Organizations: State Key Laboratory for Novel Software Technology, Nanjing University · College of Computer Science and Software Engineering, Hohai University · School of Mathematics, Nanjing University · Nanjing Normal University
Gradient matching attacks (GMAs) in LLM split learning (SL) rely on a critical yet underexplored assumption: the gradient exposed at the split interface is a faithful derivative of the client's full-label training objective. This gradient-objective consistency allows a curious server to recover private labels by searching for a sequence whose induced gradient explains the observation. We propose Gradient Mirage, a defense that breaks this consistency without discarding the optimization utility of the backward signal. Our key idea is to induce the adversary to solve a misspecified inverse problem, in which no plausible label sequence in the sequence space can explain the observed gradients. Concretely, Gradient Mirage achieves this by inducing inconsistency across three dimensions: objective, direction, and scale. Selective Autoregressive Supervision derives the exposed gradient from a masked surrogate loss rather than the full-label objective assumed by the attacker; Scale Blinding then applies randomized multiplicative rescaling, obscuring the gradient's natural magnitude; and Directional Privatization further randomizes the gradient direction while preserving its magnitude through the von Mises-Fisher (vMF) mechanism under a directional metric differential privacy guarantee. Crucially, utility is preserved: the Top segment still learns from all target tokens via Dual-Track Backpropagation, the exposed gradient remains informative since each supervised token retains its complete autoregressive context, and Bottom-Gradient Recovery restores the effective gradient for Bottom-segment optimization. Extensive experiments show that Gradient Mirage provides substantially stronger protection than existing defenses under comparable fine-tuning performance, achieving a better privacy-utility trade-off.
Figures & tables
Figure 1: Illustration of label leakage in label-shielded split learning. Given the gradient returned from the client’s Top segment to the Trunk segment, a curious-but-honest server can recover the label sequence by optimization.
Figure 2: Two classical split learning paradigms: label-exposed split learning and label-shielded split learning.
Figure 3: Classical gradient-matching attack with a frozen parameter snapshot. At training step t , the adversary fixes the model parameters θ(t) (the snapshot) and optimizes dummy inputs xdum and labels ydum .
Figure 4: Gradient matching attack in split learning (GMA-SL). The adversary observes the gradient with respect to the cut-layer representation ∇xtrk , produced by the victim’s Top segment, then optimizes a dummy label ydum using a differentiable proxy top model F(⋅;θpro) , such that the proxy-induced gradient ∇xtrkL(F(xtrk;θpro),y~) matches the observed one. The schematic computation graph is shown on the right side.
Figure 5: Illustration of Gradient Mirage against GMA-SL. The private track (red) remains local, while the exposed track (blue-to-cyan) is protected before transmission. The numbered markers indicate the corresponding processing stages.
Dataset
CodeAlpaca
PIQA
GSM8K
Model
Method
RougeL-F
Meteor
PPL
RougeL-F
Meteor
PPL
RougeL-F
Meteor
PPL
Llama3 -8B
GP
1.00 ± .00
.99 ± .00
5.29 ± .54
.96 ± .01
.94 ± .02
11.50 ± 2.16
1.00 ± .00
1.00 ± .01
12.23 ± 1.13
GD
.94 ± .01
.94 ± .01
4.78 ± .10
.95 ± .01
.91 ± .00
7.76 ± .03
.95 ± .01
.94 ± .01
12.48 ± .97
LDP(10240)
.56 ± .03
.57 ± .02
4.67 ± .00
.80 ± .03
.76 ± .05
7.74 ± .06
.90 ± .01
.92 ± .01
11.04 ± .03
LDP(12288)
.66 ± .03
.66 ± .04
4.61 ± .04
.81 ± .03
.77 ± .05
7.20 ± .02
.89 ± .02
.89 ± .02
11.12 ± .04
Top-Only
-
-
4.83 ± .01
-
-
8.87 ± .02
-
-
12.00 ± .01
Table 1: Comparison between Gradient Mirage and existing privacy-preserving methods across three models.
Figure 6: Effect of GP against GMA-SL under different PRs.
Figure 7: Effect of GD against GMA-SL under different drop rates and Gaussian noise standard deviations.
Figure 8: Comparison between Top-only FT and SL FT under GradSeq-LDP. The left two panels correspond to 1-decoder and the right two to 5-decoder. Experiments were conducted on Llama3-8B using the CodeAlpaca dataset.
Figure 9: Gradient utility of GradSeq-LDP under different privacy budgets across three datasets. Even at large ε , the privatized gradients retain limited signal strength and salient-coordinate information.
Figure 10: Seed sensitivity of SL FT across random seeds.
