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EAP-GP: Mitigating Saturation Effect in Gradient-based Automated Circuit Identification
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Proposes EAP-GP, a gradient-based circuit discovery method that builds an adaptive integration path from clean to corrupted activations to avoid gradient saturation, improving circuit faithfulness over EAP and EAP-IG on GPT-2 models.
Problem
Gradient-based edge attribution for automated circuit discovery in transformer LMs (EAP, EAP-IG) suffers from the zero-gradient problem and saturation effects along fixed straight-line integration paths, yielding unreliable edge attributions and unfaithful circuits.
Approach
Replace EAP-IG's fixed straight-line integration path with GradPath, a model-dependent path built by iterative gradient-descent steps on the squared output distance to the corrupted activation, normalized by gradient norm, so that the path avoids saturated regions where gradients vanish.
Key results
- At 97.5% edge sparsity on GPT-2 Small, EAP-GP reaches 80.1% NFS on IOI versus 62.4% for EAP-IG and 56.9% for EAP.
- On Greater-Than at 97.5% sparsity, EAP-GP reaches 99.8% NFS versus 97.6% for EAP-IG and 96.3% for EAP (Table 1).
- EAP-GP is roughly five times slower than EAP-IG (232.5 s vs 49.7 s on IOI at 97.5% sparsity).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace EAP-IG's fixed straight-line integration path with adaptive GradPath | EAP-GP · IOI (97.5% sparsity), GPT-2 Small | NFS: 62.47% -> 80.08% | Helped |
| Replace EAP-IG's fixed straight-line integration path with adaptive GradPath | EAP-GP · SVA (97.5% sparsity), GPT-2 Small | NFS: 84.57% -> 96.14% | Helped |
| Replace EAP-IG's fixed straight-line integration path with adaptive GradPath | EAP-GP · Gender-Bias (97.5% sparsity), GPT-2 Small | NFS: 90.95% -> 91.05% | Helped |
| Replace EAP-IG's fixed straight-line integration path with adaptive GradPath | EAP-GP · Country-Capital (97.5% sparsity), GPT-2 Small | NFS: 91.62% -> 93.67% | Helped |
| Replace EAP-IG's fixed straight-line integration path with adaptive GradPath | EAP-GP · Hypernymy (97.5% sparsity), GPT-2 Small | NFS: 55.62% -> 67.24% | Helped |
| Replace EAP-IG's fixed straight-line integration path with adaptive GradPath | EAP-GP · Greater-Than (97.5% sparsity), GPT-2 Small | NFS: 99.45% -> 98.98% | Hurt |
| Use adaptive GradPath instead of fixed-path EAP-IG | EAP-GP · IOI (97.5% sparsity), GPT-2 Small | time: 49.7 -> 232.5 | Hurt |
| Increase the GradPath step count beyond 5 (ablation) | EAP-GP · IOI and Gender-Bias | faithfulness metric | Mixed |
| Use 4 or 5 GradPath steps rather than fewer steps (ablation) | EAP-GP · IOI and Gender-Bias | faithfulness | Helped |
| Set the GradPath step count to 1 (equivalent to EAP) (ablation) | EAP-GP · IOI and Gender-Bias | faithfulness | Hurt |
Surprising findings
- EAP generates fully unfaithful (score 0) circuits at 99.0-99.9% sparsity on IOI due to parentless heads being pruned.
- Increasing the number of GradPath steps beyond about 5, or reducing sparsity, can decrease faithfulness, attributed to amplified high-frequency oscillations in the path.
Limitations
- Runtime is roughly five times that of EAP-IG due to the extra forward and backward passes for constructing the path.
- Gains on Greater-Than and Gender-Bias are small, and manual-circuit precision/recall results are mixed, with EAP-GP initially worse on IOI.
- Faithfulness can decline with more steps or lower sparsity, possibly from selecting noise-encoding edges.
Experimental setup
Datasets: Indirect Object Identification (IOI) Subject-Verb Agreement (SVA) Gender-Bias Capital-Country Hypernymy Greater-Than
Benchmarks: IOI SVA Gender-Bias Capital-Country Hypernymy Greater-Than
Metrics: Normalized Faithfulness Score (NFS) runtime (s) precision-recall vs manual circuits
Baselines: EAP EAP-IG ACDC
Builds on: Edge Attribution Patching (EAP) EAP-IG Integrated Gradients Automated Circuit Discovery (ACDC)
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