Bioinspired Computing Lecture 7 Alternative Neural Networks M. De Kamps, Netta Cohen

2 Attractor networks: Two examples Jets and Sharks network –Weights set by hand –Demonstrates recall Generalisation Prototypes Graceful degradation Robustness Kohonen networks –Unsupervised learning: Self-Organizing Maps

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5 Dynamics o: output of a node act > 0: o = act act <=0: o = 0 act: activity of a node –i >0:Δa u = (max – a u )*i – decay*(a u -rest) –i <=0:Δa u = (a u - min)*i – decay*(a u -rest) i: input of a node –i u = 0.1Σw ui o i ext u

6 Jets and Sharks Units Weights (excitatory: +1; inhibitory -1) Activation -0.2, 1.0 –Resting activation: -0.1 Dynamics

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9 Activate “ART”

10 Jets and Sharks NameGangAgeEducationMar.Occupation ArtJets40sJ.HSing.Pusher AlJets30sJ.H.Mar.Burglar ClydeJets40sJ.HSing.Bookie MikeJets30sJ.H.Sing.Bookie PhilSharks30sCol.MarPusher DonSharks30sColMar.Burglar DaveSharks30sH.S.Div.Pusher

11 Properties Retrieving a name from other properties –Content Addressable Memory Categorisation and prototype formation –Activating sharks will activate person units of shark members –Phil is quintessential shark: 30s Pusher (wins out in the end!)

12 Activate “Shark”

13 Properties Can activate 20s and pusher and find persons who match best Robust –Graceful degradation –Noise Weight set by hand

14 Last time Biologically inspired associative memories moves away from bio- realistic model Unsupervised learning Working examples and applications Pros, Cons & open questions Today Attractor neural nets: SOM (Competitive) Nets Neuroscience applications GasNets. Robotic control Other Neural Nets

15 Spatial Codes Natural neural nets often code similar things close together. The auditory and visual cortex provide examples. Neural Material Low Freq. High Freq. Frequency Sensitivity Orientation Sensitivity Neural Material 0°359° Another example: touch receptors in the human body. "Almost every region of the body is represented by a corresponding region in both the primary motor cortex and the somatic sensory cortex" (Geschwind 1979:106). "The finger tips of humans have the highest density of receptors: about 2500 per square cm!" (Kandel and Jessell 1991:374). This representation is often dubbed the homunculus (or little man in the brain) Picture from

16 Input Nodes Fully Connected Output Pattern In a Kohonen net, a number of input neurons feed a single lattice of neurons. The output pattern is produced across the lattice surface. Lattice Kohonen Nets Large volumes of data are compressed using spatial/ topological relationships within the training set. Thus the lattice becomes an efficient distributed representation of the input.

17 Kohonen Nets Important features: Self-organisation of a distributed representation of inputs. This is a form of unsupervised learning: The underlying learning principle: competition among nodes known as “winner takes all”. Only winners get to “learn” & losers decay. The competition is enforced by the network architecture: each node has a self-excitatory connection and inhibits all its neighbours. Spatial patterns are formed by imposing the learning rule throughout the local neighbourhood of the winner. also known as self-organising maps (SOMs)

18 Training Self-Organising Maps A simple training algorithm might look like this: 1.Randomly initialise the network input weights 2.Normalise all inputs so they are size-independent 3.Define a local neighbourhood and a learning rate 4.For each item in the training set Find the lattice node most excited by the input Alter the input weights for this node and those nearby such that they more closely resemble the input vector, i.e., at each node, the input weight update rule is:  w = r (x-w) 5.Reduce the learning rate & the neighbourhood size 6.Goto 2 (another pass through the training set)

19 Training Self-Organising Maps (cont) Gradually the net self-organises into a map of the inputs, clustering the input data by recruiting areas of the net for related inputs or features in the inputs. The size of the neighbourhood roughly corresponds to the resolution of the mapped features.

