Ciyaaraha waxaa loo soo saarka GPU-ka ah oo ku simuleertaa qiyaasadda brainstorm 1500x ka badan

Authors: Yichen Zhang Gan He Lei Ma Xiaofei Liu J. J. Johannes Hjorth Alexander Kozlov Yutao He Shenjian Zhang Jeanette Hellgren Kotaleski Yonghong Tian Sten Grillner Kai Du Tiejun Huang Haku: Qalabka Zhang Haku Lei Ma Shiinaha Liu J. J. Johannes Hjorth Alexander Kozlov Yutao He Shenjian Zhang Marka: Jeanette Hellgren Kotaleski Yonghong Tian Kaftansiga Kai Du Tiejun Huang Haku Biophysically detailed multi-compartment models are powerful tools to explore computational principles of the brain and also serve as a theoretical framework to generate algorithms for artificial intelligence (AI) systems. However, the expensive computational cost severely limits the applications in both the neuroscience and AI fields. The major bottleneck during simulating detailed compartment models is the ability of a simulator to solve large systems of linear equations. Here, we present a novel endritic Qalabka cheduling (DHS) method to markedly accelerate such a process. We theoretically prove that the DHS implementation is computationally optimal and accurate. This GPU-based method performs with 2-3 orders of magnitude higher speed than that of the classic serial Hines method in the conventional CPU platform. We build a DeepDendrite framework, which integrates the DHS method and the GPU computing engine of the NEURON simulator and demonstrate applications of DeepDendrite in neuroscience tasks. We investigate how spatial patterns of spine inputs affect neuronal excitability in a detailed human pyramidal neuron model with 25,000 spines. Furthermore, we provide a brief discussion on the potential of DeepDendrite for AI, specifically highlighting its ability to enable the efficient training of biophysically detailed models in typical image classification tasks. D H S Introduction Sida loo isticmaali karaa in ay u isticmaali karaa in ay u isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa in ay isticmaali karaa. , in which neurons were regarded as simple summing units, is still widely applied in neural computation, especially in neural network analysis. In recent years, modern artificial intelligence (AI) has utilized this principle and developed powerful tools, such as artificial neural networks (ANN) . However, in addition to comprehensive computations at the single neuron level, subcellular compartments, such as neuronal dendrites, can also carry out nonlinear operations as independent computational units , , , , Markaas ka mid ah, dendritic spines, mid ka mid ah mid ka mid ah mid ka mid ah dendrites ee neurons dendrites, waxay ka mid ah dhererka synaptic, si ay u isticmaali karaa in ay ka mid ah mid ka mid ah dendrites dadka ex vivo iyo in vivo , , , . 1 2 3 4 5 6 7 8 9 10 11 Simulations using biologically detailed neurons provide a theoretical framework for linking biological details to computational principles. The core of the biophysically detailed multi-compartment model framework , Waxaad ka heli doontaa in ay u dhismaha neurons la morphologies dendritic realist, conducctance ionic intrinsic, iyo inducts synaptic extrinsic. The dhismaha dhismaha multi-compartment dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha , which models the biophysical membrane properties of dendrites as passive cables, providing a mathematical description of how electronic signals invade and propagate throughout complex neuronal processes. By incorporating Cable theory with active biophysical mechanisms such as ion channels, excitatory and inhibitory synaptic currents, etc., a detailed multi-compartment model can achieve cellular and subcellular neuronal computations beyond experimental limitations , . 12 13 12 4 7 In addition to its profound impact on neuroscience, biologically detailed neuron models recently were utilized to bridge the gap between neuronal structural and biophysical details and AI. The prevailing technique in the modern AI field is ANNs consisting of point neurons, an analog to biological neural networks. Although ANNs with “backpropagation-of-error” (backprop) algorithm achieve remarkable performance in specialized applications, even beating top human professional players in the games of Go and chess , , the human brain still outperforms ANNs in domains that involve more dynamic and noisy environments , Qalabka dhismaha ugu horeysay oo ku yaalaa in ay ku yaalaa dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha , , Waxaa kale oo ka mid ah, model multi-compartment ah oo ah waxaa laga yaabaa in ay ka mid ah wax soo saarka nonlinear ee network-level for neurons by adjusting only the synaptic strength. , , demonstrating the full potential of the detailed models in building more powerful brain-like AI systems. Therefore, it is of high priority to expand paradigms in brain-like AI from single detailed neuron models to large-scale biologically detailed networks. 14 15 16 17 18 19 20 21 22 One long-standing challenge of the detailed simulation approach lies in its exceedingly high computational cost, which has severely limited its application to neuroscience and AI. The major bottleneck of the simulation is to solve linear equations based on the foundational theories of detailed modeling , , . To improve efficiency, the classic Hines method reduces the time complexity for solving equations from O(n3) to O(n), which has been widely applied as the core algorithm in popular simulators such as NEURON and GENESIS . However, this method uses a serial approach to process each compartment sequentially. When a simulation involves multiple biophysically detailed dendrites with dendritic spines, the linear equation matrix (“Hines Matrix”) scales accordingly with an increasing number of dendrites or spines (Fig. ), making Hines method no longer practical, since it poses a very heavy burden on the entire simulation. 12 23 24 25 26 1E Dhismaha Neurone ah ee layer-5 ee dhismaha pyramidal iyo dhismaha macluumaadka ee loo isticmaali karaa in dhismaha neurone ee dhismaha dhismaha. Workflow when numerically simulating detailed neuron models. The equation-solving phase is the bottleneck in the simulation. Qalabka linear ee simulators. Data dependency of the Hines method when solving linear equations in Haku The size of the Hines matrix scales with model complexity. The number of linear equations system to be solved undergoes a significant increase when models are growing more detailed. Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Shuruudaha ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah. Computational cost of three methods in when solving equations of a pyramidal model with spines. Run time of different methods on solving equations for 500 pyramidal models with spines. The run time indicates the time consumption of 1 s simulation (solving the equation 40,000 times with a time step of 0.025 ms). p-Hines parallel method in CoreNEURON (on GPU), Branch based branch-based parallel method (on GPU), DHS Dendritic hierarchical scheduling method (on GPU). a b c d c e f g h g i During past decades, tremendous progress has been achieved to speed up the Hines method by using parallel methods at the cellular level, which enables to parallelize the computation of different parts in each cell , , , , , Sida loo yaqaan "Cellular-level parallel methods" (methods parallel) waa mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah. 27 28 29 30 31 32 Here, we develop a fully automatic, numerically accurate, and optimized simulation tool that can significantly accelerate computation efficiency and reduce computational cost. In addition, this simulation tool can be seamlessly adopted for establishing and testing neural networks with biological details for machine learning and AI applications. Critically, we formulate the parallel computation of the Hines method as a mathematical scheduling problem and generate a Dendritic Hierarchical Scheduling (DHS) method based on combinatorial optimization and parallel computing theory Waayo, sidoo kale, waxaan ku dhigi karaa DHS ka mid ah macluumaadka GPU-ka ah oo ka mid ah macluumaadka macluumaadka GPU iyo macluumaadka macluumaadka macluumaadka. ) si loo yaqaan simulators classic Neuron while maintaining identical accuracy. 33 34 1 25 To enable detailed dendritic simulations for use in AI, we next establish the DeepDendrite framework by integrating the DHS-embedded CoreNEURON (an optimized compute engine for NEURON) platform as the simulation engine and two auxiliary modules (I/O module and learning module) supporting dendritic learning algorithms during simulations. DeepDendrite runs on the GPU hardware platform, supporting both regular simulation tasks in neuroscience and learning tasks in AI. 35 Sida loo yaqaan 'Dendritic Spine Inputs' (Dendritic Spine Inputs) waxaa loo yaqaan 'Dendritic Neuroscience' (Dendritic Neuroscience) (Dendritic Neuroscience) iyo 'Dendritic Spine Inputs' (Dendritic Spine Neuroscience' (Dendritic Spine Neuroscience) (Dendritic Neuroscience) (Dendritic Spine Neuroscience) (Dendritic Spine Neuroscience) (Dendritic Spine Neuroscience) (Dendritic Spine Neuroscience) (Dendritic Spine) (Dendritic Spine Inputs) (Dendritic Spine Neuroscience) (Dendritic Spine) (Dendritic Cudarada dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha Qalabka dhismaha synaptic burst-dependent , and learning with spike prediction . Overall, our study provides a complete set of tools that have the potential to change the current computational neuroscience community ecosystem. By leveraging the power of GPU computing, we envision that these tools will facilitate system-level explorations of computational principles of the brain’s fine structures, as well as promote the interaction between neuroscience and modern AI. 21 20 36 Results Dendritic Hierarchical Scheduling (DHS) method Computing ionic currents and solving linear equations are two critical phases when simulating biophysically detailed neurons, which are time-consuming and pose severe computational burdens. Fortunately, computing ionic currents of each compartment is a fully independent process so that it can be naturally parallelized on devices with massive parallel-computing units like GPUs . As a consequence, solving linear equations becomes the remaining bottleneck for the parallelization process (Fig. Haku 37 1A-F To tackle this bottleneck, cellular-level parallel methods have been developed, which accelerate single-cell computation by “splitting” a single cell into several compartments that can be computed in parallel , , Sidaas, ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah wax soo saarka ugu horeysay si ay u isticmaali karaa si ay u isticmaali karaa macluumaadka macluumaadka (Fig. Qalabka Qalabka Fig. Sidaas, waxaa laga yaabaa in ay ka mid ah wax soo saarka ee neurons la morphology asymmetrical, sidaas, neurons pyramidal iyo neurons Purkinje. 