上浦 尚武

Defect-tolerance, the ability to overcome unreliability of components in a system, will be essential to realize computers built by nanotechnology. This paper reviews two approaches to defect-tolerance for nanocomputers that are based on self-timed cellular automata, a type of asynchronous cellular automaton, where the cells' defects are assumed to be of the stuck-at fault type. One approach for detecting and isolating defective components (cells) is ill a so-called off-line manner, i.e., through isolating defective cells and laying out circuits in the cellular space. Ill the other approach, defective cells can be detected and isolated while computation takes place, i.e., in an on-line manner. We show how to cope with defects in the cellular space in a self-contained ways while a computation task is conducted on it.

共焦点レーザ顕微鏡によって得られた2次元画像から神経細胞の3次元形態を再構成するシステムを開発した．神経回路の構造や特性を調べるには，まず，2次元画像から細胞の形状を抽出し，次に，抽出結果より3次元形態を再構成しなければならない．これらの作業は，これまで，実験者によって手作業で行われることが多いため，多大な時間と労力が浪費されてきた．これに対して，本システムでは単一点距離変換法を用いて樹状突起の構造と直径を自動的に抽出し，その結果を用いてモデルを再構築している．また，グラフィカル・ユーザ・インタフェースを用いることにより，実験者の作業手順も簡単化されている．この結果，本システムは直観的，かつ，効率的にユーザを支援できる．

The system for reconstructing of the 3D morphological structure of an insect neuron has been developed. Since the conventional operation of the reconstruction has been almost executed manually, large-scale time and work have been wasted. In contrast, in the developed system, the 3D morphological structure is automatically extracted by using the single-seed distance transform method. In addition, the setting of all parameters is simplified by use of the graphical user interface. From the above results, the developed system can support a user intuitively and effectively.

A power-aware voltage-scheduling heuristic with offline and online components is presented for a hard real-time multi-processor system supporting multiple voltage levels. The offline component determines a voltage configuration for each task in a graph according to the worst-case scenario of task execution, to speed up paths with tasks. Once some path is speeded up, it next chooses and speeds up one of the paths sharing tasks with that path. The online component reclaims the slack, which occurs when some task actually finishes, to slow down the execution speed of its successor. Simulations are made to show the effectiveness of the proposed heuristic.

This paper presents map-based data classification for hematopoietic tumor patients. A set of squarely arranged neurons in the map is defined as a block, and previously proposed block-matching-based learning constructs the map used for data classification. This paper incorporates pseudo-learning processes, which employ block reference vectors as quasi-training data, in the above training processes. Pseudo-learning improves the accuracy of classification. Experimental results establish that the percentage of missing the screening data of the tumor patients is very low.

Associative memory networks based on quaternionic Hopfield neural network are investigated in this paper. These networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic networks.

In this paper, a scheme of recognizing hematopoietic tumor patients is presented, using self-organizing maps constructed by fast block-matching-based learning. This fast learning is referred to as T-BMSOM leaning. To classify the patients, screening data of examinees are presented to a constructed map. In T-BMSOM learning, a set of neurons arranged in square is regarded as a block, and one of the blocks is chosen as a winner per the presented data. It is assumed that members of a training data set to construct the map never change in static environments, whereas the data set is suddenly updated during learning in dynamic environments. While adopting the concept of blocks makes it possible to construct well-organized maps in dynamic environments, it lengthens the time for learning. To overcome this issue, T-BMSOM learning is based on a decision-tree-like winner search and a batch process. The screening data of an examinee frequently lacks several of the item values, and hence the data is presented to the map after averages of non-missing item values substitute for items with no values. The class of the data to be classified is basically judged by observing the label of a winner block. Simulation results establish that the proposed scheme achieves high accuracy of correctly recognizing the data of hematopoietic tumor patients, even if training the map is conducted in a dynamic environment.

This paper proposes the video object segmentation using block-matching-based self-organization maps and a kernel function. A window covering a target object in a frame is split into units with some pixels. A vector with two elements is provided a unit to quantify its color attributes, and is presented to train a map. It is also presented to classify the units. The trained map then judges the class of the unit corresponding to the presented vector. The value of the kernel function supports the mechanism of winner search from the viewpoint of a spatial feature. Experimental results show that the proposed scheme works well for the video sequence in which the viewing direction of camera moves.

