Desegregation of neuronal predictive processing.
Paper
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The authors' code
MATLAB · 233 lines · 9.1 KB · no license
- (* ::Package:: *)
- IneuronRate[lambda_,mu_,p_,size_]:=Module[{theta,b,deltax,deltay,idxdiag,e,mulnormal,w,v,iemis,iemisy,iefull,rmis,rmisy,rfull,s,sign,stimVec,J0,J0p,side,chiral,idp,a0,thre,a,hImis,hImisy,hIfull,kappa,interp},
- theta = 0;
- b=150;
- deltax[b_,x_,y_]:=((1+b/2) x-b/2 Sqrt[mu] y)/(1+b+(1-mu) b^2/4);
- deltay[b_,x_,y_]:=((1+b/2) y-b/2 Sqrt[mu] x)/(1+b+(1-mu) b^2/4);
- idxdiag = Table[{i,i},{i,1,size}];
- e =Table[1,{i,1,size}];
- (*Calculate the weight*)
- mulnormal = RandomVariate[\[ScriptD]=MultinormalDistribution[{3,3},{{1,Sqrt[mu]},{Sqrt[mu],1}}],{p,size}];
- w = Ramp[mulnormal[[;;,;;,1]]];
- v = Ramp[mulnormal[[;;,;;,2]]];
- (*Calculate E neurons' response*)
- iemis=(w[[1]]-Mean[w[[1]]])*deltax[b,1,0]+(v[[1]]-Mean[v[[1]]])*deltay[b,1,0];
- iemisy=(w[[1]]-Mean[w[[1]]])*deltax[b,0,1]+(v[[1]]-Mean[v[[1]]])*deltay[b,0,1];
- iefull=(w[[1]]-Mean[w[[1]]])*deltax[b,1,1]+(v[[1]]-Mean[v[[1]]])*deltay[b,1,1];
- rmis=b*Ramp[iemis-theta];
- rmisy=b*Ramp[iemisy-theta];
- rfull=b*Ramp[iefull-theta];
- s=(rmis-Mean[rmis])*(rfull-Mean[rfull]);
- (*Calculate stimulus input vector and put in the matrix*)
- stimVec = Join[Table[w[[i]],{i,1,p}],Table[v[[i]],{i,1,p}]];
- J0 = IdentityMatrix[size];
- side=stimVec[[1;;2 p,2p+1;;]];
- J0p=stimVec[[1;;2 p,1;;2 p]];
- (*The order*)
- chiral = Det[J0p];
- idp=IdentityMatrix[2 p];
- If[chiral<= 0,
- idp=ReplacePart[idp,{1->idp[[2]],2->idp[[1]]}]
- ];
- (*Diagonal elements*);
- thre=0.8-Log[0.5]/4;
- a0=HeavisideTheta[-s](1.4+12Exp[1.5s])+0.2HeavisideTheta[s](0.01+HeavisideTheta[s-thre]);
- kappa =lambda;
- a =kappa*a0+(1-kappa)*e;
- interp=kappa*J0p/size+(1-kappa)*idp;
- J0=ReplacePart[J0,{i_,i_}:>a[[i]]];
- J0[[1;;2 p,1;;2 p]] = interp;
- J0[[1;;2 p,2p+1;;]] = kappa*side/size;
- hImis = J0 . rmis;
- hImisy = J0 . rmisy;
- hIfull = J0 . rfull;
- {hImis,hImisy,hIfull}
- ]
- IneuronJie[lambda_,mu_,p_,size_]:=Module[{theta,b,deltax,deltay,idxdiag,e,mulnormal,w,v,Jout,iemisx,iemisy,iefull,rmisx,rmisy,rfull,s,sign,stimVec,J0p,Jie,Jei,side,chiral,idp,a0,thre,a,hImisx,hImisy,hIfull,alambda,kappa,interp},
- theta = 0;
- b=150;
- deltax[b_,x_,y_]:=((1+b/2) x-b/2 Sqrt[mu] y)/(1+b+(1-mu) b^2/4);
- deltay[b_,x_,y_]:=((1+b/2) y-b/2 Sqrt[mu] x)/(1+b+(1-mu) b^2/4);
- idxdiag = Table[{i,i},{i,1,size}];
- e =Table[1,{i,1,size}];
- (*Calculate the weight*)
- mulnormal = RandomVariate[\[ScriptD]=MultinormalDistribution[{3,3},{{1,Sqrt[mu]},{Sqrt[mu],1}}],{p,size}];
- w = Ramp[mulnormal[[;;,;;,1]]];
- v = Ramp[mulnormal[[;;,;;,2]]];
- Jout = (w\[Transpose] . w+v\[Transpose] . v)/size;
- (*Calculate E neurons' response*)
