{"id":"46b717b1-2509-491e-a5f5-bc5a13047585","arxiv_id":"2506.08169","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A federated learning algorithm that trains local stochastic neural networks to capture both the true function and the noise in each client's data.","lead":"This paper proposes FedStNN, a federated learning method that uses stochastic neural networks as local models, so each client learns both a prediction and a measure of its data noise. It is a candidate approach for handling noisy and non-IID client data without sharing raw data with a central server.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (39) asserts that parameter-averaging local diffusion networks preserves global noise calibration, but no proof or quantitative check is given; visual 'bandwidth' evidence cannot rule out systematic bias.","rationale":"The reader identified the same weakest assumption: that the weighted average of local diffusion networks, Eq. (39), yields a global diffusion network that faithfully represents total observation noise. My stress-test agrees and sharpens the concern by noting that parameter averaging of a nonlinear diffusion network is not variance averaging, so the assertion requires either a proof or a direct quantitative check. The concern is load-bearing because the paper's novelty over plain FedAvg rests on the noise-quantification claim. However, this does not force a change of verdict: the mathematics of the SNN/SMP framework is coherent, the experiments are reproducible in principle, and a concrete quantitative validation could resolve the issue. Therefore the reader's CONDITIONAL verdict remains appropriate. I would not escalate to REJECT or lower to ACCEPT without the proposed test. The paper does include some independent support: the SDE/BSDE machinery is standard and previous work on SNN convergence is cited, but there is no formal verification and no released code, which makes the missing quantitative noise check the decisive gap.","tokens_in":18701,"tokens_out":3648,"duration_ms":51122,"concrete_test":"Using the final global model from the 1D experiment in Section 5.1, fix 50 evenly spaced inputs x_i in [0, 2π]. For each x_i, run 1,000 independent forward simulations of the trained global SNN (sampling new Brownian paths per Eq. (12)) and compute the empirical variance of the predicted outputs at that input. Then compare the median of these variances to the true observation-noise variance sigma^2 = 0.01, and also regress the squared diffusion-network output h·g_global(x_i)^2 against the empirical variances. If the median ratio of empirical variance to sigma^2 deviates from 1 by more than 20%, or if the R^2 of the regression is poor, then Eq. (39) does not preserve noise calibration and the paper's headline claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central added claim is that the global FedStNN model quantifies latent noise: Section 4 states that the global model from Eq. (39) 'can effectively measure noise across the entire training dataset as well.' This claim is load-bearing because it distinguishes FedStNN from deterministic FedAvg, yet it is supported only by qualitative statements such as 'the predicted plot almost has the same bandwidth as the observation data' (Section 5.1). No theorem connects the aggregation rule in Eq. (39) to a calibrated global diffusion term. In the SNN forward model, Eq. (12), the per-step conditional variance of X is h g(u)^2; the diffusion network g(u) is a nonlinear function of its parameters. The global diffusion network is obtained by weighted averaging of the parameters u_beta, which does not generally equal a weighted average of the local noise amplitudes g_k(u), nor does it account for the fact that in the non-IID experiments each local g_k is trained mainly on a biased subset of the domain and may be poorly constrained elsewhere. Even if every local model were perfectly calibrated on its own local noise variance, parameter averaging of nonlinear diffusion networks is not variance averaging. The experiments never compare the learned global diffusion variance (or the empirical variance of repeated global-model predictions) with the known sigma^2 = 0.01 used to generate the data, so the central claim remains empirically unverified. This is a genuine soft spot, not a matter of disagreeing with a consensus: it is a missing validation of the exact quantity the method claims to deliver.