arXiv:2509.09679v3 Announce Type: replace-cross
Abstract: Large language models require massive memory footprints, severely limiting deployment on consumer hardware. Quantization reduces memory through lower numerical precision, but extreme 2-bit quantization suffers from catastrophic performance loss due to outliers in activations. Rotation-based methods such as QuIP and QuaRot apply orthogonal transforms to eliminate outliers before quantization, using computational invariance: $mathbf{y} = mathbf{Wx} = (mathbf{WQ}^T)(mathbf{Qx})$ for orthogonal $mathbf{Q}$. However, these methods use fixed transforms–Hadamard matrices achieving optimal worst-case coherence $mu = 1/sqrt{n}$–that cannot adapt to specific weight distributions. We identify that different transformer layers exhibit distinct outlier patterns, motivating layer-adaptive rotations rather than one-size-fits-all approaches. In this work, we propose ButterflyQuant, which replaces Hadamard rotations with learnable butterfly transforms parameterized by continuous Givens rotation angles. Unlike Hadamard’s discrete ${+1, -1}$ entries that are non-differentiable and thus prohibit gradient-based learning, butterfly transforms’ continuous parameterization enables smooth optimization while guaranteeing orthogonality by construction. This orthogonal constraint ensures theoretical guarantees in outlier suppression while achieving $O(n log n)$ computational complexity with only $frac{n log n}{2}$ learnable parameters. We further introduce a uniformity regularization on post-transformation activations to promote smoother distributions amenable to quantization. Learning requires only 128 calibration samples and converges in minutes on a single GPU. Read More