- iemisx=(w[[1]]-Mean[w[[1]]])*deltax[b,1,0]+(v[[1]]-Mean[v[[1]]])*deltay[b,1,0];
- iemisy=(w[[1]]-Mean[w[[1]]])*deltax[b,0,1]+(v[[1]]-Mean[v[[1]]])*deltay[b,0,1];
- iefull=(w[[1]]-Mean[w[[1]]])*deltax[b,1,1]+(v[[1]]-Mean[v[[1]]])*deltay[b,1,1];
- rmisx=b*Ramp[iemisx-theta];
- rmisy=b*Ramp[iemisy-theta];
- rfull=b*Ramp[iefull-theta];
- s=(rmisx-Mean[rmisx])*(rfull-Mean[rfull]);
- (*Calculate stimulus input vector and put in the matrix*)
- stimVec = Join[Table[w[[i]],{i,1,p}],Table[v[[i]],{i,1,p}]];
- side=stimVec[[1;;2 p,2p+1;;]];
- J0p=stimVec[[1;;2 p,1;;2 p]];
- (*The order*)
- chiral = Det[J0p];
- idp=IdentityMatrix[2 p];
- If[chiral<= 0,
- idp=ReplacePart[idp,{1->idp[[2]],2->idp[[1]]}]
- ];
- (*Diagonal elements*);
- thre=0.8-Log[0.5]/4;
- a0=HeavisideTheta[-s](1.4+12Exp[1.5s])+0.2HeavisideTheta[s](0.01+HeavisideTheta[s-thre]);
- Jie = IdentityMatrix[size];
- Jei = ConstantArray[0,{size,size}];
- Jei[[All,1;;2p]]=stimVec\[Transpose];
- kappa =lambda;
- a =kappa*a0+(1-kappa)*e;
- interp=kappa*J0p/size+(1-kappa)*idp;
- Jie=ReplacePart[Jie,{i_,i_}:>a[[i]]];
- Jie[[1;;2 p,1;;2 p]]=interp;
- Jie[[1;;2 p,2p+1;;]] = kappa*side/size;
- hImisx =Jie . rmisx;
- hImisy =Jie . rmisy;
- hIfull =Jie . rfull;
- alambda = DiagonalMatrix[(1-kappa)/a];
- Jei[[All,2p+1;;]]=Jout[[All,2p+1;;]] . alambda[[2p+1;;,2p+1;;]];
- {{iemisx,iemisy,iefull,hImisx,hImisy,hIfull},Jie,Jei}
- ]
- EImeanRate[mu_,p_,size_]:=Module[{theta,b,deltax,deltay,e,mulnormal,w,v,iemis,iemisy,iefull,rmis,rmisy,rfull,Jee,Ji,Jfull},
- theta = 0;
- b=150;
- deltax[b_,x_,y_]:=((1+b/2) x-b/2 Sqrt[mu] y)/(1+b+(1-mu) b^2/4);
- deltay[b_,x_,y_]:=((1+b/2) y-b/2 Sqrt[mu] x)/(1+b+(1-mu) b^2/4);
- e =Table[1,{i,1,size}];
- (*Calculate the weight*)
- mulnormal = RandomVariate[\[ScriptD]=MultinormalDistribution[{3,3},{{1,Sqrt[mu]},{Sqrt[mu],1}}],{p,size}];
- w = Ramp[mulnormal[[;;,;;,1]]];
- v = Ramp[mulnormal[[;;,;;,2]]];
- (*Calculate E neurons' response*)
- iemis=(w[[1]]-Mean[w[[1]]])*deltax[b,1,0]+(v[[1]]-Mean[v[[1]]])*deltay[b,1,0];
- iemisy=(w[[1]]-Mean[w[[1]]])*deltax[b,0,1]+(v[[1]]-Mean[v[[1]]])*deltay[b,0,1];
- iefull=(w[[1]]-Mean[w[[1]]])*deltax[b,1,1]+(v[[1]]-Mean[v[[1]]])*deltay[b,1,1];
- rmis=b*Ramp[iemis-theta];
- rmisy=b*Ramp[iemisy-theta];
- rfull=b*Ramp[iefull-theta];
- Jee=((w\[Transpose] . w+v\[Transpose] . v)+Mean[w[[1]]] (w\[Transpose] . {e}+{e}\[Transpose] . w)+Mean[v[[1]]](v\[Transpose] . {e}+{e}\[Transpose] . v))/size;
- Ji=(2(w\[Transpose] . w+v\[Transpose] . v)+Mean[w[[1]]]^2+Mean[v[[1]]]^2)/size;
- {Jee . rmis,Jee . rmisy,Jee . rfull,Ji . rmis,Ji . rmisy,Ji . rfull,iemis,iemisy,iefull}
- ]
