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Preserving predictive information under biologically plausible compression.

Code ↔ Paper

2 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 2 matches
  1. [1] § Materials and methods › Optimization methods ↔ examplescript.m, lines 1–46 · score 0.69 · GradObj, firing rate, SQP, fmincon, MATLAB, algorithm
  2. [2] § Materials and methods › Coarse-graining functions ↔ figscript.m, lines 986–1055 · score 0.51 · maximally correlated cells, simulate, meta neuron, summed, activity, movies

Paper

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The authors' code

MATLAB · 286 lines · 8.9 KB · no license · 1 match

  1. %% example script to optimize PCG
  2. % Requires MATLAB R2016b or later (local functions in scripts)
  4. % set up and preprocessing
  5. load('multmovie_data.mat');
  6. ntrials = min(nreps); ptrials = round(ntrials*0.5); nsamp = 50; % for bootstrapping
  7. rng(0); N = 4; cutoff = 20;
  8. load("maxpredgroupsall.mat"); % create mixed group of ranked pred cells and overlapping groups
  9. maxpredgroups = reshape(maxpredgroupsall(1:92),N,[]); maxpredgroups = maxpredgroups';
  10. y = randsample(maxpredgroupsall(1:cutoff),N*30,true); randgroups1 = reshape(y,[],N);
  11. y = randsample(ncell,N*20,true); randgroups2 = reshape(y,[],N);
  12. maxpredgroups = [maxpredgroups; randgroups1; randgroups2];
  13. ngroups = size(maxpredgroups,1);
  15. % optimize PCG with firing rate constraint
  16. Dt = 1; nrun = 50;
  17. mov = 4; % fish movie
  18. binned = binned(1:nreps(mov),:,:,mov); % in ntrials x trialtime x ncells x movie. binned in binary
  19. binned = permute(binned,[3,2,1]);
  20. binned = reshape(binned,ncell,[]);
  21. [I_wordword,I_CCG,R_CCG,I_PCG,R_PCG,Params,Bootstrap_CCG,Bootstrap_PCG] = preallocate(maxpredgroups,nsamp);
  22. for i = 1:ngroups
  23. mycells = maxpredgroups(i,:);
  24. [I_CCG(i),R_CCG(i),I_wordword(i)] = CCGInfo(mycells,binned,Dt);
  25. fr = R_CCG(i);
  26. fun = @(params)PerceptronInfo(mycells,binned,params,Dt);
  27. con = @(params)mycon(mycells,binned,params,fr);
  29. paramsrun = nan(nrun,N+1); fvalrun = nan(1,nrun); Rrun = nan(1,nrun);
  30. for run = 1:nrun
  31. params0 = 100.*rand(1,N+1);
  32. [params,fval] = fmincon(fun,params0,[]...
  33. ,[],[],[],zeros(1,N+1),100.*ones(1,N+1),con,optimset('GradObj','off','Algorithm','sqp','Display','off'));
  34. paramsrun(run,:) = params; fvalrun(run) = fval; Rrun(run) = PerceptronFR(mycells,binned,params);
  35. end
  36. [fval,runidx] = min(fvalrun); params = paramsrun(runidx,:);
  37. I_PCG(i) = -fval; Params(:,i) = params; R_PCG(i) = Rrun(runidx);
  39. for j = 1:nsamp
  40. allptrials = randsample(ntrials,ptrials);
  41. Bootstrap_CCG(i,j) = LMInfosample(mycells,allptrials,Dt,mov);
  42. Bootstrap_PCG(i,j) = PerceptronInfosample(mycells,allptrials,params,Dt,mov);
  43. end
  44. end
  45. err_CCG = std(Bootstrap_CCG,0,2)./sqrt(2);
  46. err_PCG = std(Bootstrap_PCG,0,2)./sqrt(2);
  50. function [I_wordword,I_CCG,R_CCG,I_PCG,R_PCG,Params,Bootstrap_CCG,Bootstrap_PCG] = preallocate(groups,nsamp)
  51. % PREALLOCATE sets up and preallocates vectors
  53. ngroups = size(groups,1); N = size(groups,2);
  54. I_wordword = nan(1,ngroups); I_CCG = nan(1,ngroups); R_CCG = nan(1,ngroups);
  55. I_PCG = nan(1,ngroups); R_PCG = nan(1,ngroups); Params = nan(N+1,ngroups);
  56. Bootstrap_CCG = nan(ngroups,nsamp); Bootstrap_PCG = nan(ngroups,nsamp);
  57. end
  59. function [P_wt,condprob] = CondProb(mycells,binned,Dt)
  60. %CONDPROB gets the probability of words wt and the conditional probability
  61. % matrix for every wt+dt given wt
