ලේඛකයෝ : ජෝන් Zhang Gan He Lei Ma ශ් රීලනිපය J. J. Johannes Hjorth Alexander Kozlov Yutao He Shenjian චාන් Jeanette Hellgren Kotaleski ඉංජිනේරු Tian Sten Grillner නුඹේ Tiejun Huang ලේඛකයෝ : ජෝන් Zhang ගෙන් ඔහු ලී මා ශ් රීලනිපය J. J. ජෝන්සන්ස් හර්ස් ඇලෙක්සැන්ඩර් කොස්ලොව් යූටෝ ඔහු Shenjian චාන් ජැනේට් Hellgren Kotaleski ඉංජිනේරු Tian ස්ටීන් ග් රීකර් නුඹේ චාමනා Huang abstract පිලිබඳ 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 ඇන්ඩ්රොක් ඉරාකික එවැනි ක්රියාවලිය වේගවත් කිරීමට cheduling (DHS) ක්රමයක්. අපි තාක්ෂණිකව ඔප්පු කරන්නේ DHS ක්රියාත්මක කිරීම පරිගණකයෙන් හොඳම සහ නිවැරදි බවයි. මෙම GPU පදනම් ක්රමයක් සාමාන්ය CPU වේදිකාවේ ක්රියාකාරී ශ්රේණිගත Hines ක්රමයට වඩා ශ්රේණිගත වේගය වැඩි වේගයෙන් 2-3 ක් වේගයෙන් ක්රියාත්මක කරයි. අපි DHS ක්රමය සහ NEURON සමුදායෙහි GPU පරිගණක යන්ත්රය ඇතුළත් කරන DeepDendrite ක්රමයක් ගොඩනැගීම සහ neuroscience කාර්යයන් තුළ DeepDendrite හි යෙදුම් ප්රදර්ශනය කිරීම. අපි පර්යේෂණ කරන්නේ 25,000 spins සහිත විස්තරිත මනුෂ් ය pyramidal neuron ආකෘතියක D H S ඇතුළත් කිරීම neuron coding and computational principles is essential to neuroscience. මත්ද් රව් ය මොළය අමුද් රව් ය හා biophysical properties with unique morphological and biophysical properties, thousands of different types of neurons. , neurons simple summing units ලෙස හැඳින්වේ, තවමත් පුළුල් ලෙස අර්ධ පරිගණක, විශේෂයෙන් අර්ධ ජාල විශ්ලේෂණය. කෙසේ වෙතත්, තනි neuron මට්ටමේ සම්පූර්ණ පරිගණක වලට අමතරව, neuronal dendrites වැනි subcellular compartments, ස්වාධීන පරිගණක සමාගම් ලෙස nonlinear මෙහෙයුම් සිදු කළ හැකිය. , , , , එපමණක් නොව, dendritic spines, dendrites වල dendrites ගැඹුරින් සකස් කරන කුඩා ප්රචලිතයන්, synaptic සංඥා compartmentalize කළ හැකි අතර, ඔවුන් ex vivo සහ in vivo ඔවුන්ගේ දෙමාපිය dendrites වෙන් කළ හැකි. , , , . 1 2 3 4 5 6 7 8 9 10 11 ජීව විද්යාත්මකව විස්තරිත neurons භාවිතා සමුදායන් පරිගණක මූලධර්මය සමග ජීව විද්යාත්මක විස්තර සම්බන්ධ කිරීම සඳහා ප්රමුඛ පද්ධතියක් සපයයි. , සැබෑ dendritic morphologies, intrinsic ionic conductance, and extrinsic synaptic inputs සහිත neurons ආකෘති කිරීමට අපට හැකි වේ. dendrites 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 cellular and subcellular neuronal calculations beyond experimental limitations. , . 12 13 12 4 7 neuroscience මත එහි ගැඹුරු බලපෑම අමතරව, මෑතකදී neuronal ව්යුහය හා biophysical විස්තර සහ AI අතර වෙනස සීමා කිරීම සඳහා ජීව විද්යාත්මකව විස්තරිත neuron models භාවිතා කර ඇත.The prevalent technique in the modern AI field is ANNs consisting of point neurons, an analog to biological neural networks.Al ANNs with “backpropagation-of-error” (backprop) algorithm remarkable performance in specialized applications, even beating top human professional players in games of Go and chess , මනුෂ් ය මොළය තවමත් ANNs වඩා දෛනික හා ශබ්දීය පරිසරයන් ඇතුළත් ප්රදේශවල ක්රියාත්මක කරයි , මෑත න්යාය විද්යාත්මක අධ්යයන පෙන්වා දෙන්නේ dendritic ඇතුළත් කිරීම න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ න්යාය ඉගැන්වීමේ , , මීට අමතරව, තනි විස්තරාත්මක multi-compartment ආකෘතිය