Understanding Federated Learning from IID to Non-IID dataset: An Experimental Study

Chunming Rong; Ferhat Ozgur Catak; Jungwon Seo

REVIEW 3 major objections 4 minor 1 cited by

Understanding Federated Learning from IID to Non-IID dataset: An Experimental Study

T0 review · 3 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read This paper argues that inconsistent client loss landscapes are the primary cause of federated learning performance degradation under non-IID data, and that existing remedies either adjust parameter update paths or modify the loss…

desk verdict A useful organizing taxonomy for non-IID FL, but the paper's central causal claim about loss-landscape inconsistency is not supported by its own evidence. read the letter →

arxiv 2502.00182 v3 pith:X6M3IMN5 submitted 2025-01-31 cs.LG cs.AIstat.ML

Jungwon Seo , Ferhat Ozgur Catak , Chunming Rong This is my paper · ORCID

classification cs.LGcs.AIstat.ML

keywords federatedlearningnon-IIDdataclientdriftlosslandscapeFedAvggradientdescentpartialparticipationDirichletdistribution

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the performance drop in federated learning when client data are non-IID is primarily caused by inconsistencies among clients' loss landscapes—the surfaces mapping model parameters to loss—rather than by optimization noise or client drift alone. It supports this with experiments tracing training from a single centralized learner to FedAvg on CIFAR-10 under IID and non-IID partitions. Along the way it isolates a quantity, effective updates per round $u = \eta E|D|/(BK)$, that must be matched when comparing different numbers of clients, and it shows that under IID conditions client updates align while non-IID clients follow divergent loss-decrease curves. The authors then classify existing remedies: adjusting the path parameters take through parameter space, or modifying the loss landscapes themselves so clients' local optima overlap. If the claim is right, future non-IID methods should be evaluated by how well they align client loss landscapes, not just by aggregate accuracy.

What carries the argument

The load-bearing mechanism is the comparison between two views of federated optimization. The first is an identity for the amount of effective parameter updates per communication round, $u = \eta E|D|/(BK)$, where $\eta$ is the learning rate, $E$ the number of local epochs, $B$ the batch size, $|D|$ the total dataset size, and $K$ the number of clients; the authors use it to keep comparisons fair when the number of clients changes. The second is the loss-landscape interpretation: since each client minimizes its own loss on its own data, divergence in training is read as evidence that the clients' loss landscapes differ. The quantitative proxy for landscape inconsistency is the layer-wise cosine similarity between pairs of client updates, which is systematically lower under non-IID partitioning. These two pieces organize the paper's taxonomy: methods either adjust the update path (e.g., control variates, server-side optimizers) or modify the loss landscape (e.g., regularization, contrastive terms).

What would settle it

A concrete test: for a fixed Dirichlet split with $\alpha = 0.1$, project each client's loss surface near its own local optimum onto a shared two-dimensional subspace and measure whether the basins overlap. If the basins overlap even while pairwise update cosine similarity is low, the claimed causal role of landscape inconsistency is not supported; if they are disjoint, it is. A companion check would add matched pure gradient noise to an IID run and see whether accuracy degrades as much as under non-IID, separating optimization noise from landscape structure.

Watch

Extended reading notes

Core claim

The central claim is that inconsistencies in client loss landscapes primarily cause performance degradation in non-IID scenarios. In the paper's account, FedAvg is structured gradient descent: each client's update is a gradient-like step over its own dataset, so each client effectively optimizes its own loss landscape. When client data are IID, these landscapes are similar, local update directions have high cosine similarity, and aggregation behaves like centralized training. When data are non-IID, client losses decrease at different rates and update directions become less aligned, so the averaged model lands in a poor region relative to the global objective. The paper does not claim to visualize FL loss landscapes directly; the evidence is indirect, through per-client training loss trajectories and pairwise cosine similarity of updates across layers.

Load-bearing premise

The claim collapses if divergence in clients' training losses and lower cosine similarity between their updates are not reliable proxies for inconsistency among the underlying loss landscapes, or if that inconsistency is an accompaniment of non-IID data rather than the primary cause of the performance gap.

