushma, Yudou Tian, Harshvardhan Mestha et al.

Deep state-space models (Deep SSMs) are becoming popular as effective approaches to model sequence data. They have also been shown to be capable of in-context learning, much like transformers. However, a complete picture of how SSMs might be able to do in-context learning has been missing. In this study, we provide a direct and explicit construction to show that state-space models can perform gradient-based learning and use it for in-context learning in much the same way as transformers. Specifically, we prove that a single structured state-space model layer, augmented with multiplicative input and output gating, can reproduce the outputs of an implicit linear model with least squares loss after one step of gradient descent. We then show a straightforward extension to multi-step linear and non-linear regression tasks. We validate our construction by training randomly initialized augmented SSMs on linear and non-linear regression tasks. The empirically obtained parameters through optimization match the ones predicted analytically by the theoretical construction. Overall, we elucidate the role of input- and output-gating in recurrent architectures as the key inductive biases for enabling the expressive power typical of foundation models. We also provide novel insights into the relationship between state-space models and linear self-attention, and their ability to learn in-context.

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.

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.

Reza Sedghi, Anand Subramoney, David Kappel

Efficient inference with transformer-based models remains a challenge, especially in vision tasks like object detection. We analyze the inherent sparsity in the MLP layers of DETR and introduce two methods to exploit it without retraining. First, we propose Static Indicator-Based Sparsification (SIBS), a heuristic method that predicts neuron inactivity based on fixed activation patterns. While simple, SIBS offers limited gains due to the input-dependent nature of sparsity. To address this, we introduce Micro-Gated Sparsification (MGS), a lightweight gating mechanism trained on top of a pretrained DETR. MGS predicts dynamic sparsity using a small linear layer and achieves up to 85 to 95% activation sparsity. Experiments on the COCO dataset show that MGS maintains or even improves performance while significantly reducing computation. Our method offers a practical, input-adaptive approach to sparsification, enabling efficient deployment of pretrained vision transformers without full model retraining.

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.

Sebastian Billaudelle, Benjamin Cramer, Mihai A. Petrovici et al.

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.

Lukas Hahne, Timo Lüddecke, Florentin Wörgötter et al.

Attention mechanisms have been boosting the performance of deep learning models on a wide range of applications, ranging from speech understanding to program induction. However, despite experiments from psychology which suggest that attention plays an essential role in visual reasoning, the full potential of attention mechanisms has so far not been explored to solve abstract cognitive tasks on image data. In this work, we propose a hybrid network architecture, grounded on self-attention and relational reasoning. We call this new model Attention Relation Network (ARNe). ARNe combines features from the recently introduced Transformer and the Wild Relation Network (WReN). We test ARNe on the Procedurally Generated Matrices (PGMs) datasets for abstract visual reasoning. ARNe excels the WReN model on this task by 11.28 ppt. Relational concepts between objects are efficiently learned demanding only 35% of the training samples to surpass reported accuracy of the base line model. Our proposed hybrid model, represents an alternative on learning abstract relations using self-attention and demonstrates that the Transformer network is also well suited for abstract visual reasoning.

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.

Guillaume Bellec, David Kappel, Wolfgang Maass et al.

Neuromorphic hardware tends to pose limits on the connectivity of deep networks that one can run on them. But also generic hardware and software implementations of deep learning run more efficiently for sparse networks. Several methods exist for pruning connections of a neural network after it was trained without connectivity constraints. We present an algorithm, DEEP R, that enables us to train directly a sparsely connected neural network. DEEP R automatically rewires the network during supervised training so that connections are there where they are most needed for the task, while its total number is all the time strictly bounded. We demonstrate that DEEP R can be used to train very sparse feedforward and recurrent neural networks on standard benchmark tasks with just a minor loss in performance. DEEP R is based on a rigorous theoretical foundation that views rewiring as stochastic sampling of network configurations from a posterior.

David Kappel, Robert Legenstein, Stefan Habenschuss et al.

Synaptic connections between neurons in the brain are dynamic because of continuously ongoing spine dynamics, axonal sprouting, and other processes. In fact, it was recently shown that the spontaneous synapse-autonomous component of spine dynamics is at least as large as the component that depends on the history of pre- and postsynaptic neural activity. These data are inconsistent with common models for network plasticity, and raise the questions how neural circuits can maintain a stable computational function in spite of these continuously ongoing processes, and what functional uses these ongoing processes might have. Here, we present a rigorous theoretical framework for these seemingly stochastic spine dynamics and rewiring processes in the context of reward-based learning tasks. We show that spontaneous synapse-autonomous processes, in combination with reward signals such as dopamine, can explain the capability of networks of neurons in the brain to configure themselves for specific computational tasks, and to compensate automatically for later changes in the network or task. Furthermore we show theoretically and through computer simulations that stable computational performance is compatible with continuously ongoing synapse-autonomous changes. After reaching good computational performance it causes primarily a slow drift of network architecture and dynamics in task-irrelevant dimensions, as observed for neural activity in motor cortex and other areas. On the more abstract level of reinforcement learning the resulting model gives rise to an understanding of reward-driven network plasticity as continuous sampling of network configurations.

Zhaofei Yu, David Kappel, Robert Legenstein et al.

Synaptic plasticity is implemented and controlled through over thousand different types of molecules in the postsynaptic density and presynaptic boutons that assume a staggering array of different states through phosporylation and other mechanisms. One of the most prominent molecule in the postsynaptic density is CaMKII, that is described in molecular biology as a "memory molecule" that can integrate through auto-phosporylation Ca-influx signals on a relatively large time scale of dozens of seconds. The functional impact of this memory mechanism is largely unknown. We show that the experimental data on the specific role of CaMKII activation in dopamine-gated spine consolidation suggest a general functional role in speeding up reward-guided search for network configurations that maximize reward expectation. Our theoretical analysis shows that stochastic search could in principle even attain optimal network configurations by emulating one of the most well-known nonlinear optimization methods, simulated annealing. But this optimization is usually impeded by slowness of stochastic search at a given temperature. We propose that CaMKII contributes a momentum term that substantially speeds up this search. In particular, it allows the network to overcome saddle points of the fitness function. The resulting improved stochastic policy search can be understood on a more abstract level as Hamiltonian sampling, which is known to be one of the most efficient stochastic search methods.

David Kappel, Stefan Habenschuss, Robert Legenstein et al.

General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features of synaptic plasticity and spine motility enable cortical networks of neurons to carry out probabilistic inference by sampling from a posterior distribution of network configurations. This model provides a viable alternative to existing models that propose convergence of parameters to maximum likelihood values. It explains how priors on weight distributions and connection probabilities can be merged optimally with learned experience, how cortical networks can generalize learned information so well to novel experiences, and how they can compensate continuously for unforeseen disturbances of the network. The resulting new theory of network plasticity explains from a functional perspective a number of experimental data on stochastic aspects of synaptic plasticity that previously appeared to be quite puzzling.