සංකේත මට්ටමේ අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය සඳහා අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය අමුද්රව්ය , එබැවින්, මොළයට සමාන AI ආකෘති පුළුල් කිරීම, තනි විස්තරිත neuron ආකෘති වලින් විශාල ප්රමාණවත් ජීව විද්යාත්මක විස්තරිත ජාලවලට. 14 15 16 17 18 19 20 21 22 දිගුකාලීන අභියෝගයක් විස්තරාත්මක සංයුක්ත ප්රවේශය එහි අතිශයින් ඉහළ පරිගණක වියදම, එය සංකීර්ණ ආකෘති විද්යාව හා AI සඳහා එහි යෙදුම බරපතල ලෙස සීමා කර ඇත. , , ඵලදායීත්වය වැඩි කිරීම සඳහා, ශ් රීලනිප හයිනස් ක්රමය O(n3) සිට O(n) දක්වා යුධ විසඳීම සඳහා කාල සංකීර්ණතාව අඩු කරයි, එය Neuron වැනි ජනප්රිය සිහිනකරණවල ප්රධාන ඇල්ගාටරි ලෙස පුළුල් ලෙස භාවිතා කර ඇත. and GENESIS කෙසේ වෙතත්, මෙම ක්රමයේ සංකීර්ණ ප්රවේශයක් භාවිතා කරන්නේ සෑම කාමරයක්ම අනුකූලව ක්රියාත්මක කිරීම සඳහා ය.එහෙත්, මෙම ක්රමයට dendritic spines සහිත බොහෝ biophysically විස්තරිත dendrites ඇතුළත් කරන විට, සංකීර්ණ සමානකරණ මැට්රික් (“Hines Matrix”) dendrites හෝ spines (හී. ), Hines ක්රමය තවදුරටත් ප්රයෝජනවත් නොවේ, එය මුළු සමුදාය මත ඉතා බර බර බර තැබූ නිසා. 12 23 24 25 26 1E ප් රතිසංස්කරණය කර ඇති පිරමීඩ නයිරෝන් මට්ටමේ 5 ආකෘතිය සහ විස්තරිත නයිරෝන් ආකෘති සමඟ භාවිතා කරන මාතෘකාව. සංකේතය විසඳීමේ පියවර සංකේතය විසඳීමේ පියවරයි.The equation-solving phase is the bottleneck in the simulation. Simulator වල linear equations වල උදාහරණ Hines Method Data Dependency (Hines Method) Linear Equations විසඳන විට 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.එය විසඳා ගත යුතු සංකේත පද්ධති සංඛ් යාව වඩාත් විස්තරාත්මක වේ. පරිගණක වියදම (නිර්මාණ විසඳුම් පියවර) විවිධ වර්ගයේ neuron ආකෘති මත Hines පද්ධතිය. විවිධ විසඳුම් ක්රම ආදර්ශයක්.නොරෝනයේ විවිධ කොටස් සමන්විත ක්රමවල (සහ, දකුණ), විවිධ වර්ණවල පෙන්වනු ලැබේ.විශාල ක්රමයේ (මුළුවට), සියලු කාමරයක් එක් එක් එක් එක් සමග ගණනය කරනු ලැබේ. 3 පරිගණක ගාස්තු පිරමීඩ ආකෘතියක සමානකම් විසඳන විට. ක්රියාත්මක කාලය spin සමග 500 පිරමීඩ ආකෘති විසඳීම මත විවිධ ක්රම ක්රියාත්මක කාලය. ක්රියාත්මක කාලය 1 s අනුකූලතා විසඳීම 40,000 වතාවක් 0.025 ms කාලය පියවර සමග කාලය ගත කරන බව පෙන්වයි. p-Hines අනුකූල ක්රමය CoreNEURON (GPU මත), Branch මත පදනම්ව අර්ධ මත පදනම්ව අනුකූල ක්රමය (GPU මත), DHS Dendritic අනුකූල සැලසුම් ක්රමය (GPU මත). a b c d c e f g h g i පසුගිය දශක ගණනාවක් තිස්සේ, සෛල මට්ටමේ සෘජුවම ක්රම භාවිතා කිරීමෙන් හයිනස් ක්රමයේ වේගවත් කිරීම සඳහා විශාල දියුණුවක් සිදු කර ඇත, සෑම සෛලයකම විවිධ කොටස් ගණනය කිරීම සෘජුවම කළ හැකිය. , , , , , කෙසේ වෙතත්, වර්තමානයේ සෛල මට්ටමේ සෘජු ක්රම බොහෝ විට ඵලදායී සෘජු ක්රමයක් නැති හෝ ප්රථම Hines ක්රමයට වඩා ප්රමාණවත් සංඛ්යාත්මක නිවැරදිතාවයක් නැති වේ. 27 28 29 30 31 32 මෙහිදී, අපි පරිගණක ඵලදායීතාව වැඩි දියුණු කිරීමට සහ පරිගණක වියදම් අඩු කිරීමට හැකි සම්පූර්ණයෙන්ම ස්වයංක්රීය, සංඛ්යාත්මකව නිවැරදි, සහ පරිගණක ආකෘතිය වැඩි දියුණු කිරීම සඳහා මෙවලමක් සංවර්ධනය කර ඇත. අමතරව, මෙම සමුදාය මෙවලමක් පරිගණක අධ්යයයනය සහ AI යෙදුම් සඳහා ජීව විද්යාත්මක විස්තර සහිත ස්නායු ජාල ස්ථාපනය කිරීම සහ පරීක්ෂා කිරීම සඳහා සම්පූර්ණයෙන්ම අනුකූලව භාවිතා කළ හැකිය. සංකීර්ණ පරිගණක තාක්ෂණය අපගේ ආකෘතිය නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිතව නිශ්චිත වේ. Neuron Simulator සමාන කිරීම 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 Simulation Engine සහ දෙකක් (I/O Module සහ Learning Module) යන සහාය මොඩියුලයක් ලෙස Simulations තුළ dendritic learning algorithms සහාය වේ.DeepDendrite යනු GPU Hardware Platform මත ක්රියාත්මක වන අතර, Neuroscience වල සාමාන් ය Simulation Task සහ AI හි Learning Task දෙකම සහාය වේ. 