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 demonstrated superior rate-distortion (R-D) performance compared to traditional codecs, but is challenged by training inefficiency that could incur more than two weeks to train a state-of-the-art model from scratch. Existing LIC methods overlook the slow convergence caused by compacting energy in learning nonlinear transforms. In this paper, we first reveal that such energy compaction consists of two components, \emph{i.e.}, feature decorrelation and uneven energy modulation. On such basis, we propose a linear auxiliary transform (AuxT) to disentangle energy compaction in training nonlinear transforms. The proposed AuxT obtains coarse approximation to achieve efficient energy compaction such that distribution fitting with the nonlinear transforms can be simplified to fine details. We then develop wavelet-based linear shortcuts (WLSs) for AuxT that leverages wavelet-based downsampling and orthogonal linear projection for feature decorrelation and subband-aware scaling for uneven energy modulation. AuxT is lightweight and plug-and-play to be integrated into diverse LIC models to address the slow convergence issue. Experimental results demonstrate that the proposed approach can accelerate training of LIC models by 2 times and simultaneously achieves an average 1\% BD-rate reduction. To our best knowledge, this is one of the first successful attempt that can significantly improve the convergence of LIC with comparable or superior rate-distortion performance.

End-to-end optimization via deep neural networks has facilitated lossy image compression. Existing neural network-based entropy models for end-to-end optimized image compression are limited by parameterized Gaussian distributions with deterministic mean and variance and cannot achieve accurate rate estimation for bottleneck representation with varying statistics. In this paper, we propose a novel entropy model based on deep Gaussian process regression (DGPR) to address this problem. Specifically, the proposed entropy model leverages autoregressive DGPR to flexibly predict the channel-wise posterior distributions of high-dimensional bottleneck representation for entropy coding. Consequently, we develop a well-established bit-rate estimation scheme via posterior inference of DGPR using the learned probabilistic distribution. Furthermore, scalable training is achieved via tensor train decomposition and Monte Carlo sampling to enable tractable variational inference of DGPR. To our best knowledge, this paper is the first attempt to develop the learnable probabilistic model for flexible parameter estimation in entropy modeling. Experimental results show that the proposed model outperforms conventional image compression methods (e.g., JPEG2000 and BPG) as well as recent end-to-end optimized methods on the Kodak and Tecnick datasets in terms of rate-distortion performance.

Entropy modeling is the core component of learned image compression (LIC) that models the distribution of latent representation learned from input images via neural networks for bit-rate estimation. However, existing entropy models employ presumed parameterized distributions such as Gaussian models and are limited for the learned latent representation characterized by complex distributions. To address this problem, in this paper, we for the first time achieve generative probabilistic entropy modeling of latent representation based on conditional diffusion models. Specifically, we propose a conditional diffusion-based probabilistic entropy model (CDPEM) to parameterize the latent representation with distributions of arbitrary forms that are generated by well designed training-test consistent denoising diffusion implicit model (TC-DDIM) without introducing any presumption. TC-DDIM is designed to leverage ancestral sampling to gradually approximate the distribution of latent representation with guaranteed consistency in generation for training and test. Furthermore, we develop a hierarchical spatial-channel context model to incorporate with TC-DDIM to sufficiently exploit spatial correlations with the approximate contextual information produced by ancestral sampling and channel-wise correlations using channel-wise information aggregation with reweighted training loss. Experimental results demonstrate that the proposed entropy model achieves state-of-the-art performance on the Kodak, CLIC, and Tecnick datasets compared to existing LIC methods. Remarkably, when incorporated with recent baselines, the proposed model outperforms latest VVC standard by an evident gain in R-D performance.

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.