{"id":"2175a455-1792-46ed-9c48-67a2a9df7d7a","arxiv_id":"2506.14053","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Using simulations of two neuron models with known critical points, the authors show that PRG signatures appear only near criticality when time bins are chosen adaptively from the mean interspike interval.","lead":"This paper tests a widely used data-analysis method, the phenomenological renormalization group, on computer models of neuron networks with known critical points. It finds that the method detects critical behavior only very close to the transition, and that an adaptive time-binning step removes false alarms caused by fixed bin sizes.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The sharp PRG kurtosis peak at criticality rests on a hand-tuned active-bin density; without a sweep over f or ρ_bin, the peak may be a preprocessing artifact rather than a genuine critical signature.","rationale":"The reader's weakest_assumption identifies exactly the same load-bearing concern: Eq. (9) with a hand-picked target density is not justified as an unbiased preprocessing rule, and no sensitivity analysis is provided. My read agrees fully. The central claim is that PRG scaling signatures, when obtained with adaptive binning, are reliable indicators of near-critical dynamics. That claim logically requires that the observed narrow kurtosis peak at criticality is not an accident of the specific binning parameter. Since the paper shows only one value of ρ_bin (≈0.15) and gives no evidence that the peak survives other choices, the conclusion is conditional. A concrete test—sweeping f over a wide range and checking the peak's height and position—would settle whether the result is robust or an artifact. The paper's strengths (clear demonstration of fixed-bin artifacts, use of two models with known critical points) do not resolve this gap. Therefore the conditional verdict remains appropriate, but no further change is needed.","tokens_in":9197,"tokens_out":5791,"duration_ms":59158,"concrete_test":"Repeat the Fig. 4A and Fig. 4C analysis for a grid of f values such that the active-bin density ρ_bin ranges from about 0.02 to 0.8, using several random subsamples of 256 neurons. For each f, record the value and location of the maximum kurtosis as the control parameter is swept. If the maximum stays at σ = 1 (or g = 1.5) and the peak remains comparably narrow over the whole f-range, the binning choice is not responsible for the conclusion. If the peak shifts away from criticality or broadens when ρ_bin deviates from ~0.15, the paper's central claim must be qualified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that PRG kurtosis 'peaks sharply ... centered precisely at criticality' (Sec. III B, Fig. 4) depends on the adaptive binning rule Δt = f⟨ISI⟩, Eq. (9), with f chosen to yield an active-bin density ρ_bin ≈ 0.15. This value is set by hand; no sweep over f (or equivalently over target ρ_bin) is reported. Without such a sweep one cannot distinguish a genuine property of PRG from an artifact of the preprocessing tune. Specifically, if the kurtosis peak at criticality appears only when ρ_bin lies in a narrow band around 0.15, then the statement 'genuine scale-invariant behavior emerges only within a narrow range around the known critical point' is not a universal PRG signature but a consequence of the chosen operating point. The risk is heightened because fixed-bin artifacts are themselves caused by occupancy extremes (near zero or near one), so the adaptive rule merely picks a middle ground; any middle value might generically produce a peak near criticality where fluctuations are largest.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies how phenomenological renormalization group (PRG) scale-invariance signatures behave when two neuronal models with known mean-field directed-percolation critical points are tuned across their phase transitions. It first demonstrates that fixed time-binning produces spurious kurtosis peaks in the PRG coarse-grained activity because of extreme occupancy (too few or too many active bins), then proposes an adaptive binning rule, \\Delta t = f \\langle ISI \\rangle, tuned to keep the active-bin density near 0.15. With this rule, the paper reports that the PRG kurtosis peaks sharply at the known critical point and that the real-space exponent \\alpha peaks more gradually, while shuffled surrogate data remains near the Gaussian baseline. The authors argue that these results validate PRG applications to experimental data provided that preprocessing respects the intrinsic timescale of the dynamics.","tokens_in":9434,"tokens_out":3961,"duration_ms":42340,"significance":"If the central claim holds, this is a useful calibration result: it would show that PRG's scale-invariance signatures are specific to a narrow vicinity of a true critical point in models with exactly known criticality, thereby strengthening the interpretation of kurtosis peaks in experimental neural data. The paper has clear strengths: it uses two mechanistically different models with exactly known MF-DP critical points, it demonstrates the fixed-bin artifacts concretely, and it includes shuffled surrogate controls throughout. The main risk is that the central 'narrow critical window' claim rests on a hand-picked binning target and on curves shown without uncertainty quantification, so the claimed robustness is not yet established.","major_comments":[{"comment":"The adaptive binning rule is anchored to a target active-bin density of \\rho_bin \\approx 0.15, but this target is