Modeling Emergence by Design

Transcript

1. Modeling emergence by design (task 2.1) • Milestone M1 at month 12: model runs • Deliverable D2.1 at month 24: report on models and results
2. What models can do • models may • Allow predictions • Allow one to see the unfolding of hypotheses • Be useful to understand • …
3. Models to understand • Even strongly simplified models can lead to important results and insights
4. Emergence • Marangoni-Benard instability • A two-level phenomenon • The phenomenon is described by the existing theory
5. Sandwiched emergence • But most often emergence takes place between pre- existing levels (in physics, biology, social science) – Lane, 2006, 2009; White, 2009
6. emergence of mesolevels • Sandwiched emergence poses formidable problems to the theory of complex systems • In the usual bottom-up story, the upper layer, if it exists, only provides fixed boundary conditions • Now both the upper and the lower levels affect the intermediate one • And viceversa!
7. SEM: to develop a theory and a set of mathematical models of SE • Theory development • Mathematical and computational models • In-depth case studies • A model: cell differentiation • The model was built before SE • It shows a way in which SE can develop • Noise-induced emergence
8. SEM: other models and case studies • Autocatalytic reaction sets in protocells • Cognitive properties of agents in ABMs • Mesolevel structures in chromosomes and genomes • Development of stone-tool technology • Concept formation in the medical web of knowledge
9. SE in MD • Emergence takes place at levels that are intermediate between that of the individual agents and that of the whole system • We will investigate the formation of mesolevel structures – able to carry on subtasks, perhaps even in a different context • A phenomenon to be investigated with abstract models, amenable to theoretical analysis – Not simply mimicking “interacting agents”, either human-like or company-like • An abstract network model
10. Start simple • Further modifications are possible • A single variable is associated to each node • Time is discrete: at each time step the new value of a variable is a function of its immediate past value, and of the immediate past values of its input nodes B A C
11. A network of connected nodes The global state of the network is X  x 1 ,x 2 ...x N  
12. • Each node computes its new state by means of its transition function • The rule is deterministic • The global state of the network at time t+1 is a function of its state at time t – Plus external inputs, if any  x i (t 1)  F i x i1 (t),x i2 (t)...x iK (t)  
13. • A family of networks is defined by • The parameters of the topology – i.e. number and type of connections – e.g. regular, random, scale-free, small-world… • The set of values that x can take – E.g. boolean, discrete, continuous in a range… • The type of transition functions – e.g. sigmoid, threshold, boolean … – For example, a feedforward neural network has a regular layered topology, continuous x values and sigmoid transition function
14. Random networks • The connections are drawn at random • According to a given probability distribution • E.g. completely random with uniform probability, power-law.. • The transition functions are chosen at random for every node – E.g. with uniform probability in a given set of allowed functions • Surprisingly enough, random networks can describe very interesting real-world phenomena – The distribution of perturbations of gene expression after knock- out (Serra, Villani & Semeria, 2004, 2007) – The rich phenomenology of cell differentiation (Villani, Barbieri & Serra, 2011)
15. An alternative: evolved networks • It is possible to evolve a family of networks, in order to improve performances on a given task, e.g. – passing through a certain state – reaching a final state (attractor) with certain features, or even developing a set of final states with desired properties – Classifying a given input – Controlling a robot – …
16. • There are several evolution algorithms for achieving this goal • E.g. genetic algorithms – start from a family of networks generated at random – Evaluate each member of the family assigning it a “fitness value” – Create a new generation of networks by combining the best individuals from the previous one, chosen at random with a fitness-dependent probability distribution – Evaluate each member of the new generation, etc.
17. Sandwiched emergence • The network can self-organize during its evolution, giving rise to structures at a level that is intermediate between the single nodes and the whole network – E.g. “motifs” in genetic regulatory networks – or sets of nodes that remain frozen at fixed values, under a wide set of conditions – Or sets of nodes that oscillate in synchrony
18. SE in evolving networks • We will study the way in which the overall network self- organizes in specific modules – in a set of different tasks – Looking for “generic” properties, common to a wide class of tasks – Comparing random vs evolved networks • Which model features favour the formation of certain types of structures? • A conceptual move towards “design for emergence” – Monitoring the emergence of motifs • Higher-level structures?
19. A specific aspect, relevant for MD • The networks are not built to perform a single specific task, but with some directedness (to support innovation) – Communication is important • We will consider also to develop networks that maximize mutual information among their parts – M(X,Y) = I(X) + I(Y) – I(X,Y) • We will verify whether these networks outperform the others in learning various tasks • Whether their mesolevel structures are significantly different • We will also consider different information-theoretical measures
20. In synthesis • Develop models of dynamical networks – We know where to start… • Analyze the generic features of a set of random nets • Evolve networks for specific tasks and compare them with the random ones • Evolve networks to maximize mutual information and compare them with the other ones