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Bioinspired Computing Lecture 3

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1 Bioinspired Computing Lecture 3
Biological Neural Networks and Artificial Neural Networks Based on slides from Netta Cohen lecture 2008

2 Last week: Today... We introduced swarm intelligence.
We saw how many simple agents can follow simple rules that allow them to collectively perform more complex tasks. Today... Biological systems whose manifest function is information processing: computation, thought, memory, communication and control. We begin a dissection of a brain: How different is a brain from an artificial computer? How can we build and use artificial neural networks? lecture 2008

3 Investigating the brain
Imagine landing on an abandoned alien planet and finding thousands of alien computers. You and your crew’s mission is to find out how they work. What do you do? Summon Scottie, your engineer Summon Data - your software wiz to disassemble the machines into component parts, test each part (electronically, optically, chemically…), decode the machine language, and study how components are connected. to connect to the input & output ports of a machine, find a language to communicate with it & write computer programs to test the system’s response by measuring its speed, efficiency & performance at different tasks. part #373a Inputs Outputs The computer Input program Output lecture 2008

4 The brain as a computer Higher level functions in animal behaviour
Gathering data (sensation) Inferring useful structures in data (perception) Storing and recalling information (memory) Planning and guiding future actions (decision) Carrying out the decisions (behaviour) Learning consequences of these actions Hardware functions and architectures 10 billion neurons in human cortex 10,000 synapses (connections) per neuron Machine language: 100mV, 1-2msec spikes (action potential) Specialised regions & pathways (visual, auditory, language…) lecture 2008

5 The brain as a computer versus
Special task: program often hard-coded into system. Hardware not hard: plastic, rewiring. No clear hierarchy. Bi-directional feedback up & down the system. Unreliable components. Parallelism, redundancy appear to compensate. Output doesn’t always match input: Internal state is important. Development & evolutionary constraints are crucial. Universal, general-purpose. Software: general, user-supplied. Hardware is hard: Only upgraded in discrete units. Obvious hierarchy: each component has a specific function. Once burned in, circuits run without failure for extended lifetimes. Input-output relations are well-defined. Engineering design depends on engineer. Function is not an issue. lecture 2008

6 Neuroscience pre-history
200 AD: Greek physician Galen hypothesises that nerves carry signals back & forth between sensory organs & the brain. 17th century: Descartes suggests that nerve signals account for reflex movements. 19th century: Helmholtz discovers the electrical nature of these signals, as they travel down a nerve. 1838-9: Schleiden & Schwann systematically study plant & animal tissue. Schwann proposes the theory of the cell (the basic unit of life in all living things). Mid-1800s: anatomists map the structure of the brain. but… The microscopic composition of the brain remains elusive. A raging debate surrounds early neuroscience research, until... lecture 2008

7 The neuron doctrine Ramon y Cajal (1899)
1) Neurons are cells: distinct entities (or agents). 2) Inputs & outputs are received at junctions called synapses. 3) Input & output ports are distinct. Signals are uni-directional from input to output. Today, neurons (or nerve cells) are regarded as the basic information processing unit of the nervous system. neuron Inputs Outputs lecture 2008

8 lecture 2008

9 Neuron details lecture 2008

10 Organisation of neurons
lecture 2008

11 Ion channels and spiking
Membrane potential negative (inside /outside) Na+ would like to rush in but can’t Depolarisation opens Na+ channels, Na+ flows in Chain reaction! More Na+ flows in! This opens K+ channels, K+ flows out: hyperpolarisation lecture 2008

12 Macaque brain (Felleman & van Essen 1991)
lecture 2008

13 lecture 2008

14 The neuron as a transistor
Both have well-defined inputs and outputs. Both are basic information processing units that comprise computational networks. If transistors can perform logical operations, maybe neurons can too? Neuronal function is typically modelled by a combination of a linear operation (sum over inputs) and a nonlinear one (thresholding). input  neuron  output This simple representation relies on Cajal’s concept of lecture 2008

