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When Is Shallow Enough? Adaptive Split Federated Learning with Client-Specific Sufficiency Estimation

Wenhao Yuan, Chenchen Lin, Wenhao Hu, Jian Chen, Jinfeng Xu, Shujie Li, Edith Cheuk Han Ngai

arXiv:2608.15639v1cs.DCcs.AIcs.LG

TL;DR

In heterogeneous SFL, a static split may not suit clients whose data and adaptation states differ, leaving the sufficiency of each client's shallow interface uncertain. FedSGA estimates that sufficiency with client-specific signals and harmonizes interfaces across split depths; it reports the best performance across datasets, partitions, and backbones.

  • Problem

    In heterogeneous SFL, it remains unclear when each client’s shallow interface preserves enough task-relevant information for server-side learning, while static split points may not fit client-specific training states.

    Source: §1 · pp. 1–2

  • Method

    FedSGA combines private prompt states with semantic alignment and temporal interface stability to estimate client-specific shallow sufficiency, then harmonizes activations from different split depths.

    Source: §1 · p. 2, §5 · p. 10

  • Results

    FedSGA consistently achieves the best performance across datasets, partitions, and backbones.

    Source: §4.2 · p. 7

  • Takeaways & Limitations

    The computational benefit comes from client-specific early offloading, not uniformly enforcing the shallowest split across clients.

    Source: §3.5 · p. 6

    Existing adaptive split strategies use resource criteria that do not assess interface sufficiency or require costly repeated evaluation across candidate depths.

    Source: §1 · p. 2

Abstract

from arXiv · show

\textit{Split Federated Learning} (SFL) enables distributed model training by splitting networks between the server and clients. However, under client heterogeneity, the conventional static split strategy may be suboptimal because clients can differ in data distributions, adaptation dynamics, and representation learning progress, making a single split point insufficient to accommodate client-specific training states. In this paper, we propose \textsc{FedSGA}, a \textbf{S}ufficiency-\textbf{G}uided \textbf{A}daptive split \textbf{Fed}erated learning framework that addresses this question through client-specific shallow sufficiency estimation. First, we introduce a client-specific adaptation channel based on private prompt tokens, which tracks local adaptation dynamics separately from the shared backbone and provides a lightweight signal for detecting whether client adaptation remains active. To further avoid repeated online probing over multiple candidate depths, we design a shallow sufficiency estimator that combines cross-client semantic alignment, temporal interface stability, and prompt-state variation to estimate whether the shallowest split is already sufficient. Finally, we introduce a split-compatible interface harmonization module that projects activations from different split depths into a shared semantic space, improving the comparability of heterogeneous client interfaces before server-side prediction. Extensive experiments on multiple heterogeneous benchmarks demonstrate the effectiveness of \textsc{FedSGA} in improving model performance compared with state-of-the-art methods while reducing unnecessary client-side computation.

1 Introduction

FedSGA addresses the limits of static split points in heterogeneous SFL by estimating client-specific shallow-interface sufficiency and harmonizing activations from different split depths. Its design tracks local adaptation, evaluates interface reliability without exhaustive depth probing, and maps heterogeneous interfaces into a shared semantic space.

Introduction

  • A shared static split can be suboptimal because heterogeneous clients follow different representation-learning trajectories and expose interfaces with differing semantic maturity and geometry.Domain skew can further produce feature-distribution and semantic-structure discrepancies that impair collaborative optimization and generalization.Source: §1 · pp. 1–2
  • Resource-based split rules do not measure task-relevant interface sufficiency, while repeated depth probing adds computation and current-interface-only criteria can be unreliable during ongoing adaptation.The paper identifies reliable client-specific split decisions and compatibility across heterogeneous interfaces as two unresolved challenges.Source: §1 · p. 2
  • The estimator combines cross-client semantic alignment, temporal interface stability, and prompt-state variation to assess shallow-interface sufficiency without probing every split depth.Private prompt tokens provide a lightweight client-specific signal for whether local adaptation remains active.Source: §1 · p. 2
  • FedSGA maps activations from heterogeneous split depths into a shared semantic space, using split-depth-conditioned projections and server-maintained class prototypes.This harmonization is designed to improve interface comparability and stabilize server-side learning.Source: §1 · p. 2
  • FedSGA frames adaptive split selection as client-specific shallow sufficiency estimation rather than resource-driven partitioning.The framework combines private-prompt adaptation tracking, a shallow sufficiency estimator, and prototype-aligned interface harmonization.Source: §1 · p. 2
  • The paper reports experiments under general statistical and domain heterogeneity on CIFAR-10, CIFAR-100, Tiny-ImageNet, and DomainNet.The introduction states that these experiments demonstrate FedSGA's effectiveness, without providing quantitative comparisons here.Source: §1 · p. 2

2 Related Works

Prior work studies SFL efficiency and personalization, adaptive partitioning, and federated representation alignment, but leaves the semantic sufficiency of heterogeneous split interfaces unresolved.

