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Spiking neural models for decision-making tasks with learning.

Code ↔ Paper

4 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 4 matches
  1. [1] § The experiment › Single participant analysis ↔ functions_simulator.py, lines 226–358 · score 0.59 · weight updates, learning phase, zero, mistake, answer, neurons
  2. [2] § The experiment › Participants ↔ plot_answer_times.ipynb, lines 248–317 · score 0.58 · Middle school students, undergraduate students
  3. [3] § The experiment › Analysis ↔ functions_simulator.py, lines 96–224 · score 0.57 · transfer phase, learning phase, speed, threshold, answer, weights
  4. [4] § The experiment › Procedure ↔ plot_answer_times.ipynb, lines 248–317 · score 0.57 · Middle school students, undergraduate students

Paper

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The authors' code

Python · 359 lines · 12 KB · GPL-3.0 · 2 matches

  1. import numpy as np
  2. import scipy.stats as stats
  3. import matplotlib.pyplot as plt
  4. import scipy.special as spe
  5. import torch
  8. def inA(object):
  9. return object[0]==0
  11. def inB(object):
  12. return not inA(object)
  14. def ObjLearningTransfer(n):
  15. """
  16. Returns the list of the n objects used for the learning phase and the ntot - n objects used for the transfer phase (here n = 10 and 6 objects for the transfer phase)
  17. """
  18. obj = np.array([
  19. [1,0,1,0,1,0,1,0],
  20. [1,0,1,0,1,0,0,1],
  21. [1,0,1,0,0,1,1,0],
  22. [1,0,1,0,0,1,0,1],
  23. [1,0,0,1,1,0,1,0],
  24. [1,0,0,1,1,0,0,1],
  25. [1,0,0,1,0,1,1,0],
  26. [1,0,0,1,0,1,0,1],
  27. [0,1,1,0,1,0,1,0],
  28. [0,1,1,0,1,0,0,1],
  29. [0,1,1,0,0,1,1,0],
  30. [0,1,1,0,0,1,0,1],
  31. [0,1,0,1,1,0,1,0],
  32. [0,1,0,1,1,0,0,1],
  33. [0,1,0,1,0,1,1,0],
  34. [0,1,0,1,0,1,0,1],
  35. ])
  36. #8 first in B, 8 last in A
  38. A = obj[8:, :]
  39. B = obj[:8, :]
  41. A2 = np.copy(A)
  42. np.random.shuffle(A2)
  43. B2 = np.copy(B)
  44. np.random.shuffle(B2)
  45. n2 = int(n/2)
  46. learning = np.concatenate((A2[:n2,:],B2[:n2,:])) # 8,10
  47. transfer = np.concatenate((A2[n2:,:], B2[n2:,:])) # 8, 4
  48. np.random.shuffle(learning)
  49. np.random.shuffle(transfer)
  50. return transfer, learning
  52. def GainOutput(P_mid, obj): #target = label of current image
  53. gain = np.zeros((2, 8))
  54. if inA(obj):
  55. gain[0,:] = 2 * P_mid
  56. gain[1,:] = - gain[0,:]
  57. else:
  58. gain[1,:] = 2 * P_mid
  59. gain[0,:] = - gain[1,:]
  60. return gain
  62. def EWA(W_not_renorm, eta, cred):
  63. """
  64. Updates the weights `W_not_renorm` using the Exponentially Weighted Average (EWA) method.
  65. """
  66. res = W_not_renorm.copy()
  67. res[:, :] *= np.exp(eta * cred[:, :])
  68. return res
  70. def Poisson(lamb, T):
  71. nb_points = stats.poisson.rvs(lamb*T)
  72. points = stats.uniform.rvs(0,T, size = nb_points)
  73. return points
  77. def discrete_Hawkes(input_neurons, W, g):
  78. """
  79. input_neurons: np matrix (nI, N) with N = T/dt
  80. W: matrix (nJ, nI)
  81. g: np array (A)
  82. """
  83. nJ, nI = W.shape
  84. A = g.shape[0]
  85. N = input_neurons.shape[1]
  87. # Initialize the probability output matrix
  88. prob_output = np.zeros((nJ, N))
  90. # Accumulate the weighted sums over the lag values in g
  91. for s in range(A):
  92. if s < N:
  93. prob_output[:, s:] += g[s] * np.dot(W, input_neurons[:, :N-s])
  96. def simulator_vectorized(eta_output, s, f = 300, N = 5000, nb_obj_max = 100): #s = threshold (proportion to reach, between 0 and 1), f = firing rate (freq of spikes, nb by second)
  98. K_input = 8
  99. K_output = 2
  100. s = N*s
  101. p = 5 * f / N #0.3
  104. transfer, learning = ObjLearningTransfer(10) #gives the 10 learning objects and 6 transfer objects
  105. cond = True #when a bloc is correctly classified it becomes false
  106. answers = []
  107. accuracy = []
  108. times = np.zeros(nb_obj_max)
  109. W_output = np.zeros((K_output, K_input)) + 1/K_input
  110. cum_gain = np.zeros((K_output, K_input))
  111. nb_obj = 0
