arXiv:2608.23889math.OCcs.LG2026-08

用深度学习模拟生物可塑性,发现两个无量纲参数决定学习效果。

Dimensionless Controls of Plasticity Under Alternating Tasks: From Evolutionary Biology to Continual Learning

论文配图:Dimensionless Controls of Plasticity Under Alternating Tasks: From Evolutionary Biology to Continual Learning
图 1 · 摘自论文原文
  • 将生物可塑性机制转化为训练动态量,提炼出任务分歧率和学习率-切换周期乘积两个核心参数。
  • 在9720次实验中验证:任务分歧率决定学习极限,两者共同限制遗忘程度。
  • 适用于研究持续学习、神经演化或物理类比系统的研究人员。

在变化环境中的可塑性是进化生物学与持续学习的核心问题。受基因型-表型映射研究启发,我们构建了一个最小化深度学习模型,交替训练两个布尔标签集,探究生物可塑性控制机制在梯度下降下的保留情况。将四种生物因素重解释为训练动态量,发现系统可简化为两个无量纲控制变量:任务分歧率 $r$(不一致标签比例)和可达性 $ηT$(学习率与切换周期的乘积)。我们推导出两个可塑性边界:仅 $r$ 决定乌托邦距离的几何下限;$r$ 与 $ηT$ 共同约束遗忘程度。在9,720条轨迹中,方差分析确认 $r$、$η$、$T$ 起主导作用,而中性集大小(生物设定中强调)影响可忽略。最优可达性满足近似反幂律关系 $ηT^{*}/propto r^{-1.18}$,可仅凭任务分歧率估算最优 $ηT^*$。因此,保留下来的类比是动力学而非几何性的,该框架为可塑性提供了物理学与工程学驱动系统的视角。

原文摘要 · Abstract (English)

Plasticity under changing environments is central to both evolutionary biology and continual learning. Motivated by recent work on genotype--phenotype maps, we study a minimal deep-learning analogue where a network is trained alternately on two Boolean label sets, and ask which biological controls of plasticity survive the translation to gradient descent. Reinterpreting four proposed biological factors as quantities of training dynamics, we find the system reduces to two dimensionless controls: the task disagreement $r$, the fraction of disagreeing labels, and the reach $ηT$, the product of learning rate and switching period. We derive two bounds on plasticity: $r$ alone fixes an extremal geometric floor on the utopia distance, while $r$ and $ηT$ jointly bound forgetting. Across 9,720 trajectories, an ANOVA confirms that $r$, $η$, and $T$ dominate, while the effect of neutral-set size (emphasized in the biological setting) is negligible. The optimal reach itself follows an approximate inverse power law $ηT^{*}\propto r^{-1.18}$, yielding a heuristic that sets the optimal reach $ηT^*$ from the task disagreement alone. The analogy that survives is therefore dynamical rather than geometric, and our setting enables a view of plasticity through the lens of other driven systems in physics and engineering.

持续学习可塑性深度学习动力系统

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