set by hand and no sensitivity analysis over f or \\rho_bin is reported. Since the fixed-bin artifacts are themselves driven by occupancy extremes, the rule effectively selects an intermediate occupancy, and without a sweep over that intermediate value one cannot exclude that the sharp kurtosis peak at criticality is a property of the chosen operating point rather than of PRG itself. A demonstration that the peak location and narrowness survive over a range of f and target densities is load-bearing for the paper's central claim.","section":"Section III B, Eq. (9), Fig. 4"},{"comment":"The abstract and Discussion state that genuine scale-invariant behavior emerges only within a narrow range around the known critical point, but the adaptive-binning parameter sweeps are explicitly limited to within ten percent of the critical values. No adaptive-binning data are shown for control-parameter distances larger than 10%, so the 'only' claim is not supported by the measurements as presented; the authors should either extend the sweeps or reword the claim to match the range actually explored.","section":"Section III B and Discussion"},{"comment":"The kurtosis and exponent curves are presented without error bars or replicate statistics, and the manuscript does not state how many independent simulations or trials were used to produce the PRG estimators. Kurtosis estimates from binned binary data with 256 subsampled neurons can have sizable finite-sample fluctuations, so the statements that the peak is 'sharp' and 'centered precisely at criticality' and that surrogate data remain 'consistently close' to the Gaussian baseline are not quantitatively established without uncertainty quantification.","section":"Fig. 4 and Section II D 1"}],"minor_comments":[{"comment":"The normalization factor Z_i(N_cutoff) is introduced but its explicit form is not given; please provide it so the reader can verify that var(\\psi)=1 is enforced.","section":"Eq. (4)"},{"comment":"The definition of the step function is unclear as written ('\\Theta(x>1)=0 (null otherwise)'); please define \\Theta with the standard convention or with an explicit piecewise expression.","section":"Eq. (8)"},{"comment":"The simulation section specifies 10^4 neurons and trials of 5\\times 10^3 time steps but does not state the number of trials used; please report this number, as it is needed to assess the statistical reliability of the kurtosis and exponent estimates.","section":"Section II D 1"},{"comment":"The Discussion claims that the results remain unaffected by heavy subsampling, but no comparison across different subsampled neuron counts is shown; please support this statement or qualify it.","section":"Discussion"},{"comment":"The text does not describe the parameter values, axis ranges, or line styles in panels C and D in enough detail for the reader to reproduce the 'nearly constant active bin density' claim; please clarify the figure contents.","section":"Fig. 3"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable contribution to PRG methodology, and the core idea is not circular: the critical points come from external model definitions. However, the central claim currently depends on an unsupported choice of the target active-bin density and on curves without error bars. I recommend major revision with the expectation that the authors can provide the requested sensitivity sweeps and statistical details; if those are supplied, the paper could be publishable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take on the Nascimento et al. preprint. The key thing to know: it demonstrates convincingly that fixed time bins can create false PRG criticality signatures in neuronal models, and it offers a data-driven fix based on mean ISI. The adaptive binning recovers the known critical point in two models with known MF-DP transitions. That is a useful methodological contribution, and the cautionary examples in Fig. 2 are well constructed.\n\nWhat is actually new: this is the first systematic sweep of a PRG control parameter through a known critical point in spiking neuronal models, and the adaptive binning rule (Δt = f〈ISI〉) is new for PRG, though borrowed from avalanche analysis. The use of two models—a minimal cellular automaton and a stochastic integrate-and-fire network with inhibition—gives the test some teeth. The surrogate controls are the right comparison.\n\nSoft spots, in rough order of importance. First, the target active-bin density ρ_bin ≈ 0.15 is set by hand, and there is no sensitivity analysis over f or the resulting ρ_bin. The central claim—that the kurtosis peak sits precisely at criticality—depends on this binning rule. It is plausible that the peak survives for a range of f values, but the paper does not show that. A referee should ask for this. Second, the parameter sweep is limited to within 10% of criticality. The abstract and discussion say the scaling emerges 'only within a narrow range around the known critical point,' but the data only cover 10% on either side. To support 'narrow,' they need to show kurtosis returns to baseline farther away. Third, there are no error bars on the kurtosis curves, and no code or data are shared. These are minor but would strengthen the paper.\n\nI don't think the stress-test concern about circularity is damning. The adaptive binning uses the data's mean ISI, but the target density is not tuned to force the peak at the known critical point; the known critical points come from the model definitions. The hand-tuned ρ_bin is a genuine gap in robustness evidence, not a fatal flaw in the argument.