  112. bloc = np.copy(learning)
  114. #Learning phase
  115. while cond:
  116. m = 0
  117. condbis = True #becomes false when there is a mistake
  118. np.random.shuffle(bloc)
  119. if np.sum(accuracy[-10:])==10:
  120. num = 5
  121. else:
  122. num = 10
  123. while condbis and m < num:
  124. #Simulation input neurons
  125. prob_input = np.transpose(np.array([p*bloc[m,:] for i in range(N)])) #proba until max time
  126. input_neurons_out = stats.bernoulli.rvs(prob_input) #simu until max time (K_input, N)
  128. #Simulation output neurons
  129. prob_output = np.sum(W_output[:,None,:] * input_neurons_out.T, axis = 2)
  130. output_neurons = stats.bernoulli.rvs(prob_output)
  132. #Approximated BM
  133. S = np.cumsum(output_neurons, axis = 1)
  135. #reac time and classif
  136. SA = S[0,:]
  137. SB = S[1,:]
  138. timesA = np.where(SA >= s)[0]
  139. timesB = np.where(SB >= s)[0]
  140. if np.shape(timesA)[0]==0 and np.shape(timesB)[0] == 0:
  141. times[nb_obj] = N
  142. answers.append(-1)
  143. elif np.shape(timesA)[0]==0: #B reaches threshold first
  144. times[nb_obj] = timesB[0]
  145. answers.append(1)
  146. elif np.shape(timesB)[0]==0:
  147. times[nb_obj] = timesA[0]
  148. answers.append(0)
  149. else:
  150. if timesA[0] < timesB[0]:
  151. times[nb_obj] = timesA[0]
  152. answers.append(0)
  153. else:
  154. times[nb_obj] = timesB[0]
  155. answers.append(1)
  156. if answers[-1] == bloc[m,0] :
  157. accuracy.append(1)
  158. else:
  159. accuracy.append(0)
  161. N_time_steps = int(times[nb_obj])
  162. P_input = np.sum(input_neurons_out[:,:N_time_steps], axis = 1) / N_time_steps
  163. #Weights update
  164. gain_output = GainOutput(P_input, bloc[m,:])
  165. cum_gain += gain_output
  166. W_output = spe.softmax(eta_output * cum_gain, axis = 1)
  167. #W_output_tot[:,:,nb_obj] = W_output
  169. nb_obj += 1
  170. m+=1
  171. if nb_obj == nb_obj_max - 18 :
  172. return nb_obj_max + 1, times, accuracy
  173. condbis = condbis and (accuracy[-1] == 1)
  175. #condition update
  176. if np.sum(accuracy[-15:])==15 or nb_obj == nb_obj_max - 18:
  177. cond = False
  179. #Transfer phase
  180. transfer_objects = np.zeros((18,8))
  181. bloc_transfer = np.copy(transfer)
  182. np.random.shuffle(bloc_transfer)
  183. transfer_objects[:6,:] = bloc_transfer
  184. transfer_objects[6:12,:] = bloc_transfer
  185. transfer_objects[12:,:] = bloc_transfer
  187. prob_input = np.transpose(np.array([p*transfer_objects for i in range(N)]))
  188. input_neurons_out = stats.bernoulli.rvs(prob_input) #(K_input, 18, N)
  190. prob_output = np.einsum('imt, ki -> kmt', input_neurons_out, W_output)
  191. output_neurons = stats.bernoulli.rvs(prob_output) #(K_output, 18, N)
  192. S = np.cumsum(output_neurons, axis = 2) #(K_output, 18, N)
  193. #reac time and classif
  195. for m in range(18):
  196. SA = S[0,m,:]
  197. SB = S[1,m,:]
  198. timesA = np.where(SA >= s)[0]
  199. timesB = np.where(SB >= s)[0]
  200. if np.shape(timesA)[0]==0 and np.shape(timesB)[0] == 0:
  201. times[nb_obj] = N
  202. answers.append(-1)
  203. elif np.shape(timesA)[0]==0: #B reaches threshold first
  204. times[nb_obj] = timesB[0]
  205. answers.append(1)
  206. elif np.shape(timesB)[0]==0:
  207. times[nb_obj] = timesA[0]
  208. answers.append(0)
  209. else:
  210. if timesA[0] < timesB[0]:
  211. times[nb_obj] = timesA[0]
  212. answers.append(0)
  213. else:
  214. times[nb_obj] = timesB[0]
  215. answers.append(1)
  216. nb_obj +=1
  218. n = nb_obj
  219. fill_time = np.sum(times[n-18:n])/18 #average time transfer phase
  220. times[n:]+=fill_time
  222. #conversion in seconds (max time = 5s)
  223. times = 5 * times / N
  224. return n, times, accuracy
  226. def simulator_vectorized_fix_nb_obj(eta_output, s, nb_obj_learning, f = 300, N = 5000): #s = threshold (proportion to reach, between 0 and 1), f = firing rate (freq of spikes)
  227. """
  228. nb_obj_learning: objects before the transfer phase
  229. """
  230. K_input = 8
  231. K_output = 2
  232. s = N*s
  233. p = 5 * f / N #0.3
  235. #W_output_tot = np.zeros((K_output, K_input, nb_obj_max))