2.1 Split Federated Learning

  • SFL research addresses system efficiency, personalization [39], and feature alignment or distillation, but mostly relies on fixed splits or resource-oriented partitioning.The split interface also shapes which client representations the shared server model receives.Source: §2.1 · pp. 2–3

2.2 Adaptive Split Learning with Heterogeneity

  • Adaptive split methods allow client-specific offloading depths [29] [30], but often optimize resources [30] rather than semantic sufficiency; repeated online probing adds overhead [40] [59].Representation-level signals may also be unreliable when an apparently aligned interface comes from a client that is still adapting.Source: §2.2 · p. 3

2.3 Representation Alignment in FL

  • Federated alignment methods use feature, prototype, contrastive, or distillation objectives [14] [26], but heterogeneous split depths produce activations with different semantic granularity [29] [30] [4].Thus, alignment for adaptive SFL must account for abstraction-level differences as well as domain semantics.Source: §2.3 · p. 3

3 Methodology

FedSGA treats split selection under client heterogeneity as client-specific shallow-sufficiency estimation, combining local adaptation signals, semantic alignment, and interface stability to decide whether the shallowest split is sufficient. It also harmonizes activations from different split depths in a shared semantic space before server-side prediction.

3.1 Preliminaries and Notation

  • Split federated learning divides the model between clients and a shared server, while heterogeneous client distributions and representation trajectories make a single fixed split potentially unsuitable.Clients send intermediate activations to the server and receive interface gradients; domain skew can produce client-specific feature characteristics and representation-learning trajectories.Source: §3.1 · p. 3

3.2 Client-Specific Adaptation Channel

  • Client-specific prompt tokens form a private adaptation channel that tracks local adaptation separately from the shared backbone and noisy, batch-dependent interface features.The prompts are updated only through the corresponding client’s local objective, and their descriptor’s temporal variation provides a low-cost signal of changing adaptation patterns.Source: §3.2 · p. 4

3.3 Shallow Sufficiency Estimation

  • Sparse calibration compares the shallowest interface with one fixed, moderately deep reference, then lets clients estimate sufficiency online instead of repeatedly probing candidate depths.The shallow interface is judged relative to the deeper reference with a tolerance margin; the learned estimate is converted to a split depth by a budget-aware policy that can favor deeper local computation or earlier offloading.Source: §3.3 · p. 5
  • FedSGA estimates shallow-split sufficiency from cross-client semantic alignment, interface stability, and prompt-state variation, requiring all three signals to support a reliable shallow interface.Its low-capacity monotone estimator increases with prototype alignment and decreases with representation drift and prompt-state variation, reflecting whether local adaptation remains unresolved.Source: §3.3 · p. 5

1 Initialize 𝒘0 𝑠, {𝒘0

FedSGA harmonizes interfaces from different split depths in a shared semantic space and uses sparse calibration to guide client-specific offloading, reducing repeated depth probing without imposing the shallowest split on every client.

3.4 Split-Compatible Interface Harmonization

  • A depth-aware projector conditions pooled interface features on the selected split depth, while prototype alignment anchors projected representations to shared class-level semantics.The module improves cross-depth comparability but is not intended to eliminate all mismatch from heterogeneous split depths and client adaptation states.Source: §3.4 · p. 6

3.5 Discussion

  • Sparse calibration compares only p1 and pref at selected rounds, amortizing depth-comparison cost at O(|Tcal|) rather than O(KT) for exhaustive probing.The estimator runs once per client in ordinary rounds; prompt summarization costs O(m), and prototype alignment costs O(B|Y|) per client batch.Source: §3.5 · pp. 6–7
  • Clients estimated to have sufficient shallow interfaces can offload earlier and avoid unnecessary deeper local computation, rather than uniformly using the shallowest split.The discussion cautions that aggressive shallow splitting for all clients may lower computation while degrading transmitted-interface quality.Source: §3.5 · p. 6

4 Numerical Experiments · 4.1 Experiment Setups

The numerical experiments are designed to evaluate FedSGA against federated and split-federated baselines, assess its components and adaptive split strategy, and test performance and client-side computation across heterogeneous settings. The setup spans four datasets, two backbone architectures, and shared training protocols.

