Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 5 of 5
Full-Text Articles in Mathematics
When Is Deep Learning Better And When Is Shallow Learning Better: Qualitative Analysis, Salvador Robles Herrera, Martine Ceberio, Vladik Kreinovich
When Is Deep Learning Better And When Is Shallow Learning Better: Qualitative Analysis, Salvador Robles Herrera, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, deep neural networks work better than the traditional "shallow" ones, however, in some cases, the shallow neural networks lead to better results. At present, deciding which type of neural networks will work better is mostly done by trial and error. It is therefore desirable to come up with some criterion of when deep learning is better and when shallow is better. In this paper, we argue that this depends on whether the corresponding situation has natural symmetries: if it does, we expect deep learning to work better, otherwise we expect shallow learning to be more effective. …
Why Daubechies Wavelets Are So Successful, Solymar Ayala Cortez, Laxman Bokati, Aaron Velasco, Vladik Kreinovich
Why Daubechies Wavelets Are So Successful, Solymar Ayala Cortez, Laxman Bokati, Aaron Velasco, Vladik Kreinovich
Departmental Technical Reports (CS)
In many applications, including analysis of seismic signals, Daubechies wavelets perform much better than other families of wavelets. In this paper, we provide a possible theoretical explanation for the empirical success of Daubechies wavelets. Specifically, we show that these wavelets are optimal with respect to any optimality criterion that satisfies the natural properties of scale- and shift-invariance.
Many Known Quantum Algorithms Are Optimal: Symmetry-Based Proofs, Vladik Kreinovich, Oscar Galindo, Olga Kosheleva
Many Known Quantum Algorithms Are Optimal: Symmetry-Based Proofs, Vladik Kreinovich, Oscar Galindo, Olga Kosheleva
Departmental Technical Reports (CS)
Many quantum algorithms have been proposed which are drastically more efficient that the best of the non-quantum algorithms for solving the same problems. A natural question is: are these quantum algorithms already optimal -- in some reasonable sense -- or they can be further improved? In this paper, we review recent results showing that many known quantum algorithms are actually optimal. Several of these results are based on appropriate invariances (symmetries).
Why Kappa Regression?, Julio C. Urenda, Orsolya Csiszár, József Dombi, György Eigner, Olga Kosheleva, Vladik Kreinovich
Why Kappa Regression?, Julio C. Urenda, Orsolya Csiszár, József Dombi, György Eigner, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
A recent book provide examples that a new class of probability distributions and membership functions -- called kappa-regression distributions and membership functions -- leads to better data processing results than using previously known classes. In this paper, we provide a theoretical explanation for this empirical success -- namely, we show that these distributions are the only ones that satisfy reasonable invariance requirements.
Why Min-Based Conditioning, Salem Benferhat, Vladik Kreinovich
Why Min-Based Conditioning, Salem Benferhat, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we do not have full information about which alternatives are possible and which are not. In such situations, an expert can estimate, for each alternative, the degree to which this alternative is possible. Sometimes, experts can produce numerical estimates of their degrees, but often, they can only provide us with qualitative estimates: they inform us which degrees are higher, but do not provide us with numerical values for these degrees. After we get these degrees from the experts, we often gain additional information, because of which some alternatives which were previously considered possible are now excluded. …