Researchers have identified two distinct factors that influence what physical learning rules remember. One factor is related to the conservation of mass in the system, while the other is tied to the circuit's invariance under rescaling. The study found that when not all elements are trainable, the initialization scale has a significant impact on the learned function. This suggests that physical learning carries two independent biases: one from the circuit and one from the rule. The conservation law does not necessarily protect the function, but rather influences solution quality. --- Why it matters: This research is important for engineers working with physical learning rules because it highlights the need to consider both the circuit's properties and the rule's structure when designing systems that learn from their environment. Source: https://arxiv.org/abs/2608.00097