- IneuronJieEvolve1[lambda_,mu_,p_,size_,x0_,y0_,z0_]:=Module[{theta,b,deltax,deltay,idxdiag,e,mulnormal,w,v,wv,Jout,iemisx,iemisy,iefull,rmisx,rmisy,rfull,s,sign,stimVec,J0p,Jie,Jei,side,chiral,idp,a0,thre,a,hImisx,hImisy,hIfull,alambda,kappa,interp},
- theta = 0;
- b=150;
- deltax[b_,x_,y_]:=((1+b/2) x-b/2 Sqrt[mu] y)/(1+b+(1-mu) b^2/4);
- deltay[b_,x_,y_]:=((1+b/2) y-b/2 Sqrt[mu] x)/(1+b+(1-mu) b^2/4);
- idxdiag = Table[{i,i},{i,1,size}];
- e =Table[1,{i,1,size}];
- (*Calculate the weight*)
- wv=Table[{3+Sqrt[Sqrt[mu]]x0[[i]]+Sqrt[1-Sqrt[mu]]y0[[i]],3+Sqrt[Sqrt[mu]]x0[[i]]+Sqrt[1-Sqrt[mu]]z0[[i]]},{i,1,Length[x0]}];
- w = {Ramp[wv[[All,1]]]};
- v = {Ramp[wv[[All,2]]]};
- Jout = (w\[Transpose] . w+v\[Transpose] . v)/size;
- (*Calculate E neurons' response*)
- iemisx=(w[[1]]-Mean[w[[1]]])*deltax[b,1,0]+(v[[1]]-Mean[v[[1]]])*deltay[b,1,0];
- iemisy=(w[[1]]-Mean[w[[1]]])*deltax[b,0,1]+(v[[1]]-Mean[v[[1]]])*deltay[b,0,1];
- iefull=(w[[1]]-Mean[w[[1]]])*deltax[b,1,1]+(v[[1]]-Mean[v[[1]]])*deltay[b,1,1];
- rmisx=b*Ramp[iemisx-theta];
- rmisy=b*Ramp[iemisy-theta];
- rfull=b*Ramp[iefull-theta];
- s=(rmisx-Mean[rmisx])*(rfull-Mean[rfull]);
- (*Calculate stimulus input vector and put in the matrix*)
- stimVec = Join[Table[w[[i]],{i,1,p}],Table[v[[i]],{i,1,p}]];
- side=stimVec[[1;;2 p,2p+1;;]];
- J0p=stimVec[[1;;2 p,1;;2 p]];
- (*The order*)
- chiral = Det[J0p];
- idp=IdentityMatrix[2 p];
- If[chiral<= 0,
- idp=ReplacePart[idp,{1->idp[[2]],2->idp[[1]]}]
- ];
- (*Diagonal elements*);
- thre=0.8-Log[0.5]/4;
- a0=HeavisideTheta[-s](1.4+12Exp[1.5s])+0.2HeavisideTheta[s](0.01+HeavisideTheta[s-thre]);
- Jie = IdentityMatrix[size];
- Jei = ConstantArray[0,{size,size}];
- Jei[[All,1;;2p]]=stimVec\[Transpose];
- kappa =lambda;
- a =kappa*a0+(1-kappa)*e;
- interp=kappa*J0p/size+(1-kappa)*idp;
- Jie=ReplacePart[Jie,{i_,i_}:>a[[i]]];
- Jie[[1;;2 p,1;;2 p]]=interp;
- Jie[[1;;2 p,2p+1;;]] = kappa*side/size;
- hImisx =Jie . rmisx;
- hImisy =Jie . rmisy;
- hIfull =Jie . rfull;
- alambda = DiagonalMatrix[(1-kappa)/a];
- Jei[[All,2p+1;;]]=Jout[[All,2p+1;;]] . alambda[[2p+1;;,2p+1;;]];
- {{iemisx,iemisy,iefull,hImisx,hImisy,hIfull},Jie,Jei}
- ]
- IneuronJieEvolve2[lambda_,mu_,p_,size_,x0_,y0_]:=Module[{theta,b,deltax,deltay,idxdiag,e,mulnormal,w,v,wv,Jout,iemisx,iemisy,iefull,rmisx,rmisy,rfull,s,sign,stimVec,J0p,Jie,Jei,side,chiral,idp,a0,thre,a,hImisx,hImisy,hIfull,alambda,kappa,interp},
- theta = 0;
- b=150;
- deltax[b_,x_,y_]:=((1+b/2) x-b/2 Sqrt[mu] y)/(1+b+(1-mu) b^2/4);
- deltay[b_,x_,y_]:=((1+b/2) y-b/2 Sqrt[mu] x)/(1+b+(1-mu) b^2/4);
- idxdiag = Table[{i,i},{i,1,size}];
- e =Table[1,{i,1,size}];
- (*Calculate the weight*)
- wv=Table[{3+x0[[i]],3+Sqrt[mu]x0[[i]]+Sqrt[1-mu]y0[[i]]},{i,1,Length[x0]}];
- w = {Ramp[wv[[All,1]]]};
- v = {Ramp[wv[[All,2]]]};
- Jout = (w\[Transpose] . w+v\[Transpose] . v)/size;
- (*Calculate E neurons' response*)
