phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | noise correlations in neural population coding— “Two key factors influence the quality of a population code: (1) the shape of the tuning functions of individual neurons and (2) the structure of interneuronal noise correlations.” | |
| claim-type | critique— “In summary, the notion that reducing correlations leads to a more accurate encoding is not a general principle but is only true under certain conditions.” | |
| method — evidence | — “Because only the amplitude variability model is analytically tractable, we ran numerical simulations to estimate the Fisher information for populations with other forms of heterogeneity.” | |
| object of study — evidence | — “If correlations are unavoidable, it is generally believed that reducing them improves a population code ( Zohary et al., 1994 ; Abbott and Dayan, 1999 ; Sompolinsky et al., 2001 ; Wilke and Eurich, 2002 ; Ecker et al., 2010 ). In line with this notion, a number of recent experimental studies find reduced spike count correlations under… | |
| research question — evidence | — “Most previous theoretical studies of population coding use homogeneous population models, in which all neurons have tuning functions that differ only in their preferred stimulus and are otherwise identical ( Snippe and Koenderink, 1992 ; Abbott and Dayan, 1999 ; Sompolinsky et al., 2001 ; Wilke and Eurich, 2002 ). In these models, limited… | |
| contribution — evidence | — “We found that this improvement results from a decrease in noise entropy that is associated with increasing correlations if the marginal distributions are unchanged. Surprisingly, for constant noise entropy and in the limit of large populations, the encoding accuracy is independent of both structure and magnitude of noise correlations.” | |
| transfer | from information theory: the decrease in noise entropy associated with increasing correlations, which is where the improvement in encoding accuracy comes from— “We found that this improvement results from a decrease in noise entropy that is associated with increasing correlations if the marginal distributions are unchanged. Surprisingly, for constant noise entropy and in the limit of large populations, the encoding accuracy is independent of both structure and magnitude of noise correlations.” | transfers[0] |
| transfer | from signal processing: diagonalisation of a circulant matrix in the Fourier basis, which is what makes very large populations analytically tractable— “When correlations are increased, the noise power increases in a few low-frequency Fourier components while it decreases in all higher-frequency components (it quickly asymptotes to 1 − c 0 with increasing frequency; Fig. 1 D ). Because in homogeneous populations the stimulus encoding is confined to the low-frequency Fourier components, higher… | transfers[1] |
| transfer | from estimation theory: the Cramer-Rao bound and estimator bias, used to check that the measure being compared is attainable at all— “One potential caveat that has to be addressed when using Fisher information is that it provides only a bound (the Cramér–Rao bound) on the accuracy of a population code. Unfortunately, under some conditions potentially relevant for neural coding this bound is not tight, which means there exists no estimator that achieves this performance (… | transfers[2] |
| transfer | from experimental V1 physiology: 408 measured orientation tuning curves, used to set the heterogeneity parameter rather than to test the theory— “We set κ = 0.25 as determined from a dataset of 408 orientation tuning curves of neurons recorded in macaque primary visual cortex ( Ecker et al., 2010 ). We further assume that the noise correlation between two neurons depends only on their difference in preferred direction (limited range structure) and that variances of the neurons are… | transfers[3] |
| mechanism | Raising correlations redistributes noise power out of the high-frequency Fourier components, and because heterogeneous tuning spreads the stimulus signal into exactly those components, their signal-to-noise ratio rises— “When correlations are increased, the noise power increases in a few low-frequency Fourier components while it decreases in all higher-frequency components (it quickly asymptotes to 1 − c 0 with increasing frequency; Fig. 1 D ).” | mechanisms[0] |
| mechanism | Heterogeneous tuning distributes the encoded signal across all spatial frequencies, so the high-frequency channels favoured by strong correlations carry stimulus information— “In heterogeneous populations, in contrast, the stimulus encoding is distributed among all frequencies and the high-frequency components have a better signal-to-noise ratio if correlations are strong.” | mechanisms[1] |
| mechanism | Attention improves coding by suppressing a shared noise source (raising rates, lowering Fano factors and correlations together), which lowers noise entropy, rather than by decorrelation per se— “Our analysis suggests an alternative interpretation: the higher firing rates under attention increase the signal while the reduced Fano factors and correlations indicate the suppression of a common noise source, which reduces the noise entropy and therefore leads to improved coding accuracy.” | mechanisms[2] |
| mechanism | 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— “When correlations are increased, the noise power increases in a few low-frequency Fourier components while it decreases in all higher-frequency components (it quickly asymptotes to 1 − c 0 with increasing frequency; Fig. 1 D ). Because in homogeneous populations the stimulus encoding is confined to the low-frequency Fourier components, higher… | mechanisms[3] |