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Federated Stochastic Neural Networks (FedStNN), in which each client trains a stochastic neural network that solves a data-driven SDE via the stochastic maximum principle, and the server aggregates the drift and diffusion network parameters separately using Eq. (39). The authors claim that the resulting global model captures the true underlying function and quantifies observation noise across the entire training dataset, even when local client datasets are biased and non-IID. The numerical sections demonstrate the method on 1D sine data with Gaussian noise, a 2D piecewise function, and a 2D image-reconstruction task, but the reported evidence is largely qualitative.","tokens_in":18945,"tokens_out":5063,"duration_ms":62985,"significance":"If the central claim were established, FedStNN would provide a useful way to obtain generative, uncertainty-aware global models in federated learning while retaining deterministic parameters that are easy to aggregate. The paper builds on a previously developed SNN framework and makes a reasonable architectural proposal: separating drift and diffusion networks and averaging them componentwise. The main weakness is that the load-bearing claim, namely that the aggregated diffusion network faithfully quantifies the global observation noise, is neither proven nor quantitatively validated. The strengths of the paper are its clear algorithmic presentation and reproducible experimental setup, but these do not by themselves justify the noise-quantification claim.","major_comments":[{"comment":"The paper's central added claim, that the global model u_{i+1} formed by Eq. (39) 'can effectively measure noise across the entire training dataset as well', is asserted rather than derived. In the forward model Eq. (12), the per-step conditional variance of X_{n+1} is h g(u_n)^2, and g is a nonlinear function of the diffusion-network parameters u_beta. Weighted averaging of u_beta across clients does not generally equal a weighted average of the local noise amplitudes g_k(u), nor does it account for the fact that each local diffusion network in the non-IID experiments is trained mostly on a biased subset of the domain and may be poorly constrained elsewhere. A theorem or a quantitative calibration check is needed to justify that parameter averaging preserves noise calibration.","section":"Section 4, Eq. (39)"},{"comment":"The experiments never compare the noise produced by the global model with the known sigma^2 = 0.01 used to generate the data. The statement that 'the predicted plot almost has the same bandwidth as the observation data' is qualitative and cannot rule out, for example, a global diffusion term that is systematically too wide or too narrow by a constant factor. Please report the empirical variance of repeated global-model predictions, the learned global diffusion coefficient as a function of x, or a coverage probability of prediction intervals against the true sigma^2 = 0.01.","section":"Section 5.1, Figs. 5-6"},{"comment":"None of the three experiments includes baselines, repeated trials, or error bars. There is no comparison with FedAvg, with a non-federated SNN trained on pooled data, or with a Bayesian treatment; the only quantitative number reported, MSE approximately 2.13 in Section 5.2, has no baseline to give it meaning. In addition, the IID case described in Section 5.1 is never reported, so the reader cannot assess how the non-IID results differ. Without such comparisons, the claimed advantage of FedStNN over deterministic federated learning is not demonstrated.","section":"Section 5"},{"comment":"The image experiment relies on the known number of white pixels Xi: the Psi function maps the largest Xi numerical SNN outputs to 1 and all others to 0. This prior information substantially aids the reconstruction, and the section reports no quantitative accuracy measure such as pixel error, nor any noise component. As presented, this experiment does not bear on the noise-quantification claim, and the role of the known Xi should be clarified and the reconstruction accuracy should be reported numerically.","section":"Section 5.3, Eq. (41)"}],"minor_comments":[{"comment":"The displayed identity in Eq. (4) states that the gradient of the global loss is the sum of the local gradients, but from Eq. (2) the correct expression should include the weights n_k/n, namely nabla f(u_t) = sum_{k=1}^K (n_k/n) nabla F_k(u_t).","section":"Section 2.1, Eq. (4)"},{"comment":"The aggregation step in Algorithm 4 says to update the global model 'using equation 6', but the method described in Section 4 aggregates the drift and diffusion networks separately via Eq. (39); the algorithm should reference Eq. (39) and specify that the average is applied componentwise to u_alpha and u_beta.","section":"Algorithm 4"},{"comment":"The phrases 'with 110 local training data' and 'with 60 local training data' are unclear; presumably they mean 100+10 and 50+10 points from the focus group and the other groups, but the sample sizes should be stated explicitly.","section":"Section 5.1"},{"comment":"The reference to Chen and Chao (2020) is titled 'FedDistill', but the text in Section 2.3 describes FedBE; the citation should be aligned with the described method.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the novelty of the paper rests entirely on the claim that Eq. (39) preserves the noise-quantification property of the local SNNs. That claim needs either a proof or a direct quantitative validation against the known noise variance. The experiments as they stand are qualitative and lack baselines, so I would not publish the manuscript in its current form, but the gap appears addressable within the scope of the paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: FedStNN is a clean, sensible combination of an existing stochastic neural network (SNN) with FedAvg, and the only genuinely new move is aggregating the drift and diffusion sub-networks separately. The load-bearing claim, that the averaged diffusion network quantifies the global observation noise, is not demonstrated. It is asserted in Section 4 and supported only by visual \"bandwidth\" matches. So this is a proposal with a plausible mechanism, not an established result.