  62. % Dt = # time steps in future
  63. N=length(mycells);
  64. binnedspikes = binned(mycells,:);
  66. % first find all zero words
  67. idx0 = sum(binnedspikes,1)==0;
  68. % where this is true, we want binnedwords to be 1 anyway
  69. % where it is false (0), we want to replace it with the correct word
  70. binnedwords = double(idx0);
  71. idx1 = find(idx0==0);
  72. for i = 1:length(idx1)
  73. a = num2str(binnedspikes(:,idx1(i)));
  74. a = sprintf(a);
  75. binnedwords(idx1(i)) = bin2dec(a)+1;
  76. end
  78. presbinnedwords = binnedwords(1:end-Dt);
  79. futbinnedwords = binnedwords(Dt+1:end);
  80. jointwords = (futbinnedwords-1).*2^N+presbinnedwords;
  81. N_wt = histcounts(binnedwords,1:2^N+1)';
  82. A = histcounts(jointwords,1:2^(2*N)+1)';
  83. A = reshape(A,2^N,[]);
  84. condprob = A./sum(A,2,'omitnan');
  86. % word entropy
  87. condprob = condprob./sum(condprob,2,'omitnan');
  88. P_wt = N_wt/sum(N_wt);
  90. end
  92. function [I] = WordInfo(P_wt,condprob)
  93. %WORDINFO gets the mutual information between words at time t and words at
  94. % t+dt, normalized by mean number of spikes
  95. H1 = -sum(P_wt.*log2(P_wt),'omitnan');
  96. H2 = -sum(P_wt.*condprob.*log2(condprob),'all','omitnan');
  97. I = H1-H2;
  98. end
  100. function [I_CCG,R_CCG,I_wordword,cg_spks] = CCGInfo(mycells,binned,Dt)
  101. %CCGINFO gets I(Mt;sigmat+dt)
  102. N=length(mycells);
  103. nword=2^N;
  104. binnedspikes = binned(mycells,:);
  106. % first find all zero words
  107. idx0 = sum(binnedspikes,1)==0;
  108. % where this is true, we want binnedwords to be 1 anyway
  109. % where it is false (0), we want to replace it with the correct word
  110. binnedwords = double(idx0);
  111. idx1 = find(idx0==0);
  112. for i = 1:length(idx1)
  113. a = num2str(binnedspikes(:,idx1(i)));
  114. a = sprintf(a);
  115. binnedwords(idx1(i)) = bin2dec(a)+1;
  116. end
  118. presbinnedwords = binnedwords(1:end-Dt);
  119. futbinnedwords = binnedwords(Dt+1:end);
  120. jointwords = (futbinnedwords-1).*2^N+presbinnedwords;
  121. N_wt = histcounts(binnedwords,1:2^N+1)';
  122. A = histcounts(jointwords,1:2^(2*N)+1)';
  123. A = reshape(A,2^N,[]);
  124. condprob = A./sum(A,2,'omitnan');
  125. condprob1 = condprob./sum(condprob,2,'omitnan');
  126. P_wt = N_wt/sum(N_wt);
  128. % get word-word info
  129. I_wordword = WordInfo(P_wt,condprob1);
  131. % now get cond prob of meta given word
  132. nstep = floor(log2(N)); % number of coarse-graining steps
  133. spks = binnedspikes;
  134. for i = 1:nstep
  135. R = corrcoef(spks');
  136. R(eye(size(R))==1) = nan;
  137. npairs = floor(N/(2^i)); % number of coarse-grained pairs in this step
  138. g = nan(npairs,2);
  139. % find correlated pairs
  140. if npairs ==1
  141. [row,col] = find(R==max(R,[],'all'));
  142. if length(row)>2
  143. row = [row(1) row(3)]; % if two pairs have same max corr, pick 1st pair
  144. col = [row(2) row(1)];
  145. end
  146. g(1,:) = row; % next pair of maximally correlated cells
  147. % g(1,:) = [1 2];
  148. else
  149. for l = 1:npairs
  150. [row,col] = find(R==max(R,[],'all'));
  151. if length(row)>2
  152. row = [row(1) row(3)]; % if two pairs have same max corr, pick 1st pair
  153. col = [row(2) row(1)];
  154. end
  155. g(l,:) = row; % next pair of maximally correlated cells
  156. R(row,:) = nan; R(:,col) = nan;
  157. end
  158. end
  160. % sum spike train pairs
  161. cg_spks = zeros(npairs,size(binned,2));
  162. for l = 1:npairs
  163. cg_spks(l,:) = sum(spks(g(l,:),:),1);
  164. end
  165. cg_spks = cg_spks./max(cg_spks,[],2);
  166. spks = cg_spks; % update
  167. end