  237. transfer, learning = ObjLearningTransfer(10) #gives the 10 learning objects and 6 transfer objects
  238. cond = True #when a bloc is correctly classified it becomes false
  239. answers = []
  240. accuracy = []
  241. times = np.zeros(nb_obj_learning + 18)
  242. W_output = np.zeros((K_output, K_input)) + 1/K_input
  243. cum_gain = np.zeros((K_output, K_input))
  244. nb_obj = 0
  245. bloc = np.copy(learning)
  247. #Learning phase
  248. while cond:
  249. m = 0
  250. condbis = True #becomes false when there is a mistake
  251. np.random.shuffle(bloc)
  252. if np.sum(accuracy[-10:])==10:
  253. num = 5
  254. else:
  255. num = 10
  256. while condbis and m < num:
  257. #Simulation input neurons
  258. prob_input = np.transpose(np.array([p*bloc[m,:] for i in range(N)])) #proba until max time
  259. input_neurons_out = stats.bernoulli.rvs(prob_input) #simu until max time (K_input, N)
  261. #Simulation output neurons
  262. prob_output = np.sum(W_output[:,None,:] * input_neurons_out.T, axis = 2)
  263. output_neurons = stats.bernoulli.rvs(prob_output)
  265. #Approximated BM
  266. S = np.cumsum(output_neurons, axis = 1)
  268. #reac time and classif
  269. SA = S[0,:]
  270. SB = S[1,:]
  271. timesA = np.where(SA >= s)[0]
  272. timesB = np.where(SB >= s)[0]
  273. if np.shape(timesA)[0]==0 and np.shape(timesB)[0] == 0:
  274. times[nb_obj] = N
  275. answers.append(-1)
  276. elif np.shape(timesA)[0]==0: #B reaches threshold first
  277. times[nb_obj] = timesB[0]
  278. answers.append(1)
  279. elif np.shape(timesB)[0]==0:
  280. times[nb_obj] = timesA[0]
  281. answers.append(0)
  282. else:
  283. if timesA[0] < timesB[0]:
  284. times[nb_obj] = timesA[0]
  285. answers.append(0)
  286. else:
  287. times[nb_obj] = timesB[0]
  288. answers.append(1)
  289. if answers[-1] == bloc[m,0] :
  290. accuracy.append(1)
  291. else:
  292. accuracy.append(0)
  294. N_time_steps = int(times[nb_obj])
  295. P_input = np.sum(input_neurons_out[:,:N_time_steps], axis = 1) / N_time_steps
  296. #Weights update
  297. gain_output = GainOutput(P_input, bloc[m,:])
  298. cum_gain += gain_output
  299. W_output = spe.softmax(eta_output * cum_gain, axis = 1)
  300. #W_output_tot[:,:,nb_obj] = W_output
  302. nb_obj += 1
  303. m+=1
  304. condbis = condbis and (accuracy[-1] == 1)
  306. #print(nb_obj)
  307. if nb_obj == nb_obj_learning:
  308. condbis = False
  309. #condition update
  310. if nb_obj == nb_obj_learning :
  311. cond = False
  313. #Transfer phase
  314. transfer_objects = np.zeros((18,8))
  315. bloc_transfer = np.copy(transfer)
  316. np.random.shuffle(bloc_transfer)
  317. transfer_objects[:6,:] = bloc_transfer
  318. transfer_objects[6:12,:] = bloc_transfer
  319. transfer_objects[12:,:] = bloc_transfer
  321. prob_input = np.transpose(np.array([p*transfer_objects for i in range(N)]))
  322. input_neurons_out = stats.bernoulli.rvs(prob_input) #(K_input, 18, N)
  324. prob_output = np.einsum('imt, ki -> kmt', input_neurons_out, W_output)
  325. output_neurons = stats.bernoulli.rvs(prob_output) #(K_output, 18, N)
  326. S = np.cumsum(output_neurons, axis = 2) #(K_output, 18, N)
  327. #reac time and classif
  329. for m in range(18):
  330. SA = S[0,m,:]
  331. SB = S[1,m,:]
  332. timesA = np.where(SA >= s)[0]
  333. timesB = np.where(SB >= s)[0]
  334. if np.shape(timesA)[0]==0 and np.shape(timesB)[0] == 0:
  335. times[nb_obj] = N
  336. answers.append(-1)
  337. elif np.shape(timesA)[0]==0: #B reaches threshold first
  338. times[nb_obj] = timesB[0]
  339. answers.append(1)
  340. elif np.shape(timesB)[0]==0:
  341. times[nb_obj] = timesA[0]
  342. answers.append(0)
  343. else:
  344. if timesA[0] < timesB[0]:
  345. times[nb_obj] = timesA[0]
  346. answers.append(0)
  347. else:
  348. times[nb_obj] = timesB[0]
  349. answers.append(1)
  350. nb_obj +=1
  352. n = nb_obj
  353. fill_time = np.sum(times[n-18:n])/18 #average time transfer phase
  354. times[n:]+=fill_time
  356. #conversion in seconds (max time = 5s)
  357. times = 5 * times / N
  358. return times, accuracy

