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Neural decision dynamics underlying reinforcement learning and working memory.

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The authors' code

Stan · 295 lines · 9 KB · no license

  1. functions {
  2. // ---------- utilities ----------
  3. real safe_entropy(vector p) {
  4. real H = 0;
  5. for (i in 1:num_elements(p)) {
  6. real pi = fmax(p[i], 1e-12);
  7. H -= pi * log(pi);
  8. }
  9. return fmax(H, 1.0);
  10. }
  12. real lba_pdf(real t, real b, real A, real v, real s) {
  13. real z1 = (b - A - t * v) / (t * s);
  14. real z2 = (b - t * v) / (t * s);
  15. real term1 = v * Phi(z1);
  16. real term2 = s * exp(normal_lpdf(z1 | 0, 1));
  17. real term3 = v * Phi(z2);
  18. real term4 = s * exp(normal_lpdf(z2 | 0, 1));
  19. real pdf = (1 / A) * (-term1 + term2 + term3 - term4);
  20. return fmax(pdf, 1e-12);
  21. }
  23. real lba_cdf_fn(real t, real b, real A, real v, real s) {
  24. real b_A_tv = b - A - t * v;
  25. real b_tv = b - t * v;
  26. real ts = t * s;
  27. real z1 = b_A_tv / ts;
  28. real z2 = b_tv / ts;
  29. real term1 = (b_A_tv / A) * Phi_approx(z1);
  30. real term2 = (b_tv / A) * Phi_approx(z2);
  31. real term3 = (ts / A) * exp(normal_lpdf(z1 | 0, 1));
  32. real term4 = (ts / A) * exp(normal_lpdf(z2 | 0, 1));
  33. real cdf = 1 + term1 - term2 + term3 - term4;
  34. return fmin(fmax(cdf, 1e-12), 1 - 1e-12);
  35. }
  37. real lba_survival_log(real t, real b, real A, vector v, real s) {
  38. int J = num_elements(v);
  39. real logS = 0;
  40. for (j in 1:J) {
  41. real Fj = lba_cdf_fn(t, b, A, v[j], s);
  42. logS += log1m(Fj);
  43. }
  44. return logS;
  45. }
  47. // One-trial choice/RT log likelihood
  48. real lba_trial_loglik(real RT, int y,
  49. real b, real A, vector v, real s, real tau) {
  50. real t = RT - tau;
  51. if (t <= 0) return log(1e-12);
  53. real log_pdf_chosen = log(lba_pdf(t, b, A, v[y], s));
  55. real log_surv_nonchosen = 0;
  56. for (j in 1:num_elements(v)) {
  57. if (j != y) {
  58. real Fj = lba_cdf_fn(t, b, A, v[j], s);
  59. log_surv_nonchosen += log1m(Fj);
  60. }
  61. }
  63. real log_prob_neg = 0;
  64. for (j in 1:num_elements(v)) {
  65. log_prob_neg += normal_lcdf(-v[j] / s | 0, 1);
  66. }
  67. real log_one_minus_probneg = log_diff_exp(0, log_prob_neg);
  69. return log_pdf_chosen + log_surv_nonchosen - log_one_minus_probneg;
  70. }
  72. real lba_censored_loglik(real T_deadline,
  73. real b, real A, vector v, real s, real tau) {
  74. real t = T_deadline - tau;
  75. if (t <= 0) return 0;
  76. return lba_survival_log(t, b, A, v, s);
  77. }
  79. vector lba_rng(real k, real A, vector v, real s, real tau) {
  80. int J = num_elements(v);
  81. vector[J] drift;
  82. array[J] real start;
  83. array[J] real ttf;
  84. array[J] int resp;
  85. vector[2] pred;
  87. for (j in 1:J) {
  88. drift[j] = normal_rng(v[j], s);
  89. start[j] = uniform_rng(0, A);
  90. ttf[j] = (k + A - start[j]) / drift[j];
  91. }
  93. resp = sort_indices_asc(ttf);
  94. ttf = sort_asc(ttf);
  95. for (j in 1:J) {
  96. if (ttf[j] > 0) {
  97. pred[1] = ttf[j] + tau;
  98. pred[2] = resp[j];
  99. return pred;
  100. }
  101. }
