Umbhali: Ukucinga Zhang Ukusuka Ukucinga I-Xiaopei Liu J. J. Johannes Hjorth Alexander Kozlov U-Yutao Shenjian Zhang U-Jeanette Hellgren Kotaleski Yonghong Tian Sten Grillner Kai Du Ukucinga Umbhali: Ukucinga Zhang Ukusuka Ukucinga I-Xiaopei Liu J. J. Johannes Hjorth Alexander Kozlov U-Yutao Shenjian Zhang U-Jeanette Hellgren Kotaleski Yonghong Tian Sten Grillner Kai Du Ukucinga Ukucinga Iimodeli ze-biophysically ezinxulumeneyo ze-multi-compartment zibonisa izixhobo ezinzima zokufunda iinkqubo ze-computer ye-brain kwaye zihlanganisa njengenkqubo ye-algorithms ye-artificial intelligence (AI) iinkqubo. Nangona kunjalo, i-cost ye-computing ephakeme yandisa kakhulu izicelo ezininzi kwindawo ze-neuroscience kunye ne-AI. I-bottleneck esikhulu ekusebenziseni iimodeli ze-compartment ezininzi yi-capacity ye-simulator yokufumana iinkqubo ezininzi ze-equations linear. Nazi, sinikezela i-novel Ukucinga Izixhobo Ukucaciswa kwe-cheduling (DHS) indlela yokukhuthaza inqubo efanayo. Thina kubonise ukuba ukucaciswa kwe-DHS kunokufumaneka ngempumelelo kunye nokufanelekileyo. Le nkqubo esekelwe yi-GPU ibekwe ngexesha elide ye-2-3 amaxesha engaphezulu kunokuba yi-Classic Series Hines method kwi-CPU platform. Sinikezela inkqubo ye-DeepDendrite, ebandakanya i-DHS method kunye ne-GPU computing engine ye-NEURON simulator, kwaye ibonise izicelo ze-DeepDendrite kwiinkqubo ze-neuroscience. Sinikezela ukuba iimodeli ze-spatial ye-spine inputs zibonise ukucaciswa kwe-neuronal kwimodeli ye-p D H S Ukucaciswa Ukuqhathanisa iingcebiso ze-coding kunye ne-computer ye-neurons kubalulekile kwi-neuroscience. Iingcebiso ze-animals zihlanganisa ngaphezu kwezigidi ezahlukahlukeneyo ze-neurons kunye nezakhiwo ezizodwa ze-morphological kunye ne-biophysical. Nangona kungekho kwakhona ngexabiso, i-doctrine "i-point-neuron" , apho i-neurons iye yaziwa njengoko iiyunithi ezincinane ze-summing, ibekwe ngokubanzi kwi-neural computing, ikakhulukazi kwi-analysis ye-neural network. Kwiinyanga ezidlulileyo, intloko lwe-artificial intelligence (i-AI) iye isetyenzise le ncwadi kwaye iye yenza izixhobo ezincinane, ezifana ne-artificial neural networks (ANN). Nangona kunjalo, ngaphandle kwamakhompyutha epheleleyo kwinqanaba ye-neuron ye-single, izixeko ze-subcellular, njenge-dendrites ze-neuronal, zinokufumana iinkqubo ze-nonlinear njenge-units ze-computing ezahlukileyo. , , , , . Furthermore, dendritic spines, small protrusions that densely cover dendrites in spiny neurons, can compartmentalize synaptic signals, allowing them to be separated from their parent dendrites ex vivo and in vivo , , , . 1 2 3 4 5 6 7 8 9 10 11 Simulations usebenzisa ne-neurons eziphilayo ezininzi kubonelela isakhiwo esisombululo ukuxhumanisa iinkcukacha zebhizinisi kunye nezisombululo zebhizinisi. I-core of the biophysically detailed multi-compartment model framework , leyo kuthetha ukuba iimodeli ne-neurons kunye ne-dendritic morphologies, i-conduction ionic intrinsic, kunye ne-extrinsic synaptic inputs. I-bone ye-multi-compartment model, ngoko ke, i-dendrites, ibekwe kwi-Cable theory classic , leyo ibonise izakhiwo ze-membrane ye-biophysical ye-dendrites njenge-cable ye-passive, ibonise i-description ye-mathematical 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 cellular and subcellular neuronal computations beyond experimental limitations. , . 12 13 12 4 7 Ukongezelela kwimiphumo yayo ebandayo kwi-neuroscience, iimodeli ze-neuron ezininzi ezisetyenziswa ngexesha elidlulileyo ukunciphisa ingxaki phakathi kweendaba ze-neuronal kunye ne-biophysics kunye ne-AI. I-technology ebandayo kwimveliso ye-AI yaziwayo i-ANN ezisekelwe kwi-point neurons, i-analogue ye-biological neural networks. Nangona i-ANN kunye ne-algorithm ye-backpropagation-of-error (i-backprop) zibonise ukusebenza enomdla kwi-applications ezizodwa, kwakhona ukutshintshela abadlali be-human professional kwiimidlalo ze-Go kunye ne-chess. , , the human brain still outperforms ANNs in domains that involve more dynamic and noisy environments , Izifundo ezidlulileyo zibonakalisa ukuba ukuhlanganiswa kwe-dendritic kubalulekile ekugqibeleni i-algorithms yokufunda efanelekileyo ezinokukwazi ukufumana i-backprop kwinkqubo ye-information ekugqibeleni , , Ukongezelela, i-modeli ye-multi-compartment eyodwa enokufunda i-network-level nonlinear calculations ye-point neurons ngokufanisa kuphela amandla ye-synaptic. , Ukubonisa umthamo epheleleyo yeemodeli eziqhelekileyo ekwenzeni iinkqubo ze-AI ezincinane ne-brain. Ngoko ke, kubaluleke kakhulu ukwandisa iimodeli ze-AI ezincinane ne-brain ukusuka kwiimodeli ze-neurone ezincinane ukuya kwinethiwekhi ze-biologically ezincinane ezininzi. 