Matching Objective
m
100
500
1000
1500
1750
2500
4000
TAG
.382±.026
.246±.018
.211±.012
.195±.016
.202±.002
.170±.002
.168±.010
Cosine Distance
.089±.008
.088±.006
.087±.008
.090±.003
.094±.005
.100±.004
.088±.007
Adaptive TAG
.360±.024
.248±.018
.213±.010
.197±.021
.208±.016
.187±.005
.184±.013
Table 2: Effect of the mean scale m on reconstruction quality under different matching objectives.
r
m
100
500
1000
1500
1750
2500
4000
1/5
.341±.021
.212±.014
.191±.012
.187±.012
.183±.011
.143±.013
.133±.014
1/7
.360±.024
.248±.018
.213±.010
.197±.021
.208±.016
.187±.005
.184±.013
1/10
.391±.017
.250±.011
.219±.013
.199±.023
.208±.007
.186±.011
.189±.009
1/25
.397±.024
.258±.017
.221±.023
.237±.015
.219±.010
.194±.010
.193±.010
1/50
.404±.024
.263±.017
.227±.016
.232±.022
.239±.008
.198±.005
.204±.009
Table 3: Effect of the relative token-wise variation r on reconstruction quality under different mean scales m .
BiSR(b)
CodeAlpaca
RougeL-F
Rouge2-F
Meteor
ε =128
.02±.01
.00±.00
.01±.00
ε =256
.03±.01
.00±.00
.02±.01
ε =1024
.12±.05
.05±.03
.10±.05
ε =8192
.62±.07
.48±.09
.62±.08
ε =10240
.56±.03
.41±.02
.57±.02
Table 4: Defense performance of GradSeq-LDP against GMA-SL under different privacy budgets.
Setting
RougeL-F
Rouge2-F
Meteor
w/o Scale Blinding
.71±.01
.51±.02
.69±.01
w/ Scale Blinding
.35±.02
.18±.02
.34±.02
Table 5: Impact of Scale Blinding.
Setting
RougeL-F
Rouge2-F
Meteor
Scale Blinding-Only
.55±.11
.25±.04
.43±.11
ρ =0.8
.42±.09
.11±.04
.28±.09
ρ =0.7
.41±.06
.11±.03
.28±.04
ρ =0.6
.37±.04
.09±.02
.25±.03
ρ =0.6, ε =8192
.29±.02
.05±.01
.19±.02
ρ =0.6, ε =1024
.17±.01
.01±.00
.11±.01
Table 6: Impact of SAS and Directional Privatization.
Figure 11: Fine-tuning performance under different mean scales m with fixed relative token-wise variation r=1/7 . The results are obtained on Llama-3-8B with the CodeAlpaca dataset.
Dataset
Standard PPL
Dual-Track BP ( ✗ )
Bottom-Gradient Rec ( ✗ )
Trunk Training ( ✗ )
PPL
Δ(%)
PPL
Δ(%)
PPL
Δ(%)
CodeAlpaca
4.42±.01
4.51±.05
2.04 ↑
4.51±.01
2.04 ↑
4.48±.05
1.36 ↑
PIQA
7.19±.03
7.30±.02
1.53 ↑
7.43±.03
3.34 ↑
7.23±.02
0.56 ↑
GSM8K
10.50±.01
10.61±.05
1.05 ↑
10.69±.03
1.82 ↑
10.59±.03
0.86 ↑
Table 7: Impact of Dual-Track Backpropagation, Bottom-Gradient Recovery, and Trunk Training on SL utility.
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 12: Tangent-normal decomposition in vMF sampling. The sampled direction μ~ is decomposed into an axial component t=μ~⊤μ=cosθ along μ and a tangential component of magnitude 1−t2=sinθ , where ξ∼Unif(Sn−2⊥μ) .
Figure 13: Illustration of the zero-gradient suffix induced by masking the last k target tokens in selective autoregressive supervision. The arrows indicate the direction of gradient propagation.
Figure 14: Training dynamics of the learning-based inversion decoder across five LLMs. Shown are the training loss, evaluation loss, and evaluation RougeL-F over training steps under three random seeds.
Figure 15: Training Curves of Gradient Pruning and Gradient Dropout.
Dataset
Method
Final PPL
PPL@500steps
PPL@1000steps
RougeL-F
Rouge1-F
Rouge2-F
Meteor
TRR
Code- Alpaca
Grad Pruning
5.292 ± .538
4.595±.001
4.934±.017
.995±.001
.995±.001
.981±.001
.987±.001
.990±.000
GradSeq-LDP(10240)
4.670±.002
4.962±.055
4.782±.043
.564±.032
.567±.037
.413±.020
.570±.016
.634±.007
GradSeq-LDP(12288)
4.611±.037
4.915±.022
4.804±.050
.657±.029
.661±.030
.517±.042
.664±.042
.717±.041
Grad Dropout
4.782±.104
5.341±.158
4.954±.041
.942±.008
.942±.008
.915±.012
.940±.007
.943±.013
Gradient Mirage(512)
4.451±.001
4.671±.022
4.610±.008
.202±.002
.208±.003
.108±.001
.226±.000
.255±.002
Gradient Mirage(1024)
4.421±.008
4.603±.008
4.552±.013
.351±.022
.361±.022
.177±.020
.341±.017
.371±.009
Appendix
Table 8: Comparison between Gradient Mirage and existing privacy-preserving methods with Llama3-8B.
