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- 1. A temporal classifier system using spiking neural networks<br />Gerard David Howard, Larry Bull & Pier-Luca Lanzi<br />{david4.howard, larry.bull} @uwe.ac.uk<br />pierluca.lanzi @polimi.it<br />1<br />
- 2. Contents<br />Intro & Motivation<br />System architecture – Spiking XCSF<br />Constructivism (nodes and connections)<br />Working in continuous space<br />Comparison to MLP / Q-learner<br />Taking time into consideration<br />Comparison to MLP<br />Simulated robotics<br />2<br />
- 3. Motivation<br />Many real-world tasks incorporate continuous space and continuous time<br />Autonomous robotics are an unanswered question: will require some degree of knowledge “self-shaping” or control over their internal knowledge representation<br />We introduce an LCS containing spiking networks and demonstrate the usefulness of the representation<br />Handles continuous space and continuous time<br />Representation structure dependent on environment<br />3<br />
- 4. XCSF<br />Includes computed prediction, which is calculated from input state (augmented by constant x0) and a weight vector – each classifier has a weight vector<br />Weights are updated linearly using modified delta rule<br />Main differences from canonical:<br />SNN replaces condition and calculates action<br />Self-adaptive parameters give autonomous learning control<br />Topology of networks altered in GA cycle<br />Generalisation from computed prediction, computed actions and network topologies<br />4<br />
- 5. Spiking networks<br />Spiking networks have temporal functionality<br />We use Integrate-and-Fire (IAF) neurons<br />Each neuron has a membrane potential (m) that varies through time<br />When m exceeds a threshold, the neuron sends a spike to every neuron in the network that it has a forward connection to, and resets m<br />Membrane potential is a way of implementing memory<br />5<br />
- 6. Spiking networks<br />IAF Spiking network replaces condition and action, 2 input, 3 output nodes<br />Each input state processed 5 times by spiking network. Neural outputs are spike trains: high (>=3) or low (<3) spikes in 5-element output window.<br />Classifier doesn’t match if !M node is high<br /><ul><li>Generalisation from computed prediction, computed actions and network topologies</li></ul>6<br />00101 = LOW<br />L<br />Input state <br />(one node per element)<br />R<br />01110 = HIGH<br />![M]<br />10001 = LOW<br />
- 7. Self-adaptive parameters<br />During a GA cycle, a parent’s µ value is copied to its offspring and altered<br />The offspring then applies its own µ to itself (bounded <br />[0-1]) before being inserted into the population.<br />Similar to ES mutation alteration<br />Mutate<br />µ µ * e N(0,1)<br />Insert<br />Copy µ <br />[A]<br />Mutate<br />µ µ * e N(0,1)<br />Copy µ <br />Insert<br />7<br />
- 8. Constructivism<br />Neural Constructivism - interaction with environment guides learning process by growing/pruning dendritic connectivity<br />Constructivism can add or remove neurons from the hidden layer during a GA event <br />Two new self-adaptive values control NC , ψ (probability of constructivism event occurring) and ω (probability of adding rather than removing a node). These are modified during a GA cycle as with µ<br />8<br />Randomly initialised weights<br />
- 9. Connection selection<br />Automatic feature selection often used in conjunction with neural networks – allows reduction in number of inputs to only highest utility features<br />We apply feature selection to every connection in a network, connection is enabled/disabled on satisfaction of new self-adaptive parameter τ. <br />All connections initially enabled, connections created via node addition are enabled with 50% probability per connection<br /><ul><li>Generalisation from computed prediction, computed actionsand network topologies</li></ul>9<br />
- 10. Effects of SA, NC & CS<br />Self Adaptation allows the system to control the amount of search taking place in an environmental niche without having to predetermine suitable parameter values<br />Neural Constructivism allows classifier to automatically grow networks to match task complexity<br /><ul><li>Connection Selection allows finer-grained search and tailoring of solutions, potentially reducing network size even further. Keeps only salient connections, can remove detrimental inputs/connections.</li></ul>10<br />
- 11. Continuous Grid World<br />Two dimensional continuous grid environment<br />Runs from 0 – 1 in both x and y axes<br />Goal state is where (x+y>1.9) – darker regions of grid represent higher expected payoff. Reaching goal returns a reward of 1000, else 0<br />Agent starts randomly anywhere in the grid except the goal state, aims to reach goal (moving 0.05) in fewest possible steps (avg. opt. 18.6)<br />1.00<br />0.50<br />Agent<br />0.00<br />0.50<br />1.00<br />11<br />