27 28 38 1g−i 1 We aim to develop a more efficient and precise parallel method for the simulation of biologically detailed neural networks. First, we establish the criteria for the accuracy of a cellular-level parallel method. Based on the theories in parallel computing , we propose three conditions to make sure a parallel method will yield identical solutions as the serial computing Hines method according to the data dependency in the Hines method (see Methods). Then to theoretically evaluate the run time, i.e., efficiency, of the serial and parallel computing methods, we introduce and formulate the concept of computational cost as the number of steps a method takes in solving equations (see Methods). 34 Based on the simulation accuracy and computational cost, we formulate the parallelization problem as a mathematical scheduling problem (see Methods). In simple terms, we view a single neuron as a tree with many nodes (compartments). For parallel threads, we can compute at most nodes at each step, but we need to ensure a node is computed only if all its children nodes have been processed; our goal is to find a strategy with the minimum number of steps for the entire procedure. k k Sida loo soo saarka partition optimaal, waxaan bixiyaan ka mid ah dhismaha Dendritic Hierarchical Scheduling (DHS) (ka dhismaha dhismaha ah waxaa la aasaasay in Methods). The key idea of DHS is to prioritize deep nodes (Fig. Dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha ). (2) After topology analysis, we search the candidates and pick at most deepest candidate nodes (a node is a candidate only if all its children nodes have been processed). This procedure repeats until all nodes are processed (Fig. Haku 2a 2b, c k 2d DHS work flow. DHS processes deepest candidate nodes each iteration. Illustration of calculating node depth of a compartmental model. The model is first converted to a tree structure then the depth of each node is computed. Colors indicate different depth values. Topology analysis on different neuron models. Six neurons with distinct morphologies are shown here. For each model, the soma is selected as the root of the tree so the depth of the node increases from the soma (0) to the distal dendrites. Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka with four threads. Candidates: nodes that can be processed. Selected candidates: nodes that are picked by DHS, i.e., the Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Nadiifinta: Parallelization strategy obtained by DHS after the process in . Each node is assigned to one of the four parallel threads. DHS reduces the steps of serial node processing from 14 to 5 by distributing nodes to multiple threads. Relative cost, i.e., the proportion of the computational cost of DHS to that of the serial Hines method, when applying DHS with different numbers of threads on different types of models. a k b c d b k e d f Take a simplified model with 15 compartments as an example, using the serial computing Hines method, it takes 14 steps to process all nodes, while using DHS with four parallel units can partition its nodes into five subsets (Fig. ): {{9,10,12,14}, {1,7,11,13}, {2,3,4,8}, {6}, {5}}. Because nodes in the same subset can be processed in parallel, it takes only five steps to process all nodes using DHS (Fig. ). 2D 2e Next, we apply the DHS method on six representative detailed neuron models (selected from ModelDB ) oo ka mid ah oo ka mid ah wax soo saarka (Fig. ):, including cortical and hippocampal pyramidal neurons , , , cerebellar Purkinje neurons Sida loo yaqaan striatal projection neurons (SPNs) ), and olfactory bulb mitral cells , covering the major principal neurons in sensory, cortical and subcortical areas. We then measured the computational cost. The relative computational cost here is defined by the proportion of the computational cost of DHS to that of the serial Hines method. The computational cost, i.e., the number of steps taken in solving equations, drops dramatically with increasing thread numbers. For example, with 16 threads, the computational cost of DHS is 7%-10% as compared to the serial Hines method. Intriguingly, the DHS method reaches the lower bounds of their computational cost for presented neurons when given 16 or even 8 parallel threads (Fig. ), suggesting adding more threads does not improve performance further because of the dependencies between compartments. 39 2F 40 41 42 43 44 45 2f Dhamaan, waxaan soo saarka dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha Speeding up DHS by GPU memory boosting DHS computes each neuron with multiple threads, which consumes a vast amount of threads when running neural network simulations. Graphics Processing Units (GPUs) consist of massive processing units (i.e., streaming processors, SPs, Fig. ) for parallel computing Sida loo helo, badan oo ka mid ah SPs on GPU waa in la socdaan simulaasi ah ee xarxa neural la mid ah (Fig. ). However, we consistently observed that the efficiency of DHS significantly decreased when the network size grew, which might result from scattered data storage or extra memory access caused by loading and writing intermediate results (Fig. , left). 3a, b 46 3c 3d GPU architecture and its memory hierarchy. Each GPU contains massive processing units (stream processors). Different types of memory have different throughput. Architecture of Streaming Multiprocessors (SMs). Each SM contains multiple streaming processors, registers, and L1 cache. Dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha Memory optimization strategy on GPU. Top panel, thread assignment and data storage of DHS, before (left) and after (right) memory boosting. Bottom, an example of a single step in triangularization when simulating two neurons in . Processors send a data request to load data for each thread from global memory. Without memory boosting (left), it takes seven transactions to load all request data and some extra transactions for intermediate results. With memory boosting (right), it takes only two transactions to load all request data, registers are used for intermediate results, which further improve memory throughput. Run time of DHS (32 threads each cell) with and without memory boosting on multiple layer 5 pyramidal models with spines. Speed up of memory boosting on multiple layer 5 pyramidal models with spines. Memory boosting brings 1.6-2 times speedup. a b c d d e f We solve this problem by GPU memory boosting, a method to increase memory throughput by leveraging GPU’s memory hierarchy and access mechanism. Based on the memory loading mechanism of GPU, successive threads loading aligned and successively-stored data lead to a high memory throughput compared to accessing scatter-stored data, which reduces memory throughput , . To achieve high throughput, we first align the computing orders of nodes and rearrange threads according to the number of nodes on them. Then we permute data storage in global memory, consistent with computing orders, i.e., nodes that are processed at the same step are stored successively in global memory. Moreover, we use GPU registers to store intermediate results, further strengthening memory throughput. The example shows that memory boosting takes only two memory transactions to load eight request data (Fig. , right). Furthermore, experiments on multiple numbers of pyramidal neurons with spines and the typical neuron models (Fig. ; Supplementary Fig. Waxaa la soo bandhigay in ay ka mid ah wax soo saarka iyo wax soo saarka ah oo ka mid ah wax soo saarka iyo wax soo saarka. 46 47 3d 3e, f 2 Waayo, si ay u adeegsanayo wax soo saarka DHS oo loo isticmaali karaa GPU memory boosting, waxaan ka heli karaa mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah. Dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha ). Moreover, compared to the conventional serial Hines method in NEURON running with a single-thread of CPU, DHS speeds up the simulation by 2-3 orders of magnitude (Supplementary Fig. ), while retaining the identical numerical accuracy in the presence of dense spines (Supplementary Figs. and Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka ) and different segmentation strategies (Supplementary Fig. ). 