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arXiv · 2602.16086

LGQ: Learnable Geometric Quantization for Image Tokenization

Idil Bilge Altun·Mert Onur Cakiroglu·Elham Buxton·Mehmet Dalkilic·Hasan Kurban
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Abstract

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/.

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Idil Bilge Altun, Mert Onur Cakiroglu, Elham Buxton, Mehmet Dalkilic, Hasan Kurban. 2026-02-17. LGQ: Learnable Geometric Quantization for Image Tokenization. https://arxiv.org/abs/2602.16086

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