Neural Nets with Superlinear VC-Dimension

1994 ◽  
Vol 6 (5) ◽  
pp. 877-884 ◽  
Author(s):  
Wolfgang Maass
Keyword(s):  
Lower Bound ◽  
Large Class ◽  
Neural Nets ◽  
New Method ◽  
Neural Net ◽  
Vc Dimension ◽  
Asymptotically Optimal ◽  
Linear Threshold

It has been known for quite a while that the Vapnik-Chervonenkis dimension (VC-dimension) of a feedforward neural net with linear threshold gates is at most O(w · log w), where w is the total number of weights in the neural net. We show in this paper that this bound is in fact asymptotically optimal. More precisely, we exhibit for any depth d ≥ 3 a large class of feedforward neural nets of depth d with w weights that have VC-dimension Ω(w · log w). This lower bound holds even if the inputs are restricted to Boolean values. The proof of this result relies on a new method that allows us to encode more “program-bits” in the weights of a neural net than previously thought possible.

scholarly journals Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian

2021 ◽  
Author(s):  
Jürgen Jost ◽  
Raffaella Mulas ◽  
Florentin Münch
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Spectral Gap ◽  
Complete Bipartite Graph ◽  
Graph Laplacian ◽  
New Method ◽  
Single Edge ◽  
Largest Eigenvalue ◽  
Complement Graph ◽  
The Largest Eigenvalue

AbstractWe offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least $$\frac{n+1}{n-1}$$ n + 1 n - 1 provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size $$\frac{n-1}{2}$$ n - 1 2 . With the same method, we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree, provided this is at most $$\frac{n-1}{2}$$ n - 1 2 .

The Use of Neural Nets for Matching Fixed or Variable Geometry Compressors With Diesel Engines

2003 ◽  
Vol 125 (2) ◽  
pp. 572-579 ◽  
Author(s):  
S. A. Nelson ◽  
Z. S. Filipi ◽  
D. N. Assanis
Keyword(s):  
Diesel Engine ◽  
System Optimization ◽  
Design Tool ◽  
Neural Nets ◽  
Additional Parameter ◽  
Mathematical Function ◽  
Neural Net ◽  
Variable Geometry ◽  
Entire Family ◽  
Wide Range

A technique which uses trained neural nets to model the compressor in the context of a turbocharged diesel engine simulation is introduced. This technique replaces the usual interpolation of compressor maps with the evaluation of a smooth mathematical function. Following presentation of the methodology, the proposed neural net technique is validated against data from a truck type, 6-cylinder 14-liter diesel engine. Furthermore, with the introduction of an additional parameter, the proposed neural net can be trained to simulate an entire family of compressors. As a demonstration, a family of compressors of different sizes is represented with a single neural net model which is subsequently used for matching calculations with intercooled and nonintercooled engine configurations at different speeds. This novel approach readily allows for evaluation of various options within a wide range of possible compressor configurations prior to prototype production. It can also be used to represent the variable geometry machine regardless of the method used to vary compressor characteristics. Hence, it is a powerful design tool for selection of the best compressor for a given diesel engine system and for broader system optimization studies.

Bounded Elastic Moduli Multiplier Technique for Limit Loads: Part 2 - Case Studies

2021 ◽  
Author(s):  
Sathya Prasad Mangalaramanan
Keyword(s):  
Lower Bound ◽  
Case Studies ◽  
Power Law ◽  
Elastic Moduli ◽  
New Method ◽  
Stress Distributions ◽  
Limit Loads ◽  
Elastic Plastic ◽  
Thick Cylinder ◽  
Better Than

Abstract An accompanying paper provides the theoretical underpinnings of a new method to determine statically admissible stress distributions in a structure, called Bounded elastic moduli multiplier technique (BEMMT). It has been shown that, for textbook cases such as thick cylinder, beam, etc., the proposed method offers statically admissible stress distributions better than the power law and closer to elastic-plastic solutions. This paper offers several examples to demonstrate the robustness of this method. Upper and lower bound limit loads are calculated using iterative elastic analyses using both power law and BEMMT. These results are compared with the ones obtained from elastic-plastic FEA. Consistently BEMMT has outperformed power law when it comes to estimating lower bound limit loads.

