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Attention-based representations for multi-task computation — arXiv:2608.04243

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.04243
License (as archived): CC0-1.0
Archived: 2026-10-08T09:11:44.522Z
SHA-256 of the archived text: 2cdf61fd3c4d90980aacaebfb53815d5bc85aac84100c83fac5fe88917b6c319
Stable URL of this page: https://metraipolis.com/documento/dc_cfbc2ca91680

How to cite

Attention-based representations for multi-task computation — arXiv:2608.04243 — arXiv (en), https://arxiv.org/abs/2608.04243 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cfbc2ca91680 (Metraipolis archive dc_cfbc2ca91680, sha256 2cdf61fd3c4d90980aacaebfb53815d5bc85aac84100c83fac5fe88917b6c319)

BibTeX

@misc{dccfbc2ca91680,
  title = {Attention-based representations for multi-task computation — arXiv:2608.04243},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.04243},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cfbc2ca91680; sha256 2cdf61fd3c4d90980aacaebfb53815d5bc85aac84100c83fac5fe88917b6c319},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.04243. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Multi-head attention layers produce vector representations that support multiple downstream tasks. We establish bounds on the number of heads required in two simple and concrete multi-task scenarios. In the first scenario, a vector representation is sought so that linear predictors can compute both the smallest and largest numbers in a given list. In this case, it is known two attention heads with small embedding dimension and bit precision level suffice. We prove that a single attention head requires exponentially higher embedding dimension or precision level. In the second scenario, a vector representation is sought so that a polynomial threshold function can compute the XOR of a given string of $n$ bits. This scenario is analogous to the first one for $n=2$, since XOR is readily computed by a linear function using a vector representation that encodes both the AND and the OR of the two bits. We observe that $n$-bit XOR requires the product of the number of heads and the polynomial degree to be at least $n$, and we construct multi-head attention layers that match this lower bound. These results generalize to arbitrary (symmetric) Boolean functions, where the bound is given in terms of the threshold degree.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-24 in cs.AI).
Categorie arXiv: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI); Computational Complexity (cs.CC).
Pagina del lavoro: https://arxiv.org/abs/2608.04243 — 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 2026-10-08T08:13:26.562Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-09-24?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).