15 Machine language Why Spikes?
The basic “bit” of information is represented by neurons in spikes. The cell is said to be either at rest or active. A spike (action potential) is a strong, brief electrical pulse. Since these action potentials are mostly identical, we can safely refer to them as all-or-none signals. Why Spikes? Why don’t neurons use analog signals? One answer lies in the network architecture: signals cover long distances (both within the brain and throughout the body). Reliable transmissions requires strong pulses. lecture 2008

16 Computation of a pyramidal neuron
Single all-or-none output Many inputs (dendrites) soma axon lecture 2008

17 From transistors to networks
We can now summarise our working principles: The basic computational unit of the brain is the neuron. The machine language is binary: spikes. Communication between neurons is via synapses. However, we have not yet asked how information is encoded in the brain, how it is processed in the brain, and whether what goes on in the brain is really ‘computation’. lecture 2008

18 Information codes Temporal code Neural code Rate code Population code/
Distributed code noise Examples of both neural codes and distributed representations have been found in the brain. Example in the visual system: colour representation, face recognition, orientation, motion detection, & more… lecture 2008

19 Information content Example. A spike train produced by a neuron over an interval of 100ms is recorded. Neurons can produce a spike every 2ms. Therefore, rates (individual code words) can be produced by this neuron. In contrast, if the neuron were using temporal coding, up to 250 different words could be represented. In this sense, temporal coding is much more powerful. 51 different 250 different lecture 2008

20 Circuitry depends on neural code
Temporal codes rely on a noise-free signal transmission. Thus, we would expect to find very few ‘redundant’ neurons with co-varying outputs in that network. Accordingly, an optimal temporal coding circuit might tend to eliminate redundancy in the pattern of inputs to different neurons. On the other hand, if neural information is carried by a noisy rate-based code, then noise can be averaged out over a population of neurons. Population coding schemes, in which many neurons represent the same information, would therefore be the norm in those networks. Experiments on various brain systems find either coding systems, and in some cases, combinations of temporal and rate coding are found. lecture 2008

21 Neuronal computation Having introduced neurons, neuronal circuits and even information codes with well defined inputs and outputs, we still have not mentioned the term computation. Is neuronal computation anything like computer computation? 1 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! In a computer program, variable have initial states, there are possible transitions, and a program specifies the rules. The same is true for machine language. To obtain an answer at the end of a computation, the program must HALT. Does the brain initialise variables? Does the brain ever halt? lecture 2008

22 an example of bio-computation
Association an example of bio-computation One recasting of biological brain function in these computational terms was proposed by John Hopfield in the 1980s as a model for associative memory. Question: How does the brain associate some memory with a given input? Answer: The input causes the network to enter an initial state. The state of the neural network then evolves until it reaches some new stable state. The new state is associated with the input state. lecture 2008

23 Trajectories in a schematic
Association (cont.) Trajectories in a schematic state space Whatever initial condition is chosen, the system will follow a well-defined route through state-space that is guaranteed to always reach some stable point (i.e., pattern of activity) Hopfield’s ideas were strongly motivated by existing theories of self-organisation in neural networks. Today, Hopfield nets are a successful example of bio-inspired computing (but no longer believed to model computation in the brain). lecture 2008

24 Learning body Sensory inputs brain Motor outputs environment
No discussion of the brain, or nervous systems more generally is complete without mention of learning. What is learning? How does a neural network ‘know’ what computation to perform? How does it know when it gets an ‘answer’ right (or wrong)? What actually changes as a neural network undergoes ‘learning’? environment body Sensory inputs Motor outputs brain lecture 2008

25 Learning (cont.) Learning can take many forms: Supervised learning
Reinforcement learning Association Conditioning Evolution At the level of neural networks, the best understood forms of learning occur in the synapses, i.e., the strengthening and weakening of connections between neurons. The brain uses its own learning algorithms to define how connections should change in a network. lecture 2008