35 Last but not least, we also present several applications using DeepDendrite, targeting a few critical challenges in neuroscience and AI: (1) We demonstrate how spatial patterns of dendritic spine inputs affect neuronal activities with neurons containing spines throughout the dendritic trees (full-spine models). DeepDendrite enables us to explore neuronal computation in a simulated human pyramidal neuron model with ~25,000 dendritic spines. (2) In the discussion we also consider the potential of DeepDendrite in the context of AI, specifically, in creating ANNs with morphologically detailed human pyramidal neurons. Our findings suggest that DeepDendrite has the potential to drastically reduce the training duration, thus making detailed network models more feasible for data-driven tasks. All source code for DeepDendrite, the full-spine models and the detailed dendritic network model are publicly available online (see Code Availability). Our open-source learning framework can be readily integrated with other dendritic learning rules, such as learning rules for nonlinear (full-active) dendrites Burst-dependent synaptic plasticity යනු Spike Prediction සමඟ ඉගෙන ගන්න මුළුමනින්ම, අපගේ අධ්යයනය, දැනට පවතින පරිගණක neuroscience පෞද්ගලික පරිගණක පද්ධතිය වෙනස් කිරීමට හැකියාව ඇති මෙවලම් සම්පූර්ණ සංකේතයක් සපයයි.GPU පරිගණකයේ ශක්තිය භාවිතා කිරීමෙන්, අපි මෙම මෙවලම් මොළයේ මෘදු පද්ධති මූලධර්මය පිළිබඳ පද්ධති මට්ටමේ පර්යේෂණ පහසු කරනු ඇත, මෙන්ම neuroscience හා නවීන AI අතර සබඳතාවය ප්රවර්ධනය කරනු ඇත. 21 20 36 ප් රතිඵල Dendritic Hierarchical Scheduling (DHS) ක් රමය 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 මෙම බෝතල් අංගය විසඳීමට, සෛල මට්ටමේ සමන්විත ක්රමයන් සංවර්ධනය කර ඇති අතර, සෛල මට්ටමේ සමන්විත ගණනය කළ හැකි විවිධ කාමරවලට එක් සෛලයක් "සංස්කරණය" කිරීමෙන් තනි සෛල ගණනය කිරීම වේගවත් කරයි. , , . However, such methods rely heavily on prior knowledge to generate practical strategies on how to split a single neuron into compartments (Fig. තවත් Fig. එබැවින්, එය අසාමාන්ය morphologies, උදාහරණයක් ලෙස pyramidal neurons හා Purkinje neurons සඳහා අඩු ඵලදායී බවට පත් වේ. 27 28 38 1g 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 සිතිවිලි නිවැරදිභාවය සහ පරිගණක වියදම මත පදනම්ව, අපි සංසන්දනය කිරීමේ ගැටලුව මාතෘකාව ප්රශ්නය ලෙස සකස් කරමු (මෙමෝටොඩෝස් බලන්න). parallel threads, we can compute at most සෑම පියවරකදීත්, අපි සෑම දරුවාගේ කොන්දේසි සලකා බැලූ විට පමණක් කොන්දේසි ගණනය කළ යුතුය; අපගේ ඉලක්කය සම්පූර්ණ ක්රියාවලිය සඳහා පියවර ගණන අවම ප්රමාණයක් සහිත උපායමාර්ගයක් සොයා ගැනීමයි. k k හොඳම බෙදාහැරීම නිර්මාණය කිරීම සඳහා, අපි Dendritic Hierarchical Scheduling (DHS) යන ක්රමයක් යෝජනා කරමු (මෙම ක්රමයන් තුළ ප්රදර්ශනීය සාක්ෂි ඉදිරිපත් කර ඇත). ), 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) Topology විශ්ලේෂණය කිරීමෙන් පසු, අපි candidates සොයමින් තෝරා ගනිමු ගැඹුරුම candidate කොන්දේසි (එක් කොන්දේසි සියලු දරුවන් කොන්දේසි ප්රතිකාර කර ඇත නම් පමණක් candidate වේ). ) 2a 2b, c k 2d DHS Processes - DHS ක්රියාවලිය සෑම පරිවර්තනයකටම ගැඹුරුම candidate nodes වේ. 