14 15 16 17 18 19 20 21 22 Enye ingxaki elide yeengxaki ye-simulation esifunyenwe yi-excessively-high-computational cost, nto leyo lithembisa kakhulu ukusetyenziswa kwe-neuroscience kunye ne-AI. I-bottleneck enkulu ye-simulation yenza ukutshintsha iingqungquthela ze-linear ezisekelwe kwi-theories eziphambili ze-modelling esifunyenweyo. , , Ukuphucula i-efficiency, indlela ye-Hines ye-classic sinciphisa ixesha lokuphendula i-equations ukusuka kwi-O(n3) ukuya kwi-O(n), eyayisetyenziswa ngokubanzi njenge-algorithm core kwi-simulators ezaziwayo njenge-NEURON. I-Genesis Nangona i-simulation ibandakanya i-dendrites ezininzi ezininzi ze-biophysically kunye ne-dendritic spines, i-matrix ye-equation ye-linear (“Hines Matrix”) ibandakanya inani elikhulu le-dendrites okanye i-spines (i-Fig. ), making Hines method no longer practical, since it poses a very heavy burden on the entire simulation. 12 23 24 25 26 1e I-reconstructed layer-5 pyramidal neuron model kunye ne-formula ye-mathematical esetyenziselwa iimodeli ze-neuron ezininzi. Workflow xa numerically simulating iimodeli ne-neurone ezininzi. I-equation-solving phase iyona i-bottleneck kwi-simulation. An example of linear equations in the simulation. Izixhobo ze-Data ye-Hines method ekuphenduleni iingxaki ze-linear . Ubungakanani i-Hines matrix isilinganiselo kunye ne-model complexity. Inani yinkqubo ye-equations linear ezisisombululo kubandakanya ukwandisa kakhulu xa iimodeli zangaphakathi ezininzi. Computational cost (steps taken in the equation solving phase) of the serial Hines method on different types of neuron models. I-Illustration of different solving methods. Iindawo ezahlukeneyo ye-neurone zithunyelwe kwiiyunithi ezininzi ze-processing ngexesha elifanelekileyo (i-middle, i-right), ezibonakalayo kwiimibala ezahlukeneyo. Kwi-serial method (i-left), zonke izixeko zithunyelwe nge-unity eyodwa. I-Cost Computational of Three Methods Ukuphendula i-equations ye-pyramidal model nge-spines. Ixesha lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela. Ixesha lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela. Ixesha lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela lokugqibela. a b c d c e f g h g i Kwiinyanga ezidlulileyo, izivumelwano ezininzi ziye ziye ziye ziye ziye zithunyelwe ekhawulezeni i-Hines-methode ngokusebenzisa iindlela ezinxulumene kwinqanaba ye-cellular, eziza kufumanisa i-parallelation ye-computation yeempawu ezahlukeneyo kwi-cell. , , , , , Nangona kunjalo, izindlela ezininzi zokusetyenziswa kwi-cellular-level ezinxulumene kunye ne-parallelization efanelekileyo okanye zihlanganisa i-numerical accuracy efanelekileyo kunxhomekeke ne-Hines yokuqala. 27 28 29 30 31 32 Kwakhona, le mveliso ye-simulation ingasetyenziswa ngokugqithisileyo, ngokugqithisileyo kunye nokunciphisa i-simulation tool enokusetyenziswa ngokugqithisileyo ekubunjweni kunye nokunciphisa iindleko ze-computing. Ukongezelela, le mveliso ye-simulation ingasetyenziswa ngokugqithisileyo ekubunjweni kunye nokuvavanya iinkonzo ze-networks ze-biological for machine learning kunye ne-AI applications. Ngokufanelekileyo, sincoma i-parallel computing ye-Hines method njenge-matematical scheduling problem kwaye sinikeza i-Dendritic Hierarchical Scheduling (DHS) method based on combinatorial optimization. and parallel computing theory . Sibonisa ukuba i-algorithm yethu inikeza i-charting ye-optimum ngaphandle kokuphazamiseka kwe-precision. Ukongezelela, sinikezelela i-DHS kwi-GPU chip eyenziwe ngexesha elidlulileyo ngokufanisa i-GPU memory hierarchy kunye ne-memory access mechanisms. Ngezinye, i-DHS inokufumana ukuhlaziywa kwe-60-1,500 amaxesha (i-Table Supplementary) ) ekubeni ne-simulator classic NEURON Ukubuyekeza ngokufanelekileyo. 