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Artificial neural manifolds.

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The authors' code

Python · 180 lines · 6 KB · CC-BY-4.0

  1. import numpy as np
  2. import matplotlib.pyplot as plt
  3. from scipy.io import loadmat
  4. from sklearn import preprocessing
  6. eeg = loadmat(r"./temp/Bonn_eeg_E_100.mat")
  7. Y1 = eeg['eeg_data']
  9. min_max_scaler = preprocessing.MinMaxScaler()
  10. Y = min_max_scaler.fit_transform(Y1)
  11. # Y = mylorenz(30)
  12. X1 = Y.copy()
  13. X=X1
  14. memory_factor=0.5
  16. m = X.shape[0]
  17. n = X.shape[1]
  19. for i in range(1,m):
  20. X[i,]=X1[i,:]+memory_factor*(X[i-1,:])
  22. Accurate_predictions = 0
  23. ii = 0
  24. all=[]
  25. real=[]
  27. # while ii < 2000:
  28. while ii < 1000:
  29. ii = ii + 1
  30. print(f'Case number: {ii/1}')
  32. INPUT_trainlength = 4
  33. selected_variables_idx = list(range(90))
  35. xx = X[3000 + ii:, selected_variables_idx].T
  37. noisestrength = 0
  38. xx_noise = xx + noisestrength * np.random.rand(*xx.shape)
  40. predict_len = 2
  42. start_idx = max(0, INPUT_trainlength - 3 * predict_len)
  43. traindata = xx_noise[:, start_idx:INPUT_trainlength]
  44. trainlength = traindata.shape[1]
  45. k = 60
  47. jd = 2
  49. D = xx_noise.shape[0]
  50. origin_real_y = xx[jd, :]
  51. real_y = xx[jd, start_idx:]
  52. real_y_noise = real_y + noisestrength * np.random.rand(*real_y.shape)
  53. traindata_y = real_y_noise[:trainlength]
  55. traindata_x_NN = traindata.copy()
  57. w_flag = np.zeros((traindata_x_NN.shape[0],))
  58. A = np.zeros((predict_len, traindata_x_NN.shape[0]))
  59. B = np.zeros((traindata_x_NN.shape[0], predict_len))
  61. predict_pred = np.zeros((predict_len - 1,))
  63. for iter_num in range(1000):
  64. other_idx = list(set(range(traindata_x_NN.shape[0])) - {jd})
  65. random_sample = np.random.choice(other_idx, k - 1, replace=False)
  66. random_idx = sorted([jd] + list(random_sample))
  68. traindata_x = traindata_x_NN[random_idx, :trainlength]
  70. for i in range(len(random_idx)):
  71. b = traindata_x[i, :trainlength - predict_len + 1]
  73. B_w = np.zeros((trainlength - predict_len + 1, predict_len))
  74. for j in range(trainlength - predict_len + 1):
  75. B_w[j, :] = traindata_y[j:j + predict_len]
  77. B_para = np.linalg.lstsq(B_w, b, rcond=None)[0]
  79. B[random_idx[i], :] = (B[random_idx[i], :] + B_para +
  80. B_para * (1 - w_flag[random_idx[i]])) / 2
  81. w_flag[random_idx[i]] = 1
  83. super_bb = []
  84. super_AA = []
  86. for i in range(traindata_x_NN.shape[0]):
  87. kt = 0
  88. bb = []
  89. AA = np.zeros((predict_len - 1, predict_len - 1))
  91. for j in range(trainlength - (predict_len - 1), trainlength):
  92. bb_val = traindata_x_NN[i, j]
  93. col_known_y_num = trainlength - j
  95. for r in range(col_known_y_num):
  96. bb_val = bb_val - B[i, r] * traindata_y[trainlength - col_known_y_num + r]
  98. AA[kt, :predict_len - col_known_y_num] = B[i, col_known_y_num:predict_len]
  99. bb.append(bb_val)
  100. kt += 1
  102. super_bb.extend(bb)
  103. super_AA.append(AA)
  105. super_bb = np.array(super_bb)
  106. super_AA = np.vstack(super_AA)
  108. pred_y_tmp = np.linalg.lstsq(super_AA, super_bb, rcond=None)[0]
  110. tmp_y = np.concatenate([real_y[:trainlength], pred_y_tmp])
  111. Ym = np.zeros((predict_len, trainlength))
  112. for j in range(predict_len):
  113. Ym[j, :] = tmp_y[j:j + trainlength]
  115. BX = np.hstack([B, traindata_x_NN])
  116. IY = np.hstack([np.eye(predict_len), Ym])
  117. A = IY @ np.linalg.pinv(BX)
  119. union_predict_y = []
  120. for j1 in range(predict_len - 1):
  121. tmp_y_list = []
  122. for j2 in range(j1, predict_len - 1):
  123. row = j2 + 1
  124. col = trainlength - j2 + j1 - 1
  125. tmp_y_list.append(A[row, :] @ traindata_x_NN[:, col])
  126. union_predict_y.append(np.mean(tmp_y_list))
  128. union_predict_y = np.array(union_predict_y)
  130. eof_error = np.sqrt(np.mean((union_predict_y - predict_pred) ** 2))
  131. if eof_error < 0.0001:
  132. break
  134. predict_pred = union_predict_y.copy()
  135. all=np.append(all,union_predict_y)
  136. myreal = real_y[trainlength:trainlength + predict_len - 1]
  137. real=np.append(real,myreal)
  138. RMSE = np.sqrt(np.mean((union_predict_y - myreal) ** 2))
  140. std_val = np.std(real_y[trainlength - 2 * predict_len:trainlength + predict_len - 1])
  141. RMSE = RMSE / (std_val + 0.001)
  143. if RMSE < 0.5:
  144. Accurate_predictions += 1
  146. Accurate_prediction_rate = Accurate_predictions / (ii / 2)
  147. print(f'Accurate_prediction_rate: {Accurate_prediction_rate}')
  148. print()
  150. refx = X[3000 + ii - 100:, :].T
  152. plt.figure(1, figsize=(12, 8))
  154. plt.subplot(2, 1, 1)
  155. plt.plot(refx[jd, :150], 'c-*', linewidth=2, markersize=4)
  156. plt.plot(range(100, 100 + INPUT_trainlength),
  157. origin_real_y[:INPUT_trainlength], 'b-*', linewidth=2, markersize=4)
  158. plt.title(f'Original attractor. Init: {ii}, Noise strength: {noisestrength}',
  159. fontsize=18)
  160. plt.grid(True, alpha=0.3)
  162. plt.subplot(2, 1, 2)
  163. plt.plot(range(INPUT_trainlength),
  164. origin_real_y[:INPUT_trainlength], 'b-*', linewidth=2, markersize=4,
  165. label='Training data')
  166. plt.plot(range(INPUT_trainlength, INPUT_trainlength + predict_len - 1),
  167. origin_real_y[INPUT_trainlength:INPUT_trainlength + predict_len - 1],
  168. 'c-p', markersize=4, linewidth=2, label='True values')
  169. plt.plot(range(INPUT_trainlength, INPUT_trainlength + predict_len - 1),
  170. union_predict_y, 'ro', markersize=5, linewidth=2,
  171. label='predictions')
  172. plt.title(f'Pred: KnownLen={trainlength}, PredLen={predict_len-1}, RMSE={RMSE:.4f}',
  173. fontsize=18)
  174. plt.legend()
  175. plt.grid(True, alpha=0.3)
  177. plt.tight_layout()
  178. plt.pause(0.1)
  179. plt.savefig(f'./fig/result_case_{ii//2}.png', dpi=100, bbox_inches='tight')
  180. plt.close()

