Efficient Orthogonal Fine-Tuning with Principal Subspace Adaptation (PSOFT)

Introduction (Paper, code)

PSOFT aims to preserve the geometric relationships among pre-trained weight column vectors—a core principle of OFT—while achieving a balanced trade-off across parameter, computation, and memory efficiency. Unlike existing OFT variants (e.g., OFTv2, BOFT, and GOFT) that rely on sparsity-based designs, PSOFT adopts a low-rank principal subspace perspective, bridging the gap between LoRA and OFT. PSOFT confines orthogonal fine-tuning to a principal subspace, offering theoretical guarantees via orthogonality constraints on the down-projection matrix, while enabling practical adaptability through two low-dimensional tunable vectors.

Quick Start

import torch
from peft import PsoftConfig, get_peft_model
from transformers import AutoTokenizer, AutoModelForCausalLM
from trl import SFTConfig, SFTTrainer
from datasets import load_dataset

model_name = "facebook/opt-125m"

model = AutoModelForCausalLM.from_pretrained(model_name)
tokenizer = AutoTokenizer.from_pretrained(model_name)
tokenizer.pad_token_id = tokenizer.eos_token_id

psoft_config = PsoftConfig(
    r=32,
    psoft_alpha=32,
)

peft_model = get_peft_model(model, psoft_config)
peft_model.print_trainable_parameters()

dataset = load_dataset("imdb", split="train[:1%]")

training_args = SFTConfig(dataset_text_field="text", max_length=128)

trainer = SFTTrainer(
    model=peft_model,
    args=training_args,
    train_dataset=dataset,
    processing_class=tokenizer,
)

trainer.train()
peft_model.save_pretrained("psoft-opt-125m")

Further examples on LLaMA-3.2-3B

python psoft_finetuning.py \
  --base_model_name_or_path meta-llama/Llama-3.2-3B \
  --output_dir ./outputs/psoft-llama3.2-3b-imdb \
  --data_path imdb \
  --dataset_split "train[:1%]" \
  --max_length 128 \
  --num_train_epochs 1 \
  --per_device_train_batch_size 1 \
  --gradient_accumulation_steps 8 \
  --learning_rate 5e-4 \
  --bits bf16 \
  --r 128 \
  --psoft_alpha 128 \
  --target_modules q_proj v_proj

Best Practices

1. Rank Choice: Smaller ranks (e.g., 32–128) are suitable for simpler tasks, while larger ranks (e.g., 64–256) provide greater expressiveness for more complex tasks at the cost of increased parameters and computation.
2. Scaling Factor: The scaling factor is typically set to $r$ in PSOFT.
3. Learning Rate: Use standard learning rates (e.g., 1e-4 to 5e-3) for stable training.
4. SVD Initialization: The lowrank option is more memory- and compute-efficient than full, making it more suitable for large models.
5. Cayley–Neumann Approximation: When the rank is large, enabling the Cayley–Neumann approximation can significantly improve computational efficiency, while the benefit is less pronounced for small ranks. In practice, a small number of Neumann series terms (typically 5) usually provides a good balance between accuracy and efficiency.

Citation

@inproceedings{wu2026efficient,
title={Efficient Orthogonal Fine-Tuning with Principal Subspace Adaptation},
author={Wu, Fei and Hu, Jia and Min, Geyong and Wang, Shiqiang},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=FSHrinMArK}
}