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 "probabilistic rank and matrix rigidity"):
  Abstract: We consider a notion of probabilistic rank and probabilistic sign-rank of a matrix, which measures the extent to which a matrix can be probabilistically represented by low-rank matrices. We demonstrate several connections with matrix rigidity, communication complexity, and circuit lower bounds, including: #R##N#The Walsh-Hadamard Transform is Not Very Rigid. We give surprising upper bounds on the rigidity of a family of matrices whose rigidity has been extensively studied, and was conjectured to be highly rigid. For the $2^n \times 2^n$ Walsh-Hadamard transform $H_n$ (a.k.a. Sylvester matrices, or the communication matrix of Inner Product mod 2), we show how to modify only $2^{\epsilon n}$ entries in each row and make the rank drop below $2^{n(1-\Omega(\epsilon^2/\log(1/\epsilon)))}$, for all $\epsilon > 0$, over any field. That is, it is not possible to prove arithmetic circuit lower bounds on Hadamard matrices, via L. Valiant's matrix rigidity approach. We also show non-trivial rigidity upper bounds for $H_n$ with smaller target rank. #R##N#Matrix Rigidity and Threshold Circuit Lower Bounds. We give new consequences of rigid matrices for Boolean circuit complexity. We show that explicit $n \times n$ Boolean matrices which maintain rank at least $2^{(\log n)^{1-\delta}}$ after $n^2/2^{(\log n)^{\delta/2}}$ modified entries would yield a function lacking sub-quadratic-size $AC^0$ circuits with two layers of arbitrary linear threshold gates. We also prove that explicit 0/1 matrices over $\mathbb{R}$ which are modestly more rigid than the best known rigidity lower bounds for sign-rank would imply strong lower bounds for the infamously difficult class $THR\circ THR$.

Includes members:
  Member "polynomial representations of threshold functions and algorithmic applications":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "approximating text to pattern hamming distances")
  Member "super linear gate and super quadratic wire lower bounds for depth two and depth three threshold circuits":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a deep conditioning treatment of neural networks")
  Member "probabilistic polynomials and hamming nearest neighbors":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "algorithms for similarity search and pseudorandomness")
  Member "using elimination theory to construct rigid matrices":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "unifying known lower bounds via geometric complexity theory")
  Member "faster all pairs shortest paths via circuit complexity":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "deterministic algorithms for decremental approximate shortest paths faster and simpler")
  Member "three lines proof of the lower bound for the matrix rigidity":
    also connected through other hyperedges:
      (none)
  Member "communication complexity lower bounds by polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "sensitivity affine transforms and quantum communication complexity")

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)