33 34 1 25 Ukuvumela iimodeli ze-dendritic ezininzi ezisetyenziswa kwi-AI, siya kuqhuba i-DeepDendrite framework ngokuvumelana ne-DHS-embedded CoreNEURON (i-optimized compute engine for NEURON) platform Njengomatshini we-simulation kunye nama-module ezimbini (i-I/O module kunye ne-learning module) ezisetyenzisa i-algorithms ye-dendritic learning ngexesha le-simulations. I-DeepDendrite isebenza kwi-GPU hardware platform, ezisetyenzisa iingxaki ze-simulation ezivamile ze-neuroscience kunye neengxaki ze-learning ze-AI. 35 Last but not least, sinikezela izicelo ezininzi usebenzisa i-DeepDendrite, ezivela kwiingxaki ezininzi ezibalulekileyo kwi-neuroscience kunye ne-AI: (1) Sinikezela njani iimodeli zendawo ze-dendritic spine inputs ziyafumanisa iinkqubo ze-neuronal kunye ne-neurons eziquka i-spines kwiintlobo ze-dendritic (iimodeli ze-full-spine). I-DeepDendrite ibonakalisa ukucacisa i-neuronal in a simulated human pyramidal neuron model with ~25,000 dendritic spines. Zonke i-source code ye-DeepDendrite, iimodeli ze-full-spine kunye ne-dendritic network model ezininzi ziyafumaneka ngokubanzi kwi-intanethi (bheka i-Code Availability). I-Open-source learning framework yethu ingasetyenziswa ngempumelelo kunye nezinye imiyalezo ze-dendritic learning, njenge-learning rules ye-nonlinear (i-full-active) dendrites I-burst-dependent synaptic plasticity , kunye nokufunda nge-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 Imiphumo 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. ). 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 , , . However, such methods rely heavily on prior knowledge to generate practical strategies on how to split a single neuron into compartments (Fig. ; Supplementary Fig. ). Ngoko ke, kubaluleke ngempumelelo kwi-neurons nge-morphologies asymmetric, isib. i-neurons pyramidal kunye ne-neurons yePurkinje. 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 , sinikezela izimo ezintathu ukuqinisekisa ukuba umgangatho we-parallel iya kuba izixazululo efanayo kunye ne-serial computing Hines method ngokutsho umgangatho we-data dependency kwi-Hines method (bheka iMethods). Emva koko, ukucacisa ngokwenene ixesha lokugqibela, ngexesha lokuphumelela, i-efficiency, ye-serial kunye ne-parallel computing methods, sinikezela kwaye ilungise i-concept ye-cost computational njenge-number of steps a method takes in solving equations (bheka iMethods). 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 Ukuze kwenziwe i-partition efanelekileyo, sincoma i-methode ebizwa ngokuba yi-Dendritic Hierarchical Scheduling (DHS) (i-proof ye-theoretical ifumaneka kwi-Methods). I-IDEA esisombululo ye-DHS yi-prioritying ye-deep nodes (i-Fig. ), which results in a hierarchical schedule order. The DHS method includes two steps: analyzing dendritic topology and finding the best partition: (1) Given a detailed model, we first obtain its corresponding dependency tree and calculate the depth of each node (the depth of a node is the number of its ancestor nodes) on the tree (Fig. ) (2) Emva kokufunda i-topology, sincoma i-candidates kunye ne-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. ). 2a 2B, C k 2d DHS work flow. DHS processes deepest candidate nodes each iteration. I-Illustration of calculating node depth of a compartmental model. I-model is first converted into a tree structure then the depth of each node is calculated. Imibala ibonisa iindleko ezahlukeneyo ze-depth. Uhlalutyo lwe-topology kwiimodeli ezahlukahlukeneyo ze-neurone. Six ne-neurons kunye ne-morphologies ezahlukileyo ziyafumaneka apha. Kwiimodeli ngamnye, i-soma ifumaneka njenge-root ye-tree ukuze ububanzi be-node ifumaneka ukusuka kwi-soma (0) ukuya kwi-dendrites ze-distal. Illustration of performing DHS on the model in with four threads. Candidates: nodes that can be processed. Selected candidates: nodes that are picked by DHS, i.e., the deepest candidates. Processed nodes: nodes that have been processed before. Parallelization strategy obtained by DHS after the process in . Wonke i-node ibekwe kwi-one of the four parallel threads. I-DHS ikunciphisa i-steps ye-serial node processing ukusuka ku-14 kuya ku-5 ngokudibanisa i-node