arXiv:2609.23094v1 Announce Type: cross
Abstract: We study the number of prototypes needed to represent Boolean functions by nearest-neighbour classification. There are two distinct settings: the pro...
By Martin Anthony
arXiv:2608. 16438v1 Announce Type: new Abstract: In a world where valuable artifacts are increasingly created, completed, or processed by LLMs, the central economic question is not only what the LLM can produce, but what \emph{value} remains in the inputs (i.
By Rafael Pass
arXiv:2608. 02533v1 Announce Type: cross Abstract: We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $\Omega(n^2)$.
By Chirag Pabbaraju
arXiv:2608. 03439v1 Announce Type: cross Abstract: In recent work, Marcussen, Rubinfeld, and Sudan introduced the notion of quality control problems, which aim to capture the task of determining if a given input is truly random.
By Cassandra Marcussen, Ronitt Rubinfeld, Madhu Sudan
We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $Ω(n^2)$. By utilizing the special structure of these DNFs, we prove a lifting theorem with a constant-sized gadget that lifts the DNF to a communication problem, while losslessly translating the separation in certificate complexity to a separation in communication complexity.
arXiv:2609. 04046v1 Announce Type: cross Abstract: What can a single layer of self-attention compute?
By Rajmohan Rajaraman, Ravi Sundaram, Amanuel Tesfaye