  102. pred[1] = -1; pred[2] = -1;
  103. return pred;
  104. }
  105. }
  107. data {
  108. int<lower=1> L;
  109. int<lower=1> N;
  110. int<lower=1> Actions;
  111. int<lower=1> max_num_stim;
  113. array[N] int<lower=1> block_trial;
  114. array[N] int<lower=0,upper=1> include_density;
  115. array[N] int<upper=Actions> response;
  116. array[N] int<lower=1,upper=max_num_stim> stim;
  117. array[N] int<lower=1,upper=max_num_stim> max_stim;
  118. array[N] int<upper=1> feedback;
  119. matrix[N,2] RT;
  120. array[N] int<lower=1,upper=L> subject;
  122. int<lower=1> beta;
  123. real<lower=0> tau;
  124. real initial_value;
  126. real mu_sd_prior;
  127. real<lower=0> sd_sd_prior;
  128. real<lower=0> sd_prior;
  130. int<lower=1> K;
  131. vector[K] Ks;
  132. }
  134. parameters {
  135. real mu_alpha; real<lower=0> sd_alpha; vector[L] z_alpha;
  136. real mu_phi; real<lower=0> sd_phi; vector[L] z_phi;
  137. real mu_rho; real<lower=0> sd_rho; vector[L] z_rho;
  138. real mu_pers; real<lower=0> sd_pers; vector[L] z_pers;
  140. real mu_logk; real<lower=0> sd_logk; vector[L] z_k;
  141. real mu_logA; real<lower=0> sd_logA; vector[L] z_A;
  142. real mu_eta; real<lower=0> sd_eta; vector[L] z_eta;
  144. real mu_C_raw; real<lower=0> sd_C; vector[L] z_C;
  145. }
  147. transformed parameters {
  148. real s = 1;
  150. vector[L] alpha_sbj;
  151. vector[L] rho_sbj;
  152. vector[L] phi_sbj;
  153. vector[L] pers_sbj;
  154. vector[L] k_sbj;
  155. vector[L] A_sbj;
  156. vector[L] eta_sbj;
  157. vector[L] C_sbj;
  159. for (l in 1:L) {
  160. alpha_sbj[l] = Phi_approx(mu_alpha + z_alpha[l] * sd_alpha);
  161. rho_sbj[l] = Phi_approx(mu_rho + z_rho[l] * sd_rho);
  162. phi_sbj[l] = Phi_approx(mu_phi + z_phi[l] * sd_phi);
  163. pers_sbj[l] = Phi_approx(mu_pers + z_pers[l] * sd_pers);
  165. k_sbj[l] = exp(mu_logk + z_k[l] * sd_logk);
  166. A_sbj[l] = exp(mu_logA + z_A[l] * sd_logA);
  167. eta_sbj[l] = exp(mu_eta + z_eta[l] * sd_eta);
  169. C_sbj[l] = 2 + 3 * inv_logit(mu_C_raw + z_C[l] * sd_C);
  170. }
  172. array[N,Actions] real drifts;
  174. {
  175. matrix[max_num_stim,Actions] q_rl = rep_matrix(initial_value, max_num_stim, Actions);
  176. matrix[max_num_stim,Actions] q_wm = rep_matrix(initial_value, max_num_stim, Actions);
  177. matrix[max_num_stim,Actions] q_wm0 = rep_matrix(initial_value, max_num_stim, Actions);
  178. matrix[max_num_stim,Actions] p_rl = rep_matrix(1.0 / Actions, max_num_stim, Actions);
  179. matrix[max_num_stim,Actions] p_wm = p_rl;
  180. matrix[max_num_stim,Actions] p = p_rl;
  182. for (t in 1:N) {
  183. int subj_t = subject[t];
  184. int nstim_t = max_stim[t];
  186. if (block_trial[t] == 1) {
  187. for (r in 1:nstim_t) {
  188. q_rl [r,] = rep_row_vector(initial_value, Actions);
  189. q_wm [r,] = rep_row_vector(initial_value, Actions);
  190. q_wm0[r,] = rep_row_vector(initial_value, Actions);
  191. p_rl [r,] = rep_row_vector(1.0 / Actions, Actions);
  192. p_wm [r,] = rep_row_vector(1.0 / Actions, Actions);
  193. p [r,] = rep_row_vector(1.0 / Actions, Actions);
  194. }
  195. }
  197. real prop_wm = rho_sbj[subj_t] * (C_sbj[subj_t] / nstim_t);
  198. prop_wm = fmin(1, fmax(0, prop_wm));
  200. {
