AI 中文总结
该研究从生物学获启发引入沙景，由相互作用的霍普菲尔德单元最小模型导出。沙景能自发产生对称破缺和分化树，借助突变理论自组织向翻转分岔发展，可作发育轨迹生成模型，揭示了自适应动力学中主体与景观反馈产生相关特性的机制。
AI 中文摘要
能量景观为描述学习、胚胎发育和集体动力学提供了一个通用框架。虽然这些景观可能随时间演变，但其动态通常由外部规定而非系统自身产生。本文从生物学中获得灵感引入沙景，即相互作用主体的运动不断重塑支配自身轨迹的景观。我们从相互作用的霍普菲尔德单元的最小模型推导出沙景，其中每个吸引子的盆地由其占有率调制。沙景自发产生顺序对称破缺和分化树，局部分支由耦合伊辛动力学描述。然后我们驱动沙景动力学并利用突变理论表明沙景自组织向翻转分岔发展，这为普遍存在的二元细胞命运决定的出现提供了一种通用机制。我们进一步证明沙景可作为发育轨迹的生成模型：仅从终端状态开始，我们重建了具有多层中间祖细胞状态的现实造血分化树。更广泛地说，我们的结果将沙景确定为自适应动力学的一般原则，解释了主体与景观之间的反馈如何在学习和生物学中产生分支、临界性和自组织。
英文摘要
Energy landscapes provide a common framework for describing learning, embryonic development, and collective dynamics. Although such landscapes may evolve over time, their dynamics are typically prescribed externally rather than generated by the system itself. Here we get inspiration from biology to introduce sandscapes : self-modifying landscapes in which the motions of interacting agents continuously reshape the landscape that governs their own trajectories. We derive sandscapes from a minimal model of interacting Hopfield units, where the basins of each attractor are modulated by their occupancies. Sandscapes spontaneously generate sequential symmetry breaking and differentiation trees, with local branching described by coupled Ising dynamics. We then drive the dynamics of sandscapes (using local proliferation common in biology) and leverage catastrophe theory to show that sandscapes self-organize toward flip bifurcations, suggesting a generic mechanism for the emergence of ubiquitous binary cell-fate decisions. We further demonstrate that sandscapes can act as generative models of developmental trajectories : starting from terminal states alone, we reconstruct realistic hematopoietic differentiation trees with multiple layers of intermediate progenitor states. More broadly, our results identify sandscapes as a general principle of adaptive dynamics, explaining how feedback between agents and landscapes produces branching, criticality, and self-organization across learning and biology.