A system for counting pedestrians in sequence images obtained from single video camera is proposed in this paper. This system has the capabilities of simultaneously detecting and tracking several groups of pedestrians. Groups can be extracted by using the background subtraction method, and a layered neural network with BP learning algorithm is applied to estimate the number of pedestrians in each of the groups. The practical applicability of the proposed system is demonstrated, applying it to the sequence images of a real scenery.

Milltistable perception phenomena in seeing ambiguous figures have been observed and their distribution curves of alternation durations are well-known as the Gamma distribution through psychophysical experiments. It is important and interesting to investigate its describable model for clarifying brain functions. In this paper, we propose a model based on the multilayered bidirectional associative memories and report good simulation results on the distribution of alternation durations.

Though the regular and fixed structure of cellular automata greatly contributes to their simplicity, it imposes a strict limitation on the applications that can be modeled by them. This paper proposes swarm networks, a model in which cells, unlike in cellular automata, have irregular neighborhoods. Timed asynchronously, a cell in this model acts like an agent that can dynamically interact with a varying set of other cells under the control of transition rules. The configurations in which cells are organized according to their neighborhoods can move around in space, following simple mechanical laws. We prove computational universality of this model by simulating a circuit consisting of asynchronously timed circuit modules. The proposed model may find applications in nanorobotic systems and artifical biological systems.

For the realization of nanocomputers it will be important to have built-in defect-tolerance, which is the ability to overcome the unreliability caused by defective components. This paper explores defect-tolerance for nanocomputers based on Self-Timed Cellular Automata-an asynchronously timed CA of which the functionality can be expressed through a small number of transition rules. The proposed method assumes that defects are coped with in an initial phase by detecting and isolating them in cellular space from non-defective cells. The phase after this-the main topic of this paper-includes a scheme to efficiently lay out circuits on the cellular space in areas that are not affected by defects. The scheme is self-contained, i.e., it is carried out through the transition rules defined for the CA and does not require external circuitry.

Unreliability will be a major issue for computers built from components at nanometer scales. Thus, it's to be expected that such computers will need a high degree of defect-tolerance to overcome components' defects which have arisen during the process of manufacturing. This paper presents a novel approach to defect-tolerance that is especially geared towards nanocomputers based on asynchronous cellular automata. According to this approach, defective cells are detected and isolated by small configurations that move around randomly in cellular space. These configurations, called random flies, will attach to configurations that are static, which is typical for configurations that contain defective cells. On the other hand, dynamic configurations, like those that conduct computations, will not be isolated from the rest of the cellular space by the random flies, and will be able to continue their operations unaffectedly. © 2007 Higher Education Press and Springer-Verlag.

Data detection based on self organizing maps is presented for hematopoietic tumor patients. Learning data for the maps are generated from the screening data of examinees. The incomplete screening data without some item values is then supplemented by substituting averaged non-missing item values. In addition, redundant items, which are common to all the data and tend to have an unfavorable influence on data detection, are eliminated by a genetic algorithm and/or an immune algorithm. It is basically judged, by observing the label of a winner neuron in the map, whether the data presented to the map belongs to the class of hematopoietic tumors. Some experimental results are provided to show that the proposed methods achieve the high probability of correctly identifying examinees as hematopoietic tumor patients.

In this paper, a systematic method based on self-organizing maps is presented to classify interneurons of silkworm moths. Denseness of branching structures and existence of thick main dendrites are quantified by six fractal dimension values and three values calculated from images to which fundamental processing techniques are applied, respectively. Such values are employed as nine elements in training data for a map. The classification result is obtained as clusters with units in the trained map. Experimental results establish that the classification executed by the proposed method is comparable in accuracy to the manually executed classification. ©2006 IEEE.

For the manufacturing of computers built by nanotechnology, defects are expected to be a major problem. This paper explores this issue for nanocomputers based on cellular automata. Known for their regular structure, such architectures promise cost-effective manufacturing based on molecular self-organization. We show how a cellular automaton can detect defects in a self-contained way, and how it configures circuits on its cells while avoiding the defects. The employed cellular automaton is asynchronous, i.e., it does not require a central clock to synchronize the updates of its cells. This mode of timing is especially suitable for the high integration densities of nanotechnology implementations, since it potentially causes less heat dissipation.