  201. row_vector[Actions] qrl_row = q_rl[stim[t]];
  202. row_vector[Actions] qwm_row = q_wm[stim[t]];
  203. vector[Actions] prl = softmax(beta * to_vector(qrl_row));
  204. vector[Actions] pwm = softmax(beta * to_vector(qwm_row));
  205. for (a in 1:Actions) {
  206. p_rl[stim[t], a] = prl[a];
  207. p_wm[stim[t], a] = pwm[a];
  208. p [stim[t], a] = prop_wm * pwm[a] + (1 - prop_wm) * prl[a];
  209. }
  210. }
  212. {
  213. vector[Actions] mean_p = rep_vector(0.0, Actions);
  214. for (a in 1:Actions) {
  215. real acc = 0;
  216. for (r in 1:nstim_t) acc += p[r, a];
  217. mean_p[a] = acc / nstim_t;
  218. }
  219. real prior_ent = safe_entropy(mean_p);
  220. for (a in 1:Actions)
  221. drifts[t, a] = eta_sbj[subj_t] * (p[stim[t], a] / prior_ent);
  222. }
  224. if (include_density[t] == 1) {
  225. real alpha_r = alpha_sbj[subj_t];
  226. real alpha_w = 1;
  227. real pers = pers_sbj[subj_t];
  228. if (feedback[t] == 1) {
  229. q_rl[stim[t], response[t]] += alpha_r * (1 - q_rl[stim[t], response[t]]);
  230. q_wm[stim[t], response[t]] += alpha_w * (1 - q_wm[stim[t], response[t]]);
  231. } else {
  232. q_rl[stim[t], response[t]] += (1 - pers) * alpha_r * (0 - q_rl[stim[t], response[t]]);
  233. q_wm[stim[t], response[t]] += (1 - pers) * alpha_w * (0 - q_wm[stim[t], response[t]]);
  234. }
  235. }
  236. q_wm = q_wm + phi_sbj[subj_t] * (q_wm0 - q_wm);
  237. }
  238. }
  239. }
  241. model {
  242. mu_alpha ~ normal(-2, mu_sd_prior); sd_alpha ~ lognormal(log(0.5), 0.35);
  243. mu_phi ~ normal(-1, mu_sd_prior); sd_phi ~ lognormal(log(0.5), 0.35);
  244. mu_rho ~ normal( 1, mu_sd_prior); sd_rho ~ lognormal(log(0.5), 0.35);
  245. mu_pers ~ normal( 1, mu_sd_prior); sd_pers ~ lognormal(log(0.5), 0.35);
  247. mu_logk ~ normal(log(1.0), 0.3); sd_logk ~ lognormal(log(0.5), 0.35);
  248. mu_logA ~ normal(log(1.2), 0.35); sd_logA ~ lognormal(log(0.5), 0.35);
  249. mu_eta ~ normal(log(5.0), 0.3); sd_eta ~ lognormal(log(0.5), 0.35);
  251. mu_C_raw ~ normal(0, 1.5); sd_C ~ lognormal(log(0.5), 0.35);
  253. z_alpha ~ normal(0, sd_prior);
  254. z_phi ~ normal(0, sd_prior);
  255. z_rho ~ normal(0, sd_prior);
  256. z_pers ~ normal(0, sd_prior);
  257. z_k ~ normal(0, sd_prior);
  258. z_A ~ normal(0, sd_prior);
  259. z_eta ~ normal(0, sd_prior);
  260. z_C ~ normal(0, sd_prior);
  262. for (t in 1:N) {
  263. if (include_density[t] == 1) {
  264. vector[Actions] v;
  265. for (a in 1:Actions) v[a] = drifts[t, a];
  266. target += lba_trial_loglik(RT[t,1], response[t],
  267. A_sbj[subject[t]] + k_sbj[subject[t]],
  268. A_sbj[subject[t]], v, 1, tau);
  269. }
  270. }
  271. }
  273. generated quantities {
  274. matrix[N,2] pred;
  275. vector[N] log_lik;
  277. for (t in 1:N) {
  278. vector[Actions] v;
  279. for (a in 1:Actions) v[a] = drifts[t, a];
  281. {
  282. vector[2] tmp = lba_rng(k_sbj[subject[t]], A_sbj[subject[t]], v, 1, tau);
  283. pred[t,1] = tmp[1];
  284. pred[t,2] = tmp[2];
  285. }
  287. if (include_density[t] == 1) {
  288. log_lik[t] = lba_trial_loglik(RT[t,1], response[t],
  289. A_sbj[subject[t]] + k_sbj[subject[t]],
  290. A_sbj[subject[t]], v, 1, tau);
  291. } else {
  292. log_lik[t] = 0;
  293. }
  294. }
  295. }