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. විවිධ neuron ආකෘති මත topology විශ්ලේෂණය. distinct morphologies සමග හය neurons මෙහි පෙන්වනු ලැබේ. සෑම ආකෘතියකටම, soma ගස් උෂ්ණත්වය ලෙස තෝරා ගනු ලැබේ, එබැවින් අංගයේ ගැඹුර soma (0) සිට distal dendrites දක්වා වැඩි වේ. DHS ක්රියාත්මක කිරීමේ ආකෘතිය මත with four threads. Candidates: nodes that can be processed. Selected candidates: nodes that are picked by DHS, i.e., the ප් රචණ්ඩත්වය සිදුවේ, නමුත් අපි පාපයට එරෙහිව ශුද්ධ විනිශ්චය සහ අපි පුද්ගලිකව අකමැති අයට එරෙහි වන පුරපැම අතර වෙනස අප හඳුනාගත යුතුය, එය උඩඟුකමේ අනිවාර්ය ප් රතිපලයයි. DHS විසින් ලබාගත් සංකේතය ප ් රතිසංස්කරණ ක්රියාවලිය . 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, එනම්, DHS හි පරිගණක වියදම් ප්රතිශතය Hines ක්රමයේ ප්රතිශතයට, විවිධ වර්ගයේ ආකෘති මත විවිධ සංඛ්යාවන් සහිත DHS භාවිතා කරන විට. a k b c d b k e d f උදාහරණයක් ලෙස 15 කාමර සහිත සරලව උදාහරණයක් ගන්න, සර්වික පරිගණක Hines ක්රමයක් භාවිතා කිරීමෙන්, සියලු කාමර ක්රියාත්මක කිරීම සඳහා පියවර 14 ක් ගත වන අතර, හතරක් සංකේතයක් සහිත DHS භාවිතා කිරීමෙන්, එහි කාමර පහකට බෙදාහැරීමට හැකි වේ. ): {{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 ) විවිධ සංඛ්යාව සමඟ අමුද්රව්ය (Fig. Cortical and Hippocampal Pyramidal Neurons ඇතුළත් , , Cerebellar Purkinje නයිරෝන STRIATAL PROJECTION NEURONS (SPN) යනු මිටරල් මිටරල් මිටරල් මිටරල් මිටරල් , සංවේදී, කොරියාකාරී, සහ subcortical ප්රදේශයේ ප්රධාන ප්රධාන neurons ආවරණය. පසුව අපි පරිගණක වියදම ප්රමාණය. මෙහි සංවේදී පරිගණක වියදම DHS හි පරිගණක වියදම Hines ක්රමයේ ප්රමාණයට ප්රමාණයෙන් සංකේත කරන ලදී. පරිගණක වියදම, එනම්, සමාගම් විසඳීමේදී සිදු කරන පියවර ගණන, පුදුමයෙන් අඩු වේ. උදාහරණයක් ලෙස, 16 අඟල් සමඟ, DHS හි පරිගණක වියදම Hines ක්රමයට වඩා 7%-10% වේ. ආකර්ෂණීයව, DHS ක්රමයේ 16 හෝ පවා 8 සංකේත අඟල් ලබා දෙන විට ඉදිරිපත් කරන අඟල් සඳහා ඔවුන්ගේ පරිගණක වියද ), suggesting adding more threads does not improve performance further because of the dependencies between compartments. 39 2f 40 41 42 43 44 45 2f එක්ව, අපි DHS ක්රමයක් නිර්මාණය කර ඇත, dendritic ටොපෝගෝලයේ ස්වයංක්රීය විශ්ලේෂණය සහ සමන්විත පරිගණක සඳහා හොඳම බෙදාහැරීමේ හැකියාව ලබා දෙයි. DHS සංකල්පය ආරම්භ කිරීමට පෙර හොඳම බෙදාහැරීමේ හැකියාව සොයා ගත යුතු අතර, සමානකම් විසඳීමට අතිරේක පරිගණක අවශ්ය නොවේ. GPU Memory Boosting මගින් DHS වේගවත් කිරීම DHS සෑම neuron එකකටම multi-threads භාවිතා කරන අතර, එය neuronal network simulations ක්රියාත්මක කරන විට විශාල ප්රමාණයක් threads භාවිතා කරයි.Graphics Processing Units (GPUs) යනු විශාල පරිශීලකයන් (එනම්, streaming processors, SPs, Fig. ) for parallel computing . In theory, many