Disentangling Computation in Multi-Task Neural Networks with the Green's Operator
Researchers use the Green's operator to map how multitask recurrent networks reuse computation across tasks and time.
The paper analyzes how computation is organized and reused in a trained multitask recurrent network using the network's global first-order perturbation response. The finite-horizon Green's operator maps perturbations along a trajectory to downstream state-space responses, giving task-to-task and time-to-time views of the same computation. In a flexible multitask RNN, task reductions show structured reuse of known motifs, while temporal reductions show causal pathways and how they emerge during training. Matrix-free products make the analysis possible without constructing the full operator.
- The finite-horizon Green's operator maps perturbations to downstream state-space responses.
- Task and time reductions reveal reused motifs and causal pathways in a multitask RNN.
- Matrix-free products make these views available without building the full operator.
From the original article
1 min read at arxiv.orgHow 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.
By James Hazelden · arxiv.org
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