FPGA Realization of the Reconfigurable Mesh Counting Algorithm

2021 ◽  
pp. 2150157
Author(s):  
Yosi Ben-Asher ◽  
Esti Stein ◽  
Vladislav Tartakovsky
Keyword(s):  
Lower Bound ◽  
Neural Nets ◽  
Processing Elements ◽  
Large Numbers ◽  
Unrealistic Assumption ◽  
Reconfigurable Mesh ◽  
Speed Up ◽  
Optimal Tree ◽  
Pass Transistor ◽  
Signal Switching

Pass transistor logic (PTL) is a circuit design technique wherein transistors are used as switches. The reconfigurable mesh (RM) is a model that exploits the power of PTLs signal switching, by enabling flexible bus connections in a grid of processing elements containing switches. RM algorithms have theoretical results proving that [Formula: see text] can speed up computations significantly. However, the RM assumes that the latency of broadcasting a signal through [Formula: see text] switches (bus length) is 1. This is an unrealistic assumption preventing physical realizations of the RM. We propose the restricted-RM (RRM) wherein the bus lengths are restricted to [Formula: see text], [Formula: see text]. We show that counting the number of 1-bits in an input of [Formula: see text] bits can be done in [Formula: see text] steps for [Formula: see text] by an [Formula: see text] RRM. An almost matching lower bound is presented, using a technique which adds to the few existing lower-bound techniques in this area. Finally, the algorithm was directly coded over an FPGA, outperforming an optimal tree of adders. This work presents an alternative way of counting, which is fundamental for summing, beating regular Boolean circuits for large numbers, where summing a vast amount of numbers is the basis of any accelerator in embedded systems such as neural-nets and streaming. a

On the braid index of links with nested diagrams

1992 ◽  
Vol 111 (2) ◽  
pp. 273-281 ◽  
Author(s):  
D. A. Chalcraft
Keyword(s):  
Lower Bound ◽  
Large Class ◽  
Upper Bound ◽  
Simple Criterion ◽  
Braid Index

AbstractThe number of Seifert circuits in a diagram of a link is well known 9 to be an upper bound for the braid index of the link. The -breadth of the so-called P-polynomial 3 of the link is known 5, 2 to give a lower bound. In this paper we consider a large class of links diagrams, including all diagrams where the interior of every Seifert circuit is empty. We show that either these bounds coincide, or else the upper bound is not sharp, and we obtain a very simple criterion for distinguishing these cases.

scholarly journals FORECASTING PRICE INCREMENTS USING AN ARTIFICIAL NEURAL NETWORK

2001 ◽  
Vol 04 (01) ◽  
pp. 45-56 ◽  
Author(s):  
FILIPPO CASTIGLIONE
Keyword(s):  
Financial Time Series ◽  
Black Box ◽  
Neural Nets ◽  
Neural Net ◽  
Forecast Method ◽  
Time Series Forecast ◽  
Simplified Approach ◽  
Financial Time ◽  
System A ◽  
Intrinsic Complexity

Financial forecasting is a difficult task due to the intrinsic complexity of the financial system. A simplified approach in forecasting is given by "black box" methods like neural networks that assume little about the structure of the economy. In the present paper we relate our experience using neural nets as financial time series forecast method. In particular we show that a neural net able to forecast the sign of the price increments with a success rate slightly above 50% can be found. Target series are the daily closing price of different assets and indexes during the period from about January 1990 to February 2000.

scholarly journals A note on the number of irrational odd zeta values

2020 ◽  
Vol 156 (8) ◽  
pp. 1699-1717
Author(s):  
Li Lai ◽  
Pin Yu
Keyword(s):  
Optimal Design ◽  
Lower Bound ◽  
Closed Form ◽  
Rational Functions ◽  
Asymptotically Optimal ◽  
Zeta Values

AbstractWe prove that, for any small $\varepsilon > 0$, the number of irrationals among the following odd zeta values: $\zeta (3),\zeta (5),\zeta (7),\ldots ,\zeta (s)$ is at least $( c_0 - \varepsilon )({s^{1/2}}/{(\log s)^{1/2}})$, provided $s$ is a sufficiently large odd integer with respect to $\varepsilon$. The constant $c_0 = 1.192507\ldots$ can be expressed in closed form. Our work improves the lower bound $2^{(1-\varepsilon )({\log s}/{\log \log s})}$ of the previous work of Fischler, Sprang and Zudilin. We follow the same strategy of Fischler, Sprang and Zudilin. The main new ingredient is an asymptotically optimal design for the zeros of the auxiliary rational functions, which relates to the inverse totient problem.

Sign in / Sign up

Export Citation Format

Share Document