This tool compresses SDXL LoRA models while experimenting with new methods for selecting singular values. The proposed method scores the singular values of the LoRA layers relative to the spectral norm of the corresponding layers from the base model checkpoint. This score, called spn_ckpt, is computed as $\sigma_i(BA) / \sigma_{\text{max}}(W_{\text{ckpt}})$, where $\sigma_i(BA)$ represents the singular values of the LoRA layer, and $\sigma_{\text{max}}(W_{\text{ckpt}})$ is the maximum singular value (spectral norm) of the base layer from the checkpoint.

• Features
• Installation
• Usage
  • Basic Command
  • Arguments
  • Recipe Format
  • Advanced Example
• Evaluation
• License
• Contributing

• Support SDXL LoRAs/LoCons only for now (This means no SD1.5, and no DoRA, LoKr, LoHa, etc).
• Base model weights for thresholding: Uses weights from the base model for thresholding the relative singular values of the LoRA.
• Multiple scoring Methods: Various scoring methods can be weighted together.
• Target size or score threshold: Specify either a target size or a score threshold.
• Batch processing: Process multiple LoRA models in one command.
• Multiple recipes: Apply multiple recipes resulting in multiple outputs per input LoRA. This allows to reuse the SVD decomposition for experimenting with a range of parameters.
• Optimized for speed: Uses 3 SVDs directly on the LoRA's weights instead of the full rank matrix. Spectral norms from the checkpoint are cached to the filesystem for faster processing.

Clone the repository:

git clone https://github.com/elias-gaeros/resize_lora.git
cd resize_lora

• Python 3.8
• torch
• safetensors
• tqdm

python resize_lora.py /path/to/checkpoint.safetensors /path/to/lora.safetensors -o /path/to/output/folder

Filters out the singular values that are 10 times smaller or more than the spectral norm of the base layer from the checkpoint.

• checkpoint_path (positional): Path to the checkpoint file.
• lora_model_paths (positional): Paths to the LoRA model files (can specify multiple files).
• -o, --output_folder (required): Folder to save the output files.
• -t, --output_dtype: Output bit-width, either 32 or 16 (default: 16).
• -d, --device: Device to run the computations on (default: 'cuda' if available, otherwise 'cpu').
• -r, --score_recipes: Score/threshold recipes separated by colons (:). Each recipe specifies weights and either a target size or threshold. The default is spn_ckpt=1,thr=-1.2.
• -v, --verbose: Increase verbosity level (e.g., -v for INFO, -vv for DEBUG).

The score recipe string is a comma-separated list of key-value pairs. It specifies the weights for the geometric average of various score metrics and the threshold or the target file size. At least one score type and one selection method must be specified. Valid keys are:

Selection methods:

• size: Target output size in MiBs (required if thr is not specified).
• thr: Log base 10 threshold for scores (required if size is not specified). A threshold of -1.2 (the default) will select the singular values $> 10^{-1.2} \times \text{reference}$, at least 1/16th of the reference. Typically negative except for subspace denominator.

Scoring method weights:

• spn_ckpt: Weight for the score relative to the spectral norm of the layer from the checkpoint. The score is $\sigma_i(BA) / \sigma_\text{max}\left(W_\text{ckpt}\right)$.
• spn_lora: Weight for the score relative to the spectral norm of the layer from the LoRA model. The score is $\sigma_i(BA) / \sigma_\text{max}\left(BA\right)$.
• fro_ckpt: Weight for the score relative to the Frobenius norm of the layer from the checkpoint. The score is $\sigma_i(BA) / |W_\text{ckpt}|_\text{F}$.
• fro_lora: Weight for the score relative to the Frobenius norm of the layer from the LoRA model. The score is $\sigma_i(BA) / |BA|_\text{F}$.
• subspace: Weight for the subspace score, computed as $\sigma_i(BA) / \left\langle \mathbf{u}_i, W_\text{ckpt} \mathbf{v}_i \right\rangle$.
• params: Divide the score by the number of parameters required by ranks: $\sigma_i(BA) / (n m)$. A low weight, like params=0.1, favors layers with fewer parameters per rank. Used with size=, this does a greedy knapsack approximation.

A weight of 1 is used if no weight is specified. Weights are normalized to sum to 1. For example, fro_ckpt=3,spn_lora is equivalent to fro_ckpt=0.75,spn_lora=0.25.

spn_lora scoring should be equivalent to kohya-ss/sd-scripts/networks/resize_lora.py --dynamic_method="sv_ratio".

Unlike spn_lora, spn_ckpt and fro_ckpt can remove LoRA layers completely. It is expected to generalize better across LoRAs and doesn't depend on the amount of training.

subspace is experimental and hasn't performed well alone. It favors singular subspaces that gets contracted by the base weights. It remains to be seen if low weights can improve other methods.

The Frobenius norm of a matrix $W \in \mathbb{R}^{n \times m}$ can be expressed as the euclidean norm its singular values. A typical weight matrix from a neural network has a complete numerical rank and singular values that are slowly decreasing. Under this assumption we get the following scaling law relating the spectral norm $|W|F$ to the spectral norm $\sigma{\max}$:

$$ |W|^2_F = \sum_i \sigma_i^2(W) \propto \min(n, m) \cdot \sigma_{\max}^2(W) $$

This means that the score fro_ckpt ($\sigma_i(BA) / |W_\text{ckpt}|_\text{F}$) tends to behave little like the score spn_ckpt=2,params=1, which is:

$$ \frac{\sigma_i(BA)}{\left( \left(n m\right) \cdot |W_\text{ckpt}|^2_\text{F} \right)^\frac{1}{3}} $$

python resize_lora.py /path/to/checkpoint.safetensors /path/to/loras/*.safetensors -o /path/to/output/folder \
    -v -r spn_lora=1,thr=-0.7:spn_ckpt=1,thr=-1.2:subspace=0.5,spn_ckpt=0.5,size=32

Process multiple LoRAs from a folder. For each, outputs:

• spn_lora=1,thr=-0.7: a LoRA with singular values greater than $10^{-0.7} \simeq $ 1/5th of the largest one. This is equivalent to kohya-ss/sd-scripts/networks/resize_lora.py --dynamic_method="sv_ratio" --dynamic_param=5.
• spn_ckpt=1,thr=-1.2: a LoRA with singular values greater than $10^{-1.2} \simeq $ 1/16th of the largest singular value of the base layer (spectral norm). This is the default and recommended setting for a strong compression with relatively limited effects on the quality.
• subspace=0.5,spn_ckpt=0.5,size=32: a 32MiB LoRA with a dynamic threshold applied on the geometric mean of:
  • The singular values divided by the scaling of base layer on the singular subspaces.
  • The singular values divided by the spectral norm of the base layer.

(TBD) General procedure:

1. Compress a LoRA with default parameters -r spn_ckpt=1,thr=-1.2, note the file size.
2. Compress the same original LoRA with -r spn_lora=1,size=<file size of the first output>, note the threshold.
3. Compress the same original LoRA using kohya-ss/sd-scripts/networks/resize_lora.py --dynamic_method="sv_ratio" --dynamic_param=<10**-threshold noted from 2.>.

LoRAs from steps 2 and 3 should give similar results. Evaluation of spn_ckpt scoring compares step 1 against steps 2 and 3.

This project is licensed under the MIT License. See the LICENSE file for details.

Contributions are welcome! Please open an issue or submit a pull request on GitHub.