Editorial extensions

If this is right

Under IID conditions, reducing client participation from 10 to 1 barely changes final accuracy, so a single client's update remains valid for others; under non-IID conditions, participation level strongly affects outcome.
Matching the effective update amount $u = \eta E|D|/(BK)$ across client counts makes performance comparable from centralized to federated settings; unequal effective updates explain why imbalanced weighted aggregation converges faster under IID data.
Larger learning rates and smaller batch sizes improve final non-IID accuracy more than in the IID setting, which the paper attributes to update-path adjustment that tends toward flatter minima.
The two-strategy taxonomy implies that any non-IID remedy can be classified as adjusting update paths, modifying client loss landscapes, or both, and that hybrid methods such as FedDyn combine the two strategies.
Because lower $\alpha$ in the Dirichlet partition makes clients' loss landscapes more distinct, performance degrades monotonically as $\alpha$ decreases, from about 69% to 55% accuracy in the paper's CIFAR-10 experiments.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A consequence the paper leaves implicit: if loss-landscape overlap is the causal variable, non-IID performance should track a measurable overlap among per-client loss basins (for example, Hessian similarity or low-dimensional basin overlap) more closely than it tracks raw gradient variance across Dirichlet $\alpha$ values.
A testable extension: the two-strategy taxonomy predicts that pure update-path methods such as control-variate corrections will plateau when client loss surfaces remain disjoint, and that combining them with landscape-reshaping regularization should outperform either alone on strongly skewed partitions.
A practical calibration consequence of the $u$ identity: FL comparisons across client counts should hold the ratio of effective updates per round fixed, otherwise hyperparameter effects will be confused with non-IID effects; this follows from the paper's Eq. (3) but is not drawn out there.
Since the experiments deliberately exclude weight decay, data augmentation, momentum, and adaptive optimizers, the landscape-consistency conclusion may shift under modern training recipes; direct low-dimensional landscape visualization would test whether the flatter-minima interpretation generalizes beyond plain SGD.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The real contribution here is the two-strategy taxonomy: methods that adjust the update path versus methods that modify the client loss landscape. That framing is genuinely useful for structuring the literature and for newcomers to FL. The paper is also clearly written, and the progression from gradient descent to FedAvg is a sensible pedagogical route. The IID experiments are systematic, and the "effective updates per round" control (Eq. 3) is a reasonable way to compare across client counts.

What the paper does not do is establish its headline claim. Section 5 says inconsistencies in client loss landscapes "primarily cause" non-IID degradation, but the evidence is Fig. 12 (client training losses diverge) and Fig. 13 (lower cosine similarity of updates). Both are measured after local multi-epoch training, so they conflate the static landscape property with the dynamics of the update rule. Under non-IID data, clients doing several local epochs will show divergent losses and updates even if the landscape inconsistency is mild. The authors themselves acknowledge they cannot visualize the FL loss landscape, so the causal step rests on proxies that are basically the phenomena to be explained. They also never rule out gradient variance from partial participation or local overfitting as primary drivers. The stress-test note is right: this is a correlational claim, plausible but not proven.

That said, the paper is honest about its limitations, and the taxonomy does not depend on the strong causal claim. You can accept the organizing frame without accepting "primarily cause." The classification of existing methods is coarse but not misleading; SCAFFOLD and FedOpt do adjust update paths, and regularizers like FedDyn do modify the loss landscape (with a hybrid element, as noted).

Minor soft spots: no code or data, no error bars in most figures, and the imbalance model (SGM) is described only in a caption. The Dirichlet experiments average three runs, which is fine, but the single-run figures elsewhere are harder to interpret.

Who is this for? FL researchers wanting a quick conceptual map, or anyone writing a related-methods section. It is not a breakthrough result, but it is a fair experimental study with a sensible framing. I would send it to peer review for a workshop or a mid-tier conference, with a request to temper the causal language and either add code/data or at least detail the seed and imbalance protocol.

Recommendation: conditionally accept after revision. The taxonomy is worth publishing; the causal claim should be softened or properly tested with controls that separate landscape inconsistency from update drift.

Referee Report

3 major / 4 minor

Summary. This manuscript presents an experimental study of FedAvg across centralized, IID, and non-IID settings, systematically varying the number of clients K, local epochs E, batch size B, learning rate η, partial participation, and data imbalance. Its central claim is that inconsistencies in client loss landscapes primarily cause performance degradation in non-IID scenarios, and it proposes that existing non-IID FL methods fall into two strategies: adjusting parameter update paths or modifying client loss landscapes. The supporting evidence for the central claim consists of two proxy measurements: per-client training-loss traces (Fig. 12) and pairwise cosine similarity of local updates (Fig. 13), with the authors explicitly noting in Section 5 that direct visualization of the FL loss landscape is difficult.

