The Evolution of Lexical Usage Profiles in Social Networks
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(2) The Evolution of Lexical Usage Profiles in Social Networks Gerhard Schaden gerhard.schaden@gmx.net Université Lille 3 & CNRS UMR 8163 STL. Complete Networks: Contact Creates Uniformity Within a simulation run in a complete network, the lexical usage profiles of the agents are extremely similar, even though they can be very dissimilar across simulation runs. Complete Networks Create Similar Lexical Representations. ua lia 2 1Q W or d. ia 2 ua l d2 Q W or. lia d1. Q ua. lia Q ua d1. 2. Word1Qualia3. 2 W or. W or. Word1Qualia3. 2. 2. lia ua. lia. Q d2. ua Q d2 W or. W or. lia Q ua d1 W or. 2 lia ua Q d2 W or. Word1Qualia3. ua lia 2 1Q. ia 2 ua l d2 Q W or. 2. Word1Qualia3. lia Q ua d1 W or. W or d. 1Q W or d. ia 2 ua l d2 Q W or. 2. Word1Qualia3. 2 lia ua Q d2 W or. Word1Qualia3. ua lia 2. Word1Qualia3. ua lia 2 1Q W or d. ia 2 ua l d2 Q W or. lia Q ua d1 W or. 2 lia ua Q d2 W or. Word1Qualia3. ua lia 2 1Q 2. Word1Qualia3. lia Q ua W or. 2 lia ua Q d2 W or. W or d. ia 2 ua l d2 Q W or. 2. Word1Qualia3. d1. d1 W or. Word1Qualia3. ua lia 2 1Q W or d. ia 2 ua l W or. d2 Q. Q ua. lia. 2. Word1Qualia3. 2 lia ua Q d2 W or. lia ua Q d2. Word1Qualia3. ua lia 2 1Q W or d. ia 2 ua l d2 Q W or. d1 W or. 2. 2 lia ua Q. Word1Qualia3. ua lia 2 1Q lia Q ua. lia Q ua d1. 2. Word1Qualia3. 2. Word1Qualia3. lia Q ua d1. W or d. ia 2 ua l d2 Q W or. ia 2 ua l d2 Q W or. 2. Word1Qualia3. Word1Qualia3. ua lia 2 W or d. 1Q W or d. 1Q. Word1Qualia3. ua lia 2. Word1Qualia3. ia 2 ua l d2 Q W or. W or. W or. W or. 4. lia. 4. lia. ua Q. d2. d