SPs on the GPU should support efficient simulation for large-scale neural networks (Fig. කෙසේ වෙතත්, DHS හි ඵලදායීතාවය අන්තර්ජාල ප්රමාණය වර්ධනය වන විට වැදගත් ලෙස අඩු වී ඇති බව අපි නිශ්චිතව නිරීක්ෂණය කර ඇති අතර, එය මධ් යම ප්රතිඵල ලියාපදිංචි කිරීම සහ ලිවීමට හේතුවෙන් දත්ත ගබඩා කිරීම හෝ අතිරේක මතකය ප්රවේශය නිසා ඇති විය හැකිය. වම් පස ) 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. Streaming Multiprocessors (SMs) ආකෘතිය - සෑම SM එකකටම Multi Streaming Processors, Registers සහ L1 Cache ඇතුළත් වේ. DHS ක්රියාත්මක කිරීම, සෑම neuron එකකටම හතරක් ඇත.During simulation, each thread executes on one stream processor. GPU මත මත මතය ආයෝජනය උපාය මාර්ග. Top panel, thread assignment and data storage of DHS, before (left) and after (right) memory boosting.Bottom, a 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. ස්පර්ශ වේගයේ මතකය වර්ධනය multi-layer 5 පිරමීඩ ආකෘති සමග spin. 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 , උදාහරණයක් ලෙස, අපි මුලින්ම පරිගණක ඇණවුම් හුවමාරු කර, ඔවුන් මත අඟල් සංඛ්යාව අනුව අඟල් හුවමාරු කරමු. ඉන්පසු අපි පරිගණක ඇණවුම් සමග අනුකූලව ගෝලීය මතකය තුළ දත්ත ගබඩා ප්රමාණවත් කරමු, එනම්, එකම පියවරකදී පරිශීලක කරන ලද අඟල් ගෝලීය මතකය තුළ අනුකූලව ගබඩා කරනු ලැබේ. අමතරව, අපි මධ්යම ප්රතිඵල ගබඩා කිරීම සඳහා GPU ලැයිස්තු භාවිතා කරමු, තවදුරටත් මතකය ගබඩා ප්රමාණය ශක්තිමත් කිරීම. ඊට අමතරව, පිඟාන් සහ සාමාන්ය neuron ආකෘති සමග පිරමීඩයේ neurons කිහිපයක් පිළිබඳ අත්හදා බැලීම් (එළිදරව්. තවත් Fig. ) show that memory boosting achieves a 1.2-3.8 times speedup as compared to the naïve DHS. 46 47 3D 3e, f 2 GPU මතකය වැඩි දියුණු කිරීම සමඟ DHS ක්රියාකාරීත්වය සම්පූර්ණයෙන්ම පරීක්ෂා කිරීම සඳහා, අපි සෑම ආකෘතියක විශාල සංඛ්යාව මත කේබල් සමානකම් විසඳීමේ ක්රියාකාරී කාලය අගය කරන ලද සාමාන්ය neuron ආකෘති හයක් තෝරා ගනිමු. DHS-4, DHS-16 සහ CoreNEURON හි GPU ක්රමයට ගැලපෙන පරිදි, DHS-4 සහ DHS-16 ක්රමයට ගැලපෙන පරිදි 5 සහ 15 වතාවක් වේගවත් විය හැකිය. එපමණක් නොව, NEURON හි සම්ප් රදායික ශ්රේණිගත Hines ක්රමයට වඩා, CPU හි එක් තනි අංගයක් සහිතව ක්රියාත්මක වන අතර, DHS සංයුක්තය 2-3 ශ්රේණිගත කිරීම් විසින් වේගවත් කරයි (විශේෂ රූපය. ), සමාන සංඛ්යානීය නිවැරදිතාවය පවත්වාගෙන යන අතර, ගැඹුරු ස්පින්ස් (පිරිතාලික ෆයිග්ස්. සහ ), active dendrites (Supplementary Fig. ) සහ විවිධ බෙදාහැරීමේ උපාය මාර්ග (Supplementary Fig. ) 4 4A 3 4 8 7 7 GPU මත 1 s සකසා ගැනීම සඳහා සමානතා විසඳීමේ ක්රියාකාරී කාලය (dt = 0.025 ms, සම්පූර්ණයෙන්ම 40,000 iterations).CoreNEURON: CoreNEURON හි භාවිතා කරන සංකල්ප විසඳීමේ ක්රමය; DHS-4: DHS සෑම neuron සඳහා හතර අඟල් සමග; DHS-16: DHS සෑම neuron සඳහා 16 අඟල් සමග. , DHS-4 සහ DHS-16 විසින් බෙදාහැරීමේ දර්ශනය, සෑම වර්ණයක්ම එක් තනි අඟහරුවක් පෙන්වයි. a b c DHS ස්වයංක්රීය ස්වයංක්රීය ස්වයංක්රීය Partitioning නිර්මාණය කරයි 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. පින්තූරයක් පෙන්වා දෙන්නේ තනි අංගයක් විවිධ අංග අතර නිතර මාරු කරන බවයි (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. ), DHS තනි කාමර ප්රමාණයේ (එනම්, ගස් නෝඩ්) තනි කාමර ප්රමාණයේ (එනම්, ගස් නෝඩ්) තනි කාමර ප්රමාණයේ (එනම්, ගස් නෝඩ්) තනි කාමරයේ (එනම්, ගස් නෝඩ්) තනි වේ. 