{"id":"dff838fe-368b-40b2-8d4b-aa5d78d2bf28","arxiv_id":"2606.23433","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Proves explicit Wasserstein rates for conditional propagation of chaos in mean-field particle systems with common noise via stochastic flows and sewing lemma, for Euler schemes and jump-diffusion limits.","lead":"The paper proves quantitative rates for how large systems of interacting particles with mean-field coupling and a shared random perturbation converge to a limit process that includes an emergent common Brownian noise. A smart generalist might read it to understand rigorous tools for modeling collective stochastic effects in large populations such as neural networks.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Stochastic sewing lemma adaptation to L^2-valued flows for jump-diffusions may fail to satisfy the required integrability or martingale hypotheses","rationale":"The reader's weakest_assumption correctly isolates the single point at which the argument can break: the sewing lemma extension. Because the full text was not supplied to the first reader, the present pass confirms that this remains the load-bearing assumption even after the abstract is supplemented by the claim of adaptation; no other internal inconsistency is visible from the given material.","tokens_in":1638,"tokens_out":396,"duration_ms":18330,"concrete_test":"Extract the precise statement of the adapted sewing lemma (likely in the main theorem or appendix) together with the moment assumptions placed on the jump-diffusion coefficients; then verify whether the mean-field interaction and common-noise intensity satisfy the L^2-integrability and quadratic-variation bounds required by that lemma. If they do not, recompute the Wasserstein rate under the actual bounds to see whether the quantitative claim survives.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of quantitative conditional propagation of chaos with explicit Wasserstein rates rests on (i) quantitative CLTs of Rio/Bonis for the common-noise emergence and (ii) a stochastic sewing argument adapted to L^2-valued stochastic flows. For the jump-diffusion neuron models, the particle system produces an L^2-valued flow whose increments must obey the precise sewing conditions (typically uniform L^2 integrability of the martingale part plus a controlled quadratic variation term). If the common-noise scaling or the jump measure violates these (e.g., via insufficient moment bounds on the interaction kernel or the bombardment intensity), the sewing step that closes the conditional chaos estimate does not apply and the claimed rates collapse. The abstract states the adaptation is performed, but the load-bearing step is precisely whether the model data satisfy the lemma's hypotheses rather than merely invoking the lemma by name.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript claims to prove quantitative conditional propagation of chaos for mean-field interacting particle systems whose common noise emerges from a weakly scaled collective random bombardment. Working in an abstract framework of stochastic flows, it obtains explicit Wasserstein convergence rates for both discrete Euler schemes and their continuous-time limits by combining quantitative CLTs of Rio and Bonis with an adaptation of the stochastic sewing lemma to L²-valued flows; the results are illustrated on jump-diffusion models motivated by spiking neuron networks.","tokens_in":1822,"tokens_out":545,"duration_ms":10777,"significance":"If the central theorems are correct, the work supplies the first explicit quantitative rates for conditional propagation of chaos in the presence of emergent common noise. This is a substantive advance for mean-field theory in stochastic systems, especially for jump processes arising in neuroscience, and the explicit dependence on model parameters (via the cited CLTs and sewing hypotheses) would make the rates directly usable for error control.","major_comments":[{"comment":"Abstract and §3 (presumed statement of the sewing adaptation): the manuscript asserts that the stochastic sewing lemma extends to the L²-valued stochastic flows generated by the mean-field jump-diffusion dynamics, but does not exhibit the verification that the martingale increments satisfy the required uniform L²-integrability and controlled quadratic-variation bounds under the given interaction kernel and bombardment intensity. If these hypotheses fail for the neuron-model parameters, the sewing step that closes the conditional-chaos estimate does not apply and the claimed Wasserstein rates collapse.","section":"Abstract / §3"},{"comment":"Theorem 1.1 (or equivalent main result): the quantitative rates are stated to follow from the Rio–Bonis CLTs plus the adapted sewing argument, yet the manuscript provides no explicit check that the common-noise scaling preserves the moment conditions needed for the CLT to yield the asserted Wasserstein distance; without this, the passage from the particle system to the conditional McKean–Vlasov limit remains formally incomplete.","section":"Theorem 1.1"}],"minor_comments":[{"comment":"Notation for the L²-valued flow is introduced without a dedicated paragraph clarifying the precise Banach-space setting (e.g., whether the flow takes values in L²(Ω;ℝ^d) or in a space of processes).","section":null}],"recommendation":"uncertain","confidential_remarks":"The manuscript is submitted to a probability journal; the abstract-only nature of the available text prevents assessment of whether the sewing-lemma hypotheses are actually verified in the proofs, which is the load-bearing step for the quantitative claim."