arXiv:2608.00097cond-mat.softcond-mat.dis-nn2026-08被引 1

物理学习中,不可训练元件决定模型记忆,而非守恒律。

Untrainable elements determine what physical learning remembers

  • 区分电路缩放不变性与规则质量守恒,发现不可训练元件破坏前者
  • 单个固定忆阻器使学习结果随初始化变化12%,全可训练时仅0.00003%
  • 适合研究神经形态计算、硬件感知学习的读者关注

如平衡传播(EP)、耦合学习(CL)和伴随耦合学习(AL)等物理学习规则通过局部测量训练电阻网络,其学习函数取决于训练落在解流形的哪个位置。两个可能影响该结果的特性未被分离:电路在所有电导缩放下的不变性,以及规则对质量 K = (1/2) sum_e kappa_e^2 的守恒性。本文将其分离。当所有元件可训练时,三种向量场在电导上均为齐次,初始尺度可证明无关。但规则不调整的元件无论其本构关系如何,均破坏齐次性。在二十种拓扑中,固定整流器时学习函数随初始尺度变化中位数达12%,固定线性电阻时为8%,而全可训练时仅为3×10⁻⁸;一个固定整流器即产生全部效应。守恒律并非记忆保护机制:我们证明AL以自身损失两倍速率耗散质量,却仍与守恒规则一样强地保留初始记忆,且在K保守至1×10⁻⁴时记忆仍存。将固定元件数从1增至8使守恒漂移增大五千倍,但记忆不变;而全可训练电路在AL下漂移相当却无记忆。规则守恒结构实际控制的是解的质量:在六种小电路中,相同训练损失下AL性能比EP和CL差3%~7%,排序不稳定且在50节点时不复现。因此,物理学习包含两个独立归纳偏置:一个属于电路,一个属于规则,且只有前者是设备构建方式的记忆。

原文摘要 · Abstract (English)

Physical learning rules such as equilibrium propagation (EP), coupled learning (CL), and adjoint coupled learning (AL) train resistive networks through local measurements. The learned function is decided by where on the solution manifold training lands. Two properties could decide it, and they have not been separated: the circuit's invariance under rescaling every conductance, and the rule's conservation of the mass K = (1/2) sum_e kappa_e^2. We separate them. When every element is trainable, all three vector fields are homogeneous in the conductances, so the initialization scale is provably inert. An element the rule does not adjust breaks that homogeneity whatever its constitutive law. Across twenty topologies the learned function moves with the initialization scale by a median of twelve percent with fixed rectifiers and eight with fixed linear resistors, against 3e-8 when every element is trainable; a single fixed rectifier produces the whole effect. The conservation law is not what protects the function: AL, which we prove dissipates the mass at exactly twice its own loss, remembers its initialization as strongly as the rules that conserve it, and the memory survives in runs where K is conserved to 1e-4. Raising the fixed-element count from one to eight multiplies the conservation drift by five thousand and leaves the memory unchanged, while the all-trainable circuit under AL drifts comparably and remembers nothing. What the rule's conservation structure does control is solution quality: at matched training loss AL is worse than EP and CL in four of six small circuits, by a median of three to seven percent, though the ordering is not stable across checkpoints and does not reproduce at fifty nodes. Physical learning therefore carries two independent inductive biases, one belonging to the circuit and one to the rule, and only the first is a memory of how the device was built.

物理学习忆阻网络记忆机制

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。