rlwm_lba_model.stan, no license · at the source

Overview

Authors: Mads L Pedersen1,2, Erik R Frogner1,2, Lars T Westlye1,2,3, Torgeir Moberget2,4
ORCID iDs: Mads L Pedersen
  1. Department of Psychology, University of Oslo, Oslo, Norway
  2. Center for Precision Psychiatry, Division of Mental Health and Addiction, Oslo University Hospital, Oslo, Norway
  3. KG Jebsen Centre for Neurodevelopmental Disorders, University of Oslo, Oslo, Norway
  4. Department of Psychology, Pedagogy and Law, Kristiania University of Applied Sciences, Oslo, Norway
Institutions: Oslo University Hospital (Norway); University of Oslo (Norway); Høyskolen Kristiania (Norway)
Journal: iScience, volume 29, issue 5, article 115471
Dates: received 16 October 2025; accepted 20 March 2026; published online 27 March 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1016/j.isci.2026.115471 · PMID 42016315 · PMCID PMC13092874 · OpenAlex W7141718068
Open access: gold, a free copy (OpenAlex)
Status: code verified (how the code is found and verified)
Categories: EEG (modality), cognitive (subfield)
Methods: Connectivity, Statistics, Smoothing, state filtering, decompositions, Machine learning, Evoked potentials, fMRI & imaging
Keywords: biological sciences, clinical neuroscience, natural sciences, neuroscience
Topic: Neural and Behavioral Psychology Studies (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: Research Council of Norway (273345, 249795, 300767); Horizon 2020 Framework Programme (802998); European Commission; South-Eastern Norway Regional Health Authority (2018076, 2021040, 2019101); European Research Council (802998); Stiftelsen Kristian Gerhard Jebsen; Bundesministerium für Forschung, Technologie und Raumfahrt (01ZX1904A); Horizon Europe (101057429); Universitetet i Oslo
Citations: not cited yet (Europe PMC); 66 references in the paper
Research resources: MATLAB RRID:SCR_001622, R RRID:SCR_001905, Psychtoolbox RRID:SCR_002881, EEGLAB RRID:SCR_007292, Python RRID:SCR_008394, Stan RRID:SCR_018459