4 Numerical Experiments

  • Five research questions cover comparative performance, component contributions, hyperparameter sensitivity, client-side computation, and sufficiency-guided split selection.The comparisons target heterogeneous environments and ask whether computational cost can be reduced while maintaining strong collaborative learning performance.Source: §4 · p. 7

4.1 Experiment Setups

  • Experiments use CIFAR-10, CIFAR-100, Tiny-ImageNet, and DomainNet [38] with ResNet-18 [16] and ViT-B/16 [7].The datasets cover general statistical and domain-level heterogeneity; Non-IID partitions use a Dirichlet concentration of 0.1, while DomainNet also applies the protocol within its multi-domain data.Source: §4.1.1 · p. 7

4.1.2 Baselines.

  • Federated baselines include FedAvg [35], FedProx, FedBABU, FedGH, and FedAS.They represent federated optimization, personalization, prototype-guided classifier optimization, and approaches to client inconsistency and stragglers.Source: §4.1.2 · p. 7
  • Split-federated baselines include SplitFed, MergeSFL, FedMut, MU-SplitFed [27], and MultiSFL.MultiSFL is identified as the primary adaptive SFL baseline.Source: §4.1.2 · p. 7
  • All clients participate in each round; the default setup uses 20 clients, 5 local epochs, batch size 64, and SGD.CIFAR-10 uses learning rate 0.1 for 100 global rounds; CIFAR-100, Tiny-ImageNet, and DomainNet use learning rate 0.01 for 300 rounds, with methods sharing backbones, partitions, and training protocols.Source: §4.1.3 · p. 7
  • FedSGA uses backbone block boundaries as candidate splits and defaults to the middle-depth reference split, with 4 client-specific prompt tokens.Other defaults are ρ=0.1, β=0.05, λ=0.1, τ_a=0.5, τ_m=0.5, EMA coefficient μ=0.9, calibration every 5 rounds, and lightweight two-layer MLPs for the estimator and projector.Source: §4.1.3 · p. 7

4.2 Main Results and Analysis (RQ1)

FedSGA achieves the best accuracy across datasets, data partitions, and both backbones, with stronger advantages under Non-IID settings and especially challenging visual domains.

4.2 Main Results and Analysis (RQ1)

  • Compared with conventional FL and SFL baselines, FedSGA’s advantages are more pronounced under Non-IID settings with stronger client distributional and representation-level discrepancies.The findings indicate that client update aggregation or a fixed split interface alone is insufficient when client representations evolve at different rates.Source: §4.2 · p. 7
  • FedSGA achieves the best accuracy across all datasets, data partitions, and both ResNet-18 and ViT-B/16 backbones.Tables 2 and 3 report the overall accuracy comparisons.Source: §4.2 · p. 7, Table 2 · p. 8, Table 3 · p. 8
  • FedSGA’s gains are particularly evident on Tiny-ImageNet and DomainNet, where heterogeneous semantics and complex visual domains challenge split-interface reliability.By estimating shallow-interface sufficiency per client and harmonizing heterogeneous-depth activations before server-side prediction, it supports more stable training across convolutional and transformer backbones.Source: §4.2 · p. 8

4.3 Ablation Study (RQ2) · 4.4 Hyperparameter Sensitivity Analysis (RQ3)

FedSGA’s ablations support the contributions of all three modules, while sensitivity results indicate that balanced settings for split selection and interface harmonization perform best across datasets and backbones.

4.3 Ablation Study (RQ2)

  • The full model performs best in all ablation cases, and Adapt., Suff. Est., and Harmon. each contribute positively across datasets, partitions, and backbones.The ablation results support combining client-local adaptation awareness with split-compatible server-side interface modeling.Source: §4.3 · p. 8, Table 4 · p. 9
  • Removing Suff. Est. consistently reduces performance with ResNet-18 and ViT-B/16, indicating that adaptive splitting needs explicit shallow-interface sufficiency estimates for reliable split decisions.The estimator is central to split selection.Source: §4.3 · p. 8
  • Adapt. yields stable gains, especially on Non-IID and DomainNet data, while Harmon. improves comparability across split depths and its removal consistently lowers accuracy.Prompt-state variation captures residual local adaptation; harmonization addresses interface mismatch that adaptive split selection alone cannot handle.Source: §4.3 · p. 8