4 4a 3 4 8 7 7 Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ka mid ah. , Dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha a b c Dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha To gain insights into the working mechanism of the DHS method, we visualized the partitioning process by mapping compartments to each thread (every color presents a single thread in Fig. Shuruudaha ugu horeysay ee loo yaabaa in ay ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah. ). Interestingly, DHS generates aligned partitions in morphologically symmetric neurons such as the striatal projection neuron (SPN) and the Mitral cell (Fig. ). By contrast, it generates fragmented partitions of morphologically asymmetric neurons like the pyramidal neurons and Purkinje cell (Fig. ), indicating that DHS splits the neural tree at individual compartment scale (i.e., tree node) rather than branch scale. This cell-type-specific fine-grained partition enables DHS to fully exploit all available threads. 4b, c 4B, C 4b, c 4B, C Dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha DHS enables spine-level modelling Sida dendritic spines waxay ka mid ah dhismaha qiyaasta ah ee dhismaha pyramidal cortical iyo hippocampal, dhismaha proyection striatal, iwm, morfology iyo plasticity waa mid ka mid ah qiyaasta dhismaha neuronal. , , , , . However, spines are too small ( ~ 1 μm length) to be directly measured experimentally with regard to voltage-dependent processes. Thus, theoretical work is critical for the full understanding of the spine computations. 10 48 49 50 51 We can model a single spine with two compartments: the spine head where synapses are located and the spine neck that links the spine head to dendrites . The theory predicts that the very thin spine neck (0.1-0.5 um in diameter) electronically isolates the spine head from its parent dendrite, thus compartmentalizing the signals generated at the spine head Sida loo yaqaan 'Dendrites' iyo 'Dendrites' (Dendrites) waxaa loo yaqaan 'Dendrites' (Dendrites) iyo 'Dendrites' (Dendrites) waxaa loo yaqaan 'Dendrites' (Dendrites) iyo 'Dendrites' (Dendrites). Haku Spine Sida loo isticmaali karaa, waxaa loo isticmaali karaa in ka mid ah wax soo saarka ah. spine factor aims at approximating the spine effect on the biophysical properties of the cell membrane . 52 53 F 54 F 54 Inspired by the previous work of Eyal et al. , we investigated how different spatial patterns of excitatory inputs formed on dendritic spines shape neuronal activities in a human pyramidal neuron model with explicitly modeled spines (Fig. ). Noticeably, Eyal et al. employed the spine factor to incorporate spines into dendrites while only a few activated spines were explicitly attached to dendrites (“few-spine model” in Fig. ). The value of spine in their model was computed from the dendritic area and spine area in the reconstructed data. Accordingly, we calculated the spine density from their reconstructed data to make our full-spine model more consistent with Eyal’s few-spine model. With the spine density set to 1.3 μm-1, the pyramidal neuron model contained about 25,000 spines without altering the model’s original morphological and biophysical properties. Further, we repeated the previous experiment protocols with both full-spine and few-spine models. We use the same synaptic input as in Eyal’s work but attach extra background noise to each sample. By comparing the somatic traces (Fig. ) and spike probability (Fig. ) in full-spine and few-spine models, we found that the full-spine model is much leakier than the few-spine model. In addition, the spike probability triggered by the activation of clustered spines appeared to be more nonlinear in the full-spine model (the solid blue line in Fig. ) than in the few-spine model (the dashed blue line in Fig. ). These results indicate that the conventional F-factor method may underestimate the impact of dense spine on the computations of dendritic excitability and nonlinearity. 51 5a F 5a F 5b, c 5d 5d 5d Experiment setup. We examine two major types of models: few-spine models and full-spine models. Few-spine models (two on the left) are the models that incorporated spine area globally into dendrites and only attach individual spines together with activated synapses. In full-spine models (two on the right), all spines are explicitly attached over whole dendrites. We explore the effects of clustered and randomly distributed synaptic inputs on the few-spine models and the full-spine models, respectively. Somatic voltages recorded for cases in . Colors of the voltage curves correspond to , scale bar: 20 ms, 20 mV. Color-coded voltages during the simulation in at specific times. Colors indicate the magnitude of voltage. Somatic spike probability as a function of the number of simultaneously activated synapses (as in Eyal et al.’s work) for four cases in . Background noise is attached. Run time of experiments in with different simulation methods. NEURON: conventional NEURON simulator running on a single CPU core. CoreNEURON: CoreNEURON simulator on a single GPU. DeepDendrite: DeepDendrite on a single GPU. a b a a c b d a e d In the DeepDendrite platform, both full-spine and few-spine models achieved 8 times speedup compared to CoreNEURON on the GPU platform and 100 times speedup compared to serial NEURON on the CPU platform (Fig. ; Supplementary Table ) while keeping the identical simulation results (Supplementary Figs. and Sidaas, dhismaha DHS waxay ku habboonay in ay ku habboonay dendritic excitability oo ka mid ah warshadaha anatomics ugu realist ah. 5e 1 4 8 Discussion In this work, we propose the DHS method to parallelize the computation of Hines method and we mathematically demonstrate that the DHS provides an optimal solution without any loss of precision. Next, we implement DHS on the GPU hardware platform and use GPU memory boosting techniques to refine the DHS (Fig. ). When simulating a large number of neurons with complex morphologies, DHS with memory boosting achieves a 15-fold speedup (Supplementary Table ) as compared to the GPU method used in CoreNEURON and up to 1,500-fold speedup compared to serial Hines method in the CPU platform (Fig. ; Supplementary Fig. and Supplementary Table ). Furthermore, we develop the GPU-based DeepDendrite framework by integrating DHS into CoreNEURON. Finally, as a demonstration of the capacity of DeepDendrite, we present a representative application: examine spine computations in a detailed pyramidal neuron model with 25,000 spines. Further in this section, we elaborate on how we have expanded the DeepDendrite framework to enable efficient training of biophysically detailed neural networks. To explore the hypothesis that dendrites improve robustness against adversarial attacks , we train our network on typical image classification tasks. We show that DeepDendrite can support both neuroscience simulations and AI-related detailed neural network tasks with unprecedented speed, therefore significantly promoting detailed neuroscience simulations and potentially for future AI explorations. 55 3 1 4 3 1 56 Decades of efforts have been invested in speeding up the Hines method with parallel methods. Early work mainly focuses on network-level parallelization. In network simulations, each cell independently solves its corresponding linear equations with the Hines method. Network-level parallel methods distribute a network on multiple threads and parallelize the computation of each cell group with each thread , . With network-level methods, we can simulate detailed networks on clusters or supercomputers . In recent years, GPU has been used for detailed network simulation. Because the GPU contains massive computing units, one thread is usually assigned one cell rather than a cell group , , . With further optimization, GPU-based methods achieve much higher efficiency in network simulation. However, the computation inside the cells is still serial in network-level methods, so they still cannot deal with the problem when the “Hines matrix” of each cell scales large. 57 58 59 35 60 61 Cellular-level parallel methods further parallelize the computation inside each cell. The main idea of cellular-level parallel methods is to split each cell into several sub-blocks and parallelize the computation of those sub-blocks , . However, typical cellular-level methods (e.g., the “multi-split” method Marka aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan yahay. , , or making approximations on some crucial compartments, while solving linear equations , . These finer-grained parallelization strategies can get higher efficiency but lack sufficient numerical accuracy as in the original Hines method. 27 28 28 29 38 62 63 64 Unlike previous methods, DHS adopts the finest-grained parallelization strategy, i.e., compartment-level parallelization. By modeling the problem of “how to parallelize” as a combinatorial optimization problem, DHS provides an optimal compartment-level parallelization strategy. Moreover, DHS does not introduce any extra operation or value approximation, so it achieves the lowest computational cost and retains sufficient numerical accuracy as in the original Hines method at the same time. Dendritic spines waa mid ka mid ah microstructures ugu caawin ah ee brainstorms for proyection neurons in the cortex, hippocampus, cerebellum, iyo ganglia basal. Sida spines waxay ka mid ah in ay ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah nidaamka caawin ah, qalabka elektric ka mid ah oo ka mid ah spines waa qalabka ugu caawin ah ee macluumaadka caawin ah ee forebrain iyo cerebellum , . The structure of the spine, with an enlarged spine head and a very thin spine neck—leads to surprisingly high input impedance at the spine head, which could be up to 500 MΩ, combining experimental data and the detailed compartment modeling approach , . Due to such high input impedance, a single synaptic input can evoke a “gigantic” EPSP ( ~ 20 mV) at the spine-head level , , thereby boosting NMDA currents and ion channel currents in the spine . However, in the classic single detailed compartment models, all spines are replaced by the coefficient modifying the dendritic cable geometries . This approach may compensate for the leak currents and capacitance currents for spines. Still, it cannot reproduce the high input impedance at the spine head, which may weaken excitatory synaptic inputs, particularly NMDA currents, thereby reducing the nonlinearity in the neuron’s input-output curve. Our modeling results are in line with this interpretation. 