Significance. If the causal claim were established, the paper would usefully reframe non-IID FL as a loss-landscape-alignment problem and provide an intuitive organizing principle for method design. The experimental sweep is systematic and internally consistent, and the effective-update control u = ηE|D|/(BK) in Eq. (3) is a thoughtful device for fair comparison across K. The proposed taxonomy, while post-hoc, is clear enough to be helpful to practitioners and newcomers. The manuscript does not provide code, proofs, or a quantitative landscape metric, so its value is as an empirical/interpretive study rather than a definitive causal analysis.

major comments (3)

[Section 5, Figs. 12-13] The paper's load-bearing claim that "inconsistencies in client loss landscapes primarily cause performance degradation" is supported only by proxy measurements taken after E local training epochs (Algorithm 4, lines 6-9). Divergent per-client loss traces and lower pairwise cosine similarity of local updates conflate the static loss-landscape inconsistency with the multi-step dynamics of local training: under non-IID data, clients performing several local updates on different datasets will produce divergent losses and updates even if the underlying landscape inconsistency is mild. The authors themselves note that direct visualization is difficult (Section 5), and the two additional experiments do not isolate the landscape property. I recommend adding a control experiment that measures cosine similarity of one-step gradients computed at the same global parameter before any local multi-step training, and comparing it with the post-local-update similarity. Without such a control, the "primarily cause" wording should be weakened to a correlational claim such as "is associated with" or "is consistent with."
[Section 4.3, Fig. 9] The partial-participation result in the non-IID setting is attributed to the statement that "updates from different clients are not valid for others," but partial participation also increases gradient variance due to client sampling. Under non-IID conditions, gradients are more diverse, so sampling fewer clients naturally increases the variance of the aggregated update even if the loss landscapes are not inconsistent in any deeper sense. To support the landscape-inconsistency interpretation, the authors should include a control that separates sampling variance from update misalignment, for example by comparing PP=1 with full participation while holding the total number of contributing updates per round approximately fixed, or by computing the expected gradient variance under a null model of client sampling. As written, the PP experiments do not rule out gradient variance as the primary driver of the observed degradation.
[Section 5, taxonomy paragraph] The proposed taxonomy of existing methods into "adjusting parameter update paths" and "modifying client loss landscapes" is not operationalized. No explicit criterion is given for deciding which category a method belongs to, so the classifications of SCAFFOLD, FedOpt, FedDyn, and others are subjective interpretations rather than testable claims. For example, a proximal term in the client objective is classified as landscape modification, while a server-side optimizer is classified as update-path adjustment, but the boundary is not formally defined. I suggest stating a precise criterion based on whether the method changes the objective function minimized by each client or changes only the aggregation/optimization trajectory; this would make the taxonomy reproducible and falsifiable.

minor comments (4)

[References] References [1] and [5] appear to be the same paper (Acar et al., "Federated learning based on dynamic regularization") listed under different author spellings; this duplicate should be consolidated.
[Section 2, header] The section title "From Gradient Descent to FedA vg" contains a rendering artifact; it should read "FedAvg."
[Section 3.2, Eq. (3)] The notation in Eq. (3) is not fully introduced: |D| is the total dataset size, but the text should explicitly state that each client holds |D|/K samples and that u is the expected number of effective parameter updates per round; this will help readers understand why the B, E, and η adjustments in Fig. 3 are meant to hold u fixed.
[Section 4.3, first paragraph] The shaded regions in Fig. 9 are said to represent the min-max range across three independent runs, but the caption and text do not state whether the same three runs are used for all hyperparameter settings; clarifying this would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the paper's central claim is an experimental interpretation, not a derivation from fitted inputs; it contains no self-citations and no equation reduces to its own inputs.

full rationale

The paper makes no formal derivation of a prediction from fitted inputs. Its central claim—that inconsistencies in client loss landscapes primarily cause non-IID performance degradation—is presented as an interpretation of controlled experiments comparing IID and non-IID conditions, not as a quantity derived from a fitted parameter. Equation (3) defines an effective-update control variable u = η·E·|D|/(B·K), used to match update budgets across different client counts; it is a definition employed to set experimental hyperparameters, and the experiments' outcomes are not fed back into Equation (3) to produce a prediction. Figures 12 and 13 report observed client training-loss traces and cosine similarities of local updates; these are measurements offered as supporting evidence, and the paper explicitly acknowledges the limitation that direct FL loss-landscape visualization is not performed (Section 5). The two-strategy taxonomy (adjusting update paths vs. modifying client loss landscapes) is a classification of existing methods, not a derived result that assumes what it concludes; no equation in the paper reduces to another by construction, and no argument relies on a self-citation or an imported uniqueness theorem. The reference list contains no work by the present authors. The main weakness of the paper is evidential—the proxy measures for landscape inconsistency may be confounded by multi-step local-update dynamics—but that is a validity limitation, not circular reasoning, and per the review rules it does not raise the circularity score.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a standard loss-landscape view, an assumed transferability of CIFAR-10 results, an ad hoc effective-update quantity used for fair comparisons, and an unproven proxy link between observable divergence metrics and invisible loss landscapes. No free parameters are fitted to data. No new entities are introduced.

