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 ...
367 Accesses 42 Citations Explore all metrics Abstract The rank of a three-way array refers to the smallest number of rank-one arrays (outer products of three vectors) that generate the array as their sum. It is also the number of components required for a full decomposition of a three-wa...
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...
different combinations of k, vocab_size, batch_size and num devices. """ torch.set_default_device(device) typical_acceptance_sampler = TypicalAcceptanceSampler() typical_acceptance_sampler.init_gpu_tensors(rank=0) target_probs = torch.rand(batch_size, k, vocab_size, dtype=torch.float32) bon...
We study the problem of low-rank matrix completion for symmetric matrices. The minimum rank of a completion of a generic partially specified symmetric matrix depends only on the location of the specified entries, and not their values, if complex entries are allowed. When the entries are required...
Then the rank of tensors of size N1 × N2 ×···× Nl is bounded, and one can make a partition of the tensor space, according to the rank values. One can de?ne typical ranks as the ranks that are associated with subsets of nonzero volume in the latter partition. If there is a...
From this, we derive the full retarded and non-local rank-4 Coulomb tensor Uijkl(ω) for both models. Casula et al. showed that using U(ω = 0) instead of the fully retarded U(ω) is justified when renormalized hopping parameters are utilized67. The correspond- ing renormalization ...
In this paper we study typical ranks of real m × n × tensors. In the case ( m 1 ) ( n 1 ) + 1 ≤ ≤ m n the typical ranks are contained in { , + 1 } , and is always a typical rank. We provide a geometric proof of this fact. We express the probabilities of these ...
typical rank3-tensorabsolutely full column tensortensor algebra15A6915A1565F40In 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–Radon function, (2) , and , (3) , ...
We study the generic and typical ranks of 3-tensors of dimension l×m×nl×m×n using results from matrices and algebraic geometry. We state a conjecture about the exact values of the generic rank of 3-tensors over the complex numbers, which is verified numerically for l,m,n≤14l,m,...