standOff, and the article is at its publisher via the link below. When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.| second reading | alternatives | an independent re-reading of a facet, recorded whether or not it agrees |
| relation to other work | claim_relations | how this paper stands to another: agrees, contradicts, extends, qualifies |
| claim type | claim_type | the shape of the claim: existence, mechanism, method, critique, prediction, null |
| concept edge | concept_edges | an asserted relation between two concepts, with the sentence asserting it |
| concept | concepts | an idea the paper works with, quoted where the paper uses it |
| content tag | content_tags | a finding, definition, quantity, statistic or variable named in the paper |
| contribution | contribution | what the paper claims to add |
| control | controls | an experiment run to eliminate a rival explanation |
| limitation | limitations | what the paper says its evidence cannot support |
| mechanism | mechanisms | how the reported effect is said to come about |
| method | method | how the paper produced its evidence |
| object of study | object_of_study | what the paper is about — the thing it investigates |
| phenomenon | phenomenon | the effect or regularity under study |
| research question | research_question | the question the paper sets itself |
| sense | senses | a distinct use of a term, quoted where the paper fixes it |
| transfer | transfers | a method or concept carried in from another field |
| unrecordable relation | unhoused_relations | a relation the paper asserts that this vocabulary cannot express, with the reason |
Relations on this page carry a quotation for the claim. Where a relation was separately evidenced — and so tested against the vocabulary for its type — the row says so; none of 11 relations here carry that mark. The rest are the tagger’s reading of the sentence quoted beside them.
| facet | tag | field | conf. | whose words |
|---|---|---|---|---|
| object_of_study | the belief that reducing noise correlations improves a population code - and the assumption of homogeneous tuning that the belief rests on Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | object_of_study | the paper's words | |
| research_question | whether limited-range correlations are detrimental once the population is heterogeneous, large, and has stimulus-dependent variances Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | research_question | the paper's words | |
| contribution | in heterogeneous populations of more than a few hundred neurons, INCREASING correlations substantially improves encoding accuracy - and with noise entropy held constant, the accuracy is independent of correlation structure and magnitude altogether Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | contribution | the paper's words | |
| claim_type | critique Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_type | the paper's words | |
| phenomenon | noise correlations in neural population coding Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | phenomenon | the paper's words | |
| method | simulation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: simulation | method | the paper's words | |
| mechanisms | mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[0] | the tagger's words | |
| mechanisms | mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[1] | the tagger's words | |
| mechanisms | mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[2] | the tagger's words | |
| mechanisms | raising correlations moves noise power into a few low-frequency Fourier components and removes it from all the higher ones; a homogeneous population encodes only in the low frequencies and is hurt, a heterogeneous one encodes across all frequencies and is helped Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[3] | 1.0 | the tagger's words |
| mechanisms | and the two effects compete, which is why the dependence on correlation is non-monotonic and why the high frequencies win as the population grows Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[4] | 1.0 | the tagger's words |
| mechanisms | underneath it, correlating neurons at fixed marginal variances lowers the noise entropy, and lower noise entropy shrinks the variance in most directions Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[5] | 0.9 | the tagger's words |
| mechanisms | but lower entropy alone is not enough - it helps only because a heterogeneous population spreads its signal across all the directions the entropy reduction touches Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[6] | 1.0 | the tagger's words |
| limitations | Whether noise entropy is equally decisive for scenarios not modelled here (stimulus-dependent or heterogeneous correlations, multi-dimensional stimuli) is untested. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the noise-entropy conclusion outside the modelled cases: whether it holds FOR OTHER SCENARIOS NOT CONSIDERED EXPLICITLY IN THIS STUDY - STIMULUS-DEPENDENT AND HETEROGENEOUS CORRELATIONS, OR SIMULTANEOUS ENCODING OF MULTIPLE STIMULUS DIMENSIONS - REMAINS TO BE INVESTIGATED | limitations[0] | the tagger's words | |