  169. condhold = zeros(nword,1);
  170. % use final cg_spks to find P(Mt|wt)
  171. for k = 1:nword % w_t
  172. % find all indices of words(k), count
  173. idx = find(binnedwords==k);
  174. idx = idx(idx<size(binned,2));
  175. % final coarsegraining gives probility of meta neuron spiking
  176. probM = spks(idx);
  177. condhold(k) = mean(probM,'omitnan');
  178. end
  179. condprob2 = [1-condhold condhold];
  181. Joint = zeros(nword,2);
  182. for m = 1:2
  183. for j = 1:nword
  184. Joint(j,m) = sum(condprob1(:,j).*condprob2(:,m).*P_wt,'omitnan');
  185. end
  186. end
  187. Joint = Joint./sum(Joint,'all');
  188. P_Mt = sum(Joint,1);
  189. P_wt = sum(Joint,2);
  191. % calculate mutual info
  192. I_CCG = -sum(P_Mt.*log2(P_Mt),'omitnan')-sum(P_wt.*log2(P_wt),'omitnan')+sum(Joint.*log2(Joint),'all','omitnan');
  193. R_CCG = P_Mt(2);
  194. end
  196. function [I] = PerceptronInfo(mycells,binned,params,Dt)
  197. %PerceptronInfo gets the mutual information between perceptron at time t and words at
  198. % t+dt
  199. N=length(mycells);
  200. % find all 2^N possible "words"
  201. nword=2^N;
  202. vec = 0:nword-1;
  203. words=dec2bin(vec);
  204. words=double(reshape(logical(words(:)-'0'),nword,[]));
  205. words = words.';
  206. [~, wordorder] = sort(sum(words,1));
  207. words = words(:,wordorder);
  209. % first get word probability P_wt
  210. [P_wt,condprob1] = CondProb(mycells,binned,Dt);
  211. condprob1 = condprob1./sum(condprob1,2);
  213. w = params(1:N);
  214. c = params(N+1);
  215. condprob2 = zeros(nword,2); % matrix of word counts, rows = wt, col = Mt
  216. % now get cond prob of meta given word
  217. for k = 1:nword
  218. wt = words(:,k);
  219. z = sum(wt'.*w);
  220. condprob2(k,2) = (1./(1+exp(-z+c)));
  221. condprob2(k,1) = 1-condprob2(k,2);
  222. end
  224. Joint = zeros(nword,2);
  225. for m = 1:2
  226. for j = 1:nword
  227. Joint(j,m) = sum(condprob1(:,j).*condprob2(:,m).*P_wt,'omitnan');
  228. end
  229. end
  230. Joint = Joint./sum(Joint,'all');
  231. P_Mt = sum(Joint,1);
  232. P_wt = sum(Joint,2);
  234. % calculate mutual info
  235. I = -sum(P_Mt.*log2(P_Mt),'omitnan')-sum(P_wt.*log2(P_wt),'omitnan')+sum(Joint.*log2(Joint),'all','omitnan');
  236. I = -I; % return negative info
  237. end
  239. function [R_PCG] = PerceptronFR(mycells,binned,params)
  240. N=length(mycells);
  241. nword = 2^N;
  242. vec = 0:nword-1;
  243. words=dec2bin(vec);
  244. words=double(reshape(logical(words(:)-'0'),nword,[]));
  245. words = words.';
  246. [~, wordorder] = sort(sum(words,1));
  247. words = words(:,wordorder);
  249. binnedspikes = binned(mycells,:);
  251. % first find all zero words
  252. idx0 = sum(binnedspikes,1)==0;
  253. % where this is true, we want binnedwords to be 1 anyway
  254. % where it is false (0), we want to replace it with the correct word
  255. binnedwords = double(idx0);
  256. idx1 = find(idx0==0);
  257. for i = 1:length(idx1)
  258. a = num2str(binnedspikes(:,idx1(i)));
  259. a = sprintf(a);
  260. binnedwords(idx1(i)) = bin2dec(a)+1;
  261. end
  263. N_wt = histcounts(binnedwords,1:2^N+1)';
  264. P_wt = N_wt/sum(N_wt);
  266. nword = round(nword);
  267. spkproball = zeros(1,nword);
  268. w = params(1:N);
  269. c1 = params(N+1);
  270. for k = 1:nword
  271. wt = words(:,k);
  272. z = sum(wt'.*w);
  273. probM = 1./(1+exp(-z+c1));
  274. spkproball(k) = probM.*P_wt(k);
  275. end
  276. R_PCG = sum(spkproball);
  277. end
  279. function [c,ceq] = mycon(mycells,binned,params,fr)
  280. R_PCG = PerceptronFR(mycells,binned,params);
  281. tol = 1e-4;
  282. c = (R_PCG-fr)^2-tol;
  283. ceq = [];
  284. end

