LittleBit-2: Maximizing the Spectral Energy Gain in Sub-1-Bit LLMs via Latent Geometry Alignment

Banseok Lee, Youngmin Kim
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:64064-64085, 2026.

Abstract

We identify the Spectral Energy Gain in extreme model compression, where low-rank binary approximations outperform tiny-rank floating-point baselines for heavy-tailed spectra. However, prior attempts fail to realize this potential, trailing state-of-the-art 1-bit methods. We attribute this degradation to Latent Geometry Misalignment: standard singular vectors exhibit high coherence (spiky distribution), the worst-case geometry for binary quantization. To realize this gain, we propose LittleBit-2, a framework employing Internal Latent Rotation and Joint Iterative Quantization (Joint-ITQ). This approach acts as a geometric preconditioner, aligning coherent latent distributions with the binary hypercube with zero inference overhead. Empirically, LittleBit-2 establishes a new state-of-the-art in the sub-1-bit regime (1$\sim$0.1 bpp) on Llama-2 and Llama-3, matching the fidelity of leading 1-bit baselines.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-lee26y, title = {{L}ittle{B}it-2: Maximizing the Spectral Energy Gain in Sub-1-Bit {LLM}s via Latent Geometry Alignment}, author = {Lee, Banseok and Kim, Youngmin}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {64064--64085}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/lee26y/lee26y.pdf}, url = {https://proceedings.mlr.press/v306/lee26y.html}, abstract = {We identify the Spectral Energy Gain in extreme model compression, where low-rank binary approximations outperform tiny-rank floating-point baselines for heavy-tailed spectra. However, prior attempts fail to realize this potential, trailing state-of-the-art 1-bit methods. We attribute this degradation to Latent Geometry Misalignment: standard singular vectors exhibit high coherence (spiky distribution), the worst-case geometry for binary quantization. To realize this gain, we propose LittleBit-2, a framework employing Internal Latent Rotation and Joint Iterative Quantization (Joint-ITQ). This approach acts as a geometric preconditioner, aligning coherent latent distributions with the binary hypercube with zero inference overhead. Empirically, LittleBit-2 establishes a new state-of-the-art in the sub-1-bit regime (1$\sim$0.1 bpp) on Llama-2 and Llama-3, matching the fidelity of leading 1-bit baselines.} }
Endnote
%0 Conference Paper %T LittleBit-2: Maximizing the Spectral Energy Gain in Sub-1-Bit LLMs via Latent Geometry Alignment %A Banseok Lee %A Youngmin Kim %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-lee26y %I PMLR %P 64064--64085 %U https://proceedings.mlr.press/v306/lee26y.html %V 306 %X We identify the Spectral Energy Gain in extreme model compression, where low-rank binary approximations outperform tiny-rank floating-point baselines for heavy-tailed spectra. However, prior attempts fail to realize this potential, trailing state-of-the-art 1-bit methods. We attribute this degradation to Latent Geometry Misalignment: standard singular vectors exhibit high coherence (spiky distribution), the worst-case geometry for binary quantization. To realize this gain, we propose LittleBit-2, a framework employing Internal Latent Rotation and Joint Iterative Quantization (Joint-ITQ). This approach acts as a geometric preconditioner, aligning coherent latent distributions with the binary hypercube with zero inference overhead. Empirically, LittleBit-2 establishes a new state-of-the-art in the sub-1-bit regime (1$\sim$0.1 bpp) on Llama-2 and Llama-3, matching the fidelity of leading 1-bit baselines.
APA
Lee, B. & Kim, Y.. (2026). LittleBit-2: Maximizing the Spectral Energy Gain in Sub-1-Bit LLMs via Latent Geometry Alignment. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:64064-64085 Available from https://proceedings.mlr.press/v306/lee26y.html.

Related Material