Orbitofrontal noradrenaline supports adaptive learning-rate adjustment in probabilistic reversal learning.

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[1] § Results › Orbitofrontal Noradrenergic Release Reflects Internal Estimates of Volatility. ↔ simulate_figures.ipynb, lines 214–266 · score 0.52 · volatility signal, reversal criterion, Meta RL, Daw, Piray, PRL8

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The authors' code

Jupyter notebook · 374 lines · 14 KB · CC-BY-4.0 · 1 match

# %%
import numpy as np
import matplotlib.pyplot as plt
from pathlib import Path
from google.colab import drive
from models import (simulate_rl_kernel, simulate_metarl, simulate_rbpf,
compute_measures, reversal_locked)
%matplotlib inline
plt.rcParams['figure.dpi'] = 110
plt.rcParams['font.size'] = 9
plt.rcParams['axes.spines.top'] = False
plt.rcParams['axes.spines.right'] = False
# %% [markdown]
# ## Case selection
#
# Modify `CASE` and exécute notebook (Run All). Only the corresponding cell will run
# %%
CASE = 'fig3' # 'fig2' | 'fig3' | 'fig4' | 'fig5'
SEED = 42
NB_TRIALS = 200
NB_AGENTS = 100
REVERSAL_CRITERION = 8
DEFAULT_RL_KERNEL = dict(alpha=0.6, beta=1.5, kappa=0.7, tau=0.4)
DEFAULT_METARL = dict(alpha_0=0.7, alpha_l=0.45, alpha_e=0.05,
lambda_0=1.3, epsilon_0=0.25,
beta=2.75, kappa=0.0, tau=0.0)
CLAMP_METARL = dict(alpha_0=0.7, alpha_l=0.5, alpha_e=0.02,
lambda_0=1.3, epsilon_0=0.2,
beta=3.0, kappa=0.0, tau=0.0)
DEFAULT_KERNELMETARL = dict(alpha_0=0.6, alpha_l=0.35, alpha_e=0.15,
lambda_0=0.8, epsilon_0=0.2,
beta=3.0, kappa=0.6, tau=0.3)
DEFAULT_RBPF = dict(beta=3.0, lambda_v=0.3, lambda_s=0.05,
v0=0.2, s0=0.2, w0=0.1, n_particles=100)
SCHEDULES = [
('70/30', '#2ca02c', np.array([[0.70, 0.30], [0.30, 0.70]])),
('80/20', '#1f77b4', np.array([[0.80, 0.20], [0.20, 0.80]])),
('90/10', '#9467bd', np.array([[0.90, 0.10], [0.10, 0.90]])),
('100/0', '#d62728', np.array([[1.00, 0.00], [0.00, 1.00]])),
]
PRL8 = SCHEDULES[1][2] # 80/20 — contingence classique PRL8
FIG_DIR = Path('figures')
FIG_DIR.mkdir(exist_ok=True)
# %%
def aggregate(runs, n_agents, L=REVERSAL_CRITERION):
meas = [compute_measures(r, L=L) for r in runs]
phigh_post_arr = np.array([m['phigh_post'] for m in meas])
pers_arr = np.array([m['mean_pers'] for m in meas])
rev_arr = np.array([m['rev_per_100'] for m in meas])
sqrtN = np.sqrt(n_agents)
return dict(
phigh_post = np.nanmean(phigh_post_arr, axis=0),
phigh_post_sem = np.nanstd(phigh_post_arr, axis=0, ddof=1) / sqrtN,
pers = np.nanmean(pers_arr),
pers_sem = np.nanstd(pers_arr, ddof=1) / sqrtN,
rev = np.nanmean(rev_arr),
rev_sem = np.nanstd(rev_arr, ddof=1) / sqrtN,
)
# %%
if CASE == 'fig2':
np.random.seed(SEED)
# Set fitted VEH when needed
veh = DEFAULT_RL_KERNEL.copy()
# Perturbations multiplicatives (à ajuster selon les fits DCZ).
perturbations = {
'VEH': veh,
'a_down': {**veh, 'alpha': 0.5 * veh['alpha']},
'b_down': {**veh, 'beta': 0.67 * veh['beta']},
'k_up': {**veh, 'kappa': 1.5 * veh['kappa']},
't_down': {**veh, 'tau': 1.5 * veh['tau']},
}
pretty = {'VEH': 'VEH', 'a_down': r'$\alpha\!\downarrow$',
