Deep neural networks proved to be a very useful and powerful tool with many practical applications. They especially excel at learning from large data sets with labeled samples. However, in order to achieve good learning results, the network architecture has to be carefully designed. Creating an optimal topology requires a lot of experience and knowledge. Unfortunately there are no practically applicable algorithms which could help in this situation. Using an evolutionary process to develop new network topologies might solve this problem. The limiting factor in this case is the speed of evaluation of a single specimen (a single network architecture), which includes learning based on the whole large dataset. In this paper we propose to overcome this problem by using a fitness prediction technique: use subsets of the original training set to conduct the training process and use its results as an approximation of specimen's fitness. We discuss the feasibility of this approach in context of the desired fitness predictor features and analyze whether subsets obtained in an evolutionary process can be used to estimate the fitness of the network topology. Finally we draw conclusions from our experiments and outline plans for future work.
In the first case the evolution is effectively replacing the back-propagation algorithm @cite_29 . It promises to overcome the drawbacks of gradient-descent based methods like trapping in local minima or inability to find a global minimum of a nondifferentiable functions. In practice however, those problems are not commonly observed and are outweighed by advantages: speed and scalability. Furthermore, this approach still requires creating and tuning the network architecture.
@cite_29
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This paper proposes a new solution to the vehicle routing problem with time windows using an evolution strategy adopting viral infection. The problem belongs to the NP-hard class and is very difficult to solve within practical time limits using systematic optimization techniques. In conventional evolution strategies, a schema with a high degree-of-fitness produced in the process of evolution may not be inherited when the fitness of the individual containing the schema is low. The proposed method preserves the schema as a virus and uses it by the infection operation in successive generations. Experimental results using extended Solomon's benchmark problems with 1000 customers proved that the proposed method is superior to conventional methods in both its rates of searches and the probability of obtaining solutions. Further experiments using the map of the central part of Tokyo with 20000 intersections and real traffic data also gave that the rate of search of the proposed method is higher than that of the conventional method. It is widely believed that the back-propagation algorithm in neural networks, for tasks such as pattern classification, overcomes the limitations of the perceptron. The authors construct several counterexamples to this belief. They also construct linearly separable examples which have a unique minimum which fails to separate two families of vectors, and a simple example with four two-dimensional vectors in a single-layer network showing local minima with a large basin of attraction. Thus, back-propagation is guaranteed to fail in the first example, and likely to fail in the second example. It is shown that even multilayered (hidden-layer) networks can also fail in this way to classify linearly separable problems. Since the authors' examples are all linearly separable, the perceptron would correctly classify them. The results disprove the presumption, made in recent years, that, barring local minima, back-propagation will find the best set of weights for a given problem. > Evolving gradient-learning artificial neural networks (ANNs) using an evolutionary algorithm (EA) is a popular approach to address the local optima and design problems of ANN. The typical approach is to combine the strength of backpropagation (BP) in weight learning and EA's capability of searching the architecture space. However, the BP's "gradient descent" approach requires a highly computer-intensive operation that relatively restricts the search coverage of EA by compelling it to use a small population size. To address this problem, we utilized mutation-based genetic neural network (MGNN) to replace BP by using the mutation strategy of local adaptation of evolutionary programming (EP) to effect weight learning. The MGNN's mutation enables the network to dynamically evolve its structure and adapt its weights at the same time. Moreover, MGNN's EP-based encoding scheme allows for a flexible and less restricted formulation of the fitness function and makes fitness computation fast and efficient. This makes it feasible to use larger population sizes and allows MGNN to have a relatively wide search coverage of the architecture space. MGNN implements a stopping criterion where overfitness occurrences are monitored through "sliding-windows" to avoid premature learning and overlearning. Statistical analysis of its performance to some well-known classification problems demonstrate its good generalization capability. It also reveals that locally adapting or scheduling the strategy parameters embedded in each individual network may provide a proper balance between the local and global searching capabilities of MGNN. A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such minimizations, and it is often thought that a main source of difficulty for these local methods to find the global minimum is the proliferation of local minima with much higher error than the global minimum. Here we argue, based on results from statistical physics, random matrix theory, neural network theory, and empirical evidence, that a deeper and more profound difficulty originates from the proliferation of saddle points, not local minima, especially in high dimensional problems of practical interest. Such saddle points are surrounded by high error plateaus that can dramatically slow down learning, and give the illusory impression of the existence of a local minimum. Motivated by these arguments, we propose a new approach to second-order optimization, the saddle-free Newton method, that can rapidly escape high dimensional saddle points, unlike gradient descent and quasi-Newton methods. We apply this algorithm to deep or recurrent neural network training, and provide numerical evidence for its superior optimization performance.