main_eeg.py, under CC-BY-4.0 · at the source

Overview

Authors: Rui Wang1, Guolei Liu2, Saisai Wang3, Tonglong Zeng1, Xinru Yang1, Jing Sun1, Xiaohua Ma1, Bowen Zhu2,3,4, Min Qiu2,3, Hong Wang1, Yue Hao1
ORCID iDs: Bowen Zhu, Min Qiu, Hong Wang
  1. State Key Laboratory of Wide Band Gap Semiconductor Devices and Integrated Technology, School of Microelectronics, Xidian University, Xi’an, China
  2. Zhejiang Key Laboratory of 3D Micro/Nano Fabrication and Characterization, Department of Electronic and Information Engineering, School of Engineering, Westlake University, Hangzhou, China
  3. Westlake Institute for Optoelectronics, Hangzhou, China
  4. Institute of Advanced Technology, Westlake Institute for Advanced Study, Hangzhou, China
Institutions: Xidian University (China); Westlake University (China)
Journal: Nature communications, volume 17, issue 1, article 7776
Dates: received 17 September 2025; accepted 12 July 2026; published online 5 August 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1038/s41467-026-75979-6 · PMID 42557258 · PMCID PMC13443166 · OpenAlex W7172519752
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: human (organism), systems (subfield)
Methods: Machine learning, Single-unit activity, calcium imaging
Keywords: Electrical and electronic engineering, Electronic devices
MeSH: Brain*, Models, Neurological*, Neural Networks, Computer*, Neurons*, Algorithms, Animals, Humans (* major topic)
Topic: Advanced Memory and Neural Computing (Electrical and Electronic Engineering, Engineering), according to OpenAlex
Funding: National Natural Science Foundation of China (National Science Foundation of China) (62304172, 92464105)
Citations: cited by 1 paper (Europe PMC); 45 references in the paper

