Integrated Learning in Multi-net Systems

1. Integrated Learningin Multi-net Systems Neural Computing Group Department of Computing University of Surrey Matthew Casey 6th February 2004 http://www.computing.surrey.ac.uk/personal/st/M.Casey/

2. Introduction • In-situ learning in multi-net systems • Classification • Parallel combination of networks: ensemble • Sequential combination of networks: modular • Simulation • Parallel and sequential combination of networks • Quantification and addition • Formal framework and algorithm for multi-net systems

3. Introduction • Learning: • “process which leads to the modification of behaviour”1 • Biological motivation • Hebb’s neurophysiological postulate2 • Learning across cell assemblies: neural integration • Functional specialism: analogy to multi-net systems • Theoretical motivation • Generalisation improvements with multi-net systems • Ensemble and modular • Learning in collaboration with modularisation

4. Single-net Systems • Systems of one or more artificial neurons combined together in a single network • Parallel distributed processing3 • Learning to generalise • Learning algorithms • Supervised: delta4,5,6, backpropagation7,8,9 • Unsupervised: Hebbian2, SOM10

5. 1 Combination of Linear Decision Boundaries 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 True (1) False (-1) -1 -1 1 Single-nets as Multi-nets? XOR

6. From Single-nets to Multi-nets • Multi-net systems appear to be a development of the parallel processing paradigm • Can multi-net systems improve generalisation? • Modularisation with simpler networks? • Limited theoretical and empirical evidence • Generalisation: • Balance prior knowledge and training • VC Dimension11,12,13 • Bias/variance dilemma14

7. Multi-net Systems:Ensemble or Modular? • Ensemble systems: • Parallel combination • Each network performs the same task • Simple ensemble • AdaBoost15 • Modular systems: • Each network performs a different (sub-)task • Mixture-of-experts16 (top-down parallel competitive) • Min-max17 (bottom-up static parallel/sequential)

8. Categorising Multi-net Systems • Sharkey’s18,19 combination strategies: • Parallel: co-operative or competitive top-down or bottom-up static or dynamic • Sequential • Supervisory • Component networks may be20: • Pre-trained (independent) • Incrementally trained (iterative) • In-situ trained (simultaneous)

9. Multi-net Systems • Categorisation schemes appear not to support the generalisation of multi-net system properties beyond specific examples • Ensemble: bias, variance and diversity21 • Modular: bias and variance • What about measures such as the VC Dimension? • Some use of in-situ learning • ME and HME22 • Negative correlation learning23

10. Research • Multi-net systems seem to offer a way in which generalisation performance and learning speed can be improved: • Yet limited theoretical and empirical evidence • Focus on parallel systems • Limited use of in-situ learning despite motivation • Existing results show improvement • Can the approach be generalised? • No general framework for multi-net systems • Difficult to generalise properties from categorisation

11. Research • Explore in-situ learning in multi-net systems: • Parallel: in-situ learning in the simple ensemble • Sequential: combining networks with in-situ learning • Does in-situ learning provide improved generalisation? • Can we combine ‘simple’ networks to solve ‘complex’ problems: ‘superordinate’ systems with faster learning? • Propose a formal framework for multi-net systems • A method to describe the architecture and learning algorithm for a general multi-net system

12. Multi-net System Framework • Previous work: • Framework for the co-operation of learning algorithms24 • Stochastic model25 • Importance Sampled Learning Ensembles (ISLE)26 • Focus on supervised learning and specific architectures • Jordan and Xu’s (1995) definition of HME27: • Generalisation of HME • Abstraction of architecture from algorithm • Theoretical results for convergence

13. Multi-net System Framework • Propose a modification to Jordan and Xu’s definition of HME to provide a generalised multi-net system framework • HME combines the output of the expert networks through a weighting generated by a gating network • Replace the weighting by the (optional) operation of a network • Can be used for parallel, sequential and supervisory systems

14. Example: HME

15. Example: Framework

16. Definition • A multi-net system consists of the ordered tree of depth r defined by the nodes , with the root of the tree associated with the output , such that:

17. Multi-net System Framework • Learning algorithm operates by modifying the state of the system as defined by associated with each node • Includes: • Pre-training • In-situ training • Incremental training (through pre- or in-situ training) • Examples demonstrate how framework can be used to describe existing types of multi-net system • However does not rely upon categorisation schemes

18. In-situ Learning • Evaluation of in-situ learning in multi-net systems • Explore parallel and sequential in-situ learning with definitions using the proposed framework • Simple learning ensemble (SLE) • Sequential learning modules (SLM) • Benchmark classification tasks28: • XOR • MONK’s problems (MONK 1, 2, 3)29 • Wisconsin Breast Cancer Database (WBCD)30 • Proben1 Thyroid (thyroid1 data set)31

19. Simple Learning Ensemble • Ensembles: • Train each network individually • Parallel combination of network outputs: mean output • Pre-training: how can we understand or control the combined performance of the ensemble? • Incremental: AdaBoost15 • In-situ: negative correlation23 • In-situ learning: • Train in-situ and assess combined performance during training using early stopping • Generalisation loss early stopping criterion32