20 How Does It Work? Imagine a 2D training set with clusters of data points Vertical Blue Red Horizontal The nodes in the lattice are initially randomly sensitive. Gradually, they will “migrate” towards the input data. Nodes that are neighbours in the lattice will tend to become sensitive to similar inputs. Effective resource allocation: dense parts of the input space recruit more nodes than sparse areas. Applet from Another example: The travelling salesman problemThe travelling salesman problem

21 The U-Matrix High dimensional clusters can only be visualized in 2D The U-height facilitates the recognition of clusters –Define a distance in weight space –For a given node n, take weight w n. For each neighbour of n, take weight w m Calculate d(w n,w m ) Add all of these distances for node n –This is the U-height of node n Colour the node map according to its U-height Clusters are areas of low U-height, separated by boundaries of high U-height

22 The U-Matrix

23 How does the brain perform classification? One area of the cortex (the inferior temporal cortex or IT) has been linked with two important functions: object recognition object classification These tasks seem to be shape/colour specific but independent of object size, position, relative motion or speed, brightness or texture. Indeed, category-specific impairments have been linked to IT injuries.

24 How does the brain perform classification (cont)? Questions: How do IT neurons encode objects/categories? e.g., local versus distributed representations/coding temporal versus rate coding at the neuronal level Can we recruit ANNs to answer such questions? Can ANNs perform classification as well given similar data? Recently, Elizabeth Thomas and colleagues performed experiments on the activity of IT neurons during an exercise of image classification in monkeys and used a Kohonen net to analyse the data.

25 The experiment Monkeys were trained to distinguish between a training set of pictures of trees and various other objects. The monkeys were considered trained when they reached a 95% success rate. Trained monkeys were now shown new images of trees and other objects. As they classified the objects, the activity in IT neurons in their brains was recorded. All in all 226 neurons were recorded on various occasions and over many different images. The data collected was the mean firing rate of each neuron in response to each image. 25% of neurons responded only to one category, but 75% were not category specific. All neurons were image-specific. Problem: Not all neurons were recorded for all images & No images were tested across all neurons. In fact, when a Table of neuronal responses for each image was created, it was more than 80% empty. E. Thomas et al, J. Cog. Neurosci. (2001)

26 Experimental Results Question: Given the partial data, is there sufficient information to classify images as trees or non-trees? Answer: A 2-node Kohonen net trained on the Table of neuronal responses was able to classify new images with an 84% success rate. E. Thomas et al, J. Cog. Neurosci. (2001) Question: Are categories encoded by category-specific neurons? Answer: Delete data of category-specific neuron responses from Table. The success rate of the Kohonen net was degraded but only minimally. A control set with random data deletions yielded similar results. Conclusion: Category- specific neurons are not important for categorisation!

27 Experimental Results (cont.) E. Thomas et al, J. Cog. Neurosci. (2001) Conclusions: The IT employs a distributed representation to encode categories of different images. The redundancy in this encoding allows for graceful degradation so that even with 80% of data missing and many neurons deleted, sufficient information is present for classification purposes. The fact that only rate information was used suggests that temporal information is less important here. Question: Which neurons are important, if any? Answer: An examination of the weights that contribute most to the output in the Kohonen net revealed that a small subset of neurons (<50) that are not category-specific yet respond with different intensities to different categories are crucial for correct classification.

28 From Biology to ANNs & Back Neuroscience and studies of animal behaviour have led to new ideas for artificial learning, communication, cooperation & competition. Simplistic cartoon models of these mechanisms can lead to new paradigms and impressive technologies. Dynamic Neural Nets are helping us understand real-time adaptation and problem-solving under changing conditions. Hopfield nets shed new insight on mechanisms of association and the benefits of unsupervised learning. Thomas’ work helps unravel coding structures in the cortex.

29 Next time… Reading Elizabeth Thomas et al (2001) “Encoding of categories by noncategory- specific neurons in the inferior temporal cortex”, J. Cog. Neurosci. 13: Phil Husbands, Tom Smith, Nick Jakobi & Michael O’Shea (1998). “Better living through chemistry: Evolving GasNets for robot control”, Connection Science, 10: Ezequiel Di Paolo (2003). Organismically-inspired robotics: Homeostatic adaptation and natural teleology beyond the closed sensorimotor loop, in: K. Murase & T. Asakura (Eds) Dynamical Systems Approach to Embodiment and Sociality, Advanced Knowledge International., Adelaide, pp Ezequiel Di Paolo (2000) “Homeostatic adaptation to inversion of the visual field and other sensorimotor disruptions”, SAB2000, MIT Press. Hopfield networks