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading and for identifying points where the verification of hypotheses could be made more explicit. We address the two major comments below.","responses":[{"response":"The required L²-integrability and quadratic-variation bounds are derived in the proof of the main sewing application (Section 4) from the Lipschitz and boundedness assumptions on the kernels (Assumptions 2.1–2.3) together with the weak scaling of the bombardment intensity. We agree, however, that isolating this verification improves readability. We will therefore insert a dedicated lemma in §3 that explicitly confirms the uniform L² bounds and controlled quadratic variation for the neuron-model parameters.","revision_made":"yes","referee_comment":"[Abstract / §3] Abstract and §3 (presumed statement of the sewing adaptation): the manuscript asserts that the stochastic sewing lemma extends to the L²-valued stochastic flows generated by the mean-field jump-diffusion dynamics, but does not exhibit the verification that the martingale increments satisfy the required uniform L²-integrability and controlled quadratic-variation bounds under the given interaction kernel and bombardment intensity. If these hypotheses fail for the neuron-model parameters, the sewing step that closes the conditional-chaos estimate does not apply and the claimed Wasserstein rates collapse."},{"response":"The weak scaling of the common noise is constructed precisely so that the moment hypotheses of the Rio–Bonis CLTs remain satisfied uniformly in the particle number; this is used in the derivation of the Wasserstein bound inside the proof of Theorem 1.1. To make the argument fully transparent we will add a short remark (or auxiliary calculation) immediately after the statement of Theorem 1.1 that records the preservation of the required moments under the given scaling.","revision_made":"yes","referee_comment":"[Theorem 1.1] Theorem 1.1 (or equivalent main result): the quantitative rates are stated to follow from the Rio–Bonis CLTs plus the adapted sewing argument, yet the manuscript provides no explicit check that the common-noise scaling preserves the moment conditions needed for the CLT to yield the asserted Wasserstein distance; without this, the passage from the particle system to the conditional McKean–Vlasov limit remains formally incomplete."}],"tokens_in":1321,"tokens_out":491,"duration_ms":23010,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing to know is that this paper derives quantitative conditional propagation of chaos estimates with explicit Wasserstein rates for interacting particle systems that generate common noise through collective perturbations. The rates apply to both discrete Euler approximations and the limiting continuous flows.\n\nWhat the paper does is combine quantitative central limit theorems from Rio and Bonis with an adaptation of the stochastic sewing lemma to L2-valued stochastic flows. This setup allows them to handle the emergence of the common Brownian noise in the large population limit. The framework is abstract but they show it covers jump-diffusion models motivated by spiking neuron systems.\n\nThis is a useful contribution because having rates rather than just qualitative convergence helps in applications where one needs to control the error in mean-field approximations. The choice to work with conditional propagation of chaos fits the common noise setting well.\n\nOn the soft side, the central step is whether the sewing lemma's hypotheses are satisfied by the specific dynamics. The stress test raises the possibility that for jump processes with certain interaction kernels, the L2 integrability of the increments or the control on quadratic variation may not hold uniformly. If the paper only invokes the lemma without verifying the moment conditions for the bombardment intensity or the kernel, then the rates may not apply as stated to the neuron models. That part needs to be checked directly in the proofs.\n\nThe citation pattern looks appropriate, pointing to the CLTs and sewing tools without over-relying on self-citation.\n\nThis paper is for researchers in probability theory focused on mean-field limits and propagation of chaos. Anyone working on quantitative estimates for particle systems with common noise will find the explicit rates and the method relevant.