\n\nWho gets value: anyone applying PRG to neural or population data, and anyone interpreting PRG kurtosis peaks as critical signatures. The paper gives a practical preprocessing rule and a warning against fixed bins.\n\nRecommendation: send it to peer review. It deserves a serious referee. Ask the authors for an f/ρ_bin sweep and a wider parameter range before acceptance; those are easy experiments for them to run.","headline":"Useful PRG methods paper with a convincing fixed-bin warning and an adaptive binning fix; missing sensitivity analysis on the binning rule before the narrow-criticality claim is fully supported.","tokens_in":9939,"tokens_out":4102,"would_cite":true,"duration_ms":39316,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"When time bins are set by the network's own average interspike interval, the phenomenological renormalization group detects scale-invariant behavior only in a narrow window around the known critical point of two neuronal models.","keywords":["phenomenological renormalization group","critical brain hypothesis","directed percolation","mean-field universality class","kurtosis","time binning","neuronal avalanches","scale invariance"],"falsifier":"Repeat the two parameter sweeps while varying f in Eq. (9), such as f ∈ {0.25, 0.5, 1, 2}, or varying the target active-bin density around 0.15, and locate the kurtosis maximum in each sweep; if the maximum shifts appreciably away from σ=1 or g=1.5, or if a broad plateau appears for some f, the claim that adaptive binning reveals a narrow genuine critical window would be falsified. A second check is to apply the same protocol to a system that is provably subcritical with slow oscillations: a persistent high kurtosis peak there would signal a binning artifact rather than criticality.","tokens_in":9014,"feed_emoji":"🧠","tokens_out":6442,"duration_ms":60118,"temperature":0.7,"pith_summary":"This paper asks how close to a phase transition a spiking network must be before the phenomenological renormalization group (PRG), a model-free coarse-graining method, reports genuine scale invariance. Simulating two neuronal models whose critical points are known exactly, the authors sweep the control parameter across the absorbing-to-active transition and apply PRG in momentum space. They find that fixed time bins produce spurious non-Gaussian signatures in both the sparse subcritical and saturated supercritical regimes. They introduce a data-driven binning rule, Δt proportional to the mean interspike interval, that keeps the active-bin density nearly constant; under this rule the kurtosis of the coarse-grained activity peaks sharply at the known critical point and scale invariance appears only within a narrow window around it. If this holds, PRG scaling signatures in experimental data can be read as indicators of near-critical dynamics, provided preprocessing follows the system's own timescale.","feed_headline":"Kurtosis peaks exactly at criticality once bins adapt","feed_subtitle":"Adaptive binning removes spurious scaling signatures that fixed time bins produce in sub- and supercritical phases.","key_machinery":"The load-bearing method is the momentum-space PRG: compute the covariance matrix of binarized spiking activity, project the data onto the top N_cutoff eigenmodes, and measure the kurtosis κ = ⟨$ψ^{4}$⟩/⟨$ψ^{2}$⟩^2 of the normalized coarse-grained variable as the cut-off is reduced. The supporting mechanism is the adaptive binning rule Δt = f⟨ISI⟩, which fixes the average fraction of occupied bins near 0.15 across all dynamical phases and prevents sparse- or saturation-induced distortions from masquerading as scale invariance. A secondary observable is the real-space exponent α from the intracluster mean variance M_2 ∝ C_size^α; it also distinguishes critical from trivial dynamics but with a broader peak.","core_discovery":"The central claim is that PRG detects genuine scale invariance in neuronal models only in a narrow vicinity of the critical point, and that a sharp kurtosis peak centered precisely on the critical value is the reliable signature. The authors show this for two mean-field directed percolation models: an excitable cellular automaton with branching ratio σ (critical at σ_c=1) and a stochastic integrate-and-fire network with inhibition strength g (critical at g_c=1.5). Fixed time bins corrupt the measurement: small bins inflate kurtosis in the quiet subcritical phase because many zeros create spurious correlations; large bins inflate it in the active phase through saturation. With bins chosen adaptively as a fixed fraction of the mean interspike interval, the active-bin density is nearly constant, and the kurtosis rises only near criticality, staying close to the Gaussian baseline elsewhere; shuffled surrogate data remain trivial throughout. The real-space exponent α also peaks near criticality but more broadly, making kurtosis the sharper diagnostic.","pith_inferences":["If the kurtosis peak remains narrow under a full sweep of f and of the target active-bin density, the method could be used as a parameter-free localizer of unknown critical points in neural data, not just a confirmatory tool.","Because both models belong to the mean-field directed percolation universality class, testing a model with finite-dimensional critical exponents would reveal whether the narrow critical window is a property of the PRG method or of this universality class.","The hand-selected target density near 0.15 could be replaced by an automatic rule that maximizes the kurtosis contrast between real and