26 Learning from experience
How do the neural networks form in the brain? Once formed, what determines how the circuit might change? In 1948, Donald Hebb, in his book, "The Organization of Behavior", showed how basic psychological phenomena of attention, perception & memory might emerge in the brain. Hebb regarded neural networks as a collection of cells that can collectively store memories. Our memories reflect our experience. How does experience affect neurons and neural networks? How do neural networks learn? lecture 2008

27 Synaptic Plasticity Definition of Learning: experience alters behaviour The basic experience in neurons is spikes. Spikes are transmitted between neurons through synapses. Hebb suggested that connections in the brain change in response to experience. Pre-synaptic cell Post-synaptic cell delay time Hebbian learning: If the pre-synaptic cell causes the post-synaptic cell to fire a spike, then the connection between them will be enhanced. Eventually, this will lead to a path of ‘least resistance’ in the network. lecture 2008

28 Today... From biology to information processing
At the turn of the 21st century, “how does it work” remains an open question. But even the kernel of understanding and simplified models we already have for various brain function are priceless, in providing useful intuition and powerful tools for bioinspired computation. Next time... Artificial neural networks (part 1) Focus on the simplest cartoon models of biological neural nets. We will build on lessons from today to design simple artificial neurons and networks that perform useful computational tasks. lecture 2008

29 The Appeal of Neural Computing
The only intelligent systems that we know of are biological. In particular most brains share the following feature in their neural architecture – they are massively parallel networks organised into interconnected hierarchies of complex structures. speed, tolerance, robustness, flexibility, self-driven dynamic activity For computer scientists, many natural systems appear to share many attractive properties: In addition, they are very good at some tasks that computers are typically poor at: recognising patterns, balancing conflicts, sensory-motor coordination, interaction with the environment, anticipation, learning… even curiosity, creativity & consciousness. lecture 2008

30 The first artificial neuron model
In analogy to a biological neuron, we can think of a virtual neuron that crudely mimics the biological neuron and performs analogous computation. A body (like the soma), sums over inputs to compute output, and Σ cell body outputs (like synapses on the axon) transmit the output downstream. output Inputs (like biological dendrites) carry signal to cell body. inputs Just like biological neurons, this artificial neuron neuron will have: The artificial neuron is a cartoon model that will not have all the biological complexity of real neurons. How powerful is it? lecture 2008

31 Early history (1943) McCulloch & Pitts (1943). “A logical calculus of the ideas immanent in nervous activity”, Bulletin of Mathematical Biophysics, 5, In this seminal paper, Warren McCulloch and Walter Pitts invented the first artificial (MP) neuron, based on the insight that a nerve cell will fire an impulse only if its threshold value is exceeded. MP neurons are hard-wired devices, reading pre-defined input-output associations to determine their final output. Despite their simplicity, M&P proved that a single MP neuron can perform universal logic operations. A network of such neurons can therefore do anything a Turing machine can do, but with a much more flexible (and potentially very parallel) architecture. lecture 2008

32 The McCulloch-Pitts (MP) neuron
inputs x1 x2 x3 xn Inputs x are binary: 0,1. Each input has an assigned weight w. w1 w2 w3 wn weights *  ( ) over all i Weighted inputs are summed  in the cell body. Neuron fires if sum exceeds (or equals) activation threshold . 1 if    0 if  <  output = Otherwise, the output=0. If the neuron fires, the output =1. The “computation” consists of "adders" and a threshold. Note: an equivalent formalism assigns =0 & instead of threshold introduces an extra bias input, such that bias * wbias = -  bias * wb lecture 2008

33 Logic gates with MP neurons
IN 1 OUT 1 1 Always 0 OUT 2 IDENTITY OUT 3 NOT OUT 4 Always 1 For binary logic gates, with only one input, possible outputs are described by the following truth tables: For example:  = -0.5 NOT x x w w = -1 Excercise: Find w and  for the 3 remaining gates. lecture 2008