| mechanism | 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— “When correlations are increased, the noise power increases in a few low-frequency Fourier components while it decreases in all higher-frequency components (it quickly asymptotes to 1 − c 0 with increasing frequency; Fig. 1 D ). Because in homogeneous populations the stimulus encoding is confined to the low-frequency Fourier components, higher… | mechanisms[4] |
| mechanism | underneath it, correlating neurons at fixed marginal variances lowers the noise entropy, and lower noise entropy shrinks the variance in most directions— “In general, increasing correlations between neurons while keeping the variances of the individual neurons fixed reduces the noise entropy of the population. Because a lower noise entropy reduces the variance in most directions, it is likely to improve the encoding.” | mechanisms[5] |
| mechanism | 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— “Because the accuracy of a population code depends on how the signal is encoded relative to the noise, a lower noise entropy by itself does not necessarily imply an improvement in coding accuracy. For instance, in the toy example in Figure 9 B , the variance along the main diagonal is larger than in the independent case in Figure 9 A .… | mechanisms[6] |
| extends | Sompolinsky et al., 2001; Shamir and Sompolinsky, 2006— “We extended the approach pioneered by Sompolinsky and colleagues ( Sompolinsky et al., 2001 ; Shamir and Sompolinsky, 2006 ) to study population codes with heterogeneous tuning functions, arbitrary mean/variance relationships (Fano factors), and a broad range of correlation structures.” | claim_relations[0] |
| extends | Shamir and Sompolinsky (2006)— “We here generalize the results of Shamir and Sompolinsky (2006) to the case with nonadditive, stimulus-dependent noise.” | claim_relations[1] |
| contradicts | Cohen and Maunsell, 2009; Mitchell et al., 2009— “The effect of different factors was assessed using highly suboptimal pooling rules ( Cohen and Maunsell, 2009 ; Mitchell et al., 2009 ) and the conclusions derived from these pooling models do not generalize to other (e.g., optimal) readout mechanisms—as our above results show.” | claim_relations[2] |
| replicates | Zohary et al., 1994; Abbott and Dayan, 1999; Sompolinsky et al., 2001; Wilke and Eurich, 2002— “Generally, small limited-range correlations decrease the accuracy compared with the independent case, consistent with previous reports ( Zohary et al., 1994 ; Abbott and Dayan, 1999 ; Sompolinsky et al., 2001 ; Wilke and Eurich, 2002 ).” | claim_relations[3] |
| contradicts | the general principle that reducing noise correlations improves a population code— “In summary, the notion that reducing correlations leads to a more accurate encoding is not a general principle but is only true under certain conditions. Assumptions about the size of the population and the way information is read out can… | claim_relations[4] |
| explains-away | the disagreement among earlier theoretical studies, as arising from different unstated noise-model and tuning assumptions | claim_relations[5] |
| 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[6] |
| 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[7] |
| supports | the use of Fisher information here specifically, having shown the maximum-likelihood estimator comes within 5% of the bound Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[8] |
| distinguishes-from | the linear-readout case, in which the original conclusion does hold Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[9] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[0] |
| sense | with the belief stated in the form it is usually held - if correlations are unavoidable, it is GENERALLY BELIEVED that reducing them improves a population code, which is why falling correlations under attention, adaptation and learning are read as better coding Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[1] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[2] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[3] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[4] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[5] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[6] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[7] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[8] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[9] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[10] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[11] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[12] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[13] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[14] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[15] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[16] |
| sense | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[17] |
| control | a second analysis holding the TOTAL noise (the noise entropy) constant while varying only the correlation structure — held — rules out 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[0] |
| differs in | the practice of treating correlation strength as a free parameter while holding tuning and variances fixed, which admits a degenerate noise-free optimum — THE AXIS IS WHETHER CORRELATION LEVEL CAN BE VARIED INDEPENDENTLY. 'we suggest that the level of correlations should not be interpreted as a free parameter that can be optimized independently while all other parameters, such as tuning functions and variances, are kept fixed.' 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[6] |
| differs in | the linear-readout case, in which the original conclusion does hold — THE AXIS IS WHETHER FISHER INFORMATION CAPTURES THE DEPENDENCE. 'Because the estimator bias depends on the correlations, the dependence of the mean squared error on correlations is not captured well by the Fisher information.' 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | claim_relations[9] |