surrogate data; the paper does not investigate such an optimization.","The adaptive-binning rule could be combined with other criticality diagnostics, such as avalanche shape collapse, to cross-validate criticality identification in a single dataset."],"forward_implications":["In the two models studied, a sharp kurtosis peak centered at the known critical point is a reliable PRG signature, while shuffled surrogate data stays near the Gaussian baseline throughout.","Fixed time bins can produce misleading PRG signatures in both the subcritical and supercritical phases, so PRG studies should avoid a single bin size when activity rates vary.","Adaptive binning based on the mean interspike interval keeps the active-bin density roughly constant and makes PRG results consistent even with heavy subsampling.","The real-space exponent α is a less precise criticality diagnostic than kurtosis; its nontrivial region extends further into the subcritical phase in the inhibitory network."],"supporting_citations":[{"why":"Defines the momentum-space PRG coarse-graining via covariance eigenmodes that the paper applies.","marker":"[43]"},{"why":"Introduces the real-space PRG procedure and the scale-invariant observables used here.","marker":"[44]"},{"why":"Originates the mean-interspike-interval binning rule adapted in Eq. (9) and the avalanche criticality context.","marker":"[2]"},{"why":"Supplies the data-driven time-binning strategy, choosing bins proportional to the mean interspike interval, that the paper adopts for PRG.","marker":"[53]"},{"why":"Further develops adaptive binning for avalanche analysis and justifies keeping active-bin density controlled.","marker":"[54]"},{"why":"Defines the excitable cellular automaton and its mean-field directed percolation critical point at σ_c=1.","marker":"[12]"},{"why":"Defines the stochastic integrate-and-fire network with inhibition and its critical point at g_c=1.5.","marker":"[56]"},{"why":"Provides the experimental PRG kurtosis analysis on cortical spiking data that motivates the 'distance to triviality' interpretation.","marker":"[48]"}],"fun_headline_variants":["Adaptive binning sharpens kurtosis at criticality","Criticality signature sharpened by adaptive bins","Kurtosis peak pinpoints critical point","Spurious scaling erased with adaptive binning","PRG detects true scale invariance near criticality"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that choosing Δt as a fixed fraction of the mean interspike interval, with the fraction set so that about 15% of bins are active, is a neutral preprocessing choice that does not itself create or hide scale invariance.","fun_headline_variants_meta":{"raw":{"variants":["Adaptive binning sharpens kurtosis at criticality","Criticality signature sharpened by adaptive bins","Kurtosis peak pinpoints critical point","Spurious scaling erased with adaptive binning","PRG detects true scale invariance near criticality"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000733,"raw_usage":{"total_tokens":3245,"prompt_tokens":875,"completion_tokens":2370,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":491,"completion_tokens_details":{"reasoning_tokens":2299}},"tokens_in":491,"tokens_out":2370,"duration_ms":15566,"temperature":1.0,"reasoning_tokens":2299,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T19:54:53.969616+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the two parameter sweeps while varying f in Eq. (9), such as f ∈ {0.25, 0.5, 1, 2}, or varying the target active-bin density around 0.15, and locate the kurtosis maximum in each sweep; if the maximum shifts appreciably away from σ=1 or g=1.5, or if a broad plateau appears for some f, the claim that adaptive binning reveals a narrow genuine critical window would be falsified. A second check is to apply the same protocol to a system that is provably subcritical with slow oscillations: a persistent high kurtosis peak there would signal a binning artifact rather than criticality.","supporting_citations":[{"cited_title":"Lotfi, A","cited_arxiv_id":null,"evidence_quote":"Defines the momentum-space PRG coarse-graining via covariance eigenmodes that the paper applies."},{"cited_title":"Lotfi, T","cited_arxiv_id":null,"evidence_quote":"Introduces the real-space PRG procedure and the scale-invariant observables used here."},{"cited_title":"This process involves successively combining the most correlated pair of neurons until no neuron is left unpaired","cited_arxiv_id":null,"evidence_quote":"Originates the mean-interspike-interval binning rule adapted in Eq. (9) and the avalanche criticality context."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the data-driven time-binning strategy, choosing bins proportional to the mean interspike interval, that the paper adopts for PRG."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Further develops adaptive binning for avalanche analysis and justifies keeping active-bin density controlled."},{"cited_title":"Plenz and E","cited_arxiv_id":null,"evidence_quote":"Defines the excitable cellular automaton and its mean-field directed percolation critical point at σ_c=1."},{"cited_title":"Interdependent scaling exponents in the human brain","cited_arxiv_id":"2411.09098","evidence_quote":"Defines the stochastic integrate-and-fire network with inhibition and its critical point at g_c=1.5."},{"cited_title":"Bradde and W","cited_arxiv_id":null,"evidence_quote":"Provides the experimental PRG kurtosis analysis on cortical spiking data that motivates the 'distance to triviality' interpretation."}],"review_version":1}