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## A Technique for Upper Bounding the Spectral Norm with Applications to Learning (1992)

Venue: | In Proceedings of the Fifth Annual Workshop on Computational Learning Theory |

Citations: | 13 - 0 self |

### Citations

1968 | A theory of the learnable.
- Valiant
- 1984
(Show Context)
Citation Context ...nique to bound spectral norms. 1.4 Applications Our main theorem has several applications to the design of efficient learning algorithms. Learning DNF. We address the problem of learning DNF formulas =-=[Va]-=-. Linial, Mansour and Nisan [LMN], Verbeurgt [Ve], and Furst, Jackson and Smith [FJS] consider (ffl; ffi; D) learning of DNF formulas: after seeing a collection of examples of the target f drawn under... |

326 |
Constant depth circuits, Fourier transform, and learnability.
- Linial, Mansour, et al.
- 1993
(Show Context)
Citation Context ...of simple functions. 7 Extensions Furst, Jackson and Smith [FJS] introduce the notion of mutually independent distributions and show how to extend the spectral techniques of Linial, Mansour and Nisan =-=[LMN]-=- (used for learning DNF under the uniform distribution) to the case of mutually independent distributions. Our techniques and results can be similarly extended to the case of mutually independent dist... |

293 | The influence of variables on boolean functions - Kahn, Kalai, et al. - 1988 |

205 | Learning decision trees using the fourier spectrum.
- Kushilevitz, Mansour
- 1993
(Show Context)
Citation Context ...e spectral norm plays a key role. One example is learning: we know that if L(f) is polynomially bounded then f is learnable (under the uniform distribution with membership queries) in polynomial time =-=[KM]-=-. Another example is in the domain of threshold circuits (or neural nets): we know that if L(f) is polynomially bounded then f can by computed by a threshold circuit of small depth [BS]. To use such t... |

140 | Threshold circuits of bounded depth. - Hajnal, Maass, et al. - 1993 |

92 | Harmonic analysis of polynomial threshold functions. - Bruck - 1990 |

51 | Fast learning of kterm DNF formulas with queries
- Blum, Rudich
- 1992
(Show Context)
Citation Context ...rnable in polynomial time. More generally, we show that a k-term DNF formula is learnable in time polynomial in n; 2 k ; ffl \Gamma1 , and lg ffi \Gamma1 . Independently of this work, Blum and Rudich =-=[BR]-=- present an algorithm which uses membership and equivalence queries to (exactly) learn a k-clause DNF formula in time polynomial in n and 2 k . Learning Decision Trees. We present a general result abo... |

46 |
On the power of threshold circuits with small weights.
- Siu, Bruck
- 1991
(Show Context)
Citation Context ... only known either for very simple functions (like parity, AND and OR) or for functions where one can compute L(f) exactly by exploiting a convenient inductive structure (like the comparison function =-=[SB]-=-). And so far there have been no general techniques to compute upper bounds: the approach used is to work directly from the definition. This paper presents a general technique to upper bound the spect... |

32 |
Polynomial threshold functions, AC functions, and spectral norms
- Bruck, Smolensky
- 1992
(Show Context)
Citation Context ...olynomial time [KM]. Another example is in the domain of threshold circuits (or neural nets): we know that if L(f) is polynomially bounded then f can by computed by a threshold circuit of small depth =-=[BS]-=-. To use such theorems, we need to first show that L(f) is small. So it is important to find ways of computing good upper bounds on the spectral norm, and thereby, in particular, identifying the funct... |

5 | The spectral norm of finite functions
- Bellare
- 1991
(Show Context)
Citation Context ...way to get small depth circuits for combinations of simple functions. We note that the theorem of [BS], and in consequence ours, are non-constructive. The results of this paper appeared previously in =-=[Be1] and [Be2]-=-. 2 Preliminaries "Boolean" for us means \Sigma1 valued. A function f : f\Gamma1; +1g n ! R is boolean if its range is f\Gamma1; +1g. The sign of x 2 R, denoted sign (x), is \Gamma1 if x ! 0... |

3 |
Learning DNF under the uniform distribution in polynomial time
- Verbeurgt
- 1990
(Show Context)
Citation Context ...ur main theorem has several applications to the design of efficient learning algorithms. Learning DNF. We address the problem of learning DNF formulas [Va]. Linial, Mansour and Nisan [LMN], Verbeurgt =-=[Ve]-=-, and Furst, Jackson and Smith [FJS] consider (ffl; ffi; D) learning of DNF formulas: after seeing a collection of examples of the target f drawn under distribution D, the algorithm must output a hypo... |

2 |
Learning AC functions sampled under mutually independent distributions
- Furst, Jackson, et al.
- 1990
(Show Context)
Citation Context ...tions to the design of efficient learning algorithms. Learning DNF. We address the problem of learning DNF formulas [Va]. Linial, Mansour and Nisan [LMN], Verbeurgt [Ve], and Furst, Jackson and Smith =-=[FJS]-=- consider (ffl; ffi; D) learning of DNF formulas: after seeing a collection of examples of the target f drawn under distribution D, the algorithm must output a hypothesis h which with probability at l... |