kwi-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 Okulandelayo, sinikezela i-DHS kwiimodeli ze-neurone ezininzi ezine (okukhetha kwi-ModelDB) ) with different numbers of threads (Fig. ):, kuquka i-cortical ne-hippocampal pyramidal neurons , , I-cerebellar Purkinje ne-neurons , striatal projection neurons (SPN ), 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 Together, we generate a DHS method that enables automated analysis of the dendritic topology and optimal partition for parallel computing. It is worth noting that DHS finds the optimal partition before the simulation starts, and no extra computation is needed to solve equations. 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 Kwi-theory, i-SPs ezininzi kwi-GPU kufuneka zithintela i-simulation efanelekileyo yeenethiwekhi ze-neuronal ye-scale (i-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. Applying DHS on two neurons, each with four threads. During simulation, each thread executes on one stream processor. I-Memory Optimization Strategy kwi-GPU. I-top panel, i-thread assignment kunye ne-data storage ye-DHS, phambi (ngaphandle) kunye emva (ngaphandle) ukwandisa i-memory. Enye, isibonelo ye-step eyodwa ye-triangularization xa i-simulating i-neurons ezimbini kwi . 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. Ukongezelela, iimvavanyo kwiinombolo ezininzi ze-neurons ye-pyramidal nge-spines kunye neemodeli ze-neuron ezijwayelekile (Imi. • I-FIG YOKUFUNDA. ) show that memory boosting achieves a 1.2-3.8 times speedup as compared to the naïve DHS. 46 47 3D 3e, f 2 Ukuvavanya ukusebenza kwe-DHS nge-GPU memory boosting, sincoma iimodeli ze-neurone ezisetyenziswa kunye nokuthintela ixesha lokugqibela sokuphendula iingcebiso ze-cable kwiinombolo ezininzi ze-model (Imi. Uyahlolwa i-DHS kunye neefayile ezine (i-DHS-4) kunye neefayile ezine (i-DHS-16) ngalinye i-neurone, ngokufanayo. Ngokuhambelana nenkqubo ye-GPU kwi-CoreNEURON, i-DHS-4 kunye ne-DHS-16 kunokukhawuleza malunga ne-5 kunye ne-15 ngokufanelekileyo, ngokufanelekileyo (i-Fig. ). 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 ), active dendrites (Supplementary Fig. ) kunye nezinye iinkqubo ze-segmentation (i-Fig. ). 4 4a 3 4 8 7 7 Run time of solving equations for a 1 s simulation on GPU (dt = 0.025 ms, 40,000 iterations in total). CoreNEURON: the parallel method used in CoreNEURON; DHS-4: DHS with four threads for each neuron; DHS-16: DHS with 16 threads for each neuron. , Visualization of the partition by DHS-4 and DHS-16, each color indicates a single thread. During computation, each thread switches among different branches. a b c DHS creates cell-type-specific optimal partitioning Ukufumana iinkcukacha kwiinkqubo yokusebenza ye-DHS, sinikezela inqubo ye-partitioning ngokuphathelene neengxaki ze-trade ye-trade ye-trade ye-trade ye-trade ye-trade ye-trade ye-trade ye-trade. ). The visualization shows that a single thread frequently switches among different branches (Fig. ). 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 In summary, DHS and memory boosting generate a theoretically proven optimal solution for solving linear equations in parallel with unprecedented efficiency. Using this principle, we built the open-access DeepDendrite platform, which can be utilized by neuroscientists to implement models without any specific GPU programming knowledge. Below, we demonstrate how we can utilize DeepDendrite in neuroscience tasks. We also discuss the potential of the DeepDendrite framework for AI-related tasks in the Discussion section. DHS enables spine-level modelling Njengoko i-spines ye-dendritic ibonelela i-input ye-excitatory kwi-cortical ne-hippocampal pyramidal neurons, i-striatal projection neurons, njl, i-morphology kunye ne-plasticity yayo kubalulekile ekulawuleni i-neuronal excitability. , , , , . 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 Uyakwazi ukucacisa i-spine eyodwa kunye namaxwebhu ezimbini: i-spine head apho i-synapses ziyafumaneka kunye ne-spine neck eyenza i-spine head kwi-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 . However, the detailed model with fully distributed spines on dendrites (“full-spine model”) is computationally very expensive. A common compromising solution is to modify the capacitance and resistance of the membrane by a I-Spine Factor , instead of modeling all spines explicitly. Here, the i-spine factor ibekwe ekubeni i-effect ye-spine kwi-biophysical properties ye-membrane ye-cell . 