34 Logic gates with MP neurons (cont.)
With two binary inputs, there are 4 possible inputs and 24 = 16 corresponding truth tables (outputs)! For example, the AND gate implemented in the MP neuron: x1 AND x2 x1 x2  = +1.5 1 IN 1 IN 2 Here is a compact, graphical representation of the same truth table: Excercise: Find w and  for OR & NAND. lecture 2008

35 Computational power of MP neurons
Universality: NOT & AND can be combined to perform any logical function; MP neurons, circuited together in a network can solve any problem that a conventional computer could. But let’s examine the single neuron a little longer. Q: Just how powerful is a single MP neuron? A: It can solve any problem that can be expressed as a classification of points on a plane by a single straight line. IN 1 IN 2 AND Even one neuron can successfully handle simple classification problem. Generalisation to many inputs: points in many dimensions are now classified, not by a line, but by a flat surface. lecture 2008

36 Classification in Action
A set of patients may have a medical problem. Blood samples are analysed for the quantities of two trace elements. trace 1 2.4 9.8 1.2 0.4 7.9 6.7 etc. trace 2 1.0 8.3 0.2 2.1 8.8 7.2 etc. problem? yes no etc. ∑ xi wi etc. output +6.6 -8.1 etc. +8.6 +7.5 -6.7 -3.9 output Yes No etc. inputs x1 bias x2 weights w1 w3 w2 sum ∑xi wi * output +ive output = problem w1=-1, w2=-1, w3=+10 & bias=+1 With correct weights, this MP neuron consistently classifies patients. lecture 2008

37 The missing step The ability of the neuron to classify inputs correctly hinges on the appropriate assignment of the weights and threshold. So far, we have done this by hand. Imagine we had an automatic algorithm for the neuron to learn the right weights and threshold on its own. In 1962, Rosenblatt, inspired by biological learning rules, did just that. lecture 2008 Frank Rosenblatt (1962). Principles of Neurodynamics, Spartan, New York

38 The perceptron algorithm
Take wj random START: Take X ε F+ U F- CHECK: if x ε F+ and Σ wjxj > 0 goto START if x ε F+ and Σ wjxj ≤ 0 goto ADD if x ε F- and Σ wjxj ≤ 0 goto START if x ε F- and Σ wjxj > 0 goto SUB ADD: wj → wj + xj goto START SUB: wj → wj - xj goto START: lecture 2008

39 The Perceptron Theorem
Says that the previous algorithm will converge on a set of weights in a finite number of steps if w* exists lecture 2008

40  Learning Rule: wi  wi + xi if output too low
Imagine a naive, randomly weighted neuron. One way to train a neuron to discriminate the sick from the healthy, is by reinforcing good behaviour and penalising bad. This carrot & stick model is the basis for the  learning rule: Compile a training set of N (say 100) sick and healthy patients. Initialise the neuronal weights (random initialisation is the standard). Run each input set in turn through the neuron & note its output. Whenever a wrong output is encountered, alter responsible weights. wi  wi + xi if output too low wi  wi  xi if output too high Repeatedly run through training set until all outputs agree with targets. When training is complete, test the neuron on a new testing set of patients. If neuron succeeds, patients whose health is unknown may be determined. lecture 2008

41 Related idea Minimize E = Σi(ti – oi )2 Here:
t is the desired output o is the observed output Find weights that minimize E Steepest gradient descent will also yield lecture 2008

42 Supervised learning The  learning rule is an example of supervised learning. Training MP neurons requires a training set, for which the ‘correct’ output is known. These ‘correct’ or ‘desired’ outputs are used to calculate the error, which in turn is used to adjust the input-output relation of the neuron. Without knowledge of the desired output, the neuron cannot be trained. Therefore, supervised learning is a powerful tool when training sets with desired outputs are available. When can’t supervised learning be used? Are biological neurons supervised? lecture 2008