| effect direction | attention —causes→ correlation — reduces Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[1] |
| evidential status | attention —causes→ correlation — REPORTED OF THE LITERATURE, and the INTERPRETATION placed on it is what this paper goes on to question Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[1] |
| edge | Fisher information —operationalised-as→ encoding accuracy Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[2] |
| audit | correlation —causes→ 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[3] |
| note | correlation —causes→ encoding accuracy — THE ANSWER REVERSES: in populations of more than a few hundred neurons, INCREASING limited range correlations can substantially IMPROVE encoding accuracy Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[3] |
| note | noise entropy —causes→ encoding accuracy — and for constant noise entropy in the large-population limit, accuracy is INDEPENDENT of both structure and magnitude of correlations Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[5] |
| audit | correlation —causes→ population code — 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[8] |
| evidential status | correlation —causes→ population code — 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[8] |
| note | correlation —causes→ population code — the belief in the form it is held - it is GENERALLY BELIEVED that reducing them improves a population code Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[8] |
| audit | heterogeneity —contrasted-with→ correlation — 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[14] |
| note | heterogeneity —contrasted-with→ correlation — asymptotically the relative performance depends only on c 0 and on the degree of heterogeneity - the more heterogeneous, the higher Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[14] |
| audit | amplitude —distinct-from→ correlation — 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[20] |
| note | amplitude —distinct-from→ correlation — 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[20] |
| effect direction | correlation —causes→ noise entropy — reduces Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[37] |
| holds when | correlation —causes→ noise entropy — at fixed marginal variances - the paper's own condition, and the claim is false without it Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[37] |
| note | correlation —causes→ noise entropy — correlating at fixed marginal variances LOWERS the noise entropy, and lower entropy shrinks the variance in most directions Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[37] |
| audit | noise entropy —causes→ population code — 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[38] |
| note | noise entropy —causes→ population code — but lower entropy ALONE is not enough - it helps only because the heterogeneous population spreads its signal across the directions the reduction touches Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[38] |
| audit | correlation —causes→ population code — 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[43] |
| effect direction | correlation —causes→ population code — reduces Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[43] |
| holds when | correlation —causes→ population code — in the low-correlation regime - below c_min, where the behaviour matches a homogeneous population Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[43] |
| note | correlation —causes→ population code — 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[43] |
| audit | correlation —causes→ population code — Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span states a regime-conditional claim (the high-correlation regime). Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[44] |
| effect direction | correlation —causes→ population code — increases Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[44] |
| holds when | correlation —causes→ population code — in the high-correlation regime - above c_min Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[44] |
| note | correlation —causes→ population code — 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[44] |
| outcome (stated by the tagger, no quotation) | control — held | controls[0] |
| for which use | limitation — 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[0] |
| for which use | limitation — 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[1] |
| for which use | limitation — every result about what correlations do to a code: OF COURSE, THE EFFECT OF CORRELATIONS CAN BE DIFFERENT FOR OTHER, COMPUTATIONALLY CONSTRAINED READOUTS Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[2] |
| for which use | limitation — 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[3] |
| for which use | limitation — the regular-grid idealisation: THE FISHER INFORMATION IS VIRTUALLY UNAFFECTED BY RANDOMLY ASSIGNING PREFERRED DIRECTIONS COMPARED WITH EQUALLY SPACING THEM (DATA NOT SHOWN) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[4] |
| for which use | limitation — the same scope as limitations[0] - the scenarios the conclusion has been tested in Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[5] |
| for which use | limitation — 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 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[6] |
| for which use | limitation — the reproduction material: it contains MATLAB CODE TO REPRODUCE ALL FIGURES AND NUMERICAL SIMULATIONS IN THIS PAPER. THIS MATERIAL HAS NOT BEEN PEER REVIEWED Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[7] |
| replication | untested | |
| no type for this | correlations → variances — 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. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | unhoused_relations[0] |