assumptions (4)

standard math Gradient descent and its variants descend the empirical loss function, and the loss landscape geometry described in Li et al. (2018) applies to the trained neural networks.
Section 5 interprets client drift geometrically using the loss landscape concept, citing [11].
domain assumption Results on CIFAR-10 with the two-layer CNN from McMahan et al. (2017) are representative enough to support general conclusions about FL behavior.
All experiments use one dataset and one architecture, as stated in Section 3.1.
ad hoc to paper The quantity u = η E |D| / (B K) controls the effective update amount and is the correct variable to hold fixed when K varies.
Section 3.2 introduces Eq. (3) to scale B, E, and η across client counts without proof.
ad hoc to paper Divergent client training losses and lower cosine similarity of client updates are valid proxies for inconsistency of client loss landscapes.
Section 5 uses Fig. 12 and Fig. 13 as evidence for landscape inconsistency, an unproven inferential step.

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Cite this review

Pith. "Pith review of Understanding Federated Learning from IID to Non-IID dataset: An Experimental Study." pith.science (2026). https://pith.science/paper/X6M3IMN5

@misc{pith2026250200182,
  author       = {Pith},
  title        = {Pith review of: Understanding Federated Learning from IID to Non-IID dataset: An Experimental Study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X6M3IMN5}},
  note         = {Machine review of arXiv:2502.00182}
}

read the original abstract

As privacy concerns and data regulations grow, federated learning (FL) has emerged as a promising approach for training machine learning models across decentralized data sources without sharing raw data. However, a significant challenge in FL is that client data are often non-IID (non-independent and identically distributed), leading to reduced performance compared to centralized learning. While many methods have been proposed to address this issue, their underlying mechanisms are often viewed from different perspectives. Through a comprehensive investigation from gradient descent to FL, and from IID to non-IID data settings, we find that inconsistencies in client loss landscapes primarily cause performance degradation in non-IID scenarios. From this understanding, we observe that existing methods can be grouped into two main strategies: (i) adjusting parameter update paths and (ii) modifying client loss landscapes. These findings offer a clear perspective on addressing non-IID challenges in FL and help guide future research in the field.

Figures

Figures reproduced from arXiv: 2502.00182 by the authors.

**Figure 2.** Impact of varying K with consistent hyperparameters. In this setup, as K increases, there is a noticeable decline in performance within a fixed number of communication rounds, highlighting a common oversight. When transitioning from CL to FL with a limited dataset, the critical factor that must be consistently controlled for a fair comparison is the amount [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Impact of matched B, E, and η on performance with different K. In [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (10 more)

**Figure 4.** Figure 4: Training dynamics when K = 10. The first row shows results for varying E, the second for different B, and the third for various η. are not substantial under IID conditions, they become more pronounced in nonIID settings, which we will discuss later. 4.2 Partial Partic…

**Figure 5.** Figure 5: Training Dynamics under Partial Participation with IID Condition [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: Data partitioning with IID labels across different levels of SGM [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: Performance under varying levels of data imbalance. The first row shows [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: Data partitioning with varying Dirichlet parameter [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: Performance across varying α (Top) and PP (Bottom). in IID settings, the level of PP plays a critical role in FL performance. When α is fixed at 0.1, lower levels of PP lead to significantly lower final accuracy, higher test loss, and increased fluctuations compared to…

**Figure 10.** Figure 10: Test accuracy, test loss, and training loss for [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

**Figure 11.** Figure 11: Toy example illustrating the loss landscape and update paths for two [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

**Figure 12.** Figure 12: Client training loss: Top row - IID, Bottom row - Non-IID. [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]

**Figure 13.** Figure 13: Cosine similarity of local updates from different clients for each layer [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Kuramoto-FedAvg: Using Synchronization Dynamics to Improve Federated Learning Optimization under Statistical Heterogeneity
cs.LG 2025-05 reject novelty 4.0 of 10

Kuramoto-FedAvg reweights client updates by their cosine similarity to the global update, but the paper's convergence bound is not derived and the empirical evidence is incomplete.

Reference graph

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