Analog Neural Networks模拟信号神经网络

Digital hardware maps nearly every computation onto the same underlying machinery: transistors executing long sequences of discrete instructions. This architecture is extraordinarily versatile, but it often forces the physics to imitate an algorithm designed in software. We take a different route. Instead of prescribing every intermediate step, we let a physical dynamical system carry out the computation through its own natural evolution. Information is encoded in the system’s initial state or external constraints; the system then evolves under its Hamiltonian, interactions, and dissipation, and the answer is extracted from the collective state, correlations, or equilibrium configuration that emerges. Computation becomes not merely something represented by physics, but a physical process in itself.数字计算几乎把所有问题都转化为同一种形式：由晶体管执行一连串离散指令。这一架构极其通用，但也意味着，无论问题本身来自怎样的物理过程，最终都必须被重新编码成适合数字处理器执行的算法。我们尝试走另一条路：不再规定每一步应该如何计算，而是让一个真实的物理动力系统通过自身演化直接给出答案。信息可以被写入系统的初始状态、边界条件或外部约束之中，随后系统在相互作用、非线性、耗散与涨落的共同作用下自然演化，计算结果则从最终形成的整体状态、关联或平衡构型中读取。于是，计算不再只是由物理器件执行的一串指令，而成为物理过程本身。

The opportunity lies in collective behavior. When many simple degrees of freedom interact, they can organize into structured states that are not contained in any individual component. These emergent states may encode solutions to optimization problems, linear systems, inference tasks, or other computations that are costly to reproduce through sequential digital operations. By shaping the interactions, energy landscape, and boundary conditions of the system, we guide its dynamics so that a disordered or incomplete input evolves toward a state that represents the desired result. In this framework, we do not program every operation performed by the hardware. We design—and, where possible, train—the dynamics themselves, allowing useful computational behavior to emerge from the underlying physics.这种计算方式的潜力来自集体行为。当大量简单的自由度彼此耦合时，它们可以自发形成具有结构的整体状态，而这些状态并不属于任何单个元件。通过设计系统中的相互作用、能量景观和边界条件，我们可以引导其动力学，使一个无序或不完整的初始状态逐渐演化为编码答案的目标构型。这里，我们不再逐条编程硬件，而是设计乃至训练系统的动力学本身，让所需的功能从底层物理规律中自然涌现。优化、线性方程求解、推断等任务，都可能由此获得不同于传统数字算法的实现方式。

This perspective opens a broader question: what algorithms become possible when computation is no longer constrained to the operations that conventional processors perform efficiently? Physical systems offer parallelism, fluctuations, nonlinear interactions, relaxation, and self-organization as native resources. Harnessing these processes may not only accelerate existing algorithms, but also enable new computational models built around what nature already does well.更重要的是，这一思路提出了一个更根本的问题：当计算不再受限于传统处理器最擅长的操作时，哪些新的算法和机器将成为可能？物理系统天然具备并行演化、非线性耦合、涨落、弛豫与自组织等能力。真正利用这些特性，目标不仅是更快地执行已有算法，更是围绕物理系统本身擅长的过程，发展新的计算原理与人工智能架构。