'b_down': r'$\beta\!\downarrow$',
'k_up': r'$\kappa\!\uparrow$',
't_down': r'$\tau\!\downarrow$'}
colors = {'VEH': 'k', 'a_down': '#d62728', 'b_down': '#1f77b4',
'k_up': '#2ca02c', 't_down': '#9467bd'}
results = {}
for label, params in perturbations.items():
runs = [simulate_rl_kernel(PRL8, nb_trials=NB_TRIALS,
L=REVERSAL_CRITERION, **params)
for _ in range(NB_AGENTS)]
results[label] = aggregate(runs, NB_AGENTS)
fig, axes = plt.subplots(1, 3, figsize=(11, 3.2))
x = np.arange(1, REVERSAL_CRITERION + 1)
labs = list(perturbations.keys())
ax = axes[0]
for lab in labs:
m = results[lab]
ax.plot(x, m['phigh_post'], 'o-', color=colors[lab],
label=pretty[lab], markersize=3, linewidth=1.5)
ax.fill_between(x, m['phigh_post'] - m['phigh_post_sem'],
m['phigh_post'] + m['phigh_post_sem'],
color=colors[lab], alpha=0.15, linewidth=0)
ax.axhline(0.5, color='gray', linestyle=':', alpha=0.5)
ax.set_ylim(0, 1)
ax.set_xlabel('Trials after reversal')
ax.set_ylabel('P(high)')
ax.set_title('Post-reversal recovery')
ax.legend(fontsize=8, frameon=False)
ax = axes[1]
ax.bar([pretty[l] for l in labs],
[results[l]['pers'] for l in labs],
yerr=[results[l]['pers_sem'] for l in labs],
color=[colors[l] for l in labs],
edgecolor='k', linewidth=0.5, capsize=3)
ax.set_ylabel('Perseverative errors')
ax.set_title('Perseveration')
ax = axes[2]
ax.bar([pretty[l] for l in labs],
[results[l]['rev'] for l in labs],
yerr=[results[l]['rev_sem'] for l in labs],
color=[colors[l] for l in labs],
edgecolor='k', linewidth=0.5, capsize=3)
ax.set_ylabel('Reversals / 100 trials')
ax.set_title('Reversal rate')
fig.suptitle('Figure 2 — RL+kernel: DREADD-like perturbations on PRL8 (80/20)',
fontsize=11)
fig.tight_layout()
fig.savefig(FIG_DIR / 'fig2_dreadd_hypotheses.png', dpi=150,
bbox_inches='tight')
fig.savefig(FIG_DIR / 'fig2_dreadd_hypotheses.pdf',
bbox_inches='tight')
plt.show()
# %%
if CASE == 'fig3':
np.random.seed(SEED)
model_specs = [
('RL+kernel', simulate_rl_kernel, DEFAULT_RL_KERNEL),
('Meta-RL', simulate_metarl, DEFAULT_METARL),
('Meta-RL+kernel', simulate_metarl, DEFAULT_KERNELMETARL),
('RBPF', simulate_rbpf, DEFAULT_RBPF),
]
results = {name: {} for name, _, _ in model_specs}
for name, sim_fn, params in model_specs:
for label, color, preward in SCHEDULES:
runs = [sim_fn(preward, nb_trials=NB_TRIALS,
L=REVERSAL_CRITERION, **params)
for _ in range(NB_AGENTS)]
results[name][label] = aggregate(runs, NB_AGENTS)
print(f'{name}: done')
sched_labels = [s[0] for s in SCHEDULES]
sched_colors = [s[1] for s in SCHEDULES]
x = np.arange(1, REVERSAL_CRITERION + 1)
fig, axes = plt.subplots(4, 3, figsize=(11, 8.5))
for row, (name, _, _) in enumerate(model_specs):
ax = axes[row, 0]
for lab, col in zip(sched_labels, sched_colors):
m = results[name][lab]
ax.plot(x, m['phigh_post'], 'o-', color=col, label=lab,
markersize=3, linewidth=1.5)
ax.fill_between(x, m['phigh_post'] - m['phigh_post_sem'],
m['phigh_post'] + m['phigh_post_sem'],
color=col, alpha=0.15, linewidth=0)
ax.axhline(0.5, color='gray', linestyle=':', alpha=0.5)
ax.set_ylim(0, 1)
ax.set_ylabel(f'{name}\nP(high)')
if row == 0:
ax.set_title('Post-reversal')