This paper proposes a scheme of detecting the screening data of hematopoietic tumor patients, using block-matching-based self-organizing maps. The data of an examinee frequently lacks several of the item values, and hence the data is presented to a map after averages of non-missing item values are substituted for items with no values. It is basically judged, by observing the label of a winner block in a map, whether the data presented to the map belongs to the class of hematopoietic tumors. Proposed scheme allows us to construct maps not only in stationary environments where members in a training data set never change but also in nonstationary environments where the data set is suddenly updated during learning. Simulation experiments established that the proposed scheme achieves high accuracy of correctly classifying the data, even if the map is in nonstatinary environments.

We analyze a discrete-time quaternionic Hopfield neural network with continuous state variables updated asynchronously. The state of a neuron takes quaternionic value which is four-dimensional hypercomplex number. Two types of the activation function for updating neuron states are introduced and examined. The stable states of the networks are demonstrated through an example of small network.

In this paper, systematic three-dimensional classification is presented for sets of interneuron slice images of silkworm moths, using self-organizing maps. Fractal dimension values are calculated for target sets to quantify denseness of their branching structures, and are employed as element values in training data for constructing a map. The other element values are calculated from the sets to which labeling and erosion are applied, and they quantifies whether the sets include thick main dendrites. The classification result is obtained as clusters with units in the map. The proposed classification employing only two elements in training data achieves as high accuracy as the manual classification made by neuroscientists.

A power-aware voltage-scheduling heuristic is presented for a hard real-time multi-processor system. Given a task graph, the offline component first allocates a certain percentage of worst-case execution units of some tasks to them as potions to be executed in a higher voltage. Once some path is speeded up, the rest of the offline component chooses and speeds up one of the paths sharing tasks with that path. The online component reclaims the slack, which occurs when some task actually finishes, to slow down the execution speed of its successor. Experimental results are finally provided to demonstrate the effectiveness of the proposed heuristic.

Defect-tolerance, the ability to overcome unreliability of components in a system, will be essential to realize computers built by nanotechnology. This paper presents a novel approach toward defect-tolerance for nanocomputers that are based on self-timed cellular automata. Called Macro cell model, this model represents its computational elements by large collections of cells, thus endowing them with a high level of redundancy. Computational processes in this model are conducted through the propagation of certain cell states over parts of the cell space within and between the macro cells. We show how computation can be performed on the macro cells.

This paper proposes a self-organizing neural network with hierarchical structure. In the forward phase of teaming, the training data is propagated from the top-level neuron to one of the bottom-level neurons, and a combination of a parent neuron and its children, which the training data reaches, is a target for updating their weights. In the backward phase, weights of at least two neurons in such a combination are averaged, and weights of the parent are changed for the averaged weights. The proposed network adequately realizes polysemous data clustering, which yields multiple results, while sustaining the capability of data visualization.

Data detection using self organizing maps is presented for hematopoietic tumor patients. The learning data for the maps is generated from the screening data. Redundant items, which have an unfavorable influence on data detection and are common to all the data, are eliminated by a genetic algorithm and an immune algorithm. It is basically judged by observing a label of a winner neuron in a map, whether, the data presented to the map belongs to the class of hematopoietic tumors. Quantitative evaluations show that the proposed methods achieve the high probability of correctly identifying examinees as hematopoietic tumor-patients.

Defect-tolerance, the ability to overcome unreliability of components in a system, will be essential to realize computers built by nanotechnology. This paper presents a novel approach to defect-tolerance for nanocomputers that are based on self-timed cellular automata, a type of asynchronous cellular automaton. According to this approach, defective cells are detected and isolated by configurations of random flies that move around in cellular space. We show that detection and isolation are realized in an on-line manner, i.e., while computation takes place.

Associative memory by Hopfield-type recurrent neural networks with quaternionic algebra, called quaternionic Hoplield neural network, is proposed in this paper. The variables in the network are represented by quaternions of four dimensional hypercomptex numbers. The neuron model, the energy function, and the Hebbian rule for embedding patterns into the network are introduced. The properties of this network are analyzed concretely through examples of the network with 3 and 4 quaternion neurons. It is demonstrated that there exist fixed attractors in the network, Le., the pattern association from test pattern close to a stored pattern is possible in the quaternionic network, as in real-valued Hopfield networks.

