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*What does each PEFT method believe about transformer internals?*
Note: This is an AI generated and guided literative survey, it does not speak for me but I share it in the hope that it is usefull, and I do believe these these exist and give us insight about how best to intervene in transformers
*Disclaimer: This is an AI-generated and AI-guided iterative survey. It does not speak for me, but I share it in the hope that it is useful. I do believe these themes exist and give us insight about how best to intervene in transformers.*
## Why care?
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We grade evidence on independent dimensions. Each method gets points for the dimensions it satisfies:
| Dim | Pts | Meaning |
|-----|-----|------------------------------------------|
| --- | --- | ----------------------------------------------------------- |
| PE | 1 | Parameter-efficient: competitive with full FT at <1% params |
| BL | 1 | Beats LoRA on raw performance at comparable budget |
| BF | 1.5 | Matches or beats full fine-tuning |
@@ -190,7 +190,11 @@ def pissa_forward(x, W_res, A, B):
return (W_res + A @ B) @ x # same as LoRA at inference
```
The decomposition: $W = \underbrace{U_{:r} S_{:r} V_{:r}^\top}_{\text{adapter (learned)}} + \underbrace{U_{r:} S_{r:} V_{r:}^\top}_{\text{residual (frozen)}}$. LoRA updates noise; PiSSA updates the signal.
The decomposition:
$$W = \underbrace{U_{:r} \, S_{:r} \, V_{:r}^\top}_{\text{adapter (learned)}} + \underbrace{U_{r:} \, S_{r:} \, V_{r:}^\top}_{\text{residual (frozen)}}$$
LoRA updates noise; PiSSA updates the signal.
**Evidence:** PiSSA consistently outperforms LoRA across 11 models (184M--70B) on 5 NLG and 8 NLU tasks under identical setups. Gemma-7B on GSM8K: PiSSA 77.7% vs LoRA 74.5%. QPiSSA (quantized) on LLaMA-3-70B GSM8K: 86.05% vs QLoRA 81.73%. Faster convergence because the optimizer starts in the high-signal subspace. The initialization cost is negligible (fast SVD, a few seconds).
@@ -913,6 +917,48 @@ The key: instead of $W' = W + \Delta W$, apply $h' = h + R^\top (R h + b - R h)$
---
## Scorecard
Sorted by evidence strength (max 8). See [scoring legend](#evidence-scoring) above.
| # | Method | Score | Breakdown | Theme |
| ---: | ------------- | ----: | ----------- | ---------------- |
| 6 | PiSSA | 5.0 | PE+BL+BF+DE | SVD basis |
| 4 | DoRA | 4.5 | PE+BL+BF+WA | dir/strength |
| 11 | AntiPaSTO* | 4.5 | PE+DE+OOD | SVD+rotation |
| 13 | BOFT | 4.0 | PE+BF+DE | orthogonal |
| 5 | DeLoRA | 3.5 | PE+BL+DE | dir/strength |
| 8 | SSVD | 3.5 | PE+BL+DE | SVD basis |
| 31 | CLOVER | 3.5 | PE+BL+BF | SVD+architecture |
| 32 | PSOFT | 3.5 | PE+BL+DE | SVD+orthogonal |
| 2 | OFT | 2.5 | PE+DE | orthogonal |
| 16 | RandLoRA | 2.5 | PE+BF | full-rank |
| 17 | FourierFT | 2.5 | PE+BF | spectral |
| 21 | MiSS | 2.5 | PE+DE | sharing |
| 27 | ETHER | 2.5 | PE+DE | orthogonal |
| 1 | LoRA | 2.0 | PE+WA | low-rank |
| 7 | SVFT | 2.0 | PE+BL | SVD basis |
| 33 | ReFT | 2.0 | PE+BL | activations |
| 3 | VeRA | 1.0 | PE | gain control |
| 9 | IA3 | 1.0 | PE | gain control |
| 10 | ROAD | 1.0 | PE | dir/strength |
| 12 | AdaLoRA | 1.0 | PE | low-rank |
| 14 | GOFT | 1.0 | PE | orthogonal |
| 15 | HRA | 1.0 | PE | orthogonal |
| 18 | C3A | 1.0 | PE | spectral |
| 19 | LoHa | 1.0 | PE | multiplicative |
| 20 | LoKr | 1.0 | PE | tensor product |
| 22 | VBLoRA | 1.0 | PE | sharing |
| 23 | SHiRA | 1.0 | PE | sparse |
| 24 | LN Tuning | 1.0 | PE | gain control |
| 25 | Prompt Tuning | 1.0 | PE | prompts |
| 26 | Poly/X-LoRA | 1.0 | PE | mixture |
| 28 | OFTv2 | 1.0 | PE | orthogonal |
\* own work -- read with appropriate skepticism
---
## Themes: What the Evidence Tells Us
Looking across all 33 methods, the successful adapters share a recipe: choose coordinates that align with pretrained structure, constrain updates to preserve that structure, and control update strength explicitly.
@@ -949,4 +995,4 @@ Before writing this catalog, I thought of adapters mainly as engineering trade-o
- The gain-control insight predicts a rank ordering for "how much adapter expressivity does task X need?": distribution shift (gain control suffices) < instruction following (low-rank) < novel capabilities (full-rank or high-rank sparse). Confidence: 60%.
- ReFT-style activation interventions will eventually beat weight-space adapters on parameter efficiency, but weight-space adapters will remain better for deployment (merging into weights). Confidence: 75%.
**Conflict of interest:** The strongest OOD result in this catalog is my own work ([AntiPaSTO](https://arxiv.org/abs/2601.07473)). I've tried to grade it honestly, but read the evidence for it with appropriate skepticism. I developed it with the same insights in this document, so it's not entirely suprising that it fits well.
**Conflict of interest:** The of the strongest OOD results in this catalog is my own work ([AntiPaSTO](https://arxiv.org/abs/2601.07473)). I've tried to grade it honestly, but read the evidence for it with appropriate skepticism. I developed it with the same insights in this document, so it's not entirely suprising that it fits well.