ax.legend(fontsize=7, frameon=False, loc='lower right')
if row == 2:
ax.set_xlabel('Trials after reversal')
ax = axes[row, 1]
ax.bar(sched_labels,
[results[name][l]['pers'] for l in sched_labels],
yerr=[results[name][l]['pers_sem'] for l in sched_labels],
color=sched_colors, edgecolor='k', linewidth=0.5, capsize=3)
ax.set_ylabel('Perseveration')
if row == 0:
ax.set_title('Perseverative errors')
ax = axes[row, 2]
ax.bar(sched_labels,
[results[name][l]['rev'] for l in sched_labels],
yerr=[results[name][l]['rev_sem'] for l in sched_labels],
color=sched_colors, edgecolor='k', linewidth=0.5, capsize=3)
ax.set_ylabel('Rev / 100 tr.')
if row == 0:
ax.set_title('Reversal rate')
fig.suptitle('Figure 3 — Stochasticity gradient across models', fontsize=11)
fig.tight_layout()
fig.savefig(FIG_DIR / 'fig3_stochasticity_gradient.png', dpi=150,
bbox_inches='tight')
fig.savefig(FIG_DIR / 'fig3_stochasticity_gradient.pdf',
bbox_inches='tight')
plt.show()
# %%
if CASE == 'fig4':
np.random.seed(SEED)
n_agents = 500
window_pre, window_post = 8, 8
metarl_trace = reversal_locked(
simulate_metarl,
{**DEFAULT_METARL, 'preward': PRL8,
'nb_trials': NB_TRIALS, 'L': REVERSAL_CRITERION},
latent_keys=['lambda'],
n_agents=n_agents, window_pre=window_pre, window_post=window_post)
rbpf_trace = reversal_locked(
simulate_rbpf,
{**DEFAULT_RBPF, 'preward': PRL8,
'nb_trials': NB_TRIALS, 'L': REVERSAL_CRITERION},
latent_keys=['v'],
n_agents=n_agents, window_pre=window_pre, window_post=window_post)
print(f'Meta-RL: {metarl_trace["n_reversals"]} reversals')
print(f'RBPF : {rbpf_trace["n_reversals"]} reversals')
x = np.arange(-window_pre + 1, window_post + 1)
fig, axes = plt.subplots(1, 2, figsize=(9, 3.4))
ax = axes[0]
m = metarl_trace['lambda']
e = metarl_trace['lambda_sem']
ax.plot(x, m, color='#1f77b4', linewidth=1.8)
ax.fill_between(x, m - e, m + e, color='#1f77b4', alpha=0.25, linewidth=0)
ax.axvline(0.5, color='k', linestyle='--', alpha=0.5, linewidth=0.8)
ax.set_xlabel('Trials from reversal')
ax.set_ylabel(r'$\lambda(t)$')
ax.set_title('Meta-RL volatility signal')
ax = axes[1]
m = rbpf_trace['v']
e = rbpf_trace['v_sem']
ax.plot(x, m, color='#1f77b4', linewidth=1.8)
ax.fill_between(x, m - e, m + e, color='#1f77b4', alpha=0.25, linewidth=0)
ax.axvline(0.5, color='k', linestyle='--', alpha=0.5, linewidth=0.8)
ax.set_xlabel('Trials from reversal')
ax.set_ylabel(r'$v_t$')
ax.set_title('Piray-Daw volatility signal')
fig.suptitle('Figure 4 — Reversal-locked volatility, PRL8 (80/20)',
fontsize=11)
fig.tight_layout()
fig.savefig(FIG_DIR / 'fig4_volatility_reversal_locked.png', dpi=150,
bbox_inches='tight')
fig.savefig(FIG_DIR / 'fig4_volatility_reversal_locked.pdf',
bbox_inches='tight')
plt.show()
# %%
if CASE == 'fig5':
np.random.seed(SEED)
conditions = [
('Intact', None),
('LC-OFC inh.', 0.0),
]
cmap = {'Intact': 'k', 'LC-OFC inh.': '#d62728'}
behav = {}
locked = {}
for cond_label, lam_clamp in conditions:
runs = [simulate_metarl(PRL8, nb_trials=NB_TRIALS,
L=REVERSAL_CRITERION,
lambda_clamp=lam_clamp,
**CLAMP_METARL)
for _ in range(NB_AGENTS)]
