Rethinking Autoregressive Models for Lossless Image Compression via Hierarchical Parallelism and Progressive Adaptation

Autoregressive (AR) models, the theoretical performance benchmark for learned lossless image compression, are often dismissed as impractical due to prohibitive computational cost. This work re-thinks this paradigm, introducing a framework built on hierarchical parallelism and progressive adaptation that re-establishes pure autoregression as a top-performing and practical solution. Our approach is embodied in the Hierarchical Parallel Autoregressive ConvNet (HPAC), an ultra-lightweight pre-trained model using a hierarchical factorized structure and content-aware convolutional gating to efficiently capture spatial dependencies. We introduce two key optimizations for practicality: Cache-then-Select Inference (CSI), which accelerates coding by eliminating redundant computations, and Adaptive Focus Coding (AFC), which efficiently extends the framework to high bit-depth images. Building on this efficient foundation, our progressive adaptation strategy is realized by Spatially-Aware Rate-Guided Progressive Fine-tuning (SARP-FT). This instance-level strategy fine-tunes the model for each test image by optimizing low-rank adapters on progressively larger, spatially-continuous regions selected via estimated information density. Experiments on diverse datasets (natural, satellite, medical) validate that our method achieves new state-of-the-art compression. Notably, our approach sets a new benchmark in learned lossless compression, showing a carefully designed AR framework can offer significant gains over existing methods with a small parameter count and competitive coding speeds.