On physical processes that work like learning algorithms

Adaptive behavior is a widespread phenomenon observed in both living and non-living systems, manifesting in diverse forms such as the directional growth of plants in response to sunlight and the directed aging of materials. Such diversity demands a physics-based approach. Thus, the emerging field of physical learning aims to explain these phenomena by drawing analogies between adaptive processes in nature and learning in neural networks, motivating the central question of this thesis: Can physical processes in nature function like learning algorithms? A typical learning algorithm involves two fundamental steps: signaling and weight up- dating. In the Part I of the thesis, we focus on how physical systems can perform input and feedback signaling. In Chapter 2, we draw inspiration from the remarkable adaptability of Physarum polycephalum -aka slime mold - to present a mechanism for optimizing flow net- works. This mechanism operates on the principle that each network component—specifically, the tubes—utilizes locally available information to collectively minimize a global cost function. In Chapter 5, we continue our analysis of this tuning process by constructing a comprehensive phase diagram that identifies the specific network parameters under which successful adaptation, or tuning, is achieved. We reveal a phase boundary in the phase diagram, indicating a distinct satisfiability-unsatisfiability (SAT-UNSAT) phase transition that delineates successful and unsuccessful adaptation, and propose that such a phase boundary might also exist between living and non-living systems. In Chapter 3, we introduce Multi-mechanism Learning (MML), a learning process that encodes input and feedback signals into two distinct, non-interfering physical quantities. We formulate a simple backpropagation-like learning process that uses local information to perform gradient descent on a global cost function. As biological systems possess multiple signaling pathways, we propose that this learning process can model adaptive phenomena in biology. Additionally, in Chapter 4, we introduce frequency propagation, a case of MML, where we encode feedback and feedforward signals in distinct frequency domains, and demonstrate how this algorithm can train non-linear resistor networks. In Part II of the thesis, we explore physical processes that mimic weight updates in artificial neural networks. In Chapter 6, we argue that glassy systems can be used for weight updates due to their slow, history-dependent dynamics. Recognizing that the weight update rule in Multi-mechanism Learning initially seems non-physical, we modify it to resemble aging phenomena and demonstrate its utility in training physical systems to exhibit complex behaviors, such as performing linear regression. While our modified weight update rule is now physically grounded, it still relies on an explicit update mechanism. In Chapter 7, we propose a microscopic model in which the physics of the system inherently drives the weight updates, eliminating the need for external update rules. This model allows the system to self-organize and adjust its parameters based solely on its internal dynamics and interactions. This thesis offers new insights into the potential of physical systems to emulate learn- ing algorithms, paving the way for innovative approaches to understanding and harnessing adaptive behaviors in both living and non-living systems.