meas = [compute_measures(r, L=REVERSAL_CRITERION) for r in runs]
sqrtN = np.sqrt(NB_AGENTS)
behav[cond_label] = dict(
phigh_post = np.nanmean([m['phigh_post'] for m in meas], axis=0),
phigh_post_sem = np.nanstd([m['phigh_post'] for m in meas], axis=0, ddof=1) / sqrtN,
pers = np.nanmean([m['mean_pers'] for m in meas]),
pers_sem = np.nanstd([m['mean_pers'] for m in meas], ddof=1) / sqrtN,
high_rev = np.nanmean([m['mean_high_rev'] for m in meas]),
high_rev_sem = np.nanstd([m['mean_high_rev'] for m in meas], ddof=1) / sqrtN,
high_stable = np.nanmean([m['mean_high_stable'] for m in meas]),
high_stable_sem = np.nanstd([m['mean_high_stable'] for m in meas], ddof=1) / sqrtN,
)
locked[cond_label] = reversal_locked(
simulate_metarl,
{**CLAMP_METARL, 'preward': PRL8,
'nb_trials': NB_TRIALS, 'L': REVERSAL_CRITERION,
'lambda_clamp': lam_clamp},
latent_keys=['alpha'], n_agents=500)
print(f'{cond_label}: pers={behav[cond_label]["pers"]:.2f}, '
f'high_rev={behav[cond_label]["high_rev"]:.3f}, '
f'high_stable={behav[cond_label]["high_stable"]:.3f}')
fig, axes = plt.subplots(1, 4, figsize=(13, 3.2))
x_post = np.arange(1, REVERSAL_CRITERION + 1)
x_lock = np.arange(-locked['Intact']['window_pre'] + 1,
locked['Intact']['window_post'] + 1)
labs = [c[0] for c in conditions]
ax = axes[0]
for lab in labs:
m = behav[lab]
ax.plot(x_post, m['phigh_post'], 'o-', color=cmap[lab],
label=lab, markersize=3, linewidth=1.5)
ax.fill_between(x_post, m['phigh_post'] - m['phigh_post_sem'],
m['phigh_post'] + m['phigh_post_sem'],
color=cmap[lab], alpha=0.15, linewidth=0)
ax.axhline(0.5, color='gray', linestyle=':', alpha=0.5)
ax.set_ylim(0, 1)
ax.set_xlabel('Trials after reversal')
ax.set_ylabel('P(high)')
ax.set_title('Post-reversal recovery')
ax.legend(fontsize=8, frameon=False)
ax = axes[1]
ax.bar(labs, [behav[l]['pers'] for l in labs],
yerr=[behav[l]['pers_sem'] for l in labs],
color=[cmap[l] for l in labs],
edgecolor='k', linewidth=0.5, capsize=3)
ax.set_ylabel('Perseverative errors')
ax.set_title('Perseveration')
ax = axes[2]
width = 0.35
x_groups = np.arange(2)
for k, lab in enumerate(labs):
offset = (k - 0.5) * width
means = [behav[lab]['high_rev'], behav[lab]['high_stable']]
sems = [behav[lab]['high_rev_sem'], behav[lab]['high_stable_sem']]
ax.bar(x_groups + offset, means, width, yerr=sems,
color=cmap[lab], edgecolor='k', linewidth=0.5,
capsize=3, label=lab)
ax.set_xticks(x_groups)
ax.set_xticklabels(['Post-reversal', 'Stable'])
ax.set_ylabel('P(high)')
ax.set_title('P(high) by phase')
ax.set_ylim(0, 1)
ax.legend(fontsize=8, frameon=False)
ax = axes[3]
for lab in labs:
m = locked[lab]['alpha']
e = locked[lab]['alpha_sem']
ax.plot(x_lock, m, color=cmap[lab], label=lab, linewidth=1.6)
ax.fill_between(x_lock, m - e, m + e,
color=cmap[lab], alpha=0.2, linewidth=0)
ax.axvline(0.5, color='k', linestyle='--', alpha=0.5, linewidth=0.8)
ax.set_xlabel('Trials from reversal')
ax.set_ylabel(r'$\alpha_{\rm eff}(t)$')
ax.set_title(r'Reversal-locked $\alpha_{\rm eff}$')
fig.suptitle(r'Figure 5 — Meta-RL with $\lambda$ clamped to 0 (LC-OFC inhibition)',
fontsize=11)
fig.tight_layout()
plt.show()
# %%