| limitations | The reconciliation with experiments reporting reduced correlations was not worked out in detail against those studies' actual parameters. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the reconciliation with the experiments reporting reduced correlations: WE DID NOT ASSESS THIS IN DETAIL BY TAKING INTO ACCOUNT ALL RELEVANT PARAMETERS FROM THESE STUDIES | limitations[1] | the tagger's words | |
| limitations | Results assume an optimal readout; computationally constrained (e.g. linear) readouts can behave differently. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: every result about what correlations do to a code: OF COURSE, THE EFFECT OF CORRELATIONS CAN BE DIFFERENT FOR OTHER, COMPUTATIONALLY CONSTRAINED READOUTS | limitations[2] | the tagger's words | |
| limitations | the model itself stops being valid past a critical population size once correlation coefficients are made variable, because the covariance matrix loses positive definiteness Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the large-population regime the paper is about: THE COVARIANCE MATRIX WILL BE VALID (POSITIVE DEFINITE) ONLY UP TO n ~ 1/(2 sigma)^2 ... FROM A CRITICAL n ON, THE MODEL WILL NOT BE VALID ANY MORE | limitations[3] | 1.0 | the tagger's words |
| limitations | two of the generality checks are reported without their figures Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the regular-grid idealisation: THE FISHER INFORMATION IS VIRTUALLY UNAFFECTED BY RANDOMLY ASSIGNING PREFERRED DIRECTIONS COMPARED WITH EQUALLY SPACING THEM (DATA NOT SHOWN) | limitations[4] | 1.0 | the tagger's words |
| limitations | whether noise entropy governs accuracy under stimulus-dependent or heterogeneous correlations, or with several stimulus dimensions, is left open Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the same scope as limitations[0] - the scenarios the conclusion has been tested in | limitations[5] | 1.0 | the tagger's words |
| limitations | and the heterogeneity parameter cannot be pushed arbitrarily far - amplitudes are positive, average to one, and firing rates are biophysically capped Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the heterogeneity results, in both directions: J_mean CANNOT BE INCREASED ARBITRARILY ... BECAUSE THE AMPLITUDES ARE CONSTRAINED TO BE POSITIVE, HAVE AN AVERAGE OF 1, AND NEURONS HAVE A MAXIMUM POSSIBLE FIRING RATE, while kappa = 0.25 IS LIKELY TO BE AN UNDERESTIMATE | limitations[6] | 1.0 | the tagger's words |
| limitations | the code that reproduces every figure is released, with the note that it has not been peer reviewed Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the reproduction material: it contains MATLAB CODE TO REPRODUCE ALL FIGURES AND NUMERICAL SIMULATIONS IN THIS PAPER. THIS MATERIAL HAS NOT BEEN PEER REVIEWED | limitations[7] | 1.0 | the tagger's words |
| transfers | the decrease in noise entropy associated with increasing correlations, which is where the improvement in encoding accuracy comes from Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | transfers[0] | 1.0 | the tagger's words |
| transfers | diagonalisation of a circulant matrix in the Fourier basis, which is what makes very large populations analytically tractable Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | transfers[1] | 1.0 | the tagger's words |
| transfers | the Cramer-Rao bound and estimator bias, used to check that the measure being compared is attainable at all Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | transfers[2] | 1.0 | the tagger's words |
| transfers | 408 measured orientation tuning curves, used to set the heterogeneity parameter rather than to test the theory Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | transfers[3] | 0.9 | the tagger's words |
| controls | a second analysis holding the TOTAL noise (the noise entropy) constant while varying only the correlation structure Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: the amount of noise as the driver of the coding difference - comparing correlated and uncorrelated populations changes two things at once unless the total is pinned · outcome (stated by the tagger, no quotation): held | controls[0] | 0.95 | the tagger's words |
| concepts | correlation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: correlation | concepts[0] | the paper's words | |
| concepts | noise entropy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: noise entropy | concepts[1] | the paper's words | |
| concepts | population code Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: population code | concepts[9] | the paper's words | |
| concepts | attention Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: attention | concepts[18] | the paper's words | |
