LGQ: Learnable Geometric Quantization for Image Tokenization

Recent collapse-free quantizers such as FSQ achieve stable training by replacing the learnable codebook with an engineered geometry: a fixed scalar grid whose structure is dictated by the codebook size K. We show this trade-off is unnecessary. We introduce Learnable Geometric Quantization (LGQ), which retains a learnable codebook of codes and performs soft-to-hard assignment via temperature annealing, regularized by two cheap terms: a diversity term scaled by codebook size that penalizes concentrated batch-average usage is the primary driver of collapse resistance, complemented by a peakedness term that sharpens each token's soft-assignment toward one-hot; together they prevent codebook collapse without EMA, reset heuristics, or codebook reparameterization. Under a fixed VQ-GAN backbone, we benchmark LGQ against RotVQ, FSQ, LFQ, SimVQ, and IBQ on ImageNet 256x256 at K = 16,384, and sweep LGQ over K in 4096,..., 65,536 without any per-K hyperparameter tuning. LGQ attains the best reconstruction FID at K = 16,384 while maintaining 100% codebook utilization, and continues to improve as the codebook grows to K = 65,536, holding 100% utilization at every K. Training MaskGIT on the frozen tokenizers, LGQ further attains the best class-conditional generation among the compared quantizers, leading on reconstruction and generation alike. Code is available at https://anonymous.4open.science/r/lgq-anon-E12C/.