functions_simulator.py at commit dfe76b2, under GPL-3.0 · at the source

Overview

Authors: Sophie Jaffard1, Giulia Mezzadri2, Patricia Reynaud-Bouret3, Etienne Tanré4
ORCID iDs: Sophie Jaffard, Giulia Mezzadri, Patricia Reynaud-Bouret, Etienne Tanré
  1. Center for Systems Biology Dresden, Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
  2. Centre Borelli, École Normale Supérieure Paris-Saclay, Paris, France
  3. Laboratoire J. A. Dieudonné, CNRS, Université Côte d’Azur, Nice, France
  4. Université Côte D’Azur, Inria, CNRS, LJAD, Nice, France
Institutions: Centre National de la Recherche Scientifique (France); Université Côte d'Azur (France); Laboratoire Jean-Alexandre Dieudonné (France); Center for Systems Biology Dresden (Germany); Max Planck Institute of Molecular Cell Biology and Genetics (Germany); École Normale Supérieure Paris-Saclay (France); Centre Borelli (France); Columbia University (United States); Centre Inria d'Université Côte d'Azur (France)
Journal: Journal of mathematical biology, volume 93, issue 1, article 1
Dates: received 4 June 2025; accepted 3 May 2026; published online 12 June 2026; in print 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1007/s00285-026-02415-0 · PMID 42283906 · PMCID PMC13263290 · OpenAlex W4407241639
Open access: hybrid, a free copy (OpenAlex)
Preprint: arxiv:2506.09087
Status: code verified
Categories: human (organism), cognitive (subfield)
Methods: Machine learning
Keywords: Spiking Neural Network, Decision-making, Hawkes process, Local learning rule, Drift diffusion model
MeSH: Decision Making*, Learning*, Models, Neurological*, Action Potentials, Animals, Cognition, Computer Simulation, Humans, Mathematical Concepts, Nerve Net, Neural Networks, Computer, Neurons, Poisson Distribution, Reaction Time, Stochastic Processes (* major topic)
Topic: Neural Networks and Applications (Artificial Intelligence, Computer Science), according to OpenAlex
Funding: National Research Agency (ANR-15 IDEX-01, ANR-19-P3IA-0002, ANR-19-CE40-0024-02); CNRS; NeuroMod
Citations: not cited yet (Europe PMC); 63 references in the paper