10 11 48 65 48 66 11 F 54 On the other hand, the spine’s electrical compartmentalization is always accompanied by the biochemical compartmentalization , , , resulting in a drastic increase of internal [Ca2+], within the spine and a cascade of molecular processes involving synaptic plasticity of importance for learning and memory. Intriguingly, the biochemical process triggered by learning, in turn, remodels the spine’s morphology, enlarging (or shrinking) the spine head, or elongating (or shortening) the spine neck, which significantly alters the spine’s electrical capacity , , , Sida loo yaqaan "plasticity structural" waxaa loo yaqaan "correlation morphology" waxaa loo yaqaan "plasticity structural" waxaa loo yaqaan "cortex visual" (cortex visual). , , somatosensory cortex , Marka: Motor Cortex , hippocampus , and the basal ganglia In vivo. Waayo, ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ). Therefore, it enables us to explore of structural plasticity in large-scale circuit models across diverse brain regions. 8 52 67 67 68 69 70 71 72 73 74 75 9 76 5e Another critical issue is how to link dendrites to brain functions at the systems/network level. It has been well established that dendrites can perform comprehensive computations on synaptic inputs due to enriched ion channels and local biophysical membrane properties , , . For example, cortical pyramidal neurons can carry out sublinear synaptic integration at the proximal dendrite but progressively shift to supralinear integration at the distal dendrite Dhamaan, dendrites distal waxaa loo isticmaali karaa wax soo saarka sida dendritic sodium spikes, calcium spikes, iyo NMDA spikes/plateau potentials. , . Such dendritic events are widely observed in mice or even human cortical neurons in vitro, which may offer various logical operations , or gating functions , . Recently, in vivo recordings in awake or behaving mice provide strong evidence that dendritic spikes/plateau potentials are crucial for orientation selectivity in the visual cortex , sensory-motor integration in the whisker system , , and spatial navigation in the hippocampal CA1 region . 5 6 7 77 6 78 6 79 6 79 80 81 82 83 84 85 To establish the causal link between dendrites and animal (including human) patterns of behavior, large-scale biophysically detailed neural circuit models are a powerful computational tool to realize this mission. However, running a large-scale detailed circuit model of 10,000-100,000 neurons generally requires the computing power of supercomputers. It is even more challenging to optimize such models for in vivo data, as it needs iterative simulations of the models. The DeepDendrite framework can directly support many state-of-the-art large-scale circuit models , , , which were initially developed based on NEURON. Moreover, using our framework, a single GPU card such as Tesla A100 could easily support the operation of detailed circuit models of up to 10,000 neurons, thereby providing carbon-efficient and affordable plans for ordinary labs to develop and optimize their own large-scale detailed models. 86 87 88 Waayo, wax soo saarka ugu horeysay ee wax soo saarka dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha , and exploring full learning potentials on more realistic neuron , . However, there lies a trade-off between model size and biological detail, as the increase in network scale is often sacrificed for neuron-level complexity , , . Moreover, more detailed neuron models are less mathematically tractable and computationally expensive . 20 21 22 19 20 89 21 There has also been progress in the role of active dendrites in ANNs for computer vision tasks. Iyer et al. . proposed a novel ANN architecture with active dendrites, demonstrating competitive results in multi-task and continual learning. Jones and Kording used a binary tree to approximate dendrite branching and provided valuable insights into the influence of tree structure on single neurons’ computational capacity. Bird et al. . proposed a dendritic normalization rule based on biophysical behavior, offering an interesting perspective on the contribution of dendritic arbor structure to computation. While these studies offer valuable insights, they primarily rely on abstractions derived from spatially extended neurons, and do not fully exploit the detailed biological properties and spatial information of dendrites. Further investigation is needed to unveil the potential of leveraging more realistic neuron models for understanding the shared mechanisms underlying brain computation and deep learning. 90 91 92 In response to these challenges, we developed DeepDendrite, a tool that uses the Dendritic Hierarchical Scheduling (DHS) method to significantly reduce computational costs and incorporates an I/O module and a learning module to handle large datasets. With DeepDendrite, we successfully implemented a three-layer hybrid neural network, the Human Pyramidal Cell Network (HPC-Net) (Fig. ). This network demonstrated efficient training capabilities in image classification tasks, achieving approximately 25 times speedup compared to training on a traditional CPU-based platform (Fig. ; Supplementary Table ). 6a, b 6f 1 The illustration of the Human Pyramidal Cell Network (HPC-Net) for image classification. Images are transformed to spike trains and fed into the network model. Learning is triggered by error signals propagated from soma to dendrites. Training with mini-batch. Multiple networks are simulated simultaneously with different images as inputs. The total weight updates ΔW are computed as the average of ΔWi from each network. Comparison of the HPC-Net before and after training. Left, the visualization of hidden neuron responses to a specific input before (top) and after (bottom) training. Right, hidden layer weights (from input to hidden layer) distribution before (top) and after (bottom) training. Shuruudaha wax soo saarka ee shuruudaha wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax saarka wax soo saarka wax saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax saarka wax soo saarka Prediction accuracy of each model on adversarial samples after training 30 epochs on MNIST (left) and Fashion-MNIST (right) datasets. HPC-Net waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah a b c d e f Additionally, it is widely recognized that the performance of Artificial Neural Networks (ANNs) can be undermined by adversarial attacks —intentionally engineered perturbations devised to mislead ANNs. Intriguingly, an existing hypothesis suggests that dendrites and synapses may innately defend against such attacks . Our experimental results utilizing HPC-Net lend support to this hypothesis, as we observed that networks endowed with detailed dendritic structures demonstrated some increased resilience to transfer adversarial attacks compared to standard ANNs, as evident in MNIST and Fashion-MNIST datasets (Fig. ). This evidence implies that the inherent biophysical properties of dendrites could be pivotal in augmenting the robustness of ANNs against adversarial interference. Nonetheless, it is essential to conduct further studies to validate these findings using more challenging datasets such as ImageNet . 93 56 94 95 96 6d, e 97 In conclusion, DeepDendrite has shown remarkable potential in image classification tasks, opening up a world of exciting future directions and possibilities. To further advance DeepDendrite and the application of biologically detailed dendritic models in AI tasks, we may focus on developing multi-GPU systems and exploring applications in other domains, such as Natural Language Processing (NLP), where dendritic filtering properties align well with the inherently noisy and ambiguous nature of human language. Challenges include testing scalability in larger-scale problems, understanding performance across various tasks and domains, and addressing the computational complexity introduced by novel biological principles, such as active dendrites. By overcoming these limitations, we can further advance the understanding and capabilities of biophysically detailed dendritic neural networks, potentially uncovering new advantages, enhancing their robustness against adversarial attacks and noisy inputs, and ultimately bridging the gap between neuroscience and modern AI. Haku Simulation with DHS CoreNEURON simulator ( Ku saabsan Neuron architecture and is optimized for both memory usage and computational speed. We implement our Dendritic Hierarchical Scheduling (DHS) method in the CoreNEURON environment by modifying its source code. All models that can be simulated on GPU with CoreNEURON can also be simulated with DHS by executing the following command: 35 https://github.com/BlueBrain/CoreNeuron 25 Coreneuron_exec -d /path/to/models -e waqti --cell-permute 3 --cell-nthread 16 --gpu The usage options are as in Table . 