Figure 16: Comparison between the training dynamics with and without Trunk segment updates on Llama3-8B across three datasets. Updating the Trunk segment generally leads to lower validation perplexity across random seeds.
Dataset
Method
Final PPL
PPL@500steps
PPL@1000steps
RougeL-F
Rouge1-F
Rouge2-F
Meteor
TRR
Code- Alpaca
Grad Pruning
5.000±.089
4.864±.088
4.765±.044
.993±.003
.993±.003
.988±.006
.989±.005
.995±.003
GradSeq-LDP(10240)
4.804±.083
5.141±.149
4.991±.155
.775±.033
.776±.034
.656±.048
.741±.043
.886±.018
GradSeq-LDP(12288)
4.853±.131
5.132±.143
5.024±.172
.820±.037
.821±.037
.725±.052
.795±.043
.909±.018
Grad Dropout
6.979±1.575
7.329±.929
82.223±129.115
.902±.017
.902±.016
.859±.026
.890±.016
.932±.008
Gradient Mirage(512)
4.817±.098
5.186±.124
5.066±.068
.095±.012
.097±.012
.016±.002
.112±.005
.199±.010
Gradient Mirage(1024)
4.772±.049
5.031±.136
5.061±.124
.174±.020
.177±.019
.042±.007
.146±.008
.297±.004
Appendix
Table 9: Comparison between Gradient Mirage and existing privacy-preserving methods with Llama2-7B.
Dataset
Method
Final PPL
PPL@500steps
PPL@1000steps
RougeL-F
Rouge1-F
Rouge2-F
Meteor
TRR
Code- Alpaca
Grad Pruning
5.389±.050
5.305±.027
5.475±.094
.991±.001
.991±.001
.968±.004
.967±.001
.976±.002
GradSeq-LDP(8192)
5.045±.049
5.319±.125
5.358±.099
.598±.015
.605±.015
.376±.028
.540±.026
.738±.015
GradSeq-LDP(10240)
5.000±.098
5.327±.100
5.252±.160
.741±.020
.746±.018
.637±.024
.709±.030
.844±.014
Grad Dropout
6.328±.333
6.371±.575
7.167±1.046
.681±.040
.682±.040
.584±.041
.682±.041
.718±.044
Gradient Mirage(512)
5.304±.223
5.397±.158
5.404±.028
.070±.023
.071±.024
.030±.013
.045±.015
.163±.030
Gradient Mirage(1024)
5.149±.135
5.260±.160
5.292±.024
.105±.007
.107±.008
.028±.008
.062±.009
.204±.011
Appendix
Table 10: Comparison between Gradient Mirage and existing privacy-preserving methods with DeepSeek-LLM-7B.
Dataset
CodeAlpaca
PIQA
GSM8K
Model
Method
RougeL-F
Rouge2-F
Meteor
RougeL-F
Rouge2-F
Meteor
RougeL-F
Rouge2-F
Meteor
Llama3 -8B
GP(0.7)
.488±.006
.181±.002
.347±.002
.691±.003
.444±.007
.601±.001
.473±.008
.179±.012
.307±.011
GD(0.6, 5e-3)
.089±.016
.009±.009
.061±.010
.237±.010
.088±.012
.186±.007
.066±.012
.000±.000
.039±.003
LDP(10240)
.103±.012
.010±.005
.071±.010
.309±.007
.106±.003
.234±.008
.073±.006
.003±.002
.046±.003
LDP(12288)
.132±.005
.018±.007
.093±.004
.322±.012
.114±.005
.247±.011
.080±.002
.003±.001
.046±.003
Standard
.557±.012
.254±.015
.416±.013
.716±.007
.448±.009
.625±.009
.469±.016
.177±.016
.317±.016
Appendix
Table 11: Comparison of defense performance against the BiSR(b) attack paradigm using cosine distance as the matching objective across three models.
Figure 17: Fine-tuning performance under extremely large mean scales m with the Trunk-Frozen Training strategy, evaluated on Llama-3-8B with the CodeAlpaca dataset. The proposed strategy maintains stable convergence across all tested scales and random seeds.
Figure 18: Qualitative comparison of reconstructed inputs under different privacy-preserving methods across Llama-3-8B, Llama-2-7B, and DeepSeek-LLM-7B. Compared with existing defenses, Gradient Mirage yields substantially more distorted and incoherent reconstructions.
Figure 19: Qualitative results of GMA-SL under instruction fine-tuning across CodeAlpaca, PIQA, and GSM8K. Although the query tokens are excluded from supervision during user-side training, GMA-SL successfully reconstructs the supervised answer portion.