Gradient Mirage: Trainable yet Label-Unidentifiable Gradients in Large Language Model Split Learning
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
Abstract
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
| 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 | |
| Matching Objective | |||||||
| 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 |
| 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 |
| BiSR(b) | CodeAlpaca | ||
| RougeL-F | Rouge2-F | Meteor | |
| =128 | .02±.01 | .00±.00 | .01±.00 |
| =256 | .03±.01 | .00±.00 | .02±.01 |
| =1024 | .12±.05 | .05±.03 | .10±.05 |
| =8192 | .62±.07 | .48±.09 | .62±.08 |
| =10240 | .56±.03 | .41±.02 | .57±.02 |
| 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 |
| Setting | RougeL-F | Rouge2-F | Meteor |
| Scale Blinding-Only | .55±.11 | .25±.04 | .43±.11 |
| =0.8 | .42±.09 | .11±.04 | .28±.09 |
| =0.7 | .41±.06 | .11±.03 | .28±.04 |
| =0.6 | .37±.04 | .09±.02 | .25±.03 |
| =0.6, =8192 | .29±.02 | .05±.01 | .19±.02 |
| =0.6, =1024 | .17±.01 | .01±.00 | .11±.01 |
| Dataset | Standard PPL | Dual-Track BP ( ✗ ) | Bottom-Gradient Rec ( ✗ ) | Trunk Training ( ✗ ) | |||
| PPL | PPL | PPL | |||||
| 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 |
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
| 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 |
| 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 |
| 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 |
| 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 | |
Privacy-Preserving Language Models
Privacy-preserving language models protect sensitive data during training, inference, personalization, and information sharing.
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