Abstract

In cognition, response times and choices in decision-making tasks are commonly modeled using Drift Diffusion Models (DDMs), which describe the accumulation of evidence for a decision as a stochastic process, specifically a Brownian motion, with the drift rate reflecting the strength of the evidence. In the same vein, the Poisson counter model describes the accumulation of evidence as discrete events whose counts over time are modeled as Poisson processes. This model has a spiking neurons interpretation as these processes are used to model neuronal activities. However, these models lack a learning mechanism and are limited to tasks where participants have prior knowledge of the categories. To bridge the gap between cognitive and biological models, we propose a biologically plausible Spiking Neural Network (SNN) model for decision-making that incorporates a learning mechanism and whose neurons activities are modeled by a multivariate Hawkes process. First, we show a coupling result between the DDM and the Poisson counter model, establishing that these two models provide similar categorizations and reaction times and that the DDM can be approximated by spiking Poisson neurons. To go further, we show that a particular DDM with correlated noise can be derived from a Hawkes network of spiking neurons governed by a local learning rule. In addition, we designed an online categorization task to evaluate the model predictions. This work provides a significant step toward integrating biologically relevant neural mechanisms into cognitive models, fostering a deeper understanding of the relationship between neural activity and behavior.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above, with 4 matches between paragraphs and lines of code.

SophieJaffard/MEL

License: GPL-3.0
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: dfe76b2e73f60a32bca7fcab5442909207f784da, 2 February 2025
Languages: Jupyter (4), Python (1)
Size: 113 files, 5 scripts
Software Heritage: not archived
Found in: the text, “Conclusion”
Holds: license file, 4 notebooks
Not found: README, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: NumPy (5 files), PyTorch (5 files), Matplotlib (3 files), SciPy (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
6 files
At the source: github.com/SophieJaffard/MEL

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 5 scripts, each with its path and the digest of its content;
  • 4 matches between paragraphs of the paper and lines of the code (method lexical-v1);
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

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Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 2, 28 September 2026

  • Publisher: n/a → Springer Science+Business Media

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 5 keywords, 15 MeSH terms, 3 funders, 38 references.

Cite

This paper

Jaffard, S., Mezzadri, G., Reynaud-Bouret, P., & Tanré, E. (2026). Spiking neural models for decision-making tasks with learning. Journal of mathematical biology, 93(1), 1. https://doi.org/10.1007/s00285-026-02415-0

BibTeX

@article{jaffard2026spiking,
author = {Jaffard, Sophie and Mezzadri, Giulia and Reynaud-Bouret, Patricia and Tanré, Etienne},
title = {{Spiking neural models for decision-making tasks with learning}},
journal = {Journal of mathematical biology},
year = {2026},
month = jun,
volume = {93},
number = {1},
pages = {1},
publisher = {Springer Science+Business Media},
issn = {0303-6812},
doi = {10.1007/s00285-026-02415-0},
url = {https://doi.org/10.1007/s00285-026-02415-0},
pmid = {42283906},
pmcid = {PMC13263290}
}

RIS

TY - JOUR
AU - Jaffard, Sophie
AU - Mezzadri, Giulia
AU - Reynaud-Bouret, Patricia
AU - Tanré, Etienne
TI - Spiking neural models for decision-making tasks with learning
T2 - Journal of mathematical biology
J2 - J Math Biol
PY - 2026
DA - 2026/06/12
VL - 93
IS - 1
SP - 1
SN - 0303-6812
PB - Springer Science+Business Media
DO - 10.1007/s00285-026-02415-0
UR - https://doi.org/10.1007/s00285-026-02415-0
LA - en
ER -

CSL-JSON

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"id": "10.1007/s00285-026-02415-0",
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"title": "Spiking neural models for decision-making tasks with learning",
"container-title": "Journal of mathematical biology",
"author": [
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"family": "Jaffard",
"given": "Sophie"
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"container-title-short": "J Math Biol",
"volume": "93",
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"page": "1",
"DOI": "10.1007/s00285-026-02415-0",
"PMID": "42283906",
"PMCID": "PMC13263290",
"ISSN": "0303-6812",
"publisher": "Springer Science+Business Media",
"URL": "https://doi.org/10.1007/s00285-026-02415-0",
"language": "en",
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"date-parts": [
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