| unhoused_relations | correlations → variances Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. THE TWO CANNOT BE SEPARATED IN THIS STUDY - the DESIGN form / It bounds what the paper's own results can mean, and it lives in a methods paragraph where nothing downstream will find it. And the span adds the part that matters for interpretation: 'neither of both is more important than the other' - the authors decline to rank the two causes they cannot separate. | unhoused_relations[0] | the tagger's words | |
| senses | THE FIELD'S CONCLUSION WAS A PROPERTY OF ITS SIMPLIFYING ASSUMPTION: most previous studies use HOMOGENEOUS population models in which neurons differ only in preferred stimulus, and heterogeneity CRITICALLY ALTERS the properties of a population code - 'this has not been sufficiently appreciated' Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[0] | 1.0 | the tagger's words |
| senses | with the belief stated in the form it is usually held - if correlations are unavoidable, Quotation withheld, which is why falling correlations under attention, adaptation and learning are read as better coding Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[1] | 1.0 | the tagger's words |
| senses | AND THE ANSWER REVERSES: in populations with more than a few hundred neurons, INCREASING limited-range correlations can substantially IMPROVE encoding accuracy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[2] | 1.0 | the tagger's words |
| senses | PUBLISHED PAPERS DISAGREE AND THE PARAMETER THEIR DISAGREEMENT TURNS ON IS NAMED: 'The apparent discrepancy arises from subtle differences in the assumptions that were made about the population activity, such as for instance the noise model (additive vs Poisson-like)' Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[3] | 1.0 | the tagger's words |
| senses | and the two conditions are stated exactly: the information saturates ONLY IF the variances do not depend on the stimulus AND all neurons have identical tuning curves - fail either and it grows linearly Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[4] | 1.0 | the tagger's words |
| senses | A FREE PARAMETER THAT SHOULD NEVER HAVE BEEN FREE: the level of correlations cannot be optimized on its own with tuning functions and variances held fixed, because that drives the model to a DEGENERATE, biologically implausible solution Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[5] | 1.0 | the tagger's words |
| senses | stated against its own model too - MOST MODELS USED IN PREVIOUS STUDIES, INCLUDING OUR ABOVE MODEL, are not well constrained, because they permit the noise entropy to be made arbitrarily small Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[6] | 1.0 | the tagger's words |
| senses | AND ONCE THE RIGHT THING IS HELD CONSTANT, THE QUANTITY THE WHOLE LITERATURE MEASURES DROPS OUT: with noise entropy fixed, the information depends ONLY on amplitude variability and is INDEPENDENT of both the structure and the magnitude of correlations Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[7] | 1.0 | the tagger's words |
| senses | with the conclusion drawn in the field's own terms - accuracy is set by the amount of heterogeneity and the overall noise entropy, and the specific noise structure is NOT AS IMPORTANT AS COMMONLY ASSUMED Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[8] | 1.0 | the tagger's words |
| senses | A BOUND IS ONLY A BOUND UNTIL YOU SHOW IT IS TIGHT: Fisher information gives the Cramer-Rao bound, the bound is not always attainable, and COMPARING LOOSE UPPER BOUNDS IS MEANINGLESS Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[9] | 1.0 | the tagger's words |
| senses | so the measure is validated before it is used - the maximum-likelihood estimator comes within 5% of the bound for every population above 64 neurons Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[10] | 1.0 | the tagger's words |
| senses | THE SAME MODEL GIVES THE OPPOSITE ANSWER UNDER A DIFFERENT DECODER: the OLE does not improve with correlations at any population size, so under a linear readout REDUCING correlations increases accuracy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[11] | 1.0 | the tagger's words |
| senses | and a standard interpretation is refused on the way - the linear part of the Fisher information is often called the portion readable by linear methods, and that notion is PROBLEMATIC because the linear estimator is BIASED Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[12] | 1.0 | the tagger's words |
| senses | TWO QUANTITIES THAT MOVE TOGETHER AND CANNOT BE APPORTIONED: removing one common noise source changes correlations by 50% and variances by 5%, and CONSIDERING EACH ONE IN ISOLATION IS NOT MEANINGFUL Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[13] | 1.0 | the tagger's words |
| senses | with the published comparison called out by name - the relative importance of correlations was assessed using HIGHLY SUBOPTIMAL POOLING RULES, and conclusions from those do not generalize Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[14] | 1.0 | the tagger's words |
