Neural Computation 0368-4149-01

1. Neural Computation0368-4149-01 Prof. Nathan Intrator TA: Yehudit Hasson Tuesday 16:00-19:00 Dan David 111 Office hours: Wed 4-5 nin@tau.ac.il

2. Neural Computation • Neuroscience • The objective is to understand the human brain • Biologically azrealistic models of neurons • Biologically realistic connection topologies • Neural computation • The objective is to develop learning, representation and computation methods • Novel architectures for data representation and processing

3. The goals of neural computation • To understand how the brain actually works • Its big and very complicated and made of yukky stuff that dies when you poke it around • To understand a new style of computation • Inspired by neurons and their adaptive connections • Very different style from sequential computation • should be good for things that brains are good at(e.g. vision) • Should be bad for things that brains are bad at(e.g. 23 x 71) • To solve practical problems by using novel learning algorithms • Learning algorithms can be very useful even if they have nothing to do with how the brain works

4. The Brain The brain - that's my second most favorite organ! - Woody Allen

5. The Brain: Fundamental Questions • What kind of information is extracted from the environment? • How is information represented, e.g. visual? • How is information stored? • How is information altered (learning & memory)? • How is information processed and manipulated?

7. The Brain: Simpler Questions • How is 3D information stored • How is relational information stored: • The child is on the floor • The book is in the bag • How are verbs associated with adjectives • How is information bound together: • Collections of items which are on the table • Collection of edges which form an object

8. Physiological experiments help us learn how a new scene is analyzed, in particular the eye movement is used to learn about the analysis strategy In this unseen set of images, it takes very long time to detect the changes between the bear and microscope. How do we observe changes in familiar scenes very fast?

9. Man versus Machine (hardware)

10. Man versus Machine (information processing) No memory management, No hardware/software/data distinction

11. Brain Performance

12. Flies have a better stabilizing mechanism than a Boeing 747Their gyroscope is being studied in a wind tunnel http://www.kyb.mpg.de/publications/pdfs/pdf340.pdf

13. The bat’s external ears pick up both the emitted sounds and the returning echoes to serve as the receiving antennas. Echo delay estimation 20 nanoSec!!

14. Movies: NavigationDARPA Robot Race

15. Dolphin’s sonar properties • Send up to 200 clicks per second! • Frequency range 15 kHz – 120 kHz • Excellent sensor array (whole face) • Discriminate between alloys of aluminum • ‘See’ a tennis ball from 75 meters • Distinguish between a penny and dime from 3 meters • Detect fish buried .5 meter underground • Excellent shape discrimination (same material) W. W. L. Au (1993) The sonar of dolphins. (Springer).

16. Brief Outline • Unsupervised Learning • Short bio motivation • Unsupervised Neuronal Model • Connection with Projection Pursuit and advanced feature extraction • Supervised Learning Schemes • Perceptron and Multi Layer Perceptron • RBF, SVM, Trees • Training and optimization • Model Selection and Validation (advanced training methods) • Cross Validation, Regularization, Noise injection • Ensembles • Brain Machine Interface • EEG, fMRI modalities • Brain state interpretation based on machine learning model • Recent Research in BMI

17. Introduction to the Brain By: Geoffrey Hinton www.cs.toronto.edu/~hinton/csc321/notes/lec1.ppt

18. A typical cortical neuron • Gross physical structure: • There is one axon that branches • There is a dendritic tree that collects input from other neurons • Axons typically contact dendritic trees at synapses • A spike of activity in the axon causes charge to be injected into the post-synaptic neuron • Spike generation: • There is an axon hillock that generates outgoing spikes whenever enough charge has flowed in at synapses to depolarize the cell membrane axon body dendritic tree

19. A Neuron

20. The synaptic junction Synapses, Ca influx, release of neurotransmitter, opening of post-synaptic channels

21. Axon, dendrite Ion channels Membrane rest potential Action potential, refractory period Some relevant terms

22. billion synapses in human brain • Chemical transmission and modulation of signals • Inhibitory synapses • Excitatory synapses The Biological Neuron • 10 billion neurons in human brain • Summation of input stimuli • Spatial (signals) • Temporal (pulses) • Threshold over composed inputs • Constant firing strength

23. Biological Neural Networks • 10,000 synapses per neuron • Computational power = connectivity • Plasticity • new connections (?) • strength of connections modified

24. Neural Dynamics Action potential Action potential ≈ 100mV Activation threshold ≈ 20-30mV Rest potential ≈ -65mV Spike time ≈ 1-2ms Refractory time ≈ 10-20ms Refractory time

25. The Artificial Neuron x1(t) Stimulus wi1 x2(t) wi2 wi3 x3(t) yi(t) wi4 Response x4(t) wi5 x5(t) Neuron i urest = resting potential xj(t) = output of neuron j at time t wij = connection strength between neuron i and neuron j u(t) = total stimulus at time t

26. Artificial Neural Models • McCulloch Pitt-type Neurons (static) • Digital neurons: activation state interpretation (snapshot of the system each time a unit fires) • Analog neurons: firing rate interpretation (activation of units equal to firing rate) • Activation of neurons encodes information • Spiking Neurons (dynamic) • Firing pattern interpretation (spike trains of units) • Timing of spike trains encodes information (time to first spike, phase of signal, correlation and synchronicity

27. Binary Neurons Stimulus Response on “Hard” threshold off • = threshold • ex: Perceptrons, Hopfield NNs, Boltzmann Machines • Main drawbacks: can only map binary functions, biologically implausible.