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 ). Therefore, the DHS method enables explorations of dendritic excitability under more realistic anatomic conditions. 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 ) pay less attention to the parallelization strategy. The lack of a fine parallelization strategy results in unsatisfactory performance. To achieve higher efficiency, some studies try to obtain finer-grained parallelization by introducing extra computation operations , , 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 are the most abundant microstructures in the brain for projection neurons in the cortex, hippocampus, cerebellum, and basal ganglia. As spines receive most of the excitatory inputs in the central nervous system, electrical signals generated by spines are the main driving force for large-scale neuronal activities in the forebrain and 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 , , , . Such experience-dependent changes in spine morphology also referred to as “structural plasticity”, have been widely observed in the visual cortex , , somatosensory cortex , I-Motor Cortex yeMoto , hippocampus , and the basal ganglia in vivo. They play a critical role in motor and spatial learning as well as memory formation. However, due to the computational costs, nearly all detailed network models exploit the “F-factor” approach to replace actual spines, and are thus unable to explore the spine functions at the system level. By taking advantage of our framework and the GPU platform, we can run a few thousand detailed neurons models, each with tens of thousands of spines on a single GPU, while maintaining ~100 times faster than the traditional serial method on a single CPU (Fig. ). 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 . Moreover, distal dendrites can produce regenerative events such as dendritic sodium spikes, calcium spikes, and 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 Izixhobo ezidlulileyo ze-dendritic roles kwi-task-specific learning ziya kufumana imiphumo emangalisayo kwiiyunithi ezimbini, i-i-solving iingxaki ezininzi ezifana ne-image classification dataset ImageNet kunye ne-dendritic networks ezilula , 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. Workflow of the transfer adversarial attack experiment. We first generate adversarial samples of the test set on a 20-layer ResNet. Then use these adversarial samples (noisy images) to test the classification accuracy of models trained with clean images. Prediction accuracy of each model on adversarial samples after training 30 epochs on MNIST (left) and Fashion-MNIST (right) datasets. Run time of training and testing for the HPC-Net. The batch size is set to 16. Left, run time of training one epoch. Right, run time of testing. Parallel NEURON + Python: training and testing on a single CPU with multiple cores, using 40-process-parallel NEURON to simulate the HPC-Net and extra Python code to support mini-batch training. DeepDendrite: training and testing the HPC-Net on a single GPU with DeepDendrite. a b c d e f Ukongezelela, kuxhomekeke kakhulu ukuba ukusebenza ne-Artificial Neural Networks (ANNs) ingangena ngenxa yeengxaki ze-adversarial —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. Ukucinga Simulation with DHS CoreNEURON simulator ( ) uses the 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 time --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 , i-algorithm parallel iya kwenza imiphumo efanayo ne-algorithm ye-serial efanelekileyo, ukuba kwaye kuphela ukuba umgangatho we-processing yedatha kwi-algorithm parallel ibekwe ne-dependence yedatha kwi-serial method. I-Hines method ineemiphumo ezimbini: i-triangularization kunye ne-back-substitution. Nge-analyzing i-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 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 follows: given a tree