4B, C 4B, C 4B, C 4B, C සම්පූර්ණයෙන්ම, DHS සහ මතකය වැඩිදියුණු කිරීම දර්ශනීයව ඔප්පු කර ඇති මාර්ගගත යුධ විසඳුම් විසඳීම සඳහා වඩාත් හොඳ විසඳුමක් සංකීර්ණව හා අනාවැකියක් නොමැතිව ඵලදායී ලෙස සකස් කරයි. මෙම මූලධර්මය භාවිතා කිරීමෙන්, අපි විවෘත ප්රවේශය වන DeepDendrite වේදිකාව ගොඩනඟා, neuroscientists විසින් කිසිදු විශේෂිත GPU වැඩසටහන් දැනුම නොමැතිව ආකෘති ක්රියාත්මක කිරීම සඳහා භාවිතා කළ හැකිය. DHS ස්පෙන්සර් මට්ටමේ ආකෘතිය ලබා ගත හැකිය As dendritic spines receive most of the excitatory input to cortical and hippocampal pyramidal neurons, striatal projection neurons, etc., their morphologies and plasticity are crucial for regulating 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 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 Theory predicts that the very thin spinal neck (0.1-0.5 um in diameter) electronically isolates the spinal head from its parent dendrite, thus compartmentalizing the signals generated at the spinal head. කෙසේ වෙතත්, dendrites මත සම්පූර්ණයෙන් බෙදාහැරෙන spines සහිත විස්තරාත්මක ආකෘතිය (“full-spine ආකෘතිය”) පරිගණකයෙන් ඉතා මිල අධික වේ. ස්පෙන්සර් සාධක ඒ වෙනුවට, සියලුම ආකෘති සකස් කිරීම සඳහා, මෙහිදී, ස්පෙන්සර් ෆැක්ටරය සලකා බැලිය යුතු වන්නේ සෛල මාලිංගයේ biophysical properties මත ස්පෙන්සර් බලපෑම අවම කිරීමයි. . 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. ) සහ ස්පීක් අවදානම (පීග්. ) 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 එක ඇතුලත් වෙනවා. 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 , කෙසේ වෙතත්, සාමාන් ය සෛල මට්ටමේ ක්රම (උදාහරණයක් ලෙස, "multi-split" ක්රමය) ) 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. spines receive most of the excitatory inputs in the central nervous system, spines generated electrical signals 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 , , motor cortex , 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 Recent works on unraveling the dendritic roles in task-specific learning have achieved remarkable results in two directions, i.e., solving challenging tasks such as image classification dataset ImageNet with simplified dendritic networks , 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 පරිගණක දර්ශන කාර්යයන් සඳහා ANNs තුළ ක්රියාකාරී dendrites ක්රියාකාරී ක්රියාකාරීත්වය පිළිබඳ දියුණුවක් සිදු වී ඇත. . 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 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. Methods 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 , 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. එබැවින්, අපි විවිධ අර්බුදවල සංකේත ගණනය කළ හැක, ඔවුන්ගේ අගය මත රඳා පවතී නොවන නිසා. 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 and threads (basic computational units) to perform triangularization, parallel triangularization equals to divide the node set of into subsets, i.e., = තොපි , , … } 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., 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 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 අපි Vi Vi v Vi c c v Vj j i P* V P* V Here subset සෑම පරිගණකයක්ම පරිගණකයට ඇතුළත් වේ -th step (Fig. ), so | | ≤ indicates that we can compute nodes each step at most because the number of available threads is . 