Abstract

The abstract is not reproduced here: the paper's license (CC BY-NC-ND) does not allow it. Read it in the paper, at the publisher or on Europe PMC.

Repositories

Its files are read in the Code ↔ Paper reader above.

Zenodo 20688765

License: CC-BY-4.0
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: “Data availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Matplotlib (2 files), NumPy (2 files), scikit-learn (2 files), SciPy (2 files)
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
  • 27 September 2026: the link answers (HTTP 200)
69 files
At the source:

Arvin-xd/Neural-manifold-for-short-term-prediction

License: none: the authors keep all their rights
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: ef5b4548e2ae360037f59a26ee4ba67a90f77410, 31 May 2026
Languages: C/C++ (33), C (17), C++ (16), Python (2)
Size: 102 files, 68 scripts
Software Heritage: not archived
Found in: “Code availability”
Holds: README, environment (requirements.txt)
Not found: license file, CITATION.cff, tests, continuous integration, documentation
Tools: Matplotlib (2 files), NumPy (2 files), scikit-learn (2 files), SciPy (2 files)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
69 files
At the source: github.com/Arvin-xd/Neural-manifold-for-short-term-prediction

Code availability statement

The paper has a code availability statement. Its license (CC BY-NC-ND) does not allow reproducing it here; in short, from what the harvester recognized in it:

Read it in the paper: doi.org/10.1038/s41467-026-75979-6.

Tracing map

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What the map holds:

  • 2 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 136 scripts, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
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Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

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Code and data availability statement

The paper has a code and data availability statement. Its license (CC BY-NC-ND) does not allow reproducing it here; in short, from what the harvester recognized in it:

Read it in the paper: doi.org/10.1038/s41467-026-75979-6.

Versions

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 11 authors, 2 keywords, 7 MeSH terms, 1 funder, 28 references.

Cite

This paper

Wang, R., Liu, G., Wang, S., Zeng, T., Yang, X., Sun, J., Ma, X., Zhu, B., Qiu, M., Wang, H., & Hao, Y. (2026). Artificial neural manifolds. Nature communications, 17(1), 7776. https://doi.org/10.1038/s41467-026-75979-6

BibTeX

@article{wang2026artificial,
author = {Wang, Rui and Liu, Guolei and Wang, Saisai and Zeng, Tonglong and Yang, Xinru and Sun, Jing and Ma, Xiaohua and Zhu, Bowen and Qiu, Min and Wang, Hong and Hao, Yue},
title = {{Artificial neural manifolds}},
journal = {Nature communications},
year = {2026},
month = aug,
volume = {17},
number = {1},
pages = {7776},
publisher = {Nature Publishing Group},
issn = {2041-1723},
doi = {10.1038/s41467-026-75979-6},
url = {https://doi.org/10.1038/s41467-026-75979-6},
pmid = {42557258},
pmcid = {PMC13443166}
}

RIS

TY - JOUR
AU - Wang, Rui
AU - Liu, Guolei
AU - Wang, Saisai
AU - Zeng, Tonglong
AU - Yang, Xinru
AU - Sun, Jing
AU - Ma, Xiaohua
AU - Zhu, Bowen
AU - Qiu, Min
AU - Wang, Hong
AU - Hao, Yue
TI - Artificial neural manifolds
T2 - Nature communications
J2 - Nat Commun
PY - 2026
DA - 2026/08/05
VL - 17
IS - 1
SP - 7776
SN - 2041-1723
PB - Nature Publishing Group
DO - 10.1038/s41467-026-75979-6
UR - https://doi.org/10.1038/s41467-026-75979-6
LA - en
ER -

CSL-JSON

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