Co-evolutionary Modular Neural Networks for Automatic Problem Decomposition Vineet R. Khare, Xin Yao Bernhard Sendhoff, Yaochu Jin, Heiko Wersing Natural Computation Group Honda Research Institute Europe GmbH, School of Computer Science Carl-Legien-Strasse 30 Edgbaston, Birmingham B15 2TT D-63073 Offenbach / Main, Germany {V.R.Khare, X.Yao}

{bs, yaochu.jin, heiko.wersing}

Overview • Automatic Problem Decomposition – Modular Neural Networks (MNNs) & Co-evolution

• Types of Decompositions – A Test Problem and candidate solutions

• Co-evolutionary Problem Decomposition • Experimental Results & Discussion • Conclusion

Automatic Problem Decomposition • Divide-and-conquer : MNNs & Co-evolution • With least amount of domain knowledge! – No manual crafting – Novel Solutions

• In the context of learning: – Parallel Decomposition – Sequential Decomposition

• Within Parallel Decomposition (contd.)

Types of Decompositions • One instance – one sub-task [2, 5] r r r r f ( X , Y ) = f1 ( X ) OR f 2 ( Y ) t

• Subtasks on separate outputs [1, 3] r r r r r f ( X , Y ) = { f1 ( X ), f 2 ( Y ) }

• Combination of subtasks at one output [4] r r r r f ( X , Y ) = g ( f1 ( X ), f 2 ( Y ) )

Artificial Time-series Mixture Problem r r r r f ( X , Y ) = g ( f1 ( X ), f 2 ( Y ) ) Mackey-Glass Time-series Prediction

Lorenz - z Time-series Prediction

A Few Candidate Solutions Sequential Decomposition

Parallel Decomposition

Sub-task Specialization

Co-evolutionary Problem Decomposition • Co-evolving modular neural networks alongside their constituent modules

Co-evolutionary Problem Decomposition • System Fitness • Module Fitness

F(si) = 1/ (nrmsevalid + c) 1. f ( M i ) =

∑ f (S




2. f ( M i ) = freq i ( in last 10 gen. )

Co-evolutionary Problem Decomposition

Co-evolutionary Model : Stage 1 • Only parallel decomposition • 2 Modules • AVERAGING problem • Function ‘g’ known! • Complimentarity constraint

Co-evolutionary Model : Stage 2 • Parallel & Sequential decomposition • 2 Modules • PRODUCT problem • Function ‘g’ unknown!

Parameter Values

Results & Discussion • Stage 1 : All 30 runs produce pure-modular structure. • Stage 2: Out of 10 runs, – 5 pure-modular, 2 incomplete pure modular and 3

imbalanced incomplete

Results & Discussion • Stage 1 : Feature decomposition, easily achieved • Stage 2 : Sequential and parallel decomposition is difficult – – – –

Much bigger search space Other structures close to pure-modular New structures discovered Ensemble effect

Conclusions •

A two-level co-evolutionary model to design and optimize modular neural networks with sub-task specialization.

Evolutionary pressure to increase the overall fitness of the two populations provides the needed stimulus for the emergence of the subtask specific modules.

Emergence of other good decompositions besides the intuitive ones.

Generic model can be applied to variety of problems ranging from feature decomposition and feature selection in neural network ensembles to problems which require pre-processing.

Extensions • Making the model adaptive in terms of – Number of modules per network – Structure of combining module

• Alternative uses of modularity.

References [1] Michael Husken, Christian Igel, and Marc Toussaint. Task-dependent evolution of modularity in neural networks. Connection Science, 14:219–229, 2002. [2] Robert A. Jacobs, Michael I. Jordan, and Andrew G.Barto. Task Decomposition Through Competition in a Modular Connectionist Architecture: The What and Where Vision Tasks. Cognitive Science, 15:219–250, 1991. [3] Robert A. Jacobs, Michael I. Jordan, Steven J. Nowlan, and Geoffrey E. Hinton. Adaptive Mixtures of Local Experts. Neural Computation, 3(1):79–87, 1991. [4] Yuansong Liao and John Moody. Constructing heterogeneous committees using input feature grouping: Application to economic forecasting. Advances in Neural Information Processing Systems, 12:921–927, 1999. [5] Bao-Liang Lu and Masami Ito. Task decomposition and module combination based on class relations: A modular neural network for pattern classification. IEEE Transactions on Neural Networks, 10:1244– 1256, 1999.

Co-evolutionary Modular Neural Networks for ...