In this paper, fast block-matching-based self-organizing maps (BMSOM's) are presented. Proposed learning defines a set of neurons arranged in square as a block, and find a winner block according to the decision-tree-like search. In other words, proposed learning determines a candidate out of four blocks included in the same block that has been most recently determined as another candidate. Proposed learning then chooses the candidate with the shortest Euclidean distance relative to the presented training data as the winner for it, out of such candidates. It accumulates two values associated with degrees of reference vector modifications for each member of the training data set, and updates reference vectors of all neurons at once per epoch. It copes well with the issue of reducing computational time complexity while retaining a high adaptability to a nonstationary environment. This advantage is demonstrated by experimental results obtained using artificially generated data set and object segmentation in a short video sequence.

This paper proposes the scheme of detecting the data of hematopoietic tumor patients, using Self Organizing Maps (SOM's). This scheme makes it possible to identify the 56-dimensional screening data of hematopoietic tumor patients with high probability, even if such data are irrelevant to training maps and have some missing item values. © 2005 SICE.

A block-matching-based self-organizing map (BMSOM) is presented. Finding a winner is carried out for each block, which is a set of neurons arranged in square. The proposed learning process updates the reference vectors of all of the neurons in a winner block. Then, the degrees of vector modifications are mainly controlled by the size (i.e., the number of neurons) of the winner block. To prevent a single cluster with neurons from splitting into some disjointed clusters, the restriction of the block size is imposed in the beginning of learning. At the main stage, this restriction is canceled. In BMSOM learning, the size of a winner block does not always decrease monotonically. The formula used to update the reference vectors is basically uncontrolled by time. Therefore, even if a map is in a nonstationary environment, training the map is probably pursued without interruption to adjust time-controlled parameters such as learning rate. Numerical results demonstrate that the BMSOM makes it possible to improve the plasticity of maps in a nonstationary environment and incremental learning.

Self-organizing map-based methods for the detection of confusion between blood test data are presented. Learning data for the self-organizing map (SOM) is generated by subtracting each element of complete blood count (CBC) data of the immediately previous patient's results from that of the current results. The neurons in the well-trained SOM are roughly divided into two clusters: one with neurons reacting to regular input data, and the other with neurons reacting to irregular input data generated by subtraction between confused CBC data. If a winner neuron belongs to the latter cluster, it is presumed that confusion has arisen between the CBC data of different patients. In addition, a genetic algorithm is adopted to eliminate redundant elements in the CBC data, which have an unfavorable influence on the judgment of confusion. Experimental results show that the proposed methods achieve high accuracy of detection even when the input data irrelevant to the learning of maps is applied to them.

A block-matching-based self-organizing map (BMSOM) is presented. Finding a winner is carried out for each block, which is a set of neurons arranged in square. The proposed learning process updates the reference vectors of all of the neurons in a winner block. Then, the degrees of vector modifications are mainly controlled by the size (i.e., the number of neurons) of the winner block. To prevent a single cluster with neurons from splitting into some disjointed clusters, the restriction of the block size is imposed in the beginning of learning. At the main stage, this restriction is canceled. In BMSOM learning, the size of a winner block does not always decrease monotonically. The formula used to update the reference vectors is basically uncontrolled by time. Therefore, even if a map is in a nonstationary environment, training the map is probably pursued without interruption to adjust time-controlled parameters such as learning rate. Numerical results demonstrate that the BMSOM makes it possible to improve the plasticity of maps in a nonstationary environment and incremental learning. Copyright © 2005 The Institute of Electronics, Information and Communication Engineers.

This paper proposes the scheme of detecting the screening data of hematopoietic tumor patients, using self-organizing maps. The data of an examinee frequently lacks several of the item values. In addition, there exist redundant common items that should be eliminated from all of the data because they have an unfavorable influence on classifying the data. The data imputation, which substitutes the averages of non-missing item values, and a genetic algorithm are adopted to overcome the above issues. It is basically judged, by observing a label of a winner neuron in a map, whether the data presented to the map belongs to the class of hematopoietic tumors. Quantitative evaluations show that the proposed scheme achieves the high probability of correctly identifying examinees as hematopoietic tumor patients.

