An algorithm for learning from hints

To take advantage of prior knowledge (hints) about the function one wants to learn, we introduce a method that generalizes learning from examples to learning from hints. A canonical representation of hints is defined and illustrated. All hints are represented to the learning process by examples, and examples of the function are treated on equal footing with the rest of the hints. During learning, examples from different hints are selected for processing according to a given schedule. We present two types of schedules; fixed schedules that specify the relative emphasis of each hint, and adaptive schedules that are based on how well each hint has been learned so far. Our learning method is compatible with any descent technique

Maximal codeword lengths in Huffman codes

The following question about Huffman coding, which is an important technique for compressing data from a discrete source, is considered. If p is the smallest source probability, how long, in terms of p, can the longest Huffman codeword be? It is shown that if p is in the range 0 less than p less than or equal to 1/2, and if K is the unique index such that 1/F(sub K+3) less than p less than or equal to 1/F(sub K+2), where F(sub K) denotes the Kth Fibonacci number, then the longest Huffman codeword for a source whose least probability is p is at most K, and no better bound is possible. Asymptotically, this implies the surprising fact that for small values of p, a Huffman code's longest codeword can be as much as 44 percent larger than that of the corresponding Shannon code

Maximal codeword lengths in Huffman codes

computers &amp

Maximum Resilience of Artificial Neural Networks

The deployment of Artificial Neural Networks (ANNs) in safety-critical applications poses a number of new verification and certification challenges. In particular, for ANN-enabled self-driving vehicles it is important to establish properties about the resilience of ANNs to noisy or even maliciously manipulated sensory input. We are addressing these challenges by defining resilience properties of ANN-based classifiers as the maximal amount of input or sensor perturbation which is still tolerated. This problem of computing maximal perturbation bounds for ANNs is then reduced to solving mixed integer optimization problems (MIP). A number of MIP encoding heuristics are developed for drastically reducing MIP-solver runtimes, and using parallelization of MIP-solvers results in an almost linear speed-up in the number (up to a certain limit) of computing cores in our experiments. We demonstrate the effectiveness and scalability of our approach by means of computing maximal resilience bounds for a number of ANN benchmark sets ranging from typical image recognition scenarios to the autonomous maneuvering of robots.Comment: Timestamp research work conducted in the project. version 2: fix some typos, rephrase the definition, and add some more existing wor

Multi-Scale joints roughness characterization using wavelet and shear modeling

Mechanical behavior prediction of rock joints is very important in the rock mechanics. Many models have been proposed to predict the mechanical behavior of joints at which lack of correct evaluation of effective roughness coefficient has been the most important shortage. In this research, each of the upper and lower profiles of joint surfaces is considered as a 2-dimensional wave. Then, multi-scale decomposition based on wavelet theory has been applied studying on asperities. Upper and lower profiles have been combined to produce a composite surface having asperities characteristics of both joint surfaces. Each of the composed wave components (roughness and undulation) has been characterized with statistical quantity of arithmetic mean deviation (Ra). This procedure of characterizing for 2-dimensional waves has been easily extended to 3-dimensional joint surfaces. Conformity in the results of shear and dilation modeling and laboratory tests satisfactorily verifies success of the proposed procedure

Deferring the learning for better generalization in radial basis neural networks

Proceeding of: International Conference Artificial Neural Networks — ICANN 2001. Vienna, Austria, August 21–25, 2001The level of generalization of neural networks is heavily dependent on the quality of the training data. That is, some of the training patterns can be redundant or irrelevant. It has been shown that with careful dynamic selection of training patterns, better generalization performance may be obtained. Nevertheless, generalization is carried out independently of the novel patterns to be approximated. In this paper, we present a learning method that automatically selects the most appropriate training patterns to the new sample to be predicted. The proposed method has been applied to Radial Basis Neural Networks, whose generalization capability is usually very poor. The learning strategy slows down the response of the network in the generalisation phase. However, this does not introduces a significance limitation in the application of the method because of the fast training of Radial Basis Neural Networks

One-Year Results of Simultaneous Topography-Guided Photorefractive Keratectomy and Corneal Collagen Cross-Linking in Keratoconus Utilizing a Modern Ablation Software

Purpose. To evaluate effectiveness of simultaneous topography-guided photorefractive keratectomy and corneal collagen cross-linking in mild and moderate keratoconus. Methods. Prospective nonrandomized interventional study including 20 eyes of 14 patients with grade 1-2 keratoconus that underwent topography-guided PRK using a Custom Ablation Transition Zone (CATz) profile with 0.02% MMC application immediately followed by standard 3 mw/cm2 UVA collagen cross-linking. Maximum ablation depth did not exceed 58 μm. Follow-up period: 12 months. Results. Progressive statistically significant improvement of UCVA from 0.83±0.37 logMAR preoperative, reaching 0.25±0.26 logMAR at 12 months (P<0.001). Preoperative BCVA (0.27±0.31 logMAR) showed a progressive improvement reaching 0.08±0.12 logMAR at 12 months (P=0.02). Mean Kmax reduced from 48.9±2.8 to 45.4±3.1 D at 12 months (P<0.001), mean Kmin reduced from 45.9±2.8 D to 44.1±3.2 D at 12 months (P<0.003), mean keratometric asymmetry reduced from 3.01±2.03 D to 1.25±1.2 D at 12 months (P<0.001). The safety index was 1.39 at 12 months and efficacy index 0.97 at 12 months. Conclusion. Combined topography-guided PRK and corneal collagen cross-linking are a safe and effective option in the management of mild and moderate keratoconus. Precis. To our knowledge, this is the first published study on the use of the CATz ablation system on the Nidek Quest excimer laser platform combined with conventional cross-linking in the management of mild keratoconus

Boundary and expansion effects on two-pion correlation functions in relativistic heavy-ion collisions

We examine the effects that a confining boundary together with hydrodynamical expansion play on two-pion distributions in relativistic heavy-ion collisions. We show that the effects arise from the introduction of further correlations due both to collective motion and the system's finite size. As is well known, the former leads to a reduction in the apparent source radius with increasing average pair momentum K. However, for small K, the presence of the boundary leads to a decrease of the apparent source radius with decreasing K. These two competing effects produce a maximum for the effective source radius as a function of K.Comment: 6 pages, 5 Eps figures, uses RevTeX and epsfi