| senses | THE MODEL SILENTLY STOPS BEING VALID PAST A SIZE: with variable correlation coefficients the covariance matrix is positive definite only up to a critical n, beyond which the model is not valid any more Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[15] | 1.0 | the tagger's words |
| senses | AND THE EXPLANATION THAT WOULD SAVE THE OLD READING IS TESTED AND REJECTED ON ITS OWN TERMS: it would need the read-out population to be at most a few hundred cells, which - given the number in a single cortical column - seems rather unlikely Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[16] | 0.9 | the tagger's words |
| senses | and the claim is bounded in its final sentence - reducing correlations improving encoding is NOT A GENERAL PRINCIPLE but true only under certain conditions, with the assumptions about population size and readout named as what can change it Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[17] | 1.0 | the tagger's words |
| alternatives | claim_type: critique Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. a second reading reaching the same value. Recorded: critique — note: a second reading reaching the same value from a different sentence. Not applied - a person decides. | alternatives.claim_type | the tagger's words | |
| alternatives | method: an analytic expression for the inverse covariance obtained by diagonalising a circulant correlation matrix in the Fourier basis, which makes populations of tens of thousands of neurons tractable Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. a second reading DIFFERING from the recorded value. Recorded: simulation — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides. | alternatives.method | the tagger's words | |
| alternatives | phenomenon: limited-range noise correlations, and the experimental finding that they fall under attention, adaptation and learning Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. a second reading DIFFERING from the recorded value. Recorded: noise correlations in neural population coding — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides. | alternatives.phenomenon | the tagger's words | |
| claim_relations | extends → Sompolinsky et al., 2001; Shamir and Sompolinsky, 2006 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[0] | the tagger's words | |
| claim_relations | extends → Shamir and Sompolinsky (2006) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[1] | the tagger's words | |
| claim_relations | contradicts → Cohen and Maunsell, 2009; Mitchell et al., 2009 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[2] | the tagger's words | |
| claim_relations | replicates → Zohary et al., 1994; Abbott and Dayan, 1999; Sompolinsky et al., 2001; Wilke and Eurich, 2002 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[3] | the tagger's words | |
| claim_relations | contradicts → the general principle that reducing noise correlations improves a population code Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[4] | 1.0 | the tagger's words |
| claim_relations | explains-away → the disagreement among earlier theoretical studies, as arising from different unstated noise-model and tuning assumptions Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[5] | 1.0 | the tagger's words |
| claim_relations | critiques → the practice of treating correlation strength as a free parameter while holding tuning and variances fixed, which admits a degenerate noise-free optimum Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. differs in: THE AXIS IS WHETHER CORRELATION LEVEL CAN BE VARIED INDEPENDENTLY. 'we suggest that Quotation withheld.' The earlier optimum is real inside its own assumption and vanishes outside it - the same paper whose homogeneity assumption reverses a sign, making its objection twice about what is HELD CONSTANT rather than what is measured. | claim_relations[6] | 1.0 | the tagger's words |
| claim_relations | critiques → the attention studies' attribution of improved coding to reduced correlations, since the pooling rules used were suboptimal and correlations and variances moved together Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[7] | 0.9 | the tagger's words |
| claim_relations | supports → the use of Fisher information here specifically, having shown the maximum-likelihood estimator comes within 5% of the bound Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[8] | 1.0 | the tagger's words |
| claim_relations | distinguishes-from → the linear-readout case, in which the original conclusion does hold Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. differs in: THE AXIS IS WHETHER FISHER INFORMATION CAPTURES THE DEPENDENCE. 'Quotation withheld.' The distinction is between a quantity and the tool used to measure it - the linear-readout conclusion holds, and it holds because the measure happens to be adequate there. Same paper whose homogeneity assumption reverses a sign elsewhere in this corpus. | claim_relations[9] | 1.0 | the tagger's words |