1 Accuracy of the simulation using cellular-level parallel computation To ensure the accuracy of the simulation, we first need to define the correctness of a cellular-level parallel algorithm to judge whether it will generate identical solutions compared with the proven correct serial methods, like the Hines method used in the NEURON simulation platform. Based on the theories in parallel computing , a parallel algorithm will yield an identical result as its corresponding serial algorithm, if and only if the data process order in the parallel algorithm is consistent with data dependency in the serial method. The Hines method has two symmetrical phases: triangularization and back-substitution. By analyzing the serial computing Hines method , we find that its data dependency can be formulated as a tree structure, where the nodes on the tree represent the compartments of the detailed neuron model. In the triangularization process, the value of each node depends on its children nodes. In contrast, during the back-substitution process, the value of each node is dependent on its parent node (Fig. ). Thus, we can compute nodes on different branches in parallel as their values are not dependent. 34 55 1d Based on the data dependency of the serial computing Hines method, we propose three conditions to make sure a parallel method will yield identical solutions as the serial computing Hines method: (1) The tree morphology and initial values of all nodes are identical to those in the serial computing Hines method; (2) In the triangularization phase, a node can be processed if and only if all its children nodes are already processed; (3) In the back-substitution phase, a node can be processed only if its parent node is already processed. Once a parallel computing method satisfies these three conditions, it will produce identical solutions as the serial computing method. Computational cost of cellular-level parallel computing method Waayo, si ay u baahan tahay in ay u baahan tahay in ay u baahan tahay in ay u baahan tahay in ay u baahan tahay in ay u baahan tahay in ay u baahan tahay in ay u baahan tahay in ay u baahan tahay in ay u baahan tahay in ay u baahan tahay in ay u baahan tahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay. iyo threads (basic computational units) to perform triangularization, parallel triangularization equals to divide the node set of into subsets, i.e., Haku: , , … } where the size of each subset | | ≤ , i.e., at most nodes can be processed each step since there are only threads. The process of the triangularization phase follows the order: → → … → , and nodes in the same subset can be processed in parallel. So, we define | | (the size of set , i.e., Sida loo isticmaali karaa in ay u isticmaali karaa macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluuma T k V T n V QEEBE1 V2 Vn Vi k k k V1 V2 Vn Vi V V n Mathematical scheduling problem Based on the simulation accuracy and computational cost, we formulate the parallelization problem as a mathematical scheduling problem: Given a tree = { , } and a positive integer , where is the node-set and is the edge set. Define partition ( Haku: , Haku: }, | | ≤ , 1 ≤ ≤ n, where | | indicates the cardinal number of subset , i.e., the number of nodes in Sida loo yaqaan 'Node' ∈ , all its children nodes { | ∈children( )} must in a previous subset , where 1 ≤ < . Our goal is to find an optimal partition ( ) whose computational cost | ( )| is minimal. T V E k V E P V V1 V2 Vn Vi k i Vi Vi Vi v QEEBE c c v Vj j i P* V P* V Here subset Qalabka waxaa laga yaabaa in ay ku habboonay -th step (Fig. ), so | | ≤ indicates that we can compute Qalabka ugu horeysay oo ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah. . The restriction “for each node ∈ , all its children nodes { | ∈children( )} must in a previous subset , where 1 ≤ < ” indicates that node can be processed only if all its child nodes are processed. Vi i 2e Vi k k k v Vi c c v Vj j i v DHS implementation We aim to find an optimal way to parallelize the computation of solving linear equations for each neuron model by solving the mathematical scheduling problem above. To get the optimal partition, DHS first analyzes the topology and calculates the depth ( c) Waayo, Node ∈ . Then, the following two steps will be executed iteratively until every node ∈ is assigned to a subset: (1) find all candidate nodes and put these nodes into candidate set . A node is a candidate only if all its child nodes have been processed or it does not have any child nodes. (2) if | | ≤ , i.e., the number of candidate nodes is smaller or equivalent to the number of available threads, remove all nodes in and put them into Si kastaba ha ahaado deepest nodes from and add them to subset . Label these nodes as processed nodes (Fig. ). After filling in subset , go to step (1) to fill in the next subset . d v v V v V Q Q k Q V*i k Q Vi 2d Vi Vi+1 Correctness proof for DHS After applying DHS to a neural tree = { , }, we get a partition ( ) = { , , … }, | | ≤ , 1 ≤ ≤ . Nodes in the same subset will be computed in parallel, taking steps to perform triangularization and back-substitution, respectively. We then demonstrate that the reordering of the computation in DHS will result in a result identical to the serial Hines method. T V E P V V1 V2 Vn Vi k i n Vi n The partition ( ) obtained from DHS decides the computation order of all nodes in a neural tree. Below we demonstrate that the computation order determined by ( ) satisfies the correctness conditions. ( ) is obtained from the given neural tree Qalabka dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha to . As shown in the implementation of DHS, all nodes in subset are selected from the candidate set , and a node can be put into Sida loo yaabaa, waxaa laga yaabaa in ay ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah. are in { Haku Haku: }, meaning that a node is only computed after all its children have been processed, which satisfies condition 2: in triangularization, a node can be processed if and only if all its child nodes are already processed. In back-substitution, the computation order is the opposite of that in triangularization, i.e., from to . As shown before, the child nodes of all nodes in are in { , , … }, so parent nodes of nodes in are in { , , … }, which satisfies condition 3: in back-substitution, a node can be processed only if its parent node is already processed. P V P V P V T V1 Vn QEEBE Q Q Vi V1 V2 Vi-1 Vn V1 QEEBE V1 V2 Vi-1 Vi Vi+1 Vi+2 Vn Optimality proof for DHS Dhismaha waa in uu ku yaalaa in ay ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah. For each subset in ( ), DHS moves (thread number) deepest nodes from the corresponding candidate set to . If the number of nodes in is smaller than , move all nodes from to . To simplify, we introduce , indicating the depth sum of deepest nodes in . All subsets in ( ) satisfy the max-depth criteria (Supplementary Fig. ): . We then prove that selecting the deepest nodes in each iteration makes an optimal partition. If there exists an optimal partition = { , , … } containing subsets that do not satisfy the max-depth criteria, we can modify the subsets in ( ) so that all subsets consist of the deepest nodes from and the number of subsets ( | ( )|) remain the same after modification. Vi P V k Qi Vi Qi k Qi Vi Di k Qi P V 6a P(V) P*(V) V*1 V*2 V*s P* V Q P* V Without any loss of generalization, we start from the first subset not satisfying the criteria, i.e., . There are two possible cases that will make Waxaa la heli karaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa. | < and there exist some valid nodes in that are not put to ; (2) | | = but nodes in Waxay ku saabsan deepest nodes in . V*i QEEBE QEEBE k Qi QEEBE V*i k V*i k Qi For case (1), because some candidate nodes are not put to , these nodes must be in the subsequent subsets. As | | , we can move the corresponding nodes from the subsequent subsets to , which will not increase the number of subsets and make satisfy the criteria (Supplementary Fig. , top). For case (2), | | = , these deeper nodes that are not moved from the candidate set into must be added to subsequent subsets (Supplementary Fig. , bottom). These deeper nodes can be moved from subsequent subsets to Sida loo isticmaali karaa, waxaa laga yaabaa in la soo saarka , is picked and one of the -th deepest nodes Waxaa laga yaabaa , thus will be put into a subsequent subset (Ee) > Waayo, waxaan ka mid ahay from to + QEEBE , then modify subset + as follows: if | + QEEBE Haku ≤ and none of the nodes in + QEEBE Ku saabsan Node , stop modifying the latter subsets. Otherwise, modify + as follows (Supplementary Fig. (Waa'iid wax soo saarka ah oo ka mid ah wax soo saarka) is in + , move this parent node to + QEEBE ; else move the node with minimum depth from + Haku + QEEBE . After adjusting Qalabka ugu horeysay ee subset + Haku + QEEBE , … with the same strategy. Finally, move Marka to . V*i QEEBE < k V*i V*i 6B V*i k Qi V*i 6B V*i V*i v k Qalabka Qi v’ V*j j i v V*i V*i 1 QEEBE 1 QEEBE 1 k V*i 1 v V*i 1 6C v V*i 1 QEEBE 2 QEEBE 1 V*i 2 V*i V*i 1 QEEBE 2 QEEBE 1 v’ V*j V*i Sida loo isticmaali karaa, waxaan u isticmaali karaa mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah. Waayo, la Qalabka ugu badan ee and keep the number of subsets, i.e., | ( )| the same after modification. We can modify the nodes with the same strategy for all subsets in ( ) that do not contain the deepest nodes. Finally, all subsets ∈ ( ) waxaa laga yaqaan max-dhismaha kharashka, iyo ( )| does not change after modifying. V*i k Qi P* V P* V QEEBE Haku V Haku V Qalabka dhismaha dhismaha dhismaha dhismaha ( ), and all subsets ∈ ( ) satisfy the max-depth condition: . For any other optimal partition ( ) we can modify its subsets to make its structure the same as ( ), i.e., each subset consists of the deepest nodes in the candidate set, and keep | ( ) the same after modification. So, the partition ( ) obtained from DHS is one of the optimal partitions. P V Vi P V Haku V P V P* V | P V GPU implementation and memory boosting To achieve high memory throughput, GPU utilizes the memory hierarchy of (1) global memory, (2) cache, (3) register, where global memory has large capacity but low throughput, while registers have low capacity but high throughput. We aim to boost