In various application fields, tensor type data are used recently and then a typical rank is important. There may be more than one typical ranks over the real number field. It is well known that the set of 2×n×n 2 × n × n mathContainer Loading Mathjax tensors has two typical ...
The number $(m-1)n-1$ is a minimal typical rank of $mimes nimes ((m-1)n-1)$ tensors over the real number field. We show that a typical rank of $mimes nimes ((m-1)n-1)$ tensors over the real number field is less than or equal to $(m-1)n$ and in particular, $mimes...
different combinations of k, vocab_size, batch_size and num devices. """ torch.set_default_device(device) typical_acceptance_sampler = TypicalAcceptanceSampler() typical_acceptance_sampler = get_acceptance_sampler() typical_acceptance_sampler.init_gpu_tensors(rank=0) target_probs = torch.rand(ba...
In spite of better groundedness, LaMDA exhibits many of the nuisance qualities of chatbots. It speaks in overly general ways that lack any specificity and depth. It often seems to talk in "bromides," a "trite and unoriginal idea or remark." Much of the conversation is so superficial that...
typical rankHurwitz–Radon numberperfect15A6914P1014Q20Let . We study typical ranks of tensors over the real number field. Let be the Hurwitz–Radon function defined as for nonnegative integers such that and . If , then the set of tensors has two typical ranks . In this paper, we show...
In this paper, we study typical ranks of 3-tensors and show that there are\nplural typical ranks for mimes nimes p tensors over R in the following\ncases: (1) 3\\leq m\\leq ho(n) and (m-1)(n-1)+1\\leq p\\leq (m-1)n, where ho\\\nis the Hurwitz-Radon function, (2...
Tensor ranktypical rank3-tensorabsolutely full column tensortensor algebraIn this paper, we study typical ranks of 3- tensors and show that there are plural typical ranks for m x n x p tensors over R in the following cases: (1) 3 <= m <=.(n) and (m - 1)(n - 1) + 1 <=...
typical ranktall tensorsemi-tall tensorBezout's theoremdeterminantal varietyM X NSECANT VARIETIES1)N TENSORS(MLet m, n and p be integers with and . We showed in previous papers that if , then typical ranks of -tensors over the real number field are p and p+1 if and only if there ...
Tensor rankTypical rankDeterminantal idealReal radicalBilinear mapMonomial preorderLetm,n≥3,(m−1)(n−1)+2≤p≤mn, andu=mn−p. The setRu×n×mof all real tensors with sizeu×n×mis one to one corresponding to the set of bilinear mapsRm×Rn→Ru. We show thatRm×n×phas ...
rank3-tensorabsolutelyfullcolumntensortensorIn this paper, we study typical ranks of 3-tensors and show that there are plural typical ranks for tensors over in the following cases: (1) and , where is the Hurwitz鈥揜adon function, (2) ...