| concept_edges | attention —causes→ correlation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. status: REPORTED OF THE LITERATURE, and the INTERPRETATION placed on it is what this paper goes on to question · direction on the measure: reduces · strength of the relation: 1 also in: attention · correlation | concept_edges[1] | 1.0 | the tagger's words |
| concept_edges | Fisher information —operationalised-as→ encoding accuracy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 also in: Fisher information · encoding accuracy | concept_edges[2] | 1.0 | the tagger's words |
| concept_edges | correlation —causes→ encoding accuracy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 · note: THE ANSWER REVERSES: in populations of more than a few hundred neurons, INCREASING limited range correlations can substantially IMPROVE encoding accuracy
Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span says reduced correlations do not necessarily improve coding; causes is loose. also in: correlation · encoding accuracy | concept_edges[3] | 1.0 | the tagger's words |
| concept_edges | noise entropy —causes→ encoding accuracy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 · note: and for constant noise entropy in the large-population limit, accuracy is INDEPENDENT of both structure and magnitude of correlations also in: noise entropy · encoding accuracy | concept_edges[5] | 1.0 | the tagger's words |
| concept_edges | correlation —causes→ population code Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. status: THE FIELD'S BELIEF, not a result of this paper - and the paper's own finding is that it holds in only one of two regimes · strength of the relation: 1 · note: the belief in the form it is held - Quotation withheld
Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span reports a common belief that reducing correlations improves a code; causes states it as a finding. also in: correlation · population code | concept_edges[8] | 1.0 | the tagger's words |
| concept_edges | heterogeneity —contrasted-with→ correlation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 · note: asymptotically the relative performance depends only on c 0 and on the degree of heterogeneity - the more heterogeneous, the higher
Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span says performance depends on correlation and heterogeneity; contrasted-with is loose. also in: heterogeneity · correlation | concept_edges[14] | 1.0 | the tagger's words |
| concept_edges | amplitude —distinct-from→ correlation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 · note: THE QUANTITY THE WHOLE LITERATURE MEASURES DROPS OUT - with entropy fixed the information depends ONLY on amplitude variability, and NONE of the correlation-structure parameters enter
Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span says J mean is independent of correlations; distinct-from 'amplitude' is loose. also in: amplitude · correlation | concept_edges[20] | 1.0 | the tagger's words |
| concept_edges | correlation —causes→ noise entropy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. holds when: at fixed marginal variances - the paper's own condition, and the claim is false without it · direction on the measure: reduces · strength of the relation: 1 · note: correlating at fixed marginal variances LOWERS the noise entropy, and lower entropy shrinks the variance in most directions also in: correlation · noise entropy | concept_edges[37] | 1.0 | the tagger's words |
| concept_edges | noise entropy —causes→ population code Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 · note: but lower entropy ALONE is not enough - it helps only because the heterogeneous population spreads its signal across the directions the reduction touches
Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but a lower noise entropy 'should lead to an improvement in coding accuracy'; 'causes population code' is loose. also in: noise entropy · population code | concept_edges[38] | 1.0 | the tagger's words |
| concept_edges | correlation —causes→ population code Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. holds when: in the low-correlation regime - below c_min, where the behaviour matches a homogeneous population · direction on the measure: reduces · strength of the relation: 1 · note: ONE OF A PAIR. The same relation carries the OPPOSITE sign above c_min; see the companion edge. Neither edge is the paper's claim on its own.
Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span states a regime-conditional claim (below c_min); the sign holds only in that regime. also in: correlation · population code | concept_edges[43] | the tagger's words | |
| concept_edges | correlation —causes→ population code Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. holds when: in the high-correlation regime - above c_min · direction on the measure: increases · strength of the relation: 1 · note: ONE OF A PAIR. The same relation carries the OPPOSITE sign below c_min; see the companion edge. c_min falls with population size and converges to zero, so for large populations this is the regime that applies.
Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span states a regime-conditional claim (the high-correlation regime). also in: correlation · population code | concept_edges[44] | the tagger's words | |
| content_tags | Fisher information Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Fisher information | content_tags.statistics[0] | the tagger's words | |
| content_tags | maximum likelihood estimation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: maximum likelihood estimation | content_tags.statistics[1] | the tagger's words | |
| content_tags | Cramér-Rao bound Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Cramér-Rao bound | content_tags.statistics[2] | the tagger's words | |
| content_tags | mean squared error Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: mean squared error | content_tags.statistics[3] | the tagger's words | |
| content_tags | lognormal distribution Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: lognormal distribution | content_tags.statistics[4] | the tagger's words | |
| content_tags | Fisher information Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Fisher information | content_tags.statistics[5] | 1.0 | the tagger's words |
| content_tags | maximum-likelihood Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: maximum-likelihood | content_tags.statistics[6] | 1.0 | the tagger's words |
| content_tags | Fano factor Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Fano factor | content_tags.statistics[7] | 1.0 | the tagger's words |
| content_tags | In heterogeneous populations of more than a few hundred neurons, increasing rather than decreasing limited-range noise correlations substantially improves encoding accuracy. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[0] | the tagger's words | |
| content_tags | The accuracy gain from stronger correlations is attributable to the drop in noise entropy that accompanies them when marginal distributions are held fixed. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[1] | the tagger's words | |
| content_tags | Once noise entropy is held constant, encoding accuracy in large populations no longer depends on the structure or magnitude of the correlations at all. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[2] | the tagger's words | |
| content_tags | Fisher information stops growing with population size only under the restrictive combination of stimulus-independent variances and identical tuning curves. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[3] | the tagger's words | |
| content_tags | The maximally detrimental correlation level decreases in inverse proportion to population size. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[4] | the tagger's words | |
| content_tags | The maximum-likelihood estimator comes close enough to the Cramér–Rao bound that comparing Fisher information across conditions is legitimate. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[5] | the tagger's words | |
| content_tags | For a suboptimal linear readout the conclusion reverses: the OLE gains nothing from stronger correlations even in large populations. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[6] | the tagger's words | |
| content_tags | IN HOMOGENEOUS POPULATIONS limited range correlations are highly detrimental, which is why falling correlations under attention, adaptation and learning are read as better coding Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[7] | 1.0 | the tagger's words |
| content_tags | AND THE ANSWER REVERSES: in populations with more than a few hundred neurons, INCREASING the level of limited range correlations can substantially improve encoding accuracy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[8] | 1.0 | the tagger's words |
| content_tags | with the improvement traced to a decrease in noise entropy, and - for constant entropy in the large-population limit - accuracy INDEPENDENT of both structure and magnitude of correlations Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[9] | 1.0 | the tagger's words |
| content_tags | THE CONCLUSION WAS A PROPERTY OF THE SIMPLIFYING ASSUMPTION: most previous studies use homogeneous models, and heterogeneity CRITICALLY ALTERS a population code - 'this has not been sufficiently appreciated' Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[10] | 1.0 | the tagger's words |
| content_tags | with the belief stated as it is held - it is GENERALLY BELIEVED that reducing correlations improves any population code Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. WHOSE RESULT THIS IS: studies find - THE SUBJECT OF THIS RESULT IS AN INDEFINITE STUDY, NOT THIS PAPER. 'Previous studies reported', 'studies in guinea pig showed', 'recent studies have reported' - somebody else's work under a common noun rather than a name, with a citation in the sentence and no first-person marker. The quote is verbatim and the claim is true; only the attribution is wrong. FOUND BY MEASURING MY OWN CUE'S RECALL: the first sweep required a NAMED author as the subject ('Sperling (1960) demonstrated') and found 17. Reading eleven citation-bearing findings on 'Plakke2016' by hand showed four the cue could not see - 'A study examining recognition found', 'studies of typical human subjects have demonstrated', 'A follow up study found' - so the named cue's 17 was a floor and not a count. A CUE'S FALSE POSITIVES TELL YOU NOTHING ABOUT ITS FALSE NEGATIVES, and the only way to find these was to read a record's whole layer. | content_tags.findings[11] | 1.0 | the tagger's words |
| content_tags | A NUMBER OF AUTHORS REPORTED DIFFERENT RESULTS, and the apparent discrepancy arises from subtle differences in the assumptions that were made about the population activity, such as the noise model, additive against Poisson-like Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[12] | 1.0 | the tagger's words |
