Despite strong generalization ability, large language models (LLMs) are resource-intensive to deploy. Post-training quantization (PTQ) effectively compresses pretrained LLMs without retraining. Although recent studies target extremely low-bit quantization, most methods rely on extra parameters and the effective bit-width usually exceeds 2 bits. We introduce a saliency-guided mixed-precision PTQ framework that achieves an average bit-width of 1.70 bits while maintaining competitive performance. The proposed method allocates bit-widths across weight groups under a strict total budget, guided by a cross-precision saliency metric. The key innovation is a learnable affine transformation consisting of rotation, scaling, and shifting to align quantization grids with local weight distributions to minimize error. Experiments show that the proposed method matches state-of-the-art low-bit PTQ performance, while reducing the average bit-width by approximately 0.55 bits in Table 1.

Learned image compression (LIC) has recently emerged as a promising alternative to realize transform-based coding. Contrary to widely studied transform and entropy modeling in LIC, most LIC methods are limited to uniform scalar quantization and existing vector quantization (VQ) methods are restricted by the soft-to-hard quantization strategy. In this paper, we propose a novel entropy relaxed lattice vector quantization (ERLVQ) scheme for LIC. ERLVQ achieves a tractable dimension-wise approximation to the probability mass function for the complex Voronoi regions in a general class of lattices. Instead of directly performing probabilistic estimation on the lattices, ERLVQ equivalently aligns complex Voronoi regions with a set of complete and non-overlapping hypercubes in a projected parametric domain. Space covering technique is then developed to generating hypercubes with their centers fixed to integer projected lattice points and their volumes equaling the Voronoi regions to enable separable dimension-wise estimation of multi-variate probability mass functions. The proposed ERLVQ is the first to adapt to arbitrary lattices for VQ based on LIC and can be embedded into existing LIC methods. Experimental results demonstrate that the proposed ERLVQ is superior to the uniform scalar quantization (USQ) and existing lattice VQ methods [1] on prevailing LIC baselines, as shown in Table 1 .

Existing entropy models in learned image compression are cumbersome to generate fixed mean and variance for estimating Gaussian distributions for latent representation. In this paper, we propose a novel entropy model based on Gaussian process regression (GPR) that flexibly predicts the mean of Gaussians with posterior distributions characterized by covari-ance functions spanned in the high-dimensional feature space. Furthermore, we develop the rate-distortion optimization based on the proposed entropy model by approximating the bitrates with the evidence lower bound (ELBO) derived via variational inference for GPR. The proposed model can be seamlessly integrated into existing end-to-end optimized frame-works by substituting the masked convolution based autoregressive models. Experimental results demonstrate that the proposed model outperforms conventional image compression methods such as JPEG2000 and BPG, as well as recent learning based methods on the Kodak dataset in terms of rate-distortion performance.