examplescript.m at commit 708aa67, no license · at the source

Overview

Authors: Sylvia C L Durian1, Kyle Bojanek1, Olivier Marre2, Stephanie E Palmer1,3
ORCID iDs: Sylvia C L Durian, Kyle Bojanek, Olivier Marre, Stephanie E Palmer
  1. Department of Organismal Biology and Anatomy, University of Chicago, Chicago, IL 60637, USA
  2. Institut de la Vision, Sorbonne Université, INSERM, CNRS, Paris 75012, France
  3. Physics Frontier Center for Living Systems, University of Chicago, Chicago, IL 60637, USA
Institutions: University of Chicago (United States); Centre National de la Recherche Scientifique (France); Institut de la Vision (France); Inserm (France); Sorbonne Université (France)
Journal: PNAS nexus, volume 5, issue 7, article pgag224
Dates: received 7 October 2025; accepted 4 June 2026; published online 19 June 2026
Type: Research article · Language: English
License: CC BY-NC
Identifiers: DOI 10.1093/pnasnexus/pgag224 · PMID 42403907 · PMCID PMC13329666 · OpenAlex W4408392230
Open access: gold, a free copy (OpenAlex)
Preprint: doi:10.1101/2025.03.12.642864
Status: code verified
Methods: Statistics, Smoothing, state filtering, decompositions, Connectivity, Single-unit activity, calcium imaging
Keywords: prediction, information theory, natural scenes, population coding, downstream readout
Topic: Neural Networks and Applications (Artificial Intelligence, Computer Science), according to OpenAlex
Funding: National Science Foundation (2235451); Simons Foundation (MP-TMPS- 00005320)
Citations: cited by 1 paper (Europe PMC); 99 references in the paper