| content_tags | and the two conditions are stated exactly - the information saturates ONLY IF variances are stimulus-independent AND all tuning curves identical Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[13] | 1.0 | the tagger's words |
| content_tags | TWO REGIMES, with the boundary falling as 1/n, so that for large populations increasing correlations is almost always advantageous Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[14] | 1.0 | the tagger's words |
| content_tags | asymptotically the relative performance depends only on the same-preference correlation coefficient and on the degree of heterogeneity Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[15] | 1.0 | the tagger's words |
| content_tags | and heterogeneity cannot be pushed arbitrarily far, while the value used is likely an UNDERESTIMATE because real populations vary in more than amplitude Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[16] | 1.0 | the tagger's words |
| content_tags | A FREE PARAMETER THAT SHOULD NEVER HAVE BEEN FREE: optimising correlations with tuning and variances held fixed reaches a DEGENERATE, biologically implausible solution Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[17] | 1.0 | the tagger's words |
| content_tags | said against its own model too - MOST MODELS USED IN PREVIOUS STUDIES, INCLUDING OUR ABOVE MODEL, are not well constrained Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[18] | 1.0 | the tagger's words |
| content_tags | AND THE QUANTITY THE WHOLE LITERATURE MEASURES DROPS OUT: with noise entropy fixed the information depends only on amplitude variability, and no correlation-structure parameter enters Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[19] | 1.0 | the tagger's words |
| content_tags | so accuracy is set by heterogeneity and overall noise entropy, and the specific noise structure is NOT AS IMPORTANT AS COMMONLY ASSUMED Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[20] | 1.0 | the tagger's words |
| content_tags | A BOUND IS ONLY A BOUND UNTIL YOU SHOW IT IS TIGHT: the responses here are neither independent nor identically distributed, and COMPARING LOOSE UPPER BOUNDS IS MEANINGLESS Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[21] | 1.0 | the tagger's words |
| content_tags | so it is checked before use - the maximum-likelihood estimator is within 5% of the bound for every population above 64 neurons Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[22] | 1.0 | the tagger's words |
| content_tags | THE SAME MODEL GIVES THE OPPOSITE ANSWER UNDER A DIFFERENT DECODER: under a linear readout, reducing pairwise correlations increases accuracy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[23] | 1.0 | the tagger's words |
| content_tags | and a standard interpretation is refused - calling the linear Fisher term the portion readable by linear methods is PROBLEMATIC, because that estimator is biased Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[24] | 1.0 | the tagger's words |
| content_tags | because the readout mechanism is unknown, the paper quantifies the MAXIMUM extractable information and states that a linear readout would give different conclusions Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[25] | 1.0 | the tagger's words |
| content_tags | TWO QUANTITIES THAT MOVE TOGETHER AND CANNOT BE APPORTIONED: removing one common noise source gives a 50% change in correlation and a 5% change in variance, and considering each in isolation IS NOT MEANINGFUL Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[26] | 1.0 | the tagger's words |
| content_tags | with the published comparison named - the relative importance of correlations was assessed using HIGHLY SUBOPTIMAL POOLING RULES Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[27] | 1.0 | the tagger's words |
| content_tags | THE MODEL SILENTLY STOPS BEING VALID PAST A SIZE: with variable correlation coefficients the covariance matrix is positive definite only up to a critical n Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[28] | 1.0 | the tagger's words |
| content_tags | the regular-grid assumption on preferred directions is checked and found not to matter - DATA NOT SHOWN Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[29] | 0.8 | the tagger's words |
| content_tags | with generality checked against random tuning widths and against triples drawn from real V1 tuning curves Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[30] | 1.0 | the tagger's words |
| content_tags | and the heterogeneity parameter SET from 408 measured macaque V1 tuning curves rather than tested against them Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[31] | 1.0 | the tagger's words |
| content_tags | the mechanism in Fourier terms - correlations move noise power into a few low frequencies and out of all higher ones, and the two effects COMPETE Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[32] | 1.0 | the tagger's words |
| content_tags | correlating neurons at fixed marginal variances lowers the noise entropy, which shrinks the variance in most directions Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[33] | 1.0 | the tagger's words |
| content_tags | but lower entropy alone is not enough - it helps only because a heterogeneous population spreads its signal across the directions the reduction touches Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[34] | 1.0 | the tagger's words |
| content_tags | THE ESCAPE ROUTE IS TESTED AND REJECTED ON ITS OWN TERMS: it would need the read-out population to be at most a few hundred cells, which given a single cortical column seems RATHER UNLIKELY Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[35] | 1.0 | the tagger's words |