The binding problem is a problem on the integration of perceptual properties in our brains. For describing this problem in the artificial neural network, it is necessary to introduce the temporal coding of information. In this paper, we propose a neural network model that can represent the bindings of external stimuli, based on the network that is capable of figure-ground segmentation proposed by Sompolinsky and Tsodyks. This model adopts the coupled oscillators that can represent the temporal coding and the synchronization among them.

Defects will be a major problem for manufacturing computers by nanotechnology. This paper explores this issue for nanocomputers based on cellular arrays. Known for their regular structure, such architectures promise cost-effective manufacturing based on molecular self-organization. We show a self-contained way to detect defects in a cellular array, and to configure circuits on its cells while avoiding the defects. Timing is assumed asynchronous, i.e., updating of cells is not controlled by a clock. ©2005 IEEE.

本文では, ニューロン荷重縮退故障を仮定し, ホップフィールドニューラルネットワークで実現した連想記憶に対するフォールトトレランス強化法を提案する. 強化手段として, 荷重制限と故障注入をヘブ学習に取り入れる. 前者では, 学習中に荷重値範囲を系統的に決定する. もし, ある荷重の値が定められた範囲から外れる場合, その荷重値を範囲の上限または下限に強制的に変更する. 後者の過程では, 学習中の故障注入により故障状態が仮想的に惹起され, その条件下で荷重値が決定される. 文字認識に関する実験により, 上記両過程を取り入れた学習法は, どちらか一方のみを適用する学習法よりフォールトトレランスの観点から優れていることを示す.

本文では, ニューロン荷重縮退故障を仮定し, ホップフィールドニューラルネットワークで実現した連想記憶に対するフォールトトレランス強化法を提案する.強化手段として, 荷重制限と故障注入をヘブ学習に取り入れる.前者では, 学習中に荷重値範囲を系統的に決定する.もし, ある荷重の値が定められた範囲から外れる場合, その荷重値を範囲の上限または下限に強制的に変更する.後者の過程では, 学習中の故障注入により故障状態が仮想的に惹起され, その条件下で荷重値が決定される.文字認識に関する実験により, 上記両過程を取り入れた学習法は, どちらか一方のみを適用する学習法よりフォールトトレランスの観点から優れていることを示す.

This paper proposes the re-learning for feedforward neural networks where weight faults would occur. The sequences of target outputs are encoded by means of single-parity-check codes so that a single-bit error caused by the faults can be on-line detected at the output layer. The re-leaming is made every time a network produces the error, and its lost function is retrieved. The proposed scheme can easily achieve high MTTF (Mean Time To Failure). © Springer-Verlag 2004.

This paper proposes the re-learning for feedforward neural networks where weight faults would occur. The sequences of target outputs are encoded by means of single-parity-check codes so that a single-bit error caused by the faults can be on-line detected at the output layer. The re-learning is made every time a network produces the error, and its lost function is retrieved. The proposed scheme can easily achieve high MTTF (Mean Time To Failure).

Hopfield neural networks tolerating weight faults are presented The weight I restriction and fault injection are adopted as fault-tolerant approaches. For the weight restriction, a range to which values of weights should belong is determined during the learning, and any weight being outside this range is forced to be either its upper limit or lower limit. A status Of a fault occurring is then evoked by the fault injection, anti calculating weights is made under this status. The learning based on both of the above approaches surpasses the learning based on either of them in the fault tolerance and/or in the learning time.

Hopfield neural networks tolerating weight faults are presented. The network training is made on condition some faults occur. Statuses of such faults are evoked by intentionally injecting faults into the network. The learning using the single-fault injection is shown first. Learning schemes, which are based on the double-fault injection for a couple of weights within a neuron, are then proposed to improve the fault tolerance further. Experimental results show that the learning using the random-double-fault injection allows us to complete the reasonably dependable network with the acceptable length of the learning time. In addition, the proposed schemes make the network robust against the input noise.

We propose a cost-aware method of detecting blood samples confused among different patients, using Self Organizing Maps. The map consists of a cluster reacting to confused data and that reacting to non-confused data. It is completed so that the latter cluster can become larger than the former, and allows reducing drastically the number of samples wrongly judged to be retested.