- iemisx=(w[[1]]-Mean[w[[1]]])*deltax[b,1,0]+(v[[1]]-Mean[v[[1]]])*deltay[b,1,0];
- iemisy=(w[[1]]-Mean[w[[1]]])*deltax[b,0,1]+(v[[1]]-Mean[v[[1]]])*deltay[b,0,1];
- iefull=(w[[1]]-Mean[w[[1]]])*deltax[b,1,1]+(v[[1]]-Mean[v[[1]]])*deltay[b,1,1];
- rmisx=b*Ramp[iemisx-theta];
- rmisy=b*Ramp[iemisy-theta];
- rfull=b*Ramp[iefull-theta];
- s=(rmisx-Mean[rmisx])*(rfull-Mean[rfull]);
- (*Calculate stimulus input vector and put in the matrix*)
- stimVec = Join[Table[w[[i]],{i,1,p}],Table[v[[i]],{i,1,p}]];
- side=stimVec[[1;;2 p,2p+1;;]];
- J0p=stimVec[[1;;2 p,1;;2 p]];
- (*The order*)
- chiral = Det[J0p];
- idp=IdentityMatrix[2 p];
- If[chiral<= 0,
- idp=ReplacePart[idp,{1->idp[[2]],2->idp[[1]]}]
- ];
- (*Diagonal elements*);
- thre=0.8-Log[0.5]/4;
- a0=HeavisideTheta[-s](1.4+12Exp[1.5s])+0.2HeavisideTheta[s](0.01+HeavisideTheta[s-thre]);
- Jie = IdentityMatrix[size];
- Jei = ConstantArray[0,{size,size}];
- Jei[[All,1;;2p]]=stimVec\[Transpose];
- kappa =lambda;
- a =kappa*a0+(1-kappa)*e;
- interp=kappa*J0p/size+(1-kappa)*idp;
- Jie=ReplacePart[Jie,{i_,i_}:>a[[i]]];
- Jie[[1;;2 p,1;;2 p]]=interp;
- Jie[[1;;2 p,2p+1;;]] = kappa*side/size;
- hImisx =Jie . rmisx;
- hImisy =Jie . rmisy;
- hIfull =Jie . rfull;
- alambda = DiagonalMatrix[(1-kappa)/a];
- Jei[[All,2p+1;;]]=Jout[[All,2p+1;;]] . alambda[[2p+1;;,2p+1;;]];
- {{iemisx,iemisy,iefull,hImisx,hImisy,hIfull},Jie,Jei}
- ]
IneuronRep.m at commit 01ccaa7, no license · at the source
Overview
- Department of Physics, University of California San Diego, La Jolla, CA USA
- Mortimer B. Zuckerman Mind Brain Behavior Institute, Department of Neuroscience, Kavli Institute for Brain Science, Columbia University, NY New York, USA
- Center for Neural Science, New York University, New York, NY USA
- Department of Neurobiology, University of California San Diego, La Jolla, CA USA
Abstract
Neural circuits construct internal ‘world-models’ to guide behavior. The predictive processing framework posits that neural activity signaling sensory predictions and concurrently computing prediction-errors is a signature of those internal models. To understand how the brain generates predictions for complex sensorimotor signals, we investigate the emergence of high-dimensional, multi-modal predictive representations in recurrent networks. Contrary to previous proposals of functionally specialized cell-types, stimulus and prediction-error representations are desegregated in networks performing robust predictive processing. We confirmed these model predictions by using a rich stimulus-set to violate animals’ learned expectations. We propose that predictive processing is optimal when excitation/
Reproduced under the paper's license (CC BY), from the paper cited above.
