Matches in SemOpenAlex for { <https://semopenalex.org/work/W4225414648> ?p ?o ?g. }
Showing items 1 to 63 of
63
with 100 items per page.
- W4225414648 abstract "We prove strengthened lower bounds for constant-depth set-multilinear formulas. More precisely, we show that over any field, there is an explicit polynomial $f$ in VNP defined over $n^2$ variables, and of degree $n$, such that any product-depth $Delta$ set-multilinear formula computing $f$ has size at least $n^{Omega left( n^{1/Delta}/Deltaright)}$. The hard polynomial $f$ comes from the class of Nisan-Wigderson (NW) design-based polynomials. Our lower bounds improve upon the recent work of Limaye, Srinivasan and Tavenas (STOC 2022), where a lower bound of the form $(log n)^{Omega (Delta n^{1/Delta})}$ was shown for the size of product-depth $Delta$ set-multilinear formulas computing the iterated matrix multiplication (IMM) polynomial of the same degree and over the same number of variables as $f$. Moreover, our lower bounds are novel for any $Deltageq 2$. For general set-multilinear formulas, a lower bound of the form $ n^{Omega(log n)}$ was already obtained by Raz (J. ACM 2009) for the more general model of multilinear formulas. The techniques of LST give a different route to set-multilinear formula lower bounds, and allow them to obtain a lower bound of the form $(log n)^{Omega(log n)}$ for the size of general set-multilinear formulas computing the IMM polynomial. Our proof techniques are another variation on those of LST, and enable us to show an improved lower bound (matching that of Raz) of the form $n^{Omega(log n)}$, albeit for the same polynomial $f$ in VNP (the NW polynomial). As observed by LST, if the same $n^{Omega(log n)}$ size lower bounds for unbounded-depth set-multilinear formulas could be obtained for the IMM polynomial, then using the self-reducibility of IMM and using hardness escalation results, this would imply super-polynomial lower bounds for general algebraic formulas." @default.
- W4225414648 created "2022-05-05" @default.
- W4225414648 creator A5020540233 @default.
- W4225414648 creator A5087309847 @default.
- W4225414648 date "2022-05-01" @default.
- W4225414648 modified "2023-09-27" @default.
- W4225414648 title "Improved Low-Depth Set-Multilinear Circuit Lower Bounds" @default.
- W4225414648 doi "https://doi.org/10.48550/arxiv.2205.00611" @default.
- W4225414648 hasPublicationYear "2022" @default.
- W4225414648 type Work @default.
- W4225414648 citedByCount "0" @default.
- W4225414648 crossrefType "posted-content" @default.
- W4225414648 hasAuthorship W4225414648A5020540233 @default.
- W4225414648 hasAuthorship W4225414648A5087309847 @default.
- W4225414648 hasBestOaLocation W42254146481 @default.
- W4225414648 hasConcept C114614502 @default.
- W4225414648 hasConcept C118615104 @default.
- W4225414648 hasConcept C121332964 @default.
- W4225414648 hasConcept C134306372 @default.
- W4225414648 hasConcept C140479938 @default.
- W4225414648 hasConcept C202444582 @default.
- W4225414648 hasConcept C24890656 @default.
- W4225414648 hasConcept C2524010 @default.
- W4225414648 hasConcept C2775997480 @default.
- W4225414648 hasConcept C2779557605 @default.
- W4225414648 hasConcept C33923547 @default.
- W4225414648 hasConcept C62520636 @default.
- W4225414648 hasConcept C77553402 @default.
- W4225414648 hasConcept C84392682 @default.
- W4225414648 hasConcept C90119067 @default.
- W4225414648 hasConcept C90673727 @default.
- W4225414648 hasConceptScore W4225414648C114614502 @default.
- W4225414648 hasConceptScore W4225414648C118615104 @default.
- W4225414648 hasConceptScore W4225414648C121332964 @default.
- W4225414648 hasConceptScore W4225414648C134306372 @default.
- W4225414648 hasConceptScore W4225414648C140479938 @default.
- W4225414648 hasConceptScore W4225414648C202444582 @default.
- W4225414648 hasConceptScore W4225414648C24890656 @default.
- W4225414648 hasConceptScore W4225414648C2524010 @default.
- W4225414648 hasConceptScore W4225414648C2775997480 @default.
- W4225414648 hasConceptScore W4225414648C2779557605 @default.
- W4225414648 hasConceptScore W4225414648C33923547 @default.
- W4225414648 hasConceptScore W4225414648C62520636 @default.
- W4225414648 hasConceptScore W4225414648C77553402 @default.
- W4225414648 hasConceptScore W4225414648C84392682 @default.
- W4225414648 hasConceptScore W4225414648C90119067 @default.
- W4225414648 hasConceptScore W4225414648C90673727 @default.
- W4225414648 hasLocation W42254146481 @default.
- W4225414648 hasOpenAccess W4225414648 @default.
- W4225414648 hasPrimaryLocation W42254146481 @default.
- W4225414648 hasRelatedWork W2187292610 @default.
- W4225414648 hasRelatedWork W2412308914 @default.
- W4225414648 hasRelatedWork W2744913687 @default.
- W4225414648 hasRelatedWork W2765850415 @default.
- W4225414648 hasRelatedWork W2767623943 @default.
- W4225414648 hasRelatedWork W2963154509 @default.
- W4225414648 hasRelatedWork W3000087930 @default.
- W4225414648 hasRelatedWork W3186548984 @default.
- W4225414648 hasRelatedWork W4225414648 @default.
- W4225414648 hasRelatedWork W4300097816 @default.
- W4225414648 isParatext "false" @default.
- W4225414648 isRetracted "false" @default.
- W4225414648 workType "article" @default.