In this paper, a fuzzy controller with the capability of compensating the influence of faults is discussed. A stuck-at fault in the membership function is assumed to be fault models. The proposed inference scheme locates a candidate regarded as faulty function, and then exchanges its probably false degree for one of the following values : O, the degree in the next function to the candidate, and the difference between the constant and the degree in the next function to the candidate. If a fault occurs in the consequent part, the proposed scheme shifts several fuzzy variables, and then forms the inference result by using the membership functions allocated newly to the variables. The modified deterministic output of the controller is obtained by shifting the center of gravity of the inference result. The amounts of these shifts are determined systematically. Experimental results for a commercial controller show that the proposed scheme is valid for any single stuck-at fault deviating the normal deterministic output of the controller.

Cellular automata (CAs) are suitable architectures for computers built by nanotechnology, because their regular structure allows manufacturing based on molecular self-organization. Though cost-effective, such an approach inevitably brings with it defects in manufactured structures. This paper proposes a CA model called Defect Tolerant Asynchronous Cellular Automaton (DTACA) that works around such defects and can thus achieve reliable computation.

A multistage interconnection network (MIN) with partly duplicated stages is proposed in this paper, and network performance and fault tolerance are analyzed. The MIN is a hybrid of a non-redundant baseline network and a conventional fault-tolerant MIN called an ELMIN. In the case of a MIN with N input terminals and N output terminals, switching elements (SEs) in the first and nth stages are duplicated where n = log, N. and four-input two-output SEs and two-input four-output SEs are employed in the second and (n - 1)th stages respectively. These extra SEs and links are useful in improving the fault tolerance and performance of the MIN and do not complicate the routing algorithm. A comparison of an ELMIN with the proposed MIN shows that this new approach is superior both in theoretical throughput and performance in faulty cases, even though it requires at most 1.33 times as many links and cross points in the SEs. (C) 2002 Elsevier Science B.V. All rights reserved.

In this paper, a SOM(Self-Organizing Map)-based detection of confusion of blood test data referred to as CBC (Complete Blood Count) data is proposed. Firstly, the method based on only SOM is shown. The learning data applied to SOMs are generated by subtracting the immediately anterior CBC data of subjects from the present CBC data. All the neurons in the second layer of SOM trained by applying the above learning data are roughly divided into the following two clusters: the cluster with neurons reacting to regular input data, and that reacting to irregular input data which are generated by subtraction between confused CBC data. So, if the firing neuron belongs to the latter cluster, it is presumed that the confusion arises among CBC data of some subjects. Next, a method based on both SOM and GA (Genetic Algorithm) is shown. With the exception of selecting some elements, which instruct the weights to be updated in the second layer, of CBC data by means of GA, the learning and the detection strategy adopted by this method are similar to those by the firstly proposed method. Experimental results on detecting the confusion, which arises among CBC data of 750 subjects, show that the second proposed method produces the second layer which achieves the high accuracy of detection especially when the input data, not to be employed during the learning, are applied.

In this paper, PODEM for multiple-valued logic circuits is proposed. It consists of the D-propagation, implication and backtracing operation. To guide the D-propagation (or backtracing operation), observability (or controllability) measures are introduced. They are computed by simple recursive formulas, and enable us to reduce the frequency of backtracking. In addition, the scheme of exploiting Static Testability Measures up to a certain stage of test generation and then resorting to Dynamic Testability Measures is incorporated into PODEM. The experimental results on ternary benchmark circuits show that the above scheme is useful in generating as many test patterns as possible whilst shortening the total time required for the test generation.

Learning-based on-line testing in feedforward neural networks (NNs) is discussed. After the convergence of the ordinary learning, the re-learning employing two sigmoid activation functions per neuron in the last layer of the NN is made. It sets up the range of erroneous potentials produced from the last layer, and enables us to detect faults without extra hardware.

In this paper we propose a learning algorithm to enhance the fault tolerance of feedforward neural networks (NNs for short) by manipulating the gradient of sigmoid activation function of the neuron. We assume stuck-at-0 and stuck-at-1 faults of the connection link. For the output layer, we employ the function with the relatively gentle gradient to enhance its fault tolerance. For enhancing the fault tolerance of hidden layer, we steepen the gradient of function after convergence. The experimental results for a character recognition problem show that our NN is superior in fault tolerance, learning cycles and learning time to other NNs trained with the algorithms employing fault injection, forcible weight limit and the calculation of relevance of each weight to the output error. Besides the gradient manipulation incorporated in our algorithm never spoils the generalization ability.