4.4 Hyperparameter Sensitivity Analysis (RQ3)

  • Performance is generally best near ρ=0.1 and β=0.05 in most cases; smaller ρ can trigger premature offloading, while extreme β values risk rejecting useful or accepting premature shallow splits.The sensitivity study covers CIFAR-100 and DomainNet with ResNet-18 and ViT-B/16.Source: §4.4 · pp. 8–9, Figure 2 · p. 9, Figure 3 · p. 9
  • Performance improves as λ rises from a small value but degrades when it becomes too large, suggesting prototype alignment helps harmonize split interfaces but can over-constrain task representations.The figures show hyperparameter impacts on CIFAR-100 and DomainNet.Source: §4.4 · pp. 8–9, Figure 2 · p. 9, Figure 3 · p. 9
  • τ_a performs best around 0.5; too small a temperature sharpens prototype alignment excessively, whereas too large a value weakens class-level discrimination in the shared semantic space.Overall, the results indicate stable performance across datasets and backbones with balanced sufficiency-estimation and harmonization settings.Source: §4.4 · pp. 8–9, Figure 2 · p. 9, Figure 3 · p. 9

4.5 Computational Efficiency Analysis (RQ4)

FedSGA improves accuracy over MultiSFL while reducing client-side computation across datasets. Its adaptive split balances efficiency and collaborative performance by adjusting split depth to estimated shallow-interface sufficiency and client-local adaptation.

4.5 Computational Efficiency Analysis (RQ4)

  • FedSGA consistently achieves higher accuracy than MultiSFL while reducing client-side computational cost across all datasets.Table 5 analyzes computational cost under different backbone architectures; the passage also reports fewer activated parameters, lower FLOPs, and shorter training time.Source: §4.5 · pp. 9–10, Table 5 · p. 10
  • FedSGA adjusts split depth to estimated shallow-interface sufficiency and local adaptation, letting clients offload earlier when shallow representations are reliable and retain deeper computation when needed.The adaptive mechanism avoids unnecessary deep local computation without sacrificing representation quality.Source: §4.5 · p. 10
  • Efficiency gains are more evident on larger-scale, more heterogeneous datasets such as DomainNet, where overhead falls while accuracy improves.Source: §4.5 · p. 10

4.6 Split Strategy Comparison (RQ5)

On CIFAR-100 and DomainNet, FedSGA achieves the highest accuracy across IID and Non-IID settings, outperforming fixed static and random split strategies. The comparison supports client-specific split selection guided by estimates of interface sufficiency.

4.6 Split Strategy Comparison (RQ5)

  • FedSGA achieves the highest accuracy on CIFAR-100 and DomainNet under both IID and Non-IID settings, outperforming static and random split strategies.The improvement over both alternatives is particularly clear under Non-IID settings.Source: §4.6 · p. 10
  • Fixed static splits cannot accommodate clients whose representations mature at different depths, while random splits can produce premature or incompatible interfaces.The comparison indicates that client heterogeneity makes fixed or unguided split decisions unreliable.Source: §4.6 · p. 10
  • FedSGA estimates shallow sufficiency from semantic alignment, temporal stability, and prompt-state variation to select client-specific split depths with reliable interfaces.These results attribute FedSGA’s gains to principled client-specific split decisions rather than simply varying the split point.Source: §4.6 · p. 10

5 Conclusion

FedSGA estimates client-specific shallow sufficiency to select adaptive split depths, combining private prompt-state signals with semantic alignment and temporal interface stability. It harmonizes heterogeneous client interfaces and improves performance while reducing client-side computation across heterogeneous benchmarks and backbone architectures.

5 Conclusion

  • FedSGA consistently improves model performance over state-of-the-art methods while reducing client-side computation across heterogeneous benchmarks and backbone architectures.Source: §5 · p. 10
  • FedSGA frames split selection as client-specific shallow sufficiency estimation rather than uniform static splitting or repeated probing of candidate depths.Source: §5 · p. 10
  • A private prompt-based adaptation channel uses prompt-state variation alongside semantic alignment and temporal interface stability to detect whether local adaptation remains active.Source: §5 · p. 10
  • A budget-aware monotone policy selects split depth, while prototype-regularized harmonization maps activations from different depths into a shared semantic space.Source: §5 · p. 10

GenAI Usage Disclosure

The authors state that the work is entirely original and contains no content generated by generative AI tools.

GenAI Usage Disclosure

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