| content_tags | and the claim is bounded in its last sentence - NOT A GENERAL PRINCIPLE but true only under certain conditions Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[36] | 1.0 | the tagger's words |
| content_tags | with what is left open named: stimulus-dependent and heterogeneous correlations, and several stimulus dimensions at once Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[37] | 1.0 | the tagger's words |
| content_tags | and the code that reproduces every figure released, with the note that it HAS NOT BEEN PEER REVIEWED Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[38] | 1.0 | the tagger's words |
| content_tags | limited range correlation structure Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: limited range correlation structure | content_tags.definitions[0] | the tagger's words | |
| content_tags | homogeneous population model Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: homogeneous population model | content_tags.definitions[1] | the tagger's words | |
| content_tags | relative J mean Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: relative J mean | content_tags.definitions[3] | the tagger's words | |
| content_tags | low-correlation regime Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: low-correlation regime | content_tags.definitions[4] | the tagger's words | |
| content_tags | noise entropy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: noise entropy | content_tags.definitions[5] | 1.0 | the tagger's words |
| content_tags | degenerate Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: degenerate | content_tags.definitions[6] | 0.9 | the tagger's words |
| content_tags | bound Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: bound | content_tags.definitions[7] | 1.0 | the tagger's words |
| content_tags | heterogeneity Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: heterogeneity | content_tags.definitions[8] | 0.9 | the tagger's words |
| content_tags | J mean Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: J mean | content_tags.definitions[9] | the tagger's words | |
| content_tags | J cov Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: J cov | content_tags.definitions[10] | the tagger's words | |
| content_tags | population size Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: population size | content_tags.variables[0] | the tagger's words | |
| content_tags | correlation coefficient Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: correlation coefficient | content_tags.variables[1] | the tagger's words | |
| content_tags | amplitude variability Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: amplitude variability | content_tags.variables[2] | the tagger's words | |
| content_tags | Fisher information Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Fisher information | content_tags.variables[3] | the tagger's words | |
| content_tags | correlation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: correlation | content_tags.variables[5] | 1.0 | the tagger's words |
| content_tags | noise entropy Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: noise entropy | content_tags.variables[6] | 1.0 | the tagger's words |
| content_tags | size Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: size | content_tags.variables[7] | 1.0 | the tagger's words |
| content_tags | amplitude Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: amplitude | content_tags.variables[8] | 1.0 | the tagger's words |
| content_tags | κ = 0.25 — degree of tuning-amplitude heterogeneity used throughout, taken from 408 measured macaque V1 orientation tuning curves Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[0] | the tagger's words | |
| content_tags | within 5% — how close the maximum-likelihood estimator gets to the Cramér–Rao bound for populations larger than 64 neurons Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[1] | the tagger's words | |
| content_tags | ∼0.5 bits — entropy reduction produced by correlating two neurons at r = 0.8 while leaving their marginals unchanged Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[2] | the tagger's words | |
| content_tags | 1.29 — marginal standard deviation needed to restore the independent population's entropy once a correlation of 0.8 is imposed Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[3] | the tagger's words | |
| content_tags | 4096 — number of simulated heterogeneous population realizations generated per population size for the maximum-likelihood analysis Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[4] | the tagger's words | |
| content_tags | 5% — how close the maximum-likelihood estimator comes to the bound above 64 neurons - the check that makes every later comparison of Fisher information meaningful Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[5] | 1.0 | the tagger's words |
| content_tags | 50% ... 5% — the change in correlation and in variance produced by removing ONE common noise source - two numbers from one cause, which is why neither can be credited with the effect Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[6] | 1.0 | the tagger's words |
| content_tags | 408 — measured macaque V1 tuning curves used to SET the heterogeneity parameter, so the model's key input is data and its test is not Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[7] | 1.0 | the tagger's words |
| content_tags | a few hundred — the largest read-out population that would rescue the old interpretation - stated so that it can be judged implausible against a cortical column Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.quantities[8] | 1.0 | the tagger's words |
Tags that could not be placed in the text:
What was deliberately not tagged, and why, is recorded per paper by the tagger. Where a paper has no such record, this page says so rather than implying that nothing was declined.