- 12. Discrete movement<br />Agent can make a single discrete movement (N,E,S,W) N=(HIGH,HIGH), E=(HIGH,LOW) etc…<br />Experimental parameters N=20000,γ =0.95, β=0.2, ε0=0.005, θGA=50, θDEL=50<br />XCSF parameters as normal.<br />Initial prediction error in new classifiers=0.01, initial fitness=0.1<br />Additional trial from fixed location lets us perform t-tests. “Stability” shows first step that 50 consecutive trials reach goal state from this location.<br />12<br />
- 13. Discrete movement<br />13<br /><ul><li>Stability = 50 consecutive optimals from a fixed location
- 14. Fewer macroclassifiers = greater generalisation
- 15. Lower mutation rate = more stable evolutionary process</li></li></ul><li>Taking time into account<br /><ul><li>Most real-world tasks have some temporal element</li></ul>Describes the behaviour of the agent, or state of the environment, across extended periods of time (semi-MDP!)<br />Other LCSs have attempted to tackle semi-MDPs (CXCS, DACS etc)<br />Most recent is the Temporal Classifier System<br />TCS shown able to handle real/simulated robotics tasks under ZCS and XCS, this is the first implementation with XCSF<br />14<br />
- 16. Continuous duration actions<br />Reward usually calculated as<br />Reward is now calculated as<br />Two discount factors that favour overall effectiveness and efficient state transitions respectively <br /> =0.05, ρ=0.1<br />tt = total steps for entire trial <br />ti = duration of a single action<br />Timeout=20; new steps to goal is 1.5<br />15<br />
- 17. Continuous Grid World TCS<br />16<br /><ul><li>Fewer macroclassifiers = greater generalisation
- 18. Lower mutation rate = more stable evolutionary process</li></li></ul><li>Continuous duration actions<br />17<br />Spiking networks more inclined to switch actions within the same [A]!<br />Possibly important in scenarios requiring more disjointed action selection<br />
- 19. Smaller step size<br />18<br /><ul><li>Step size reduced to 0.005, timeout = 200 – optimal steps to goal 1.5
- 20. Tabular Q-learner cannot learn – too many (s,a) combinations, long action chains!
- 21. Spiking non-TCS cannot learn – too many (s,a) combinations, long action chains!
- 22. MLP TCS cannot learn – lack of memory?
- 23. Spiking TCS canlearn to optimally solve this environment by extending an action set across multiple states and recalculating actions where necessary
- 24. Aided by temporal element of networks</li></li></ul><li>Comparing Step Sizes<br />19<br /><ul><li>Spiking TCS with step size 0.005 has higher performance than in step size 0.05! More steps = more opportunity to use temporal information</li></li></ul><li>Smaller step size Q-learner<br />20<br />Steps to goal, spiking TCS<br />Step size 0.005<br />Steps to goal, tabular Q-learner, step size 0.005<br />
- 25. Mountain-car<br />21<br /><ul><li>Multi-step reinforcement learning problem
- 26. Guide a car out of a valley, sometimes requiring non-obvious behaviour
- 27. State comprises position and velocity
- 28. Actions increase/decrease velocity: HIGH/HIGH = increase, LOW/LOW = decrease, anything else = no change.
- 29. Noise! (+/- 5% of both state elements)
- 30. TCS optimal steps to goal = 1
- 31. N=1000
- 32. Results compare favourably to XCSF work (e.g with tile coding)</li></li></ul><li>Mountain-car results<br />22<br />
- 33. Robotics<br />23<br /><ul><li>Webots robotics package, TCS spiking controller
- 34. Simulate a Khepera robot that uses 3 IR and 3 light sensors as input state
- 35. Two bump sensors detect a collision and reverse the robot/reform [M] if collision is detected
- 36. Task: similar to grid world, but with an obstacle to avoid and a light source to reach.
- 37. 3 actions possible
- 38. Problems: state space higher dimensionality and not directly linked to prediction, increased noise levels, wheel slip, robot orientation etc.</li></li></ul><li>Robotics<br />24<br /><ul><li>Parameters: 500 trials, N=3000, initially 6 hidden layer nodes, all connected with 50% probability per connection – jumps the start of the evolutionary process, allows topological network/behaviour variations
- 39. Robot start position constrained so that obstacle is always between it and the light source
- 40. Movement is much more granular than with grid(0.05) !
- 41. Self adaptive parameters initially constrained to (0<(μ,ψ,τ)≤0.02), with (0<ω≤1) as normal.</li></li></ul><li>Robotics<br />25<br />
- 42. Robotics<br />26<br />Steps to goal<br />Connected hidden layer nodes<br />Percentage enabled connections<br />Self-adaptive parameters, μ, ψ, τ all plotted on RHS axis<br />
- 43. Robotics<br />27<br />Overall:<br /><ul><li>Parameters, neurons, and connections do not vary much
- 44. Initially seeding with 6 hidden layer nodes still let’s us use connection selection to generate behavioural variation in the networks
- 45. Temporal functionality of the networks is exploited so that a single action set can</li></ul>Drop unwanted classifiers to change it’s favoured action at specific points (e.g. just before a collision)<br />Alter the action advocated action of a majority of classifiers in [A] for the same effect<br />
- 46. Thanks for your time!<br />28<br />

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