We provide an exactly solvable example for interpreting In-Context Learning (ICL) with one-layer attention models as conditional retrieval of dense associative memory models. Our main contribution is to interpret ICL as memory reshaping in the modern Hopfield model from a conditional memory set (in-context examples). Specifically, we show that the in-context sequential examples induce an effective reshaping of the energy landscape of a Hopfield model. We integrate this in-context memory reshaping phenomenon into the existing Bayesian model averaging view of ICL [Zhang et al., AISTATS 2025] via the established equivalence between the modern Hopfield model and transformer attention. Under this unique perspective, we not only characterize how in-context examples shape predictions in the Gaussian linear regression case, but also recover the known $\epsilon$-stability generalization bound of the ICL for the one-layer attention model. We also give explanations for three key behaviors of ICL and validate them through experiments.

We propose a two-stage optimization formulation for the memory retrieval dynamics of modern Hopfield models, termed $\mathtt{U\text{-}Hop}$. Our key contribution is a learnable feature map $\Phi$ which transforms the Hopfield energy function into a kernel space. This transformation ensures convergence between the local minima of energy and the fixed points of retrieval dynamics within the kernel space. Consequently, the kernel norm induced by $\Phi$ serves as a novel similarity measure. It utilizes the stored memory patterns as learning data to enhance memory capacity across all modern Hopfield models. Specifically, we accomplish this by constructing a separation loss $\mathcal{L}_\Phi$ that separates the local minima of kernelized energy by separating stored memory patterns in kernel space. Methodologically, $\mathtt{U\text{-}Hop}$ memory retrieval process consists of: **(Stage I:)** minimizing separation loss for a more uniformed memory (local minimum) distribution, followed by **(Stage II:)** standard Hopfield energy minimization for memory retrieval. This results in significant reduction of possible meta-stable states in the Hopfield energy function, thus preventing memory confusion. Empirically, with real-world datasets, we demonstrate that $\mathtt{U\text{-}Hop}$ outperforms all existing modern Hopfield models and SOTA similarity measures, achieving a substantial margin in both associative memory retrieval and deep learning tasks. Code is available at [GitHub](https://github.com/MAGICS-LAB/UHop); future updates are on [arXiv](https://arxiv.org/abs/2404.03827).