iimveliso threads (basic computational units) to perform triangularization, parallel triangularization equals to divide the node set of into subsets, i.e., = { , , … } where the size of each subset | | ≤ , i.e., at most ama-nodes ingasetyenziswa ngalinye isinyathelo njengoko kukho kuphela threads. The process of the triangularization phase follows the order: → → … → , and nodes in the same subset kungenziwa ngokuhambelana. Ngoko ke, sincoma | (the size of set , i.e., here) as the computational cost of the parallel computing method. In short, we define the computational cost of a parallel method as the number of steps it takes in the triangularization phase. Because the back-substitution is symmetrical with triangularization, the total cost of the entire solving equation phase is twice that of the triangularization phase. T k V T n V V1 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 ( ) = { , , … }, | | ≤ , 1 ≤ ≤ n, where | | indicates the cardinal number of subset , i.e., the number of nodes in , and for each node ∈ , all its children nodes { | ∈children( )} must in a previous subset , where 1 ≤ < . Our goal is to find an optimal partition ( ) whose computational cost | ( (Ukuba ingqongquthela ingqongquthela) T V E k V E P V V1 V2 Vn Vi k i Vi Vi Vi v Vi c c v Vj j i P* V P* V Here subset consists of all nodes that will be computed at -th step (Fig. ), so | | ≤ indicates that we can compute nodes each step at most because the number of available threads is . I-restriction "ngomnye 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 ( ) for all nodes ∈ . 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., inombolo yeengxaki ye-candidate ingabizi okanye i-equivalent yeenombolo yeengxaki ezikhoyo, ukutya zonke iingxaki kwi and put them into , otherwise, remove 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 = { , }, sinika i-partition ( ) = { , , … }, | iimveliso ≤ , 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 . Operations in DHS do not modify the tree topology and values of tree nodes (corresponding values in the linear equations), so the tree morphology and initial values of all nodes are not changed, which satisfies condition 1: the tree morphology and initial values of all nodes are identical to those in serial Hines method. In triangularization, nodes are processed from subset 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 only if all its child nodes have been processed. Thus the child nodes of all nodes in are in { , ... ... }, 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 Vi Q Q Vi V1 V2 Vi-1 Vn V1 Vi V1 V2 I-1 Vi Vi+1 U + 2 Vn Optimality proof for DHS The idea of the proof is that if there is another optimal solution, it can be transformed into our DHS solution without increasing the number of steps the algorithm requires, thus indicating that the DHS solution is optimal. For each subset in ( ), DHS moves (thread number) deepest nodes from the corresponding candidate set Ukucinga . If the number of nodes in is smaller than , move all nodes from to . To simplify, we introduce Ukubonisa ububanzi ububanzi Iingubo ezininzi ze-Node . All subsets in ( ) satisfy the max-depth criteria (Supplementary Fig. ): . Ngoko ke sinikezela ukuba ukhethe ama-nodes ezininzi kwi-i-iteration 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 Ukucinga 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 not satisfy the max-depth criteria: (1) | Ngathi » and there exist some valid nodes in that are not put to ; (2) | | = but nodes in are not the deepest nodes in . V*i V*i V*i k Qi V*i 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), | Uluhlu = , 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 through the following method. Assume that after filling , is picked and one of the -th deepest nodes is still in , thus will be put into a subsequent subset ( > ). We first move from Ukucinga + , then modify subset + as follows: if | + | ≤ and none of the nodes in + is the parent of node , stop modifying the latter subsets. Otherwise, modify + as follows (Supplementary Fig. ): Ukuba i node parent ye is in + , move this parent node to + ; else move the node with minimum depth from + to + . After adjusting Ukuguqulwa kwe-subset ezidlulileyo + , + , … with the same strategy. Finally, move from to . V*i V*i < k V*i V*i 6b V*i k Qi V*i 6b V*i V*i v k v’ Qi v’ V*j j i v V*i V*i 1 V*i 1 V*i 1 k V*i 1 v V*i 1 6c v V*i 1 V*i 2 V*i 1 V*i 2 V*i V*i 1 V*i 2 V*j-1 v’ V*j V * I Nge-modification strategy ebonakalayo phezulu, sinako ukuguqulwa zonke ama-nodes ezincinane with the -I-node enhle kakhulu kwi 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 ∈ ( ) can satisfy the max-depth criteria, and | ( )| does not change after modifying. V * I k Qi P* V P* V V*i P* V P* V In conclusion, DHS generates a partition ( ), kwaye zonke iingxaki ∈ ( ) ukufumana iimeko max-ububanzi: . Kuba nayiphi na enye isahluko optima ( ) 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 P* V P V P * V | P V Ukusebenza kwe-GPU kunye ne-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 . Correctly ordering the nodes is essential for this batching of computation in warps, to make sure DHS obtains identical results as the serial Hines method. When implementing DHS on GPU, we first group all cells into multiple warps based on their morphologies. Cells with similar morphologies are grouped in the same warp. We then apply DHS on all neurons, assigning the compartments of each neuron to multiple threads. Because neurons are grouped into warps, the threads for the same neuron are in the same warp. Therefore, the intrinsic synchronization in warps keeps the computation order consistent with the data dependency of the serial Hines method. Finally, threads in each warp are aligned and rearranged according to the number of compartments. 46 Xa i-warp ithawula idatha eyenziwe ngexesha elandelayo kunye neengxelo ezihlabathi kwi-memory yehlabathi yehlabathi, inokwenza ukusetyenziswa ngokupheleleyo kwe-cache, oku kuholela ukufikelela kwedatha eyenziwe ngexesha, kwaye ukufikelela kwedatha eyenziwe ngexesha elandelayo kunceda ukufikelela i-memory. Emva kokuhlaziywa kwe-compartments kunye ne-trade rearrangement, sinikezela idatha kwi-memory yehlabathi yehlabathi ukuze kwenziwe kunye ne-computing orders ukuze i-warp inokutyelela idatha eyenziwe ngexesha elandelayo ngexesha lokusebenza kwiprogram. Ngaphezu kwalokho, sinikezela iimvavanyo ezininzi Iimodeli ze-biophysical ze-full-spine kunye ne-poor-spine We used the published human pyramidal neuron . The membrane capacitance m = 0.44 μF cm-2, membrane resistance m = 48,300 Ω cm2, and axial resistivity 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 The morphologies and biophysical mechanisms of spines were the same in few-spine and full-spine models. The length of the spine neck 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 El 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 ukuchithwa kubhalwe kwi-0.3 kunye ne-1.8 ms. Kwi-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 We attached background noise to each cell to simulate a more realistic environment. Noise patterns were implemented as Poisson spike trains with a constant rate of 1.0 Hz. Each pattern started at 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 Conventional detailed neuron simulators lack two functionalities important to modern AI tasks: (1) alternately performing simulations and weight updates without heavy reinitialization and (2) simultaneously processing multiple stimuli samples in a batch-like manner. Here we present the DeepDendrite platform, which supports both biophysical simulating and performing deep learning tasks with detailed dendritic models. 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 Ukuqhathanisa umfanekiso yintlobo we-AI. Kule nqakraza, umzila kufuneka ufunde ukufumana iinkcukacha kwi-image eyodwa kunye nokuthumela i-label efanelekileyo. Kule nathi sinikezela i-HPC-Net, i-network ebandakanya iimodeli ze-human pyramidal neuron ezininzi ezinikezele ukufundisa ukwenza imisebenzi ze-image classification ngokusebenzisa i-platform DeepDendrite. 