Beyond the Codebook: A New Approach to Discrete Representation Learning
![During image reconstruction with [latex]K=1024[/latex], codebook utilization patterns diverge significantly between methods: while VQ-VAE and FSQ initially demonstrate increasing utilization followed by a notable decline, VP-VAE and FSP consistently maintain high and stable codebook engagement throughout the training process.](https://arxiv.org/html/2602.17133v1/x1.png)
A new method decouples learning representations from codebook optimization, addressing common instability issues in vector quantization techniques.
![During image reconstruction with [latex]K=1024[/latex], codebook utilization patterns diverge significantly between methods: while VQ-VAE and FSQ initially demonstrate increasing utilization followed by a notable decline, VP-VAE and FSP consistently maintain high and stable codebook engagement throughout the training process.](https://arxiv.org/html/2602.17133v1/x1.png)
A new method decouples learning representations from codebook optimization, addressing common instability issues in vector quantization techniques.

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![The study of coupled Ising chains-specifically, [latex]N=2[/latex] chains with [latex]K=0[/latex] and [latex]g=0.5[/latex]-reveals that two-point correlation functions exhibit critical behavior near phase transitions, evidenced by power-law decay-quantified as [latex]C|i-j|^{-2\Delta}[/latex] for spin correlations-and providing a means to characterize the system's susceptibility to external influence, with reference correlations decaying as [latex]C|i-j|^{-2}[/latex].](https://arxiv.org/html/2602.17029v1/x2.png)
New research reveals unexpected behavior in coupled spin chains, challenging established theories about the transitions between different phases of matter.

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