human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "on identity testing of tensors low rank recovery and compressed sensing"):
  Abstract: We study the problem of obtaining efficient, deterministic, black-box polynomial identity testing algorithms for depth-3 set-multilinear circuits (over arbitrary fields). This class of circuits has an efficient, deterministic, white-box polynomial identity testing algorithm (due to Raz and Shpilka [36]), but has no known such black-box algorithm. We recast this problem as a question of finding a low-dimensional subspace H, spanned by rank 1 tensors, such that any non-zero tensor in the dual space ker(H) has high rank. We obtain explicit constructions of essentially optimal-size hitting sets for tensors of degree 2 (matrices), and obtain the first quasi-polynomial sized hitting sets for arbitrary tensors. We also show connections to the task of performing low-rank recovery of matrices, which is studied in the field of compressed sensing. Low-rank recovery asks (say, over R) to recover a matrix M from few measurements, under the promise that M is rank ≤ r. In this work, we restrict our attention to recovering matrices that are exactly rank ≤ r using deterministic, non-adaptive, linear measurements, that are free from noise. Over R, we provide a set (of size 4nr) of such measurements, from which M can be recovered in O(rn2+r3n) field operations, and the number of measurements is essentially optimal. Further, the measurements can be taken to be all rank-1 matrices, or all sparse matrices. To the best of our knowledge no explicit constructions with those properties were known prior to this work.   We also give a more formal connection between low-rank recovery and the task of sparse (vector) recovery: any sparse-recovery algorithm that exactly recovers vectors of length n and sparsity 2r, using m non-adaptive measurements, yields a low-rank recovery scheme for exactly recovering n x n matrices of rank ≤ r, making 2nm non-adaptive measurements. Furthermore, if the sparse-recovery algorithm runs in time τ, then the low-rank recovery algorithm runs in time O(rn2+nτ). We obtain this reduction using linear-algebraic techniques, and not using convex optimization, which is more commonly seen in compressed sensing algorithms.   Finally, we also make a connection to rank-metric codes, as studied in coding theory. These are codes with codewords consisting of matrices (or tensors) where the distance of matrices M and N is rank(M-N), as opposed to the usual hamming metric. We obtain essentially optimal-rate codes over matrices, and provide an efficient decoding algorithm. We obtain codes over tensors as well, with poorer rate, but still with efficient decoding.

Includes members:
  Member "rank minimization over finite fields fundamental limits and coding theoretic interpretations":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "almost everywhere injectivity conditions for the matrix recovery problem")
  Member "recovering low rank matrices from few coefficients in any basis":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "matrix completion with prior subspace information via maximizing correlation")
  Member "subspace expanders and matrix rank minimization":
    also connected through other hyperedges:
      (none)
  Member "information theoretic bounds for tensor rank minimization over finite fields":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "rank minimization over finite fields fundamental limits and coding theoretic interpretations")
  Member "on the power of adaptivity in sparse recovery":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "stronger l2 l2 compressed sensing without iterating")
  Member "tensor rank some lower and upper bounds":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "learning representations from imperfect time series data via tensor rank regularization")
  Member "blackbox identity testing for bounded top fanin depth 3 circuits the field doesn t matter":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "a generalized sylvester gallai type theorem for quadratic polynomials")
  Member "the power of convex relaxation near optimal matrix completion":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "ell_0 motivated low rank sparse subspace clustering")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.CC(Computational Complexity)