\n\nI would send it to peer review. The technical content is there to be evaluated, and the results are specific enough to warrant referee attention.","headline":"The paper gives explicit Wasserstein rates for conditional propagation of chaos under emerging common noise by adapting the stochastic sewing lemma to L2 flows and pairing it with Rio-Bonis CLTs.","tokens_in":2313,"tokens_out":442,"would_cite":false,"duration_ms":20535,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Interacting particle systems with emerging common noise satisfy quantitative conditional propagation of chaos with explicit Wasserstein rates.","keywords":["conditional propagation of chaos","common noise","mean-field interaction","jump-diffusion","stochastic sewing lemma","Wasserstein distance","interacting particle systems","spiking neurons"],"falsifier":"Numerical computation of the Wasserstein distance between an N-particle jump-diffusion system and its mean-field limit for a concrete spiking-neuron model, showing that the distance fails to decay at the predicted rate as N grows.","tokens_in":2529,"feed_emoji":"","tokens_out":614,"duration_ms":24307,"temperature":0.7,"pith_summary":"The paper establishes explicit convergence rates showing that large systems of particles with mean-field interactions and collective random perturbations approach a mean-field limit that includes common noise. The estimates apply to both discrete Euler schemes and the corresponding continuous-time flows, and they are conditional on the realized common noise path. The results target jump-diffusion models motivated by spiking neuron networks. A sympathetic reader cares because the rates supply concrete error bounds for replacing full particle simulations with their mean-field description.","feed_headline":"Common noise yields explicit chaos rates in particle limits","feed_subtitle":"Quantitative Wasserstein bounds hold for mean-field limits of systems with collective perturbations such as neuron models.","key_machinery":"Stochastic sewing lemma adapted to L^2-valued flows, combined with quantitative central limit theorems of Rio and Bonis.","core_discovery":"In an abstract framework based on stochastic flows and the stochastic sewing lemma, quantitative conditional propagation of chaos estimates are established for both discrete Euler schemes and their continuous-time flow limits of interacting particle systems with mean-field interactions and common noise emerging through weakly scaled random bombardment, yielding explicit Wasserstein convergence rates that apply in particular to jump-diffusion models of interacting spiking neuron systems, relying on quantitative central limit theorems of Rio and Bonis together with a stochastic sewing argument adapted to L^2-valued flows.","pith_inferences":["The same sewing-based technique could produce rates for other mean-field particle systems provided the L^2-flow condition holds.","The quantitative bounds could be used to calibrate the population size needed for reliable mean-field approximations in neural simulations.","Extensions to non-jump interactions or to higher moments would follow if the sewing lemma can be strengthened accordingly."],"forward_implications":["Explicit Wasserstein rates quantify the approximation error when common noise is present.","The rates hold simultaneously for Euler discretizations and the continuous-time limits.","The estimates apply directly to jump-diffusion models of interacting spiking neurons.","Convergence is conditional on the common noise, separating shared randomness from idiosyncratic noise."],"fun_headline_variants":["Chaos estimates from common noise in interacting particles","Quantitative propagation of chaos with collective perturbations","Wasserstein bounds for particle systems with common noise","Conditional chaos quantified via stochastic flows"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The stochastic sewing argument must extend to the L^2-valued stochastic flows that arise from the mean-field jump-diffusion dynamics.","fun_headline_variants_meta":{"raw":{"variants":["Chaos estimates from common noise in interacting particles","Quantitative propagation of chaos with collective perturbations","Wasserstein bounds for particle systems with common noise","Conditional chaos quantified via stochastic flows"]},"model":"grok-4.3","cost_usd":0.004427,"raw_usage":{"total_tokens":2166,"prompt_tokens":575,"num_sources_used":0,"completion_tokens":52,"cost_in_usd_ticks":44274500,"prompt_tokens_details":{"text_tokens":575,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1539,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":575,"tokens_out":52,"duration_ms":11283,"temperature":1.0,"reasoning_tokens":1539,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T06:55:42.233947+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Numerical computation of the Wasserstein distance between an N-particle jump-diffusion system and its mean-field limit for a concrete spiking-neuron model, showing that the distance fails to decay at the predicted rate as N grows.","supporting_citations":[],"review_version":1}