LittleBit-2: Maximizing the Spectral Energy Gain in Sub-1-Bit LLMs via Latent Geometry Alignment (ICML 2026)
Banseok Lee, Youngmin Kim

LittleBit: Ultra Low-Bit Quantization via Latent Factorization (NeurIPS 2025)
Banseok Lee*, Dongkyu Kim*, Youngcheon You, Youngmin Kim

LittleBit compresses large language models into the sub-1-bit regime by factorizing each dense weight matrix into low-rank latent factors, binarizing those factors, and restoring magnitude information through lightweight learned scales. This enables extreme compression, including the 0.1 bits-per-weight setting, while preserving the original model architecture at inference time.

LittleBit-2 improves this recipe by addressing latent geometry misalignment in the initialization stage. It applies Internal Latent Rotation with Joint Iterative Quantization (Joint-ITQ), aligning the SVD-derived latent factors with the binary hypercube before QAT. LittleBit-2 initialization is available as an opt-in (--use_itq) and produces no additional inference overhead.

• Sub-1-bit compression: Designed for 1.0 to 0.1 bits per weight.
• LittleBit-2 opt-in: Enable Joint-ITQ initialization with --use_itq for improved latent geometry alignment.
• No inference-time change: LittleBit-2 modifies initialization only; the deployed factorized layer remains the same.
• QAT-friendly: Supports Quantization-Aware Training with SmoothSign and optional residual factorization.

The codebase currently supports:

• OPT
• Llama and Llama 2/3
• Phi-4
• Qwen2.5 and QwQ
• Gemma 2 and Gemma 3
• Qwen3

We recommend Python 3.12.

conda create -n littlebit python=3.12
conda activate littlebit

# Install CUDA toolkit. Adjust the CUDA version if needed.
conda install nvidia/label/cuda-12.4.1::cuda-toolkit -c nvidia/label/cuda-12.4.1

# Install PyTorch.
pip install torch==2.8.0+cu124 torchvision==0.23.0+cu124 torchaudio==2.8.0+cu124 --index-url https://download.pytorch.org/whl/cu124

# Install dependencies.
pip install -r requirements.txt

pip install "transformers==4.51.*"

Train a model with Quantization-Aware Training. By default, LittleBitLinear uses the original SVD-only initialization. To enable LittleBit-2 (Joint-ITQ), pass --use_itq True.

Single GPU

CUDA_VISIBLE_DEVICES=0 python -m main \
    --model_id meta-llama/Llama-2-7b-hf \
    --dataset c4_wiki \
    --save_dir ./outputs/Llama-2-7b-LittleBit-2 \
    --num_train_epochs 5.0 \
    --per_device_train_batch_size 4 \
    --lr 4e-05 \
    --warmup_ratio 0.02 \
    --report wandb \
    --quant_func SmoothSign \
    --quant_mod LittleBitLinear \
    --residual True \
    --eff_bit 1.0 \
    --kv_factor 1.0 \
    --min_split_dim 8 \
    --l2l_loss_scale 10.0

# Opt-in to LittleBit-2 initialization
# --use_itq True

Multi-GPU with DeepSpeed

deepspeed --num_gpus=4 main.py \
    --model_id meta-llama/Llama-2-7b-hf \
    --dataset c4_wiki \
    --save_dir ./outputs/Llama-2-7b-LittleBit-2 \
    --ds_config_path configs/zero3.json \
    --num_train_epochs 5.0 \
    --per_device_train_batch_size 4 \
    --lr 4e-05 \
    --report wandb \
    --quant_func SmoothSign \
    --quant_mod LittleBitLinear \
    --residual True \
    --eff_bit 1.0 \
    --kv_factor 1.0 \
    --min_split_dim 8

Evaluate a local checkpoint or a model hosted on the Hugging Face Hub.

# From a local directory
CUDA_VISIBLE_DEVICES=0 python eval.py \
    --model_id ./outputs/Llama-2-7b-LittleBit-2 \
    --seqlen 2048 \
    --ppl_task wikitext2,c4 \
    --zeroshot_task boolq,piqa,hellaswag,winogrande,arc_easy,arc_challenge,openbookqa

# From the Hugging Face Hub
CUDA_VISIBLE_DEVICES=0 python eval.py \
    --model_id username/littlebit-llama-7b-0.1bpw \
    --seqlen 2048 \
    --ppl_task wikitext2

Older checkpoints may not include littlebit_config.json. In that case, pass the quantization arguments explicitly:

CUDA_VISIBLE_DEVICES=0 python eval.py \
    --model_id ./outputs/Legacy-Llama-2-7b \
    --quant_func SmoothSign \
    --quant_mod LittleBitLinear \
    --split_dim 1024

Parameter loading priority:

1. Explicit CLI arguments
2. littlebit_config.json in the model directory
3. config.json fallback for older checkpoints

If you find this work useful, please cite:

@inproceedings{lee2026littlebit2,
  title={LittleBit-2: Maximizing the Spectral Energy Gain in Sub-1-Bit LLMs via Latent Geometry Alignment},
  author={Lee, Banseok and Kim, Youngmin},
  booktitle={Proceedings of the 43rd International Conference on Machine Learning},
  year={2026}
}

@inproceedings{lee2025littlebit,
  title={LittleBit: Ultra Low-Bit Quantization via Latent Factorization},
  author={Lee, Banseok and Kim, Dongkyu and You, Youngcheon and Kim, Youngmin},
  booktitle={Advances in Neural Information Processing Systems},
  year={2025}
}

This project is licensed under the CC BY-NC 4.0 license.