多任务神经网络中的计算解耦研究
Disentangling Computation in Multi-Task Neural Networks with the Green's Operator
这篇论文用格林算子解构多任务神经网络，揭示了计算如何在任务间和时间上被组织和重用。
研究人员提出使用格林算子研究多任务神经网络中的计算组织和重用。该算子将轨迹上每个源的扰动映射到下游状态空间响应，直接表示扰动路由。任务简化揭示了已知计算 motif 的结构化重用，时间简化揭示了因果路径及其在训练过程中的形成方式。研究提供了学习动态计算组织的全局响应几何框架。
Disentangling Computation in Multi-Task Neural Networks with the Green's Operator
How is computation organized and reused across tasks and time in a trained recurrent network? Most analyses emphasize the geometry of neural activity, dynamical motifs, or local perturbation growth. We instead study the network's global first-order perturbation response. The finite-horizon Green's operator maps perturbations at each source along a trajectory to their downstream state-space responses and therefore directly represents perturbation routing. Simple reductions of this operator provide task-to-task and time-to-time views of the same computation, while matrix-free products make these views accessible without constructing the full operator. In a flexible multitask recurrent network, task reductions reveal structured reuse of known computational motifs, while temporal reductions reveal causal pathways and how they emerge during training. Our main point is simple: the Green's operator provides a global response geometry for mapping the organization of learned dynamical computation.