memory throughput by leveraging the memory hierarchy of GPU. GPU employs SIMT (Single-Instruction, Multiple-Thread) architecture. Warps are the basic scheduling units on GPU (a warp is a group of 32 parallel threads). A warp executes the same instruction with different data for different threads Qalabka dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha 46 When a warp loads pre-aligned and successively-stored data from global memory, it can make full use of the cache, which leads to high memory throughput, while accessing scatter-stored data would reduce memory throughput. After compartments assignment and threads rearrangement, we permute data in global memory to make it consistent with computing orders so that warps can load successively-stored data when executing the program. Moreover, we put those necessary temporary variables into registers rather than global memory. Registers have the highest memory throughput, so the use of registers further accelerates DHS. Qalabka biophysical full-spine iyo few-spine We used the published human pyramidal neuron . The membrane capacitance m = 0.44 μF cm-2, membrane resistance m = 48,300 Ω cm2 iyo resistivity axial a = 261.97 Ω cm. In this model, all dendrites were modeled as passive cables while somas were active. The leak reversal potential l = -83.1 mV. Ion channels such as Na+ and K+ were inserted on soma and initial axon, and their reversal potentials were Na = 67.6 mV, K = -102 mV respectively. All these specific parameters were set the same as in the model of Eyal, et al. , for more details please refer to the published model (ModelDB, access No. 238347). 51 c r r E E E 51 In the few-spine model, the membrane capacitance and maximum leak conductance of the dendritic cables 60 μm away from soma were multiplied by a spine factor to approximate dendritic spines. In this model, spine was set to 1.9. Only the spines that receive synaptic inputs were explicitly attached to dendrites. F F In the full-spine model, all spines were explicitly attached to dendrites. We calculated the spine density with the reconstructed neuron in Eyal, et al. . The spine density was set to 1.3 μm-1, and each cell contained 24994 spines on dendrites 60 μm away from the soma. 51 Shuruudaha dhismaha iyo biophysical ah ee shuruudaha waa mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah. neck = 1.35 μm and the diameter neck = 0.25 μm, whereas the length and diameter of the spine head were 0.944 μm, i.e., the spine head area was set to 2.8 μm2. Both spine neck and spine head were modeled as passive cables, with the reversal potential = -86 mV. The specific membrane capacitance, membrane resistance, and axial resistivity were the same as those for dendrites. L D QEEBE Synaptic inputs We investigated neuronal excitability for both distributed and clustered synaptic inputs. All activated synapses were attached to the terminal of the spine head. For distributed inputs, all activated synapses were randomly distributed on all dendrites. For clustered inputs, each cluster consisted of 20 activated synapses that were uniformly distributed on a single randomly-selected compartment. All synapses were activated simultaneously during the simulation. AMPA-based and NMDA-based synaptic currents were simulated as in Eyal et al.’s work. AMPA conductance was modeled as a double-exponential function and NMDA conduction as a voltage-dependent double-exponential function. For the AMPA model, the specific rise and decay were set to 0.3 and 1.8 ms. For the NMDA model, rise and decay were set to 8.019 and 34.9884 ms, respectively. The maximum conductance of AMPA and NMDA were 0.73 nS and 1.31 nS. τ τ τ τ Background noise Waayo, sidoo kale waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah. start = 10 ms and lasted until the end of the simulation. We generated 400 noise spike trains for each cell and attached them to randomly-selected synapses. The model and specific parameters of synaptic currents were the same as described in , except that the maximum conductance of NMDA was uniformly distributed from 1.57 to 3.275, resulting in a higher AMPA to NMDA ratio. t Synaptic Inputs Exploring neuronal excitability We investigated the spike probability when multiple synapses were activated simultaneously. For distributed inputs, we tested 14 cases, from 0 to 240 activated synapses. For clustered inputs, we tested 9 cases in total, activating from 0 to 12 clusters respectively. Each cluster consisted of 20 synapses. For each case in both distributed and clustered inputs, we calculated the spike probability with 50 random samples. Spike probability was defined as the ratio of the number of neurons fired to the total number of samples. All 1150 samples were simulated simultaneously on our DeepDendrite platform, reducing the simulation time from days to minutes. Performing AI tasks with the DeepDendrite platform Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid DeepDendrite consists of three modules (Supplementary Fig. ): (1) an I/O module; (2) a DHS-based simulating module; (3) a learning module. When training a biophysically detailed model to perform learning tasks, users first define the learning rule, then feed all training samples to the detailed model for learning. In each step during training, the I/O module picks a specific stimulus and its corresponding teacher signal (if necessary) from all training samples and attaches the stimulus to the network model. Then, the DHS-based simulating module initializes the model and starts the simulation. After simulation, the learning module updates all synaptic weights according to the difference between model responses and teacher signals. After training, the learned model can achieve performance comparable to ANN. The testing phase is similar to training, except that all synaptic weights are fixed. 5 HPC-Net model Image classification is a typical task in the field of AI. In this task, a model should learn to recognize the content in a given image and output the corresponding label. Here we present the HPC-Net, a network consisting of detailed human pyramidal neuron models that can learn to perform image classification tasks by utilizing the DeepDendrite platform. HPC-Net has three layers, i.e., an input layer, a hidden layer, and an output layer. The neurons in the input layer receive spike trains converted from images as their input. Hidden layer neurons receive the output of input layer neurons and deliver responses to neurons in the output layer. The responses of the output layer neurons are taken as the final output of HPC-Net. Neurons between adjacent layers are fully connected. Sida loo yaabaa, waxaa laga yaabaa in ay ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah ( ) in the image, the corresponding spike train has a constant interspike interval ISI( ) (in ms) which is determined by the pixel value ( ) as shown in Eq. ( ). x, y τ x, y p x, y 1 In our experiment, the simulation for each stimulus lasted 50 ms. All spike trains started at 9 + Isis ms iyo ku yaalaa ka hor si ay u helo simulation. Markaad ka dib markii uu soo bandhigiisa oo dhan ee shuruudaha shuruudaha qiyaastii ah ee one-to-one way. The shuruudaha synaptic la yaabaa by the spike arriving at time is given by τ Haku where is the post-synaptic voltage, the reversal potential syn = 1 mV, xawaaraha synaptic ugu badan max = 0.05 μS, and the time constant = 0.5 ms. v E g τ Neurons in the input layer were modeled with a passive single-compartment model. The specific parameters were set as follows: membrane capacitance m = 1.0 μF cm-2, membrane resistance m = 104 Ω cm2, axial resistivity a = 100 Ω cm, potentado reversal ee dhismaha dhismaha l = 0 mV. c r r E The hidden layer contains a group of human pyramidal neuron models, receiving the somatic voltages of input layer neurons. The morphology was from Eyal, et al. , and all neurons were modeled with passive cables. The specific membrane capacitance m = 1.5 μF cm-2, membrane resistance m = 48,300 Ω cm2, axial resistivity a = 261.97 Ω cm, and the reversal potential of all passive cables l = 0 mV. Input neurons could make multiple connections to randomly-selected locations on the dendrites of hidden neurons. The synaptic current activated by the -th synapse of the -th input neuron on neuron ’s dendrite is defined as in Eq. ( Ku saabsan Sida loo yaqaan Synaptic Conductance, is the synaptic weight, is the ReLU-like somatic activation function, and is the somatic voltage of the -th input neuron at time . 51 c r r E k i j 4 gijk Wijk i t Neurons in the output layer were also modeled with a passive single-compartment model, and each hidden neuron only made one synaptic connection to each output neuron. All specific parameters were set the same as those of the input neurons. Synaptic currents activated by hidden neurons are also in the form of Eq. ( ). 