Abstract

Learning relies on multiple cognitive mechanisms—including reinforcement learning (RL) and working memory (WM)—forming internal value representations guiding choice. However, it remains unclear how these values are transformed into choices, and how this transformation relates to RL and WM. We analyzed electroencephalography (EEG) data from 510 participants performing the RLWM task. An RLWM-linear ballistic accumulator (RLWM-LBA) model was applied, linking RL- and WM-derived policy estimates to evidence-accumulation dynamics. With model-derived event-related potential (ERP) analyses, we tested whether neural signatures of RL and WM persist when accounting for choice dynamics, and whether a neural evidence accumulation signal—the centro-parietal positivity (CPP)—emerges in a learning context. Our findings replicate distinct neural correlates for RL and WM and reveal a CPP signal reflecting uncertainty in learned value representations. CPP signals improve model fit and are differentially linked to RL and WM across cognitive load, supporting their role in shaping learning-related decision dynamics.

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

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OSF y72kh

License: none: the authors keep all their rights
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Languages: Stan (1)
Size: 1 file, 1 script
Software Heritage: not checked
Found in: “Data and code availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Stan (1 file)
Availability: 1 check, the latest on 30 September 2026: the link answers (HTTP 200)
  • 30 September 2026: the link answers (HTTP 200)
1 file
At the source: osf.io/y72kh/

The paper's code and data availability statement is in the Data section.

Tracing map

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Data

No dataset and no data link were found in the paper.

Data and code availability

The de-identified behavioral and EEG-derived summary data supporting the findings of this study are available upon reasonable request and subject to a data transfer agreement due to ethical and privacy restrictions.

Analysis code has been deposited at the Open Science Framework (https://osf.io/y72kh/) and is publicly available as of the date of publication. The DOI and persistent link are listed in the key resources table.

This study did not generate additional unique datasets or resources.

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

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Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 4 keywords, 9 funders, 61 references, 6 RRIDs.

Cite

This paper

Pedersen, M. L., Frogner, E. R., Westlye, L. T., & Moberget, T. (2026). Neural decision dynamics underlying reinforcement learning and working memory. iScience, 29(5), 115471. https://doi.org/10.1016/j.isci.2026.115471

BibTeX

@article{pedersen2026neural,
author = {Pedersen, Mads L and Frogner, Erik R and Westlye, Lars T and Moberget, Torgeir},
title = {{Neural decision dynamics underlying reinforcement learning and working memory}},
journal = {iScience},
year = {2026},
month = mar,
volume = {29},
number = {5},
pages = {115471},
publisher = {Elsevier},
issn = {2589-0042},
doi = {10.1016/j.isci.2026.115471},
url = {https://doi.org/10.1016/j.isci.2026.115471},
pmid = {42016315},
pmcid = {PMC13092874}
}

RIS

TY - JOUR
AU - Pedersen, Mads L
AU - Frogner, Erik R
AU - Westlye, Lars T
AU - Moberget, Torgeir
TI - Neural decision dynamics underlying reinforcement learning and working memory
T2 - iScience
J2 - iScience
PY - 2026
DA - 2026/03/27
VL - 29
IS - 5
SP - 115471
SN - 2589-0042
PB - Elsevier
DO - 10.1016/j.isci.2026.115471
UR - https://doi.org/10.1016/j.isci.2026.115471
LA - en
ER -

CSL-JSON

{
"id": "10.1016/j.isci.2026.115471",
"type": "article-journal",
"title": "Neural decision dynamics underlying reinforcement learning and working memory",
"container-title": "iScience",
"author": [
{
"family": "Pedersen",
"given": "Mads L"
},
{
"family": "Frogner",
"given": "Erik R"
},
{
"family": "Westlye",
"given": "Lars T"
},
{
"family": "Moberget",
"given": "Torgeir"
}
],
"container-title-short": "iScience",
"volume": "29",
"issue": "5",
"page": "115471",
"DOI": "10.1016/j.isci.2026.115471",
"PMID": "42016315",
"PMCID": "PMC13092874",
"ISSN": "2589-0042",
"publisher": "Elsevier",
"URL": "https://doi.org/10.1016/j.isci.2026.115471",
"language": "en",
"issued": {
"date-parts": [
[
2026,
3,
27
]
]
}
}

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