arXiv subjects

Taegu Kang

Publications and source records attributed to Taegu Kang.

4 recordsLinked to original sources

arXiv2026

Fluctuations of the free energy of the Sherrington-Kirkpatrick model with ferromagnetic interaction

We study the Sherrington-Kirkpatrick model with an additional Curie-Weiss ferromagnetic interaction (SKFI), whose phase diagram in the plane of the disorder strength $\beta$ and the ferromagnetic coupling $\gamma$ consists of a paramagnetic, a ferromagnetic, and a spin glass region. Our main result is a central limit theorem for the free energy in the ferromagnetic regime: at scale $N^{-1/2}$, the fluctuations coincide with those of the Sherrington-Kirkpatrick model in an effective external field determined by the limiting magnetization. We prove this for general mixed even $p$-spin interactions, using the fluctuation theory of Chen, Dey, and Panchenko. For the pure 2-spin model we complete the picture of the phase diagram: we give a new proof of the order-$N^{-1}$ Gaussian fluctuations in the paramagnetic regime, obtained earlier by Banerjee, valid up to the critical window; we determine the limiting distribution on the critical line $\gamma = 1 + \theta N^{-1/2}$ separating the paramagnetic and ferromagnetic regimes; and we show that in the spin glass regime the fluctuations coincide with those of the zero-field SK model under a widely believed variance-divergence assumption. Our results form the Ising analogue of the fluctuation results of Baik and Lee for the spherical SKFI model.

math.PR↗

arXiv2026

Inference-Time Scaling in Diffusion Models through Iterative Partial Refinement

Inference-time scaling has emerged as a major approach for improving reasoning capabilities, and has been increasingly applied to diffusion models. However, existing inference-time scaling methods for diffusion models typically rely on external verifiers or reward models to rank and select samples, limiting their scalability to settings where such evaluators are available and reliable. Moreover, while recent diffusion models perform sequential inference with region-wise, mixed-noise conditioning, inference-time scaling tailored to this setting remains relatively underexplored. We propose Iterative Partial Refinement (IPR), an inference-time scaling method for sequential diffusion that requires no external verifier. Starting from an already-generated sample, IPR re-noises a subset of regions and regenerates them conditioned on the remaining regions, enabling the model to revise earlier decisions under a richer context than was available during the initial generation. This iterative partial refinement produces more globally consistent samples without external verification. On reasoning tasks requiring global constraint satisfaction, IPR consistently improves performance: on MNIST Sudoku, the valid solution rate increases from 55.8% to 75.0%. These results show that iterative partial refinement alone can serve as an effective inference-time scaling strategy for diffusion models in sequential, mixed-noise settings. Code is available at: https://github.com/ahn-ml/IPR

cs.LG↗

arXiv2026

Fluctuations for the Sherrington--Kirkpatrick spin glass model near the critical temperature

We consider the Sherrington--Kirkpatrick spin glass model with zero external field and at inverse temperature $\beta>0$. Let $F_N(\beta)$ be the corresponding log-partition function. Under the assumption that $c_N:=N^{1/3}(1-\beta_N^2)$ is bounded away from $0$, we prove that Var$(F_N(\beta_N)) = - \frac{1}{2} \log (1-\beta_N^2) -{\beta_N^2}/{2} + O( c_N^{-3/2}).$ As a consequence, we obtain Var$(F_N(1-c N^{-1/3})) = \frac16\log N + O(1)$ for any fixed constant $c\in(0,\infty)$. We also prove a Gaussian central limit theorem for the centered and scaled $F_N(\beta_N)$.

math.PR↗

arXiv2025

Extendable Planning via Multiscale Diffusion

Long-horizon planning is crucial in complex environments, but diffusion-based planners like Diffuser are limited by the trajectory lengths observed during training. This creates a dilemma: long trajectories are needed for effective planning, yet they degrade model performance. In this paper, we introduce this extendable long-horizon planning challenge and propose a two-phase solution. First, Progressive Trajectory Extension incrementally constructs longer trajectories through multi-round compositional stitching. Second, the Hierarchical Multiscale Diffuser enables efficient training and inference over long horizons by reasoning across temporal scales. To avoid the need for multiple separate models, we propose Adaptive Plan Pondering and the Recursive HM-Diffuser, which unify hierarchical planning within a single model. Experiments show our approach yields strong performance gains, advancing scalable and efficient decision-making over long-horizons.

cs.LG↗