simulate_figures.ipynb, under CC-BY-4.0 · at the source

Overview

Authors: Hadrien Plat¹, Coline Chevallier², Alessandro Piccin¹, Alain R. Marchand¹, Jérémie Naudé², Etienne Coutureau¹

ORCID iDs: Hadrien Plat, Coline Chevallier, Jérémie Naudé, Etienne Coutureau

Institutions: Institut de Neurosciences Cognitives et Intégratives d’Aquitaine (France); Institut de Génomique Fonctionnelle (France)

Journal: Proceedings of the National Academy of Sciences of the United States of America, volume 123, issue 29, article e2536535123

Dates: received 15 December 2025; accepted 9 June 2026; published online 13 July 2026; in print 21 July 2026

Type: Research article · Language: English

License: CC BY-NC-ND

Identifiers: DOI 10.1073/pnas.2536535123 · PMID 42441855 · PMCID PMC13389698 · OpenAlex W7168174098

Open access: hybrid, a free copy (OpenAlex)

Status: code verified

Categories: rat (organism), cognitive (subfield)

Keywords: prefrontal cortex, neuromodulation, decision making

MeSH: Norepinephrine*, Prefrontal Cortex*, Reversal Learning*, Animals, Cognitive Flexibility, Decision Making, Locus Coeruleus, Male, Rats, Rats, Long-Evans, Reinforcement Machine Learning, Uncertainty (* major topic)

Journal subjects: Biological Sciences, Neuroscience

Topic: Neural dynamics and brain function (Cognitive Neuroscience, Neuroscience), according to OpenAlex

Funding: Agence Nationale de la Recherche (French National Research Agency) (CE37-0019, CE14-0020); Institut pour la Recherche en Santé Publique (IReSP) (24Iresp017IT07)

Citations: not cited yet (Europe PMC); 60 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.

Repository

Its files are read in the Code ↔ Paper reader above, with 1 match between paragraphs and lines of code.