Co-evolutionary Model : Stage 1. • Only parallel decomposition. • 2 Modules. • AVERAGING problem. • Function 'g' known! • Complimentarity constraint ...

886KB Sizes 1 Downloads 221 Views

Recommend Documents

Co-evolutionary Modular Neural Networks for ...
School of Computer Science. Edgbaston, Birmingham B15 2TT. {V.R.Khare ... D-63073 Offenbach / Main, Germany. {bs, yaochu.jin, heiko.wersing} ...

Learning Modular Neural Network Policies for Multi ...
transfer learning appealing, but the policies learned by these algorithms lack ..... details and videos can be found at https://sites. .... An illustration of the tasks.

Neural Networks - GitHub
Oct 14, 2015 - computing power is limited, our models are necessarily gross idealisations of real networks of neurones. The neuron model. Back to Contents. 3. ..... risk management target marketing. But to give you some more specific examples; ANN ar

Learning Methods for Dynamic Neural Networks - IEICE
Email: [email protected], [email protected], [email protected]. Abstract In .... A good learning rule must rely on signals that are available ...

Recurrent Neural Networks
Sep 18, 2014 - Memory Cell and Gates. • Input Gate: ... How LSTM deals with V/E Gradients? • RNN hidden ... Memory cell (Linear Unit). . =  ...

Intriguing properties of neural networks
Feb 19, 2014 - we use one neural net to generate a set of adversarial examples, we ... For the MNIST dataset, we used the following architectures [11] ..... Still, this experiment leaves open the question of dependence over the training set.

information networks with modular experts
on information theory to address the selection, mapping, ... expert, and then mapping it correctly. .... Experiments were performed using the glass database.

Neural Graph Learning: Training Neural Networks Using Graphs
many problems in computer vision, natural language processing or social networks, in which getting labeled ... inputs and on many different neural network architectures (see section 4). The paper is organized as .... Depending on the type of the grap

Deep Neural Networks for Acoustic Modeling in Speech ... - CiteSeerX
Apr 27, 2012 - origin is not the best way to find a good set of weights and unless the initial ..... State-of-the-art ASR systems do not use filter-bank coefficients as the input ...... of the 24th international conference on Machine learning, 2007,

PDF Neural Networks for Pattern Recognition
optimisation algorithms, data pre-processing and Bayesian methods. All topics ... Pattern Recognition and Machine Learning (Information Science and Statistics).

Siamese Neural Networks for One-shot Image Recognition
Department of Computer Science, University of Toronto. Toronto, Ontario ... or impossible due to limited data or in an online prediction setting, such as web ...

Using Recurrent Neural Networks for Time.pdf
Submitted to the Council of College of Administration & Economics - University. of Sulaimani, As Partial Fulfillment for the Requirements of the Master Degree of.

Artificial neural networks for automotive air-conditioning systems (2 ...
Artificial neural networks for automotive air-conditioning systems (2).pdf. Artificial neural networks for automotive air-conditioning systems (2).pdf. Open. Extract.

fine context, low-rank, softplus deep neural networks for mobile ...
plus nonlinearity for on-device neural network based mobile ... translation. While the majority of mobile speech recognition ..... application for speech recognition.

Deep Neural Networks for Small Footprint Text ... - Research at Google
dimensional log filterbank energy features extracted from a given frame, together .... [13] B. Yegnanarayana and S.P. Kishore, “AANN: an alternative to. GMM for ...

Deep Neural Networks for Acoustic Modeling in ... - Semantic Scholar
Apr 27, 2012 - His current main research interest is in training models that learn many levels of rich, distributed representations from large quantities of perceptual and linguistic data. Abdel-rahman Mohamed received his B.Sc. and M.Sc. from the El

recurrent deep neural networks for robust
network will be elaborated in Section 3. We report our experimental results in Section 4 and conclude our work in Section 5. 2. RECURRENT DNN ARCHITECTURE. 2.1. Hybrid DNN-HMM System. In a conventional GMM-HMM LVCSR system, the state emission log-lik

Convolutional Neural Networks for Eye Detection in ...
Convolutional Neural Network (CNN) for. Eye Detection. ▫ CNN has ... complex features from the second stage to form the outputs of the network. ... 15. Movie ...

A Survey on Leveraging Deep Neural Networks for ...
data. • Using Siamese Networks. Two-stream networks, with shared weight .... “Learning Multi-domain Convolutional Neural Networks for Visual Tracking” in ...

Data Mining Using Neural Networks: A Guide for ...
network models and statistical models are related to tackle the data analysis real problem. The book is organized as follows: some basics on artificial neural ...