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. අපි 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., the number of candidate nodes is smaller or equivalent to the number of available threads, remove all nodes in 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 = { , }, 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 ( • නිවැරදිත්වය පිළිබඳ කොන්දේසි සපුරාලීම. ( (මෙය ලැබෙන්නේ neuronal tree වලින්. . 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 DHS ක්රියාත්මක කිරීමෙන් පෙන්නුම් කර ඇති පරිදි, සෑම අංගයක්ම 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 Vi-1 Vi Vi+1 Vi+2 Vn DHS සඳහා හොඳම සාක්ෂි 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 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 අපි Qi k Qi Vi ද 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) | | < 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), | | = , 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 එවැනි will be put into a subsequent subset ( > ). We first move from to + , 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. ): if the parent node of is in + , move this parent node to + ; else move the node with minimum depth from + to + . After adjusting , modify subsequent subsets + , + , … 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 ඉහත විස්තර කරන ලද සංස්කරණය උපායමාර්ගයෙන්, අපි සෑම පෘථිවියේදීම පෘථිවියේදීම පෘථිවියේදීම පෘථිවියේදීම පෘථිවියේදීම වෙනස් කළ හැකිය. with the -th deepest node in 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 ( (එහෙම එකක් නෑ.එහෙම නෑ.එහෙම නෑ.එහෙම නෑ.එහෙම නෑ.එහෙම නෑ.එහෙම නෑ.එහෙම නෑ. ∈ ( ) 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 අවසාන වශයෙන්, DHS බෙදාහැරීම නිර්මාණය කරයි ( ) සහ සෑම සමුළුවක්ම ∈ ( ) satisfy the max-depth condition: . For any other optimal partition ( ) අපි එහි උපකරණ සංයුතිය සමාන බවට පත් කිරීමට එහි උපකරණ සංයුතිය වෙනස් කළ හැකිය ( ), එනම්, සෑම සඟරාවක්ම candidate set හි ගැඹුරුම කොන්ඩ්ස් වලින් සකස් වන අතර, එය දිගටම තබා ගන්න. ( ) the same after modification. So, the partition ( ) DHS වලින් ලබා ගනු ලැබේ හොඳම බෙදාහැරීම් වලින් එකක්. P V Vi P V P * V P V P * V | P V GPU implementation and memory boosting උසස් මතකය ප්රමාණය ලබා ගැනීම සඳහා, GPU (1) ගෝලීය මතකය, (2) cache, (3) ලැයිස්තුවේ මතකය ප්රමාණය භාවිතා කරයි, එහිදී ගෝලීය මතකය විශාල ප්රමාණය නමුත් අඩු ප්රමාණය ඇති අතර, ලැයිස්තුවේ අඩු ප්රමාණය නමුත් උසස් ප්රමාණය ඇති අතර, අපි GPU හි මතකය ප්රමාණය භාවිතා කිරීමෙන් මතකය ප්රමාණය වැඩි කිරීමට අපේක්ෂා කරමු. GPU හි SIMT (Single-Instruction, Multiple-Thread) ආකෘතිය භාවිතා කරයි. Warps යනු GPU හි මූලික තැපැල් යන්ත්ර වේ (warp යනු 32 සංකේත thread එකකි). නිවැරදිව කොන්දේසි සකස් කිරීම warps හි පරිගණක මෙම පැටවුම් සඳහා අත්යවශ්ය