20. Benchmark Results • Compare SLE results with: • Simple ensemble (SE): all networks pre-trained using early stopping • Single-net: MLP with backpropagation – with and without early stopping • For SLE and SE: • From 2 to 20 MLP networks • 100 trials per configuration: mean response

21. Benchmark Results • XOR • SLE and SE equivalent training (no early stopping) • SLE uses less epochs to give equivalent responses • MONK’s problems/WBCD/Thyroid • SLE improves upon SE, SE improves upon single-net • SLE trains for longer: combined performance • Adding more networks gives better generalisation • More networks, more achieved desired performance • MONK 1/2 • SLE improves upon non-early stopping single-net

22. Sequential Learning Modules • Sequential systems: • Can a combination of (simpler) networks give good generalisation and learning speed? • Typically pre-trained and for specific processing • Sequential in-situ learning: • How can in-situ learning be achieved with sequential networks: target error/output? • Use unsupervised networks • Last network has target output and hence can be supervised

23. Benchmark Results • Compare SLM results with: • Single-net: single layer network with delta learning • Single-net: MLP with backpropagation – without early stopping • Networks: • Combine a SOM with a single layer network with delta learning • Varying map sizes of SOM used to see effect on classification performance • 100 trials per configuration: mean response

24. Benchmark Results • XOR • Cannot be solved by SOM or single layer network • Can be solved by SLM with 3x3 map • Faster learning times than MLP with backpropagation • MONK’s problems/WBCD • SLM can learn classification of training examples • Generalisation: improves upon SE with early stopping • MONK 2/3 • SLM improves upon MLP without early stopping • MONK 3 improves upon SLE

25. Benchmark Results • MONK 1/WBCD • Generalisation: similar, but slightly worse • Thyroid • Poor learning of training examples • Can SOM perform sufficient pre-processing for single layer network? • Results seem to depend upon problem type and map size

26. In-situ Learning • In-situ learning in multi-net systems: • Can give better training and generalisation performance • Comparison with SE (early stopping) and single-net systems (with and without early stopping) • Computational effort? • Ensemble systems: • Effect of training times on bias, variance and diversity? • Sequential systems: • Encouraging empirical results: theoretical results? • Automatic classification of unsupervised clusters

27. In-situ Learning

28. In-situ Learning

29. In-situ Learning and Simulation • Biological motivation for in-situ learning • Hebb’s ‘neural integration’ • Functional specialism in cognitive systems • Use in-situ learning in modular multi-net systems to simulate numerical abilities: • Quantification: subitization and counting • Addition: fact retrieval and ‘count all’ • Combine ME and SLM to allow abilities to ‘compete’

30. Strategy Learning System

31. Multi-net Simulation of Quantification • Single-net and multi-net systems • Trained on scenes consisting of ‘objects’ • Logarithmic probability model • Subitization SOM: • Ordering of numbers with compressive scheme • Limit: training data, object frequency and map size • Counting MLP with backpropagation: • Correct responses to training data • Conventional, stable non-conventional and nonstable

32. Multi-net Simulation of Quantification • MNQ: • Subitization: SOM (pre-trained) • Single layer network with delta learning • Counting: MLP with backpropagation • Successfully learnt to quantify • To subitize or count • Decision based upon input • Subitization limit attributable to interaction of modules • Lower numbers subitized, higher numbers counted

33. Multi-net Simulation ofAddition • Single-net and multi-net systems • Trained on scenes consisting of two sets of ‘objects’ • Equal probability model • Fact retrieval SOM: • Each addend associated with a map axis • Some overlap of problems • Commutative information used • ‘Count all’ MLP with backpropagation: • Correct responses to training data • Some relationship to observed human errors

34. Multi-net Simulation ofAddition • MNA: • Fact retrieval: SOM • Single layer network with delta learning • ‘Count all’: MLP with backpropagation • Successfully learnt to add • To count or from facts • Decision based upon input • Predominant use of ‘count all’, rather than facts • Does demonstrate change in strategy

35. In-situ Learning and Simulation • In-situ learning in SLS: • Simulate developmental progression • At least as capable as equivalent monolithic solutions • Competition between supervised and unsupervised learning paradigms • In-situ learning and simulation of the interaction between multiple abilities: • Interaction between different abilities: simulating psychological phenomena • Integrated learning

36. Contribution • Multi-net systems: • Seem to offer empirical and theoretical improvement to generalisation • Properties under-explored • Framework for multi-net systems • Generalisation of multi-net systems beyond categorisation schemes • Foundation to explore multi-net properties • In-situ learning • Biological and theoretical motivation

37. Contribution • Compared different multi-net techniques and the use of in-situ learning • Demonstrated that in-situ learning can lead to improved training and generalisation • SLE • Assessment of combined performance • SLM • Combining ‘simple’ networks to solve ‘complex’ tasks • ‘Superordinate’? • Also shows automatic classification using SOM

38. Contribution • Integrated learning • Simulations using modular parallel and sequential networks • In-situ learning used to explore the interaction of modules during learning • Demonstrated simulation of abilities and observed psychological phenomena

39. Future Work • Framework: • Modify learning algorithm – recursive using tree • Explore properties such as bias, variance, diversity and VC Dimension • In-situ learning: • Further comparison • SLE: does learning promote diversity? • SLM: expand and explore limitations • Simulations: • Explore further the effect of integrated learning

40. Questions?

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