| limitation | Whether noise entropy is equally decisive for scenarios not modelled here (stimulus-dependent or heterogeneous correlations, multi-dimensional stimuli) is untested. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[0] |
| limitation | The reconciliation with experiments reporting reduced correlations was not worked out in detail against those studies' actual parameters. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[1] |
| limitation | Results assume an optimal readout; computationally constrained (e.g. linear) readouts can behave differently. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[2] |
| limitation | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[3] |
| limitation | two of the generality checks are reported without their figures Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[4] |
| limitation | whether noise entropy governs accuracy under stimulus-dependent or heterogeneous correlations, or with several stimulus dimensions, is left open Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[5] |
| limitation | and the heterogeneity parameter cannot be pushed arbitrarily far - amplitudes are positive, average to one, and firing rates are biophysically capped Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[6] |
| limitation | the code that reproduces every figure is released, with the note that it has not been peer reviewed Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[7] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[0] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[1] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[2] |
| finding | Fisher information stops growing with population size only under the restrictive combination of stimulus-independent variances and identical tuning curves. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[3] |
| finding | The maximally detrimental correlation level decreases in inverse proportion to population size. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[4] |
| finding | The maximum-likelihood estimator comes close enough to the Cramér–Rao bound that comparing Fisher information across conditions is legitimate. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[5] |
| finding | For a suboptimal linear readout the conclusion reverses: the OLE gains nothing from stronger correlations even in large populations. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[6] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[7] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[8] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[9] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[10] |
| finding | with the belief stated as it is held - it is GENERALLY BELIEVED that reducing correlations improves any population code Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[11] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[12] |
| finding | and the two conditions are stated exactly - the information saturates ONLY IF variances are stimulus-independent AND all tuning curves identical Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[13] |
| finding | TWO REGIMES, with the boundary falling as 1/n, so that for large populations increasing correlations is almost always advantageous Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[14] |
| finding | asymptotically the relative performance depends only on the same-preference correlation coefficient and on the degree of heterogeneity Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[15] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[16] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[17] |
| finding | said against its own model too - MOST MODELS USED IN PREVIOUS STUDIES, INCLUDING OUR ABOVE MODEL, are not well constrained Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[18] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[19] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[20] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[21] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[22] |
| finding | THE SAME MODEL GIVES THE OPPOSITE ANSWER UNDER A DIFFERENT DECODER: under a linear readout, reducing pairwise correlations increases accuracy Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[23] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[24] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[25] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[26] |
| finding | with the published comparison named - the relative importance of correlations was assessed using HIGHLY SUBOPTIMAL POOLING RULES Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[27] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[28] |
| finding | the regular-grid assumption on preferred directions is checked and found not to matter - DATA NOT SHOWN Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[29] |
| finding | with generality checked against random tuning widths and against triples drawn from real V1 tuning curves Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[30] |
| finding | and the heterogeneity parameter SET from 408 measured macaque V1 tuning curves rather than tested against them Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[31] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[32] |
| finding | correlating neurons at fixed marginal variances lowers the noise entropy, which shrinks the variance in most directions Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[33] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[34] |
| finding | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[35] |
| finding | and the claim is bounded in its last sentence - NOT A GENERAL PRINCIPLE but true only under certain conditions Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[36] |
