Cognitive Computing 2012

1. Cognitive Computing 2012 The computer and the mind 4. CHURCHLAND Professor Mark Bishop

2. Overview • The paper looks at the neuroscience of cognition at three levels offering: • a theory to explain how brain may represent aspects of the world providing a neuro-biological reduction of qualia. • a powerful and novel style of computation capable of explaining sensorimotor co-ordination. • an explanation of brains micro-structure that illustrates how the brain actually implements its representations of the worldand how it performs computationson them. (c) Bishop: The computer and the mind

3. An ‘eliminative reductionist’ strategy of cognitive phenomena • The core idea: • The brain represents aspects of reality by a position in multi-dimensional state-space and performs computations on such representations by co-ordinate transformations of this point. • It is an ‘eliminativist’ account as it posits a world whereby propositional attitudes – hopes; desires; beliefs etc – are eliminated. • As Patricia Churchland (1986) has argued, ‘it is hard to see where in the brain we are going to find anything that even remotely resembles the sentence-like structure that appears to be essential to beliefs and other propositional attitudes’. • And that ‘qualia’– pains, aches, happiness etc. – is more properly reduced to the ‘richer explanatory language’ of, say, a specific tuple of neural firings. (c) Bishop: The computer and the mind

4. The micro-physical organisation of the brain • Most of brain is crinkled grey matter (cerebral cortex) • White matter consists of axons projecting from the cortex to deeper regions of the brain. • In humans the cortex is six layers deep. • Top layer lots of inputs; bottom lots of outputs. • Massive horizontal connectivity in each layer; also massive regularly organised vertical connectivity. • Planar cortex divided into topographically organised Brodman areas: • preserving adjacency relations but not distance. • Many areas (e.g. visual striate cortex areas 17+18) have been identified. • Many, but not all, areas of the brain are so organised (eg. LGN; hippocampus etc). (c) Bishop: The computer and the mind

5. Sensorimotor co-ordination • Churchland’s suggestion is that the organisation of the cortex is the solution to fundamental cognitive problem of sensorimotor co-ordination. • Consider a simplified ‘crab-like’ creature • The crab needs to grab what is in visual field. • The crab needs to map from a pair of eye angles to its ‘gripper’ angles. • To do this it needs to transform from eye space to gripper space • i.e. The crab needs to perform a 2D => 2D co-ordinate transformation. (c) Bishop: The computer and the mind

6. How might the cortex perform co-ordinate transformations? • The cortex needs to arrange the two grids above each other and map between them. • The state-space sandwich • Activation of a 2D point <x, y> on the eye sensor grid; • Project down onto a 2D point <x', y'> on the motor grid; • Controlling arm angles which is required to grab object. (c) Bishop: The computer and the mind

7. Biologically plausible observations • The ‘state-space sandwich’, (SSS), is: • Resistant to localised damage; • Very fast implementation of ‘sensorimotor computations’; • Co-ordination is not uniform over the field of motor activity • The theory predicts poor between eyes and at extremities. • The state-space sandwich is one solution to the problem of sensorimotor co-ordination which is biologically plausible • However it is far too simplistic a mechanism. • So is ‘cognition’ merely appropriate sensorimotor co-ordination? • Behaviourism revisited? (c) Bishop: The computer and the mind

8. A cognitive hypothesis • The Churchland’s initial hypothesis is that scattered topographic maps in the cortex are performing cognitive processes via simple co-ordinate transforms. • The hypothesis was later modified to define cognitive state, (the data to be transformed), as a pattern of activity, (a vector), rather than a simple point-to-point transformation. (c) Bishop: The computer and the mind

9. The superior colliculus, (SC) • It has been shown that the superior colliculus actually performs such transformations on the saccadic system, (secondary to areas 17/18). • It has also been demonstrated that the lower layer of the SC is a motor layer, which has also been found to be a topographic map. • Hence there is some experimental evidence to back up the notion of state space sandwich for saccadic movements • Albeit this experimental evidence suggested ‘area sandwiches’ not ‘point to point’ sandwiches. • Churchland emphasizes that this is an extremely simplistic description of the function of the SC. (c) Bishop: The computer and the mind

10. What function might other topographic areas perform? • Abstract co-ordinate transfers • E.g. Echo location in bats and binaural disparities in owl hearing. • There has long been a restriction amongst neurologists to reserve topographic maps for clearly known functionality… • … But if the cortex is performing very abstract transformations, their function might not be obvious to the experimenter. • The multi-layer cortex: • More than one layer provides a ‘multi-modal’ sensorimotor transforms; one that can: • react to different types of stimuli; • perform sensor integration to detect and act on signals that would otherwise be too weak. (c) Bishop: The computer and the mind

11. Beyond state-space sandwiches • Churchland suggests that the cerebellum can perform more complex - vector to vector - transformations using a simple array of MCP type cells. • Perhaps to perform complex bodily movements. • And further, that - unlike simple 2D sandwich where information is coded spatially - in vector notation events might be coded via neural firing frequencies • With MCP like neurons effectively performing matrix multiplication to map between different spaces. • Properties of vector-vector (v-v) transformations: • V-V transforms need not be limited to linear transforms; • Preserve the fast speed of SSS; • Preserve gradual degradation to damage. (c) Bishop: The computer and the mind

12. The representational power of state spaces: • A point in n dimensional space can represent a system of n variables. • A state-space representation preserves metrical relations and so retains notion of ‘qualia similarity’. • Consider example of visual qualia: orange is more similar to red than dark blue as the distance between the points is smaller. • The ability to discriminate stimuli is large. • Consider Land’s colour cube. If each axis quantised to 10 positions could represent 1000 colours and their relation to each other. • NB. This colour relationship is not linear. (c) Bishop: The computer and the mind

13. The qualia cube • Any sensation can more properly be reduced to - is an identification with - a specific firing triplet of neural firings. • Cf. the identification of lightening and electricity. • Genetic faults (e.g. colour blindness) are realised by the cube collapsing to a 2D surface. • The taste system is similar, (albeit this is 4D as we have 4 taste receptors); contra Nagel this allows us to say 'what it is like to be' a cat (or rat). • E.g. Cats & rats have 4D taste but their bitterness channel is more (or less respectively) sensitive • Hence rats don’t mind saccharin, but cats hate it (as it is too bitter for them). • Similarly for the olfactory system • This is at least a 6D system; in dogs it has three times the sensitivity (and is possibly 7D) which allows dogs identify everyone in the world by smell alone. (c) Bishop: The computer and the mind

14. Qualia cubes in action • Using the ‘Qualia Cube’ the ‘ineffable’ pink of the rose is more properly reduced to a chord/triplet of neural spiking frequencies. • It seems that the Churchland’s eliminative materialism leaves no room for (eliminates) folk psychology notions concerning our ‘beliefs’ about the world. • Because by learning to talk in terms of such neural chord firings we get more precise (better?) communication of belief (cf. ‘mummy, I believe my tummy hurts’). • The Churchlands demonstrate a possible extension of the theory to describe body movements as transitions pathways in state space? • Link to Dynamic Systems theory. • The Churchlands last hypothesis is that the idea could be extended to describe, say, an ‘Anglophone linguistic hyperspace’ which could be used to define hyperspaces for appropriate sets of belief. • Memories of Skinner on language? (c) Bishop: The computer and the mind