Abstract

Retinal ganglion cells show high convergence onto their downstream projections, which poses a problem for information transfer: how can information be preserved through a synaptic layer that has significantly more inputs than outputs? Lossy compression suggests many efficient, yet computation-agnostic, methods for reading out input stimuli or activity patterns. Focusing on prediction as a ubiquitous computation in the brain, we compare compressions that explicitly retain predictive information to common neural compression frameworks that do not. We find evidence that compressing retinal inputs to perform optimal predictive computations allows putative downstream neurons to predict the future near-optimally across natural scenes. Other sensory systems also exhibit compression in their processing hierarchies, and we hope that our framework will be useful in cases where it is not yet known how information about a specific computation is maintained under compression.

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

Repository

Its files are read in the Code ↔ Paper reader above, with 2 matches between paragraphs and lines of code.

sepalmer/predictive-coarse-graining

License: none: the authors keep all their rights
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: 708aa67321388895b0de567ea84ef9b79eff3959, 11 February 2026
Languages: MATLAB (2)
Size: 39 files, 2 scripts
Software Heritage: not archived
Found in: “Data availability”
Holds: README
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Statistics and Machine Learning Toolbox (2 files), Optimization Toolbox (1 file), Violinplot-Matlab (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
3 files
At the source: github.com/sepalmer/predictive-coarse-graining.git

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

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  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
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Data

Datasets cited

Data availability

The data have been published at https://doi.org/10.5061/dryad.4qrfj6qm8 (53). Corresponding code has been published at https://github.com/sepalmer/predictive-coarse-graining.git.

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

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

  • Funding: added National Science Foundation: 2235451; Simons Foundation: MP-TMPS- 00005320

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 5 keywords, 76 references.

Cite

This paper

Durian, S. C. L., Bojanek, K., Marre, O., & Palmer, S. E. (2026). Preserving predictive information under biologically plausible compression. PNAS nexus, 5(7), pgag224. https://doi.org/10.1093/pnasnexus/pgag224

BibTeX

@article{durian2026preserving,
author = {Durian, Sylvia C L and Bojanek, Kyle and Marre, Olivier and Palmer, Stephanie E},
title = {{Preserving predictive information under biologically plausible compression}},
journal = {PNAS nexus},
year = {2026},
month = jun,
volume = {5},
number = {7},
pages = {pgag224},
publisher = {Oxford University Press},
issn = {2752-6542},
doi = {10.1093/pnasnexus/pgag224},
url = {https://doi.org/10.1093/pnasnexus/pgag224},
pmid = {42403907},
pmcid = {PMC13329666}
}

RIS

TY - JOUR
AU - Durian, Sylvia C L
AU - Bojanek, Kyle
AU - Marre, Olivier
AU - Palmer, Stephanie E
TI - Preserving predictive information under biologically plausible compression
T2 - PNAS nexus
J2 - PNAS Nexus
PY - 2026
DA - 2026/06/19
VL - 5
IS - 7
SP - pgag224
SN - 2752-6542
PB - Oxford University Press
DO - 10.1093/pnasnexus/pgag224
UR - https://doi.org/10.1093/pnasnexus/pgag224
LA - en
ER -

CSL-JSON

{
"id": "10.1093/pnasnexus/pgag224",
"type": "article-journal",
"title": "Preserving predictive information under biologically plausible compression",
"container-title": "PNAS nexus",
"author": [
{
"family": "Durian",
"given": "Sylvia C L"
},
{
"family": "Bojanek",
"given": "Kyle"
},
{
"family": "Marre",
"given": "Olivier"
},
{
"family": "Palmer",
"given": "Stephanie E"
}
],
"container-title-short": "PNAS Nexus",
"volume": "5",
"issue": "7",
"page": "pgag224",
"DOI": "10.1093/pnasnexus/pgag224",
"PMID": "42403907",
"PMCID": "PMC13329666",
"ISSN": "2752-6542",
"publisher": "Oxford University Press",
"URL": "https://doi.org/10.1093/pnasnexus/pgag224",
"language": "en",
"issued": {
"date-parts": [
[
2026,
6,
19
]
]
}
}

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