28. Analog Neurons Stimulus Response on “Soft” threshold off • ex: MLPs, Recurrent NNs, RBF NNs... • Main drawbacks: difficult to process time patterns, biologically implausible.

29. Spiking Neurons Stimulus • = spike and afterspike potential urest = resting potential e(t,u(t)) = trace at time t of input at time t • = threshold xj(t) = output of neuron j at time t wij = efficacy of synapse from neuron i to neuron j u(t) = input stimulus at time t Response

30. y(t)  urest+(t-tf) Spiking Neuron Dynamics

31. Hebb’s Postulate of Learning When an axon of cell A is near enough to excite a cell and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency as one of the cells firing B is increased.

32. Hebb’s Postulate: revisited • Stent (1973), and Changeux and Danchin (1976) • have expanded Hebb’s rule such that it also models inhibitory synapses: • If two neurons on either side of a synapse are activated simultaneously (synchronously), then the strength of that synapse is selectively increased. • If two neurons on either side of a synapse are activated asynchronously, then that synapse is selectively weakened or eliminated.a

33. Synapses • When a spike travels along an axon and arrives at a synapse it causes vesicles of transmitter chemical to be released • There are several kinds of transmitter • The transmitter molecules diffuse across the synaptic cleft and bind to receptor molecules in the membrane of the post-synaptic neuron thus changing their shape. • This opens up holes that allow specific ions in or out. • The effectiveness of the synapse can be changed • vary the number of vesicles of transmitter • vary the number of receptor molecules. • Synapses are slow, but they have advantages over RAM • Very small • They adapt using locally available signals (but how?)

34. How the brain works • Each neuron receives inputs from other neurons • Some neurons also connect to receptors • Cortical neurons use spikes to communicate • The timing of spikes is important • The effect of each input line on the neuron is controlled by a synaptic weight • The weights can be positive or negative • The synaptic weights adapt so that the whole network learns to perform useful computations • Recognizing objects, understanding language, making plans, controlling the body • You have about 10 neurons each with about 10 weights • A huge number of weights can affect the computation in a very short time. Much better bandwidth than pentium. 11 3

35. Modularity and the brain • Different bits of the cortex do different things. • Local damage to the brain has specific effects • Specific tasks increase the blood flow to specific regions. • But cortex looks pretty much the same all over. • Early brain damage makes functions relocate • Cortex is made of general purpose stuff that has the ability to turn into special purpose hardware in response to experience. • This gives rapid parallel computation plus flexibility • Conventional computers get flexibility by having stored programs, but this requires very fast central processors to perform large computations.

36. Idealized neurons • To model things we have to idealize them (e.g. atoms) • Idealization removes complicated details that are not essential for understanding the main principles • Allows us to apply mathematics and to make analogies to other, familiar systems. • Once we understand the basic principles, its easy to add complexity to make the model more faithful • It is often worth understanding models that are known to be wrong (but we mustn’t forget that they are wrong!) • E.g. neurons that communicate real values rather than discrete spikes of activity.

37. Linear neurons • These are simple but computationally limited • If we can make them learn we may get insight into more complicated neurons bias th i input y 0 weight on b 0 output th input i index over input connections

38. Binary threshold neurons • McCulloch-Pitts (1943): influenced Von Neumann! • First compute a weighted sum of the inputs from other neurons • Then send out a fixed size spike of activity if the weighted sum exceeds a threshold. • Maybe each spike is like the truth value of a proposition and each neuron combines truth values to compute the truth value of another proposition! 1 1 if y 0 0 otherwise z threshold

39. Linear threshold neurons These have a confusing name. They compute a linear weighted sum of their inputs The output is a non-linear function of the total input y 0 otherwise 0 z threshold

40. Sigmoid neurons • These give a real-valued output that is a smooth and bounded function of their total input. • Typically they use the logistic function • They have nice derivatives which make learning easy (see lecture 4). • If we treat as a probability of producing a spike, we get stochastic binary neurons. 1 0.5 0 0

41. Feedforward networks These compute a series of transformations Typically, the first layer is the input and the last layer is the output. Recurrent networks These have directed cycles in their connection graph. They can have complicated dynamics. More biologically realistic. Types ofconnectivity output units hidden units input units

42. Types of learning task • Supervised learning • Learn to predict output when given input vector • Who provides the correct answer? • Reinforcement learning • Learn action to maximize payoff • Not much information in a payoff signal • Payoff is often delayed • Unsupervised learning • Create an internal representation of the input e.g. form clusters; extract features • How do we know if a representation is good?