4 Image classification with HPC-Net For each input image stimulus, we first normalized all pixel values to 0.0-1.0. Then we converted normalized pixels to spike trains and attached them to input neurons. Somatic voltages of the output neurons are used to compute the predicted probability of each class, as shown in equation Ku saabsan is the probability of -th class predicted by the HPC-Net, is the average somatic voltage from 20 ms to 50 ms of the -th output neuron, and Qalabka dhismaha iyo dhismaha iyo dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha. 6 pi i i C Synaptic plasticity rules for HPC-Net Inspired by previous work , we use a gradient-based learning rule to train our HPC-Net to perform the image classification task. The loss function we use here is cross-entropy, given in Eq. ( ), where is the predicted probability for class , indicates the actual class the stimulus image belongs to, = 1 if input image belongs to class , and = 0 if not. 36 7 pi i yi yi i yi When training HPC-Net, we compute the update for weight (the synaptic weight of the Sida loo isticmaali karaa neuron to neuron ) at each time step. After the simulation of each image stimulus, is updated as shown in Eq. ( ee: Wijk k i j Wijk 8 Here is the learning rate, is the update value at time , , are somatic voltages of neuron iyo respectively, is the -th synaptic current activated by neuron on neuron , its synaptic conductance, Sida loo yaqaan "Transfer Resistance" ee -th connected compartment of neuron on neuron Qalabka Neuron Sida loo yaqaan Soma s = 30 ms, e = 50 ms are start time and end time for learning respectively. For output neurons, the error term can be computed as shown in Eq. ( Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka ( Haku t vj vi i j Iijk k i j gijk rijk k i j j t t 10 11 Since all output neurons are single-compartment, equals to the input resistance of the corresponding compartment, . Transfer and input resistances are computed by NEURON. Mini-batch training is a typical method in deep learning for achieving higher prediction accuracy and accelerating convergence. DeepDendrite also supports mini-batch training. When training HPC-Net with mini-batch size batch, we make HPC-Net waxaa laga yaabaa in ka mid ah wax soo saarka, wax soo saarka ah waxaa laga yaabaa in ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka. DeepDendrite ka soo saarka wax soo saarka wax soo saarka oo ka mid ah oo ka mid ah wax soo saarka wax soo saarka. N N Robustness against adversarial attack with HPC-Net To demonstrate the robustness of HPC-Net, we tested its prediction accuracy on adversarial samples and compared it with an analogous ANN (one with the same 784-64-10 structure and ReLU activation, for fair comparison in our HPC-Net each input neuron only made one synaptic connection to each hidden neuron). We first trained HPC-Net and ANN with the original training set (original clean images). Then we added adversarial noise to the test set and measured their prediction accuracy on the noisy test set. We used the Foolbox , to generate adversarial noise with the FGSM method . ANN was trained with PyTorch , and HPC-Net was trained with our DeepDendrite. For fairness, we generated adversarial noise on a significantly different network model, a 20-layer ResNet . The noise level ranged from 0.02 to 0.2. We experimented on two typical datasets, MNIST and Fashion-MNIST . Results show that the prediction accuracy of HPC-Net is 19% and 16.72% higher than that of the analogous ANN, respectively. 98 99 93 100 101 95 96 Reporting summary Further information on research design is available in the linked to this article. Nature Portfolio Reporting Summary Qalabka Data Dhamaan oo loo yaabaa in ay ku yaalaa wax soo saarka ah oo loo yaabaa in ay ku yaalaa wax soo saarka, wax soo saarka, wax soo saarka iyo wax soo saarka. – are available at MNIST data set waxaa laga yaabaa in la isticmaali karaa. The Fashion-MNIST dataset waxaa laga yaabaa si aad u aragto Haku are provided with this paper. 3 6 https://github.com/pkuzyc/DeepDendrite http://yann.lecun.com/exdb/mnist https://github.com/zalandoresearch/fashion-mnist Qalabka Data Code availability The source code of DeepDendrite as well as the models and code used to reproduce Figs. – in this study are available at . 3 6 https://github.com/pkuzyc/DeepDendrite References McCulloch, W. S. & Pitts, W. A logical calculus of the ideas immanent in nervous activity. , 115–133 (1943). Bull. Math. Biophys. 5 LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. , 436–444 (2015). Nature 521 Poirazi, P., Brannon, T. & Mel, B. W. Arithmetic of subthreshold synaptic summation in a model CA1 pyramidal cell. , 977–987 (2003). Neuron 37 London, M. & Häusser, M. Dendritic computation. , 503–532 (2005). Annu. Rev. Neurosci. 28 Branco, T. & Häusser, M. The single dendritic branch as a fundamental functional unit in the nervous system. , 494–502 (2010). Curr. Opin. Neurobiol. 20 Stuart, G. J. & Spruston, N. Dendritic integration: 60 years of progress. , 1713–1721 (2015). Nat. Neurosci. 18 Poirazi, P. & Papoutsi, A. Illuminating dendritic function with computational models. , 303–321 (2020). Nat. Rev. Neurosci. 21 Yuste, R. & Denk, W. Dendritic spines as basic functional units of neuronal integration. , 682–684 (1995). Nature 375 Ingert, F. & Bonhoeffer, T. Qalabka dhismaha dhismaha Dendritic oo ku yaqaan hippocampal long-term synaptic plasticity. Nature 399, 66-70 (1999). Yuste, R. Dendritic spines and distributed circuits. , 772–781 (2011). Neuron 71 Yuste, R. Electrical compartmentalization in dendritic spines. , 429–449 (2013). Annu. Rev. Neurosci. 36 Rall, W. Branching dendritic trees and motoneuron membrane resistivity. , 491–527 (1959). Exp. Neurol. 1 Segev, I. & Rall, W. Computational study of an excitable dendritic spine. , 499–523 (1988). J. Neurophysiol. 60 Silver, D. et al. Masters game of go iyo xarxa neeraal dhererka dhererka. Nature 529, 484–489 (2016). Silver, D. et al. A general reinforcement learning algorithm that masters chess, shogi, and go through self-play. , 1140–1144 (2018). Science 362 McCloskey, M. & Cohen, N. J. Catastrophic interference in connectionist networks: the sequential learning problem. , 109–165 (1989). Psychol. Learn. Motiv. 24 French, R. M. Catastrophic forgetting in connectionist networks. , 128–135 (1999). Trends Cogn. Sci. 3 Naud, R. & Sprekeler, H. Sparse bursts optimize information transmission in a multiplexed neural code. , E6329–E6338 (2018). Proc. Natl Acad. Sci. USA 115 Sacramento, J., Costa, R. P., Bengio, Y. & Senn, W. Dendritic cortical microcircuits approximate the backpropagation algorithm. in (NeurIPS*,* 2018). Advances in Neural Information Processing Systems 31 (NeurIPS 2018) Payeur, A., Guerguiev, J., Zenke, F., Richards, B. A. & Naud, R. Burst-dependent synaptic plasticity can coordinate learning in hierarchical circuits. , 1010–1019 (2021). Nat. Neurosci. 24 Bicknell, B. A. & Häusser, M. A rule of synaptic learning for exploiting nonlinear dendritic computation. Neuron 109, 4001–4017 (2021). Moldwin, T., Kalmenson, M. & Segev, I. The gradient clusteron: a model neuron that learns to solve classification tasks via dendritic nonlinearities, structural plasticity, and gradient descent. , e1009015 (2021). PLoS Comput. Biol. 17 Hodgkin, A. L. & Huxley, A. F. A quantitative description of membrane current and Its application to conduction and excitation in nerve. , 500–544 (1952). J. Physiol. 117 Rall, W. Theory of physiological properties of dendrites. , 1071–1092 (1962). Ann. N. Y. Acad. Sci. 96 Hines, M. L. & Carnevale, N. T. The Neuron simulation environment. Neural Comput. 9, 1179-1209 (1997). Bower, J. M. & Beeman, D. in (eds Bower, J.M. & Beeman, D.) 17–27 (Springer New York, 1998). The Book of GENESIS: Exploring Realistic Neural Models with the GEneral NEural SImulation System Hines, M. L., Eichner, H. & Schürmann, F. Neuron splitting in compute-bound parallel network simulations enables runtime scaling with twice as many processors. , 203–210 (2008). J. Comput. Neurosci. 25 Hines, M. L., Markram, H. & Schürmann, F. Fully implicit parallel simulation of single neurons. , 439–448 (2008). J. Comput. Neurosci. 25 Ben-Shalom, R., Liberman, G. & Korngreen, A. Accelerating compartmental modeling on a graphical processing unit. , 4 (2013). Front. Neuroinform. 7 Tsuyuki, T., Yamamoto, Y. & Yamazaki, T. Efficient numerical simulation of neuron models with spatial structure on graphics processing units. In (eds Hirose894Akiraet al.) 279–285 (Springer International Publishing, 2016). Proc. 2016 International Conference on Neural Information Processing Vooturi, D. T., Kothapalli, K. & Bhalla, U. S. Parallelizing Hines Matrix Solver in Neuron Simulations on GPU. In 388–397 (IEEE, 2017). Proc. IEEE 24th International Conference on High Performance Computing (HiPC) Huber, F. wax soo saarka wax soo saarka ah ee matrix hines on GPU. Preprint at https://arxiv.org/abs/1810.12742 (2018). Korte, B. & Vygen, J. 6 edn (Springer, 2018). Combinatorial Optimization Theory and Algorithms Gebali, F. (Wiley, 2011). Algorithms and Parallel Computing Kumbhar, P. et al. CoreNEURON: A optimized calculation engine for the NEURON simulator. Front. Neuroinform. 13, 63 (2019). Urbanczik, R. & Senn, W. Waayo, oo ka mid ah dhismaha dendritic ee spiking somatic. Neuron 81, 521-528 (2014). Ben-Shalom, R., Aviv, A., Razon, B. & Korngreen, A. Optimizing ion channel models using a parallel genetic algorithm on graphical processors. , 183–194 (2012). J. Neurosci. Methods 206 Mascagni, M. A parallelizing algorithm for computing solutions to arbitrarily branched cable neuron models. , 105–114 (1991). J. Neurosci. Methods 36 McDougal, R. A. et al. Twenty years of modelDB and beyond: building essential modeling tools for the future of neuroscience. , 1–10 (2017). J. Comput. Neurosci. 42 Migliore, M., Messineo, L. & Ferrante, M. Dendritic Ih selectively blocks temporal summation of unsynchronized distal inputs in CA1 pyramidal neurons. , 5–13 (2004). J. Comput. Neurosci. 16 Hemond, P. et al. Distinct classes of pyramidal cells exhibit mutually exclusive firing patterns in hippocampal area CA3b. , 411–424 (2008). Hippocampus 18 Hay, E., Hill, S., Schürmann, F., Markram, H. & Segev, I. Models of neocortical layer 5b pyramidal cells capturing a wide range of dendritic and perisomatic active Properties. , e1002107 (2011). PLoS Comput. Biol. 7 Masoli, S., Solinas, S. & D’Angelo, E. Action potential processing in a detailed purkinje cell model reveals a critical role for axonal compartmentalization. , 47 (2015). Front. Cell. Neurosci. 