Unstructured tree search on SIMD parallel computers

We present new methods for load balancing of unstructured tree computations on large-scale SIMD machines, and analyze the scalability of these and other existing schemes. An efficient formulation of tree search on an SIMD machine consists of two major components: a triggering mechanism, which determines when the search space redistribution must occur to balance the search space over processors, and a scheme to redistribute the search space. We have devised a new redistribution mechanism and a new triggering mechanism. Either of these can be used in conjunction with triggering and redistribution mechanisms developed by other researchers. We analyze the scalability of these mechanisms and verify the results experimentally. The analysis and experiments show that our new load-balancing methods are highly scalable on SIMD architectures. Their scalability is shown to he no worse than that of the best load-balancing schemes on MIMD architectures. We verify our theoretical results by implementing the 15-puzzle problem on a CM-2 SIMD parallel computer     

Parallel architecture for fast transforms with trigonometric kernel

We present an unified parallel architecture for four of the most important fast orthogonal transforms with trigonometric kernel: Complex Valued Fourier (CFFT), Real Valued Fourier (RFFT), Hartley (FHT), and Cosine (FCT). Out of these, only the CFFT has a data flow coinciding with the one generated by the successive doubling method, which can be transformed on a constant geometry flow using perfect unshuffle or shuffle permutations. The other three require some type of hardware modification to guarantee the constant geometry of the successive doubling method. We have defined a generalized processing section (PS), based on a circular CORDIC rotator, for the four transforms. This PS section permits the evaluation of the CFFT and FCT transforms in n data recirculations and the RFFT and FHT transforms in n-1 data recirculations, with n being the number of stages of a transform of length N=rⁿ. Also, the efficiency of the partitioned parallel architecture is optimum because there is no cycle loss in the systolic computation of all the butterflies for each of the four transforms     

The classification, fusion, and parallelization of array languageprimitives

We present a classification scheme for array language primitives that quantifies the variation in parallelism and data locality that results from the fusion of any two primitives. We also present an algorithm based on this scheme that efficiently determines when it is beneficial to fuse any two primitives. Experimental results show that five LINPACK routines report 50% performance improvement from the fusion of array operators     

Unicast-based multicast communication in wormhole-routed networks

Multicast communication, in which the same message is delivered from a source node to an arbitrary number of destination nodes, is being increasingly demanded in parallel computing. System supported multicast services can potentially offer improved performance, increased functionality, and simplified programming, and may in turn be used to support various higher-level operations for data movement and global process control. This paper presents efficient algorithms to implement multicast communication in wormhole-routed direct networks, in the absence of hardware multicast support, by exploiting the properties of the switching technology. Minimum-time multicast algorithms are presented for n-dimensional meshes and hypercubes that use deterministic, dimension-ordered routing of unicast messages. Both algorithms can deliver a multicast message to m-1 destinations in [log ₂ m] message passing steps, while avoiding contention among the constituent unicast messages. Performance results of implementations on a 64-node nCUBE-2 hypercube and a 168-node Symult 2010 2-D mesh are given     

Weight smoothing to improve network generalization

A weight smoothing algorithm is proposed in this paper to improve a neural network's generalization capability. The algorithm can be used when the data patterns to be classified are presented on an n-dimensional grid (n>/=1) and there exists some correlations among neighboring data points within a pattern. For a fully-interconnected feedforward net, no such correlation information is embedded into the architecture. Consequently, the correlations can only be extracted through sufficient amount of network training. With the proposed algorithm, a smoothing constraint is incorporated into the objective function of backpropagation to reflect the neighborhood correlations and to seek those solutions that have smooth connection weights. Experiments were performed on problems of waveform classification, multifont alphanumeric character recognition, and handwritten numeral recognition. The results indicate that (1) networks trained with the algorithm do have smooth connection weights, and (2) they generalize better.     

Comments on “Can backpropagation error surface not have localminima?”

in the above paper Yu (IEEE Trans. Neural Networks, vol.3, no.6, p.1019-21 (1992)) claims to prove that local minima do not exist in the error surface of backpropagation networks being trained on data with t distinct input patterns when the network is capable of exactly representing arbitrary mappings on t input patterns. The commenter points out that the proof presented is flawed, so that the resulting claims remain unproved. In reply, Yu points out that the undesired phenomenon that was sited can be avoided by simply imposing the arbitrary mapping capacity of the network on lemma 1 in the article.     

Network information criterion-determining the number of hiddenunits for an artificial neural network model

The problem of model selection, or determination of the number of hidden units, can be approached statistically, by generalizing Akaike's information criterion (AIC) to be applicable to unfaithful (i.e., unrealizable) models with general loss criteria including regularization terms. The relation between the training error and the generalization error is studied in terms of the number of the training examples and the complexity of a network which reduces to the number of parameters in the ordinary statistical theory of AIC. This relation leads to a new network information criterion which is useful for selecting the optimal network model based on a given training set.     

Quantization effects in digitally behaving circuit implementationsof Kohonen networks

Implementing a neural network on a digital or mixed analog and digital chip yields the quantization of the synaptic weights dynamics. This paper addresses this topic in the case of Kohonen's self-organizing maps. We first study qualitatively how the quantization affects the convergence and the properties, and deduce from this analysis the way to choose the parameters of the network (adaptation gain and neighborhood). We show that a spatially decreasing neighborhood function is far more preferable than the usually rectangular neighborhood function, because of the weight quantization. Based on these results, an analog nonlinear network, integrated in a standard CMOS technology, and implementing this spatially decreasing neighborhood function is then presented. It can be used in a mixed analog and digital circuit implementation.     

Hierarchical models for analysis and recognition of handwritten characters

Different hierarchical models in pattern analysis and recognition are proposed, based on occurrence probability of patterns. As an important application of recognizing handprinted characters, three typical kinds of hierarchical models such asM _89-89,M _89-36 andM _36-36 have been presented, accompanied by the computer algorithms for computing recognition rates of pattern parts. Moreover, a comparative study of their recognition rates has been conducted theoretically; and numerical experiments have been carried out to verify the analytical conclusions made. Various hierarchical models deliberated in this paper can provide users more or better choices of pattern models in practical application, and lead to a uniform computational scheme (or code). The recognition rates of parts can be improved remarkably by a suitable hierarchical model. For the modelM _89-36 in which case some of the Canadian standard handprinted characters have multiple occurrence probabilities, the total mean recognition rates of the given sample may reach 120% of that by the model proposed by Li et al., and 156% of that obtained from the subjective experiments reported by Suen.