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. For each image stimulus, we first convert each normalized pixel to a homogeneous spike train. For pixel with coordinates ( ) 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 + ISI ms and lasted until the end of the simulation. Then we attached all spike trains to the input layer neurons in a one-to-one manner. The synaptic current triggered by the spike arriving at time is given by τ t0 where is the post-synaptic voltage, the reversal potential syn = 1 mV, the maximum synaptic conductance 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, reversal potential of passive compartment 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. ( ), where is the 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 Kwimeko yeenkcukacha ye-imaging ye-input, siya kuqala ukuhlaziywa zonke iindleko ze-pixel kwi-0.0-1.0. Emva koko sikuguqulwa i-pixel e-normalized kwi-spike trains kwaye zihlanganisa kwi-neurons ye-input. I-voltage ye-somatic ye-neurons ye-output isetyenziselwa ukulawula i-probability eyenziwe ngalinye le-class, njengoko kuboniswa kwi-equation , where 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 indicates the number of classes, which equals the number of output neurons. The class with the maximum predicted probability is the final classification result. In this paper, we built the HPC-Net with 784 input neurons, 64 hidden neurons, and 10 output neurons. 6 pi i i C Synaptic plasticity rules for HPC-Net Inspired by previous work , usebenzisa isiseko sokufundisa esekelwe kwi-gradient-based learning ukufundisa i-HPC-Net yokwenza umsebenzi wokufunda i-image. Ukusetyenziswa kwimfuneko yokuthintela apha i-cross-entropy, efumaneka kwi-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 -th synapse connecting neuron to neuron ) at each time step. After the simulation of each image stimulus, is updated as shown in Eq. ( ): Wijk k i j Wijk 8 Here is the learning rate, is the update value at time , , I-Somatic Voltages ye-Neuron and respectively, is the -th synaptic current activated by neuron I-Neuron , its synaptic conductance, Yintoni i-transfer resistance phakathi kwe -th connected compartment of neuron on neuron ’s dendrite to neuron ’s 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. ( ). For hidden neurons, the error term is calculated from the error terms in the output layer, given in Eq. ( ). 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 batch copies of HPC-Net. During training, each copy is fed with a different training sample from the batch. DeepDendrite first computes the weight update for each copy separately. After all copies in the current training batch are done, the average weight update is calculated and weights in all copies are updated by this same amount. 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 , ukuvelisa i-adverse noise nge-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 Data availability The data that support the findings of this study are available within the paper, Supplementary Information and Source Data files provided with this paper. The source code and data that used to reproduce the results in Figs. – are available at . The MNIST dataset is publicly available at . The Fashion-MNIST dataset is publicly available at . are provided with this paper. 3 6 https://github.com/pkuzyc/DeepDendrite http://yann.lecun.com/exdb/mnist https://github.com/zalandoresearch/fashion-mnist Source data Code availability I-source code ye-DeepDendrite kunye neemodeli kunye ne-code ezisetyenziselwa ukuvelisa i-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. Ukufundwa okuphambili. Nature 521, 436–444 (2015). 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 I-Branco, T. & Häusser, M. Iqela elinye ye-dendritic njenge-functional fundamental unit ye-nervous system. Curr. Opin. 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Proc. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Acknowledgements Iingcebiso ziye zithunyelwe yi-National Key R&D Program of China (No. 2018B030338001) to TH, 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.K.-2021-55) ziye zithunyelwa kwi-Swish Research Fund no. 945539 (HBP SGA3), kunye neKTH Digital Futures to J.H.K., J.K., A.K., PDIC, Le nqaku lula phantsi kwe-CC by 4.0 Deed (i-Attribution 4.0 International). Le nqaku lula phantsi kwe-CC by 4.0 Deed (i-Attribution 4.0 International).
