# LGQ: Learnable Geometric Quantization for Image Tokenization

arXiv: https://arxiv.org/abs/2602.16086 · HTML: https://mlsanity.com/paper/2602.16086/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 12 of 12)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Autoregressive Image Generation using Residual Quantization](https://mlsanity.com/paper/2203.01941/) (2022)
- [Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation](https://mlsanity.com/paper/2310.05737/) (2023)
- [Finite Scalar Quantization: VQ-VAE Made Simple](https://mlsanity.com/paper/2309.15505/) (2023)
- [Addressing Representation Collapse in Vector Quantized Models with One Linear Layer](https://mlsanity.com/paper/2411.02038/) (2024)
- [Restructuring Vector Quantization with the Rotation Trick](https://mlsanity.com/paper/2410.06424/) (2024)
- [Scalable Image Tokenization with Index Backpropagation Quantization](https://mlsanity.com/paper/2412.02692/) (2024)

## Abstract (arXiv)

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/.