වේ, DHS සංකේත Hines ක්රමයක් ලෙස සමාන ප්රතිඵල ලබා ගැනීමට වග බලා ගන්න. GPU මත DHS ක්රියාත්මක කරන විට, අපි මුලින්ම ඔවුන්ගේ morphologies මත පදනම්ව සියලූ සංකේතයන් විවිධ warps එකතු කර ඇත. සමාන morphologies සහිත සංකේතයන් එකම warp එකට එකතු කර ඇත. එවිට අපි DHS සෑම neuron මත ක්රියාත්මක වන අතර, සෑම neuron ප්රමාණයන් ගණනාවක් ප්රමාණයන් සඳහා ප්රමාණයන් සකස් කර ඇත. සෑම warp හි සංකේතයන් සංකේත ගණන අනුව සකස් කර ඇත. එබැවින්, warps හි අභ්යන් 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. Full-spine සහ few-spine biophysical ආකෘති 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 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 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 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. 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 Hidden layer contains a group of human pyramidal neuron models, receiving the somatic voltages of input layer neurons.අර්පෝලියාව Eyal, et al සිට විය. , 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 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 , 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 neuron ආකෘතිය සහ 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 , 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 ආදායම් ඡායාරූපය පන්තියට අයිති නම් , 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 , , are somatic voltages of neuron and respectively, is the -th synaptic current activated by neuron neuron එක , සයිටම් සයිටම් සයිටම්, is the transfer resistance between the -th connected compartment of neuron neuron එක ’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 HPC-Net කොටස් පිටපත්. පුහුණු කාලය තුළ, සෑම පිටපතක්ම කොටස් වලින් වෙනස් පුහුණු උපාංගයක් ලබා දෙයි. DeepDendrite මුලින්ම සෑම පිටපතකටම තනිව බර යාවත්කාලීන කිරීම් ගණනය කරයි. දැනට පුහුණු කොටස්වල සියලු පිටපත් කළ පසු, සාමාන් ය බර යාවත්කාලීන කිරීම් ගණනය කරනු ලැබේ. 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 හා Fashion-MNIST ප්රතිඵල පෙන්වන්නේ HPC-Net හි අනාවැකි නිශ්චිත ANN හි අනාවැකි නිශ්චිතව 19% සහ 16.72% වඩා ඉහළ බවය. 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. – ලබා ගත හැකි වේ at MNIST දත්ත සංකේතය පොදුව ලබා ගත හැක at . 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Proc. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) අනුමැතිය GPU පරිගණකයේ වටිනා තාක්ෂණික සහාය සඳහා අධ්යාපන අමාත් යාංශය ඩොක්ටර් Rita Zhang, Daochen Shi සහ NVIDIA සාමාජිකයන් වෙත ස්තුතිවන්තව ස්තුති කරති. මෙම වැඩ L.M., Guangdong ප්රදේශයේ ජාතික ප්රධාන පර්යේෂණ සහ සංවර්ධන වැඩසටහන (No. 2020AAA0130400) ට K.D. සහ T.H., චීනයේ ජාතික ස්වාභාවික විද්යා පදනම (No. 6182588102) ට ටී.එම්, චීනයේ ජාතික ප්රධාන පර්යේෂණ සහ සංවර්ධන වැඩසටහන (No. 2022ZD01163005) ටී.එම්, චීනයේ ජාතික ප්රධාන පර්යේෂණ හා සංවර්ධන වැඩසටහන (No. 2018B030338001) ටී. මෙම ලිපිය CC by 4.0 Deed (Attribution 4.0 International) බලපත්ර යටතේ ස්වභාවිකව ලබා ගත හැකිය. මෙම ලිපිය CC by 4.0 Deed (Attribution 4.0 International) බලපත්ර යටතේ ස්වභාවිකව ලබා ගත හැකිය.
