arXiv subjects

Zixin Jessie Chen

Publications and source records attributed to Zixin Jessie Chen.

3 recordsLinked to original sources

arXiv2026

Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution

Creating images from noise is image generation; reconstructing fine details from coarse inputs is super-resolution. Despite their practical differences, both can be understood as reversing information loss across scales. We introduce $\textbf{SKILD}$, a $\textbf{S}$cale-invariant $\textbf{K}$-Space $\textbf{I}$mage $\textbf{L}$earning $\textbf{D}$iffusion model that unifies generation and continuous super-resolution within a single unconditional framework. Both natural images and critical physical systems exhibit scale invariance, and we leverage it to design a forward process that attenuates image content from fine to coarse scales while injecting spectrum-matched Gaussian noise, making scale an explicit coordinate of the diffusion dynamics. The same trained reverse process performs generation and continuous super-resolution by varying only the starting timestep: $\textit{no task-specific architecture, no conditioning branch, no classifier-free guidance, no retraining per scale factor}$. Empirically, SKILD reaches FID $2.65$ and Inception Score $9.63$ on unconditional CIFAR-10, performs $2\times$--$8\times$ super-resolution on ImageNet from a single unconditional checkpoint while outperforming conditional models across perceptual metrics, and reconstructs critical Ising models whose connected four-point correlations closely track the ground truth.

cs.CV↗

arXiv2026

Emanant and emergent symmetry-topological-order from low-energy spectrum

Low-energy emanant and emergent symmetries can be anomalous, higher-group, or non-invertible. A way to systematically capture the properties of such symmetries is through the topological orders in one-higher dimension, known as symmetry topological orders (symTOs). Consequently, identifying the emergent or emanant symmetry of a system is not simply a matter of determining its group structure, but rather of computing the corresponding symTO. In this work, we develop a method to compute the symTO of 1+1D systems by analyzing their low-energy spectra under closed boundary conditions with all possible symmetry twists. Following this approach, we show that the gapless antiferromagnetic (AF) spin-$1/2$ Heisenberg model possesses an exact emanant symTO corresponding to the $D_8$ quantum double, when the global symmetry is restricted to the $\mathbb{Z}_2^x \times \mathbb{Z}_2^z$ subgroup of the $SO(3)$ spin-rotation symmetry and lattice translations. Moreover, this model exhibits an emergent $SO(4)$ symmetry, whose exact components are described jointly by automorphisms of the $D_8$ quantum double and the $SO(3)$ spin-rotations. Using the condensable algebras of the emanant symTO, we further identify several other phases that may be accessible by modifying interactions among low-energy excitations: (1) a gapped dimer phase, connected to the AF phase via an $SO(4)$ rotation, (2) a commensurate collinear ferromagnetic phase that breaks translation by one site with a $ω\sim k^2$ mode, (3) an incommensurate, translation-symmetric ferromagnetic phase featuring both $ω\sim k^2$ and $ω\sim k$ modes, (4) and an incommensurate ferromagnetic phase that breaks translation by one site with both $ω\sim k^2$ and $ω\sim k$ modes.

cond-mat.str-el↗

arXiv2026

Superposition unifies power-law training dynamics

We investigate the role of feature superposition in the emergence of power-law training dynamics using a teacher-student framework. We first derive an analytic theory for training without superposition, establishing that the power-law training exponent depends on both the input data statistics and channel importance. Remarkably, we discover that a superposition bottleneck induces a transition to a universal power-law exponent of $\sim 1$, independent of data and channel statistics. This one over time training with superposition represents an up to tenfold acceleration compared to the purely sequential learning that takes place in the absence of superposition. Our finding that superposition leads to rapid training with a data-independent power law exponent may have important implications for a wide range of neural networks that employ superposition, including production-scale large language models.

cs.LG↗