| finding | with what is left open named: stimulus-dependent and heterogeneous correlations, and several stimulus dimensions at once Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[37] |
| finding | and the code that reproduces every figure released, with the note that it HAS NOT BEEN PEER REVIEWED Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[38] |
| quantity | κ = 0.25 — degree of tuning-amplitude heterogeneity used throughout, taken from 408 measured macaque V1 orientation tuning curves Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[0] |
| quantity | within 5% — how close the maximum-likelihood estimator gets to the Cramér–Rao bound for populations larger than 64 neurons Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[1] |
| quantity | ∼0.5 bits — entropy reduction produced by correlating two neurons at r = 0.8 while leaving their marginals unchanged Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[2] |
| quantity | 1.29 — marginal standard deviation needed to restore the independent population's entropy once a correlation of 0.8 is imposed Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[3] |
| quantity | 4096 — number of simulated heterogeneous population realizations generated per population size for the maximum-likelihood analysis Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[4] |
| quantity | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[5] |
| quantity | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[6] |
| quantity | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[7] |
| quantity | 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 paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[8] |
| variable | population size (independent) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[0] |
| variable | correlation coefficient (independent) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[1] |
| variable | amplitude variability (independent) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[2] |
| variable | Fisher information (dependent) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[3] |
| variable | correlation Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[5] |
| variable | noise entropy Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[6] |
| variable | size Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[7] |
| variable | amplitude Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[8] |
| definition | limited range correlation structure Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[0] |
| definition | homogeneous population model Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[1] |
| definition | relative J mean Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[3] |
| definition | low-correlation regime Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[4] |
| definition | noise entropy Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[5] |
| definition | degenerate Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[6] |
| definition | bound Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[7] |
| definition | heterogeneity Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[8] |
| definition | J mean Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[9] |
| definition | J cov Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[10] |
| key-terms | correlation, noise entropy, Fisher information, heterogeneity, homogeneous, population, tuning, neuron, encoding accuracy, population code, readout, maximum-likelihood, linear, bias, Fano factor, variance, noise, stimulus, attention, assumption, model, parameter, constraint, Fourier, frequency, decoding, amplitude, degenerate, bound, estimator, pooling, size |
| concept | correlation — not defined in this paper's own words; the quantity the field reduces and reads as improvement Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[0] |
| concept | noise entropy — not defined in this paper's own words; the quantity that turns out to matter instead Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[1] |
| concept | population code — not defined in this paper's own words; the object of the whole debate Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[9] |
| concept | attention — not defined in this paper's own words; the experimental condition the belief is applied to Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[18] |
| Fisher information J | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[0] |
| maximum likelihood estimation | as written: maximum-likelihood decoding Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[1] |
| Cramér-Rao bound | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[2] |
| mean squared error | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[3] |
| lognormal distribution | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[4] |
| Fisher information | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[5] |
| maximum-likelihood | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[6] |
| Fano factor | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[7] |
| claim type | critique — a second reading reaching the same value; recorded: critique Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | alternatives.claim_type |
| 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 — a second reading DIFFERING from the recorded value; recorded: simulation Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | alternatives.method |
| phenomenon | limited-range noise correlations, and the experimental finding that they fall under attention, adaptation and learning — a second reading DIFFERING from the recorded value; recorded: noise correlations in neural population coding Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | alternatives.phenomenon |
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.
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