9 Lindroos, R. et al. Basal ganglia neuromodulation over multiple temporal and structural scales—simulations of direct pathway MSNs investigate the fast onset of dopaminergic effects and predict the role of Kv4.2. , 3 (2018). Front. Neural Circuits 12 Migliore, M. et al. Synaptic clusters function as odor operators in the olfactory bulb. , 8499–8504 (2015). Proc. Natl Acad. Sci. USa 112 NVIDIA. . (2021). CUDA C++ Programming Guide https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html NVIDIA. . (2021). CUDA C++ Best Practices Guide https://docs.nvidia.com/cuda/cuda-c-best-practices-guide/index.html Harnett, M. T., Makara, J. K., Spruston, N., Kath, W. L. & Magee, J. C. Synaptic amplification by dendritic spines enhances input cooperativity. , 599–602 (2012). Nature 491 Chiu, C. Q. et al. Compartmentalization of GABAergic inhibition by dendritic spines. , 759–762 (2013). Science 340 Tønnesen, J., Katona, G., Rózsa, B. & Nägerl, U. V. Spine neck plasticity regulates compartmentalization of synapses. , 678–685 (2014). Nat. Neurosci. 17 Eyal, G. et al. Human cortical pyramidal neurons: from spines to spikes via models. , 181 (2018). Front. Cell. Neurosci. 12 Koch, C. & Zador, A. The function of dendritic spines: devices subserving biochemical instead of electrical compartmentalization. J. Neurosci. 13, 413-422 (1993). Dendritic spines. in Biophysics of Computation (Oxford University Press, 1999). Rapp, M., Yarom, Y. & Segev, I. The impact of parallel fiber background activity on the cable properties of cerebellar purkinje cells. , 518–533 (1992). Neural Comput. 4 Hines, M. Efficient computation of branched nerve equations. , 69–76 (1984). Int. J. Bio-Med. Comput. 15 Nayebi, A. & Ganguli, S. Biologically inspired protection of deep networks from adversarial attacks. Preprint at (2017). https://arxiv.org/abs/1703.09202 Goddard, N. H. & Hood, G. Large-Scale Simulation Using Parallel GENESIS. In (eds Bower James M. & Beeman David) 349-379 (Springer New York, 1998). The Book of GENESIS: Exploring Realistic Neural Models with the GEneral NEural SImulation System Migliore, M., Cannia, C., Lytton, W. W., Markram, H. & Hines, M. L. Parallel network simulations with NEURON. , 119 (2006). J. Comput. Neurosci. 21 Lytton, W. W. et al. Simulation neurotechnologies for advancing brain research: parallelizing large networks in NEURON. , 2063–2090 (2016). Neural Comput. 28 Valero-Lara, P. et al. cuHinesBatch: Solving multiple Hines systems on GPUs human brain project. In Proc. 2017 Conference International on Computational Science 566-575 (IEEE, 2017). Akar, N. A. et al. Arbor—A morphologically-detailed neural network simulation library for contemporary high-performance computing architectures. In 274–282 (IEEE, 2019). Proc. 27th Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP) Ben-Shalom, R. et al. NeuroGPU: Shirkadda multi-compartment, simulators neuron biophysically dhismaha on GPUs. J. Neurosci. Methods 366, 109400 (2022). Rempe, M. J. & Chopp, D. L. A predictor-corrector algorithm for reaction-diffusion equations associated with neural activity on branched structures. , 2139–2161 (2006). SIAM J. Sci. Comput. 28 Kozloski, J. & Wagner, J. An ultrascalable solution to large-scale neural tissue simulation. , 15 (2011). Front. Neuroinform. 5 Jayant, K. et al. Targeted intracellular voltage recordings from dendritic spines using quantum-dot-coated nanopipettes. , 335–342 (2017). Nat. Nanotechnol. 12 Palmer, L. M. & Stuart, G. J. Membrane potential changes in dendritic spines during action potentials and synaptic input. , 6897–6903 (2009). J. Neurosci. 29 Nishiyama, J. & Yasuda, R. Biochemical computation for spine structural plasticity. , 63–75 (2015). Neuron 87 Yuste, R. & Bonhoeffer, T. Morphological changes in dendritic spines associated with long-term synaptic plasticity. , 1071–1089 (2001). Annu. Rev. Neurosci. 24 Holtmaat, A. & Svoboda, K. Experience-dependent structural synaptic plasticity in the mammalian brain. , 647–658 (2009). Nat. Rev. Neurosci. 10 Caroni, P., Donato, F. & Muller, D. Structural plasticity upon learning: regulation and functions. , 478–490 (2012). Nat. Rev. Neurosci. 13 Keck, T. et al. Massive restructuring of neuronal circuits during functional reorganization of adult visual cortex. , 1162 (2008). Nat. Neurosci. 11 Hofer, S. B., Mrsic-Flogel, T. D., Bonhoeffer, T. & Hübener, M. Experience leaves a lasting structural trace in cortical circuits. , 313–317 (2009). Nature 457 Trachtenberg, J. T. et al. Long-term in vivo imaging of experience-dependent synaptic plasticity in adult cortex. , 788–794 (2002). Nature 420 Marik, S. A., Yamahachi, H., McManus, J. N., Szabo, G. & Gilbert, C. D. Axonal dynamics of excitatory and inhibitory neurons in somatosensory cortex. , e1000395 (2010). PLoS Biol. 8 Xu, T. et al. Rapid formation and selective stabilization of synapses for enduring motor memories. , 915–919 (2009). Nature 462 Albarran, E., Raissi, A., Jáidar, O., Shatz, C. J. & Ding, J. B. Enhancing motor learning by increasing the stability of newly formed dendritic spines in the motor cortex. , 3298–3311 (2021). Neuron 109 Branco, T. & Häusser, M. Synaptic integration gradients in single cortical pyramidal cell dendrites. , 885–892 (2011). Neuron 69 Major, G., Larkum, M. E. & Schiller, J. Active properties of neocortical pyramidal neuron dendrites. , 1–24 (2013). Annu. Rev. Neurosci. 36 Gidon, A. et al. Dendritic action potentials and computation in human layer 2/3 cortical neurons. , 83–87 (2020). Science 367 Doron, M., Chindemi, G., Muller, E., Markram, H. & Segev, I. Timed synaptic inhibition shapes NMDA spikes, influencing local dendritic processing and global I/O properties of cortical neurons. , 1550–1561 (2017). Cell Rep. 21 Du, K. et al. Cell-type-specific inhibition of the dendritic plateau potential in striatal spiny projection neurons. , E7612–E7621 (2017). Proc. Natl Acad. Sci. USA 114 Smith, S. L., Smith, I. T., Branco, T. & Häusser, M. Dendritic spikes enhance stimulus selectivity in cortical neurons in vivo. , 115–120 (2013). Nature 503 Xu, N.-l et al. Nonlinear dendritic integration of sensory and motor input during an active sensing task. , 247–251 (2012). Nature 492 Takahashi, N., Oertner, T. G., Hegemann, P. & Larkum, M. E. Active cortical dendrites modulate perception. , 1587–1590 (2016). Science 354 Sheffield, M. E. & Dombeck, D. A. Calcium transient prevalence across the dendritic arbour predicts place field properties. , 200–204 (2015). Nature 517 Markram, H. et al. Reconstruction and simulation of neocortical microcircuitry. , 456–492 (2015). Cell 163 Billeh, Y. N. et al. Isticmaalka nidaamka ee data struktural iyo functional in model multi-scale of mouse primary visual cortex. Neuron 106, 388–403 (2020). Hjorth, J. et al. The microcircuits of striatum in silico. , 202000671 (2020). Proc. Natl Acad. Sci. USA 117 Guerguiev, J., Lillicrap, T. P. & Richards, B. A. Towards deep learning with segregated dendrites. , e22901 (2017). elife 6 Iyer, A. et al. Avoiding catastrophe: active dendrites enable multi-task learning in dynamic environments. , 846219 (2022). Front. Neurorobot. 16 Jones, I. S. & Kording, K. P. Might a single neuron solve interesting machine learning problems through successive computations on its dendritic tree? , 1554–1571 (2021). Neural Comput. 33 Bird, A. D., Jedlicka, P. & Cuntz, H. Dendritic normalisation improves learning in sparsely connected artificial neural networks. , e1009202 (2021). PLoS Comput. Biol. 17 Goodfellow, I. J., Shlens, J. & Szegedy, C. Explaining and harnessing adversarial examples. In (ICLR, 2015). 3rd International Conference on Learning Representations (ICLR) Papernot, N., McDaniel, P. & Goodfellow, I. Transferability in machine learning: from phenomena to black-box attacks using adversarial samples. Preprint at (2016). https://arxiv.org/abs/1605.07277 Lecun, Y., Bottou, L., Bengio, Y. & Haffner, P. Gradient-based learning applied to document recognition. , 2278–2324 (1998). Proc. IEEE 86 Xiao, H., Rasul, K. & Vollgraf, R. Fashion-MNIST: a novel image dataset for benchmarking machine learning algorithms. Preprint at (2017). http://arxiv.org/abs/1708.07747 Bartunov, S. et al. Waqtiga loo yaqaan "Scalability of biologically-motivated deep learning algorithms and architectures" in Advances in Neural Information Processing Systems 31 (NeurIPS 2018) (NeurIPS, 2018). Rauber, J., Brendel, W. & Bethge, M. Foolbox: A Python toolbox to benchmark the robustness of machine learning models. In Reliable Machine Learning in the Wild Workshop, 34th International Conference on Machine Learning (2017). Rauber, J., Zimmermann, R., Bethge, M. & Brendel, W. Foolbox native: fast adversarial attacks to benchmark the robustness of machine learning models in PyTorch, TensorFlow, and JAX. , 2607 (2020). J. Open Source Softw. 5 Paszke, A. et al. PyTorch: An imperative style, high-performance deep learning library. In (NeurIPS, 2019). Advances in Neural Information Processing Systems 32 (NeurIPS 2019) He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. In 770–778 (IEEE, 2016). Proc. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Acknowledgements Shirkadda ayaa ku dhamaado Shiinaha National Key R&D Program of Guangdong Province (No. 2018B030338001) to T.H., National Natural Science Foundation of China (No. 61825101) to Y.T., Swedish Research Council (VR-M-2020-01652), Swedish e-Science Research Centre (SeRC), EU/Horizon 2020 No. 945539 (HBP SGA3), KTH, Digital Futures to J.H.K., J.K., A.H., PDIC, Swedish for Simulating Research Part (K.K.M.-2021-0255) iyo Swedish Research Fund (K.K.K.A.-2033) waxaa ku dhamaan ka mid ah Shirkadda Shiinaha iyo Shirkadda Shiinaha ee Shiinaha (K.K.K Qalabka waxaa laga yaqaan CC by 4.0 Deed (Attribution 4.0 International) license. This paper is under CC by 4.0 Deed (Attribution 4.0 International) license. available on nature