Repository
Its files are read in the Code ↔ Paper reader above.
BinW3233/HDPC_code
01ccaa7e2e2de6128ad7693cc0e1fc8262ff37bf, 9 May 2026Availability: 1 check, the latest on 30 September 2026: the link answers
- 30 September 2026: the link answers
8 files
- IneuronRep.m, MATLAB, 233 lines
- Inhibitory_response.nb, Mathematica, 98 lines
- Pulse_Input_Network.m, MATLAB, 60 lines
- SS_TwoPair.m, MATLAB, 46 lines
- SS_hirachical_net.m, MATLAB, 63 lines
- SS_network.m, MATLAB, 37 lines
- Sparse_network.m, MATLAB, 39 lines
- README.md, Text, 62 lines
Code availability
Computer code to reproduce model simulations is available in the Github repository: https://
Reproduced under the paper's license (CC BY), from the paper cited above.
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:
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- 7 scripts, each with its path and the digest of its content;
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Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.
Data
No dataset and no data link were found in the paper.
Data availability
No new experimental data was collected in this study. Source Data files are provided for all figures.
Reproduced under the paper's license (CC BY), from the paper cited above.
Versions
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Version 1, 30 September 2026: the first record
Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 5 keywords, 6 MeSH terms, 8 funders, 79 references.
Cite
This paper
Wang, B., Audette, N. J., Schneider, D. M., & Aljadeff, J. (2026). Desegregation of neuronal predictive processing. Nature communications, 17(1), 3919. https://
BibTeX
@article{wang2026desegre
author = {Wang, Bin and Audette, Nicholas J and Schneider, David M and Aljadeff, Johnatan},
title = {{Desegregation of neuronal predictive processing}},
journal = {Nature communications},
year = {2026},
month = mar,
volume = {17},
number = {1},
pages = {3919},
publisher = {Nature Publishing Group},
issn = {2041-1723},
doi = {10.1038/
url = {https://
pmid = {41826318},
pmcid = {PMC13129095}
}
RIS
TY - JOUR
AU - Wang, Bin
AU - Audette, Nicholas J
AU - Schneider, David M
AU - Aljadeff, Johnatan
TI - Desegregation of neuronal predictive processing
T2 - Nature communications
J2 - Nat Commun
PY - 2026
DA - 2026/
VL - 17
IS - 1
SP - 3919
SN - 2041-1723
PB - Nature Publishing Group
DO - 10.1038/
UR - https://
LA - en
ER -
CSL-JSON
{
"id": "10.1038/
"type": "article-journal",
"title": "Desegregation of neuronal predictive processing",
"container-title": "Nature communications",
"author": [
{
"family": "Wang",
"given": "Bin"
},
{
"family": "Audette",
"given": "Nicholas J"
},
{
"family": "Schneider",
"given": "David M"
},
{
"family": "Aljadeff",
"given": "Johnatan"
}
],
"container-title-short":
"volume": "17",
"issue": "1",
"page": "3919",
"DOI": "10.1038/
"PMID": "41826318",
"PMCID": "PMC13129095",
"ISSN": "2041-1723",
"publisher": "Nature Publishing Group",
"URL": "https://
"language": "en",
"issued": {
"date-parts": [
[
2026,
3,
13
]
]
}
}
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