43 A simple example Let’s try to train a neuron to learn the logical OR operation: Decision ( le 0 or gt 0) x1 x3 x2 w1 w3 w2 ∑ xi wi output x1 OR x2 1 desired output x2 x1 x3 bias Example on white board 1 wi  wi + xi if output low wi  wi  xi if output high ∑ xi wi lecture 2008

44 The power of learning rules
The  rule is guaranteed to converge on a set of appropriate weights, if a solution exists. While it might not be the most efficient of algorithms, this proven convergence is crucial. What can be done to improve the convergence rate? Some common variations on this learning rule: Adding a learning rate 0<r<1 which “damps” weight changes (i = rxi or i = -rxi). Widrow & Hoff recognised that weight changes should be large when actual output a and target output t were very different, but smaller otherwise. They introduced an error term, ∆=t-a, such that i =r∆xi. lecture 2008

45  Learning Rule Called  rule because weight updates have the following form w → w +  x  is a measure for the error:  = 0, no weight change lecture 2008

46 The Perceptron convergence Theorem
Suppose there are two sets: F+ and F- ; F+ ∩ F- empty Goal: X ε F+ → Σ wjxj > 0 X ε F- → Σ wjxj < 0 If there are wj* for which this is true, then the following algorithm finds wj (possibly different ones) which also do the trick lecture 2008

47 The Fall of the Artificial Neuron
Before long researchers had begun to discover the neuron’s limitations. Unless input categories were “linearly separable”, a perceptron could not learn to discriminate between them. Unfortunately, it appeared that many important categories were not linearly separable. This proved a fatal blow to the artificial neural networks community. In this example, an MP neuron would not be able to discriminate between the footballers and the academics… Successful Unsuccessful Many Hours in the Gym per Week Few Hours in the Gym per Week This failure caused the majority of researchers to walk away. Footballers Academics Exercise: Which logic operation is described in this example? lecture 2008 Marvin Minsky & Seymour Papert (1969). Perceptrons, MIT Press, Cambridge.

48 Connectionism Reborn The crisis in artificial neural networks can be understood, not as an inability to connect many neurons in a network, but an inability to generalise the training algorithms to arbitrary architectures. By arranging the neurons in an ‘appropriate’ architecture, a suitable training algorithm could be invented. The solution, once found, quickly emerged as the most popular learning algorithm for nnets. Back-propagation first discovered in 1974 (Werbos, PhD thesis, Harvard) but discovery went unnoticed. In the mid-80s, it was rediscovered independently by three groups within about one year. Most influential of these was a two-volume book by Rumelhart & McClelland, who suggested a feed-forward architecture of neurons: layers of neurons, with each layer feeding its calculations on to the next. lecture 2008 David E. Rumelhart & James L. McClelland (1986). Parallel Distributed Processing, Vols. 1 & 2, MIT Press, Cambridge, MA.

49 This time… Next time… The appeal of neural computing
From biological to artificial neurons Nervous systems as logic circuits Classification with the McCulloch & Pitts neuron Developments in the 60s: The Delta learning rule & variations Simple applications The fatal flaw of linearity Next time… The disappointment with the single neuron dissipated as promptly as it dawned upon the AI community. Next time, we will see why the single neuron’s simplicity does not rule out immense richness at the network level. We will examine the simplest architecture of feed-forward neural networks and generalise the delta-learning rule to these multi-layer networks. We will also re-discover some impressive applications. lecture 2008

50 Optional reading Excellent treatments of the perceptron, the delta rule & Hebbian learning, the multi-layer perceptron and the back-propagation learning algorithm can be found in: Beale & Jackson (1990). Neural Computing, chaps. 3 & 4. Hinton (1992). How neural networks learn from experience, Scientific American, 267 (Sep): lecture 2008

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