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Disentangling Computation in Multi-Task Neural Networks with the Green's Operator — arXiv:2609.40292

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.40292
License (as archived): CC0-1.0
Archived: 2026-10-07T13:47:01.911Z
SHA-256 of the archived text: 61eb51affd1882d46ba2bcb5e6fe9c16f5e94e5d0865807aa187e06797085e4e
Stable URL of this page: https://metraipolis.com/documento/dc_bae91ef49fee

How to cite

Disentangling Computation in Multi-Task Neural Networks with the Green's Operator — arXiv:2609.40292 — arXiv (en), https://arxiv.org/abs/2609.40292 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bae91ef49fee (Metraipolis archive dc_bae91ef49fee, sha256 61eb51affd1882d46ba2bcb5e6fe9c16f5e94e5d0865807aa187e06797085e4e)

BibTeX

@misc{dcbae91ef49fee,
  title = {Disentangling Computation in Multi-Task Neural Networks with the Green's Operator — arXiv:2609.40292},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.40292},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bae91ef49fee; sha256 61eb51affd1882d46ba2bcb5e6fe9c16f5e94e5d0865807aa187e06797085e4e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.40292. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-10-01 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG) ; Neurons and Cognition (q-bio.NC).
Pagina del lavoro: https://arxiv.org/abs/2609.40292 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T13:18:10.528Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).