Zenodo 19911953

License: CC-BY-4.0

State: the link answers, verified on 27 September 2026

Evidence: files inventoried

Languages: Python (3), Jupyter (2)

Size: 9 files, 5 scripts

Software Heritage: not checked

Found in: “Data, Materials, and Software Availability”

Holds: README, 2 notebooks

Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation

Tools: NumPy (5 files), Matplotlib (3 files), pandas (3 files), SciPy (1 file)

Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)

27 September 2026: the link answers (HTTP 200)

6 files

fit_models.ipynb, Jupyter, 256 lines
models.py, Python, 556 lines
phautom_pipeline.py, Python, 1,001 lines
photometry_analysis_.py, Python, 405 lines
simulate_figures.ipynb, Jupyter, 374 lines, 1 match
README.txt, Text, 83 lines

At the source: doi.org/10.5281/zenodo.19911953

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

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Read it in the paper: doi.org/10.1073/pnas.2536535123.

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Recorded: type, language, journal, volume, issue, pages, dates, 6 authors, 3 keywords, 12 MeSH terms, 2 funders, 59 references.

Cite

This paper

Plat, H., Chevallier, C., Piccin, A., Marchand, A. R., Naudé, J., & Coutureau, E. (2026). Orbitofrontal noradrenaline supports adaptive learning-rate adjustment in probabilistic reversal learning. Proceedings of the National Academy of Sciences of the United States of America, 123(29), e2536535123. https://doi.org/10.1073/pnas.2536535123

BibTeX

@article{plat2026orbitofrontal, author = {Plat, Hadrien and Chevallier, Coline and Piccin, Alessandro and Marchand, Alain R. and Naudé, Jérémie and Coutureau, Etienne}, title = {{Orbitofrontal noradrenaline supports adaptive learning-rate adjustment in probabilistic reversal learning}}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, year = {2026}, month = jul, volume = {123}, number = {29}, pages = {e2536535123}, publisher = {National Academy of Sciences}, issn = {0027-8424}, doi = {10.1073/pnas.2536535123}, url = {https://doi.org/10.1073/pnas.2536535123}, pmid = {42441855}, pmcid = {PMC13389698} }

RIS

TY - JOUR AU - Plat, Hadrien AU - Chevallier, Coline AU - Piccin, Alessandro AU - Marchand, Alain R. AU - Naudé, Jérémie AU - Coutureau, Etienne TI - Orbitofrontal noradrenaline supports adaptive learning-rate adjustment in probabilistic reversal learning T2 - Proceedings of the National Academy of Sciences of the United States of America J2 - Proc Natl Acad Sci U S A PY - 2026 DA - 2026/07/13 VL - 123 IS - 29 SP - e2536535123 SN - 0027-8424 PB - National Academy of Sciences DO - 10.1073/pnas.2536535123 UR - https://doi.org/10.1073/pnas.2536535123 LA - en ER -

CSL-JSON

{ "id": "10.1073/pnas.2536535123", "type": "article-journal", "title": "Orbitofrontal noradrenaline supports adaptive learning-rate adjustment in probabilistic reversal learning", "container-title": "Proceedings of the National Academy of Sciences of the United States of America", "author": [ { "family": "Plat", "given": "Hadrien" }, { "family": "Chevallier", "given": "Coline" }, { "family": "Piccin", "given": "Alessandro" }, { "family": "Marchand", "given": "Alain R." }, { "family": "Naudé", "given": "Jérémie" }, { "family": "Coutureau", "given": "Etienne" } ], "container-title-short": "Proc Natl Acad Sci U S A", "volume": "123", "issue": "29", "page": "e2536535123", "DOI": "10.1073/pnas.2536535123", "PMID": "42441855", "PMCID": "PMC13389698", "ISSN": "0027-8424", "publisher": "National Academy of Sciences", "URL": "https://doi.org/10.1073/pnas.2536535123", "language": "en", "issued": { "date-parts": [ [ 2026, 7, 13 ] ] } }

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