\n\nWhat it does well: the paper is honest about its building blocks. The local SNN training, sample-wise SMP approach, and convergence results come from prior work, and the authors say so clearly. The non-IID experimental design is thoroughly described, and the visual results in 1D and 2D do show the global model capturing the drift and producing scatter that roughly falls within a two-standard-deviation band. The motivation for avoiding Bayesian neural networks in FL—because aggregating random variables is messy—is well argued. The separate aggregation of drift and diffusion parameters is not in the cited literature, so the combination is new.\n\nThe soft spots are real and are exactly where the paper's central promise lives. Eq. (39) averages the parameters of nonlinear diffusion networks. That is not the same as averaging the noise amplitudes, and no theorem connects that aggregation rule to a calibrated global diffusion term. The experiments never compare the learned diffusion variance (or the empirical variance of repeated global-model predictions) to the known sigma^2 = 0.01 used to generate the data. The \"bandwidth\" evidence is suggestive but cannot rule out systematic bias. There are also no baselines—no deterministic FedAvg or BNN comparison—and no error bars or repeated trials. The image experiment uses the true white-pixel count in its classification function, which is an oracle; the paper doesn't flag it as a limitation. These are fixable, but they are precisely the validation needed for the paper's main claim.\n\nThe citation pattern is fine. The authors rely heavily on their own earlier work for the SNN machinery, which is appropriate since those are the relevant sources. The broader FL literature is covered.\n\nWho should read this: researchers working on uncertainty quantification in federated learning. The value is the combination and the clear framing of the aggregation problem; the evidence is too thin to take the noise-quantification claim as established.\n\nRecommendation: send it to peer review. The idea is new and coherent enough to warrant referee time, but the authors should be pushed to provide a quantitative noise-calibration experiment, baselines, and code before acceptance. This would likely be a major revision.","headline":"A clean, sensible combination of SNNs with FedAvg, but the central claim that parameter-averaged diffusion networks preserve noise calibration is asserted, not proved.","tokens_in":19557,"tokens_out":2265,"would_cite":false,"duration_ms":29590,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Federated learning with stochastic neural networks can recover both the true signal and the latent noise, even from biased clients.","keywords":["federated learning","stochastic neural network","uncertainty quantification","non-IID data","stochastic maximum principle","backward SDE","drift and diffusion networks","FedStNN"],"falsifier":"Run the 1D sine experiment with a known noise level, record the variance output by the global diffusion network at many inputs, and compare it with the known $\\sigma^2$ used to generate the data; a systematic mismatch, or a variance that changes with which clients are selected, would refute the paper's claim that the aggregated model quantifies latent noise.","tokens_in":18465,"feed_emoji":"🧠","tokens_out":8283,"duration_ms":94419,"temperature":0.7,"pith_summary":"Federated learning usually averages deterministic models, so the final model can make predictions but cannot say how uncertain they are. This paper proposes FedStNN, in which every client trains a stochastic neural network, a model built as a stochastic differential equation with one network for the drift, the signal, and one for the diffusion, the noise. The server aggregates the two kinds of networks separately, and the paper argues the averaged global model still behaves as one stochastic model whose drift tracks the true function and whose diffusion measures the latent noise across the whole dataset. The experiments show this working when clients see only biased slices of the input domain, which is the hard non-IID case for federated learning.","feed_headline":"Stochastic federated nets recover signal plus noise","feed_subtitle":"Clients see only biased slices of data, yet the aggregated model tracks the true curve and reports the error width.","key_machinery":"The central object is the stochastic neural network (SNN), written as a discrete SDE $X_{n+1}=X_n+hf(X_n,u_n)+\\sqrt{h}g(u_n)\\omega_n$, where the drift network $f$ learns the underlying signal and the diffusion network $g$ learns the size of the uncertainty. Training solves a stochastic optimal control problem through the stochastic maximum principle, using an adjoint backward SDE to compute gradients of the cost. FedStNN reuses standard federated weighted averaging but applies it separately to the drift parameters and the diffusion parameters, so the aggregated global model remains an SDE whose drift and diffusion have their own learned coefficients.","core_discovery":"On its own terms, the paper's central claim is that federation does not destroy the uncertainty-quantification property of stochastic neural networks. Each client trains a local SNN using a stochastic maximum principle scheme that updates a drift network $u_\\alpha$ and a diffusion network $u_\\beta$; the server then computes a weighted average of the drift networks and, separately, a weighted average of the diffusion networks (Eq. (39)). Section 4 explicitly asserts that this updated global model can effectively measure noise across the entire training dataset. In the numerical experiments the global model's predictions lie along the true regression curve while spreading with roughly the width of the added Gaussian noise, even though every client's local dataset is concentrated in one sub-domain. The discovery, if it holds, is that the SDE meaning of the two networks survives weighted averaging.","pith_inferences":["If the paper is right, the global diffusion network could serve as a privacy-preserving data-quality diagnostic: a server could flag a client with an unusually large noise network as a low-quality data source without ever seeing its data.","The method could be tested on heteroscedastic noise, where clients have different noise levels; plain weighted averaging may then need calibration weights to avoid over-sizing the global noise estimate.","The same drift-diffusion separation might extend to other federated aggregation rules, such as adaptive or normalized averaging, by treating the diffusion weights as a second model rather than part of one parameter vector."],"forward_implications":["A global FedStNN model can give a prediction and an uncertainty band at the same time, without any client sharing raw data.","Biased local datasets still contribute to a global model that covers the whole domain, because each client's local drift and diffusion weights are averaged into a model that spans the population.","Because all SNN parameters are deterministic numbers, the standard weighted-average aggregation of FedAvg applies directly; no distribution-valued aggregation of random variables is needed.","The trained global model can generate new synthetic observations whose noise spread resembles the original data, turning federated learning into a generative tool."],"supporting_citations":[{"why":"Defines the FedAvg algorithm and the weighted client-selection procedure that FedStNN adapts for stochastic neural networks.","marker":"McMahan et al. (2016)"},{"why":"Introduces the drift/diffusion stochastic neural network and the stochastic maximum principle gradient scheme that each client runs locally.","marker":"Archibald et al. (2020a)"},{"why":"Supplies the convergence analysis for the sample-wise backpropagation method used to train the local SNN, underpinning the local optimization step.","marker":"Archibald et al. (2024)"},{"why":"Documents how FedAvg performance degrades on non-IID data, the failure mode FedStNN is designed to address.","marker":"Li et al. (2019)"},{"why":"Gives FedBE, a Bayesian ensemble alternative, and highlights the difficulty of aggregating random variables that motivates the choice of deterministic SNN parameters.","marker":"Chen and Chao (2020)"}],"fun_headline_variants":["Federated SNNs learn signal and noise","Global SNN averages still track true curve","Client noise doesn't break federated uncertainty","SNN federation preserves noise quantification"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim collapses if the weighted average of the clients' noise networks distorts the noise estimate, so that the aggregated global model's spread no longer matches the true observation noise.","fun_headline_variants_meta":{"raw":{"variants":["Federated SNNs learn signal and noise","Global SNN averages still track true curve","Client noise doesn't break federated uncertainty","SNN federation preserves noise quantification"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000568,"raw_usage":{"total_tokens":2640,"prompt_tokens":847,"completion_tokens":1793,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":463,"completion_tokens_details":{"reasoning_tokens":1739}},"tokens_in":463,"tokens_out":1793,"duration_ms":15810,"temperature":1.0,"reasoning_tokens":1739,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T05:17:55.006760+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the 1D sine experiment with a known noise level, record the variance output by the global diffusion network at many inputs, and compare it with the known $\\sigma^2$ used to generate the data; a systematic mismatch, or a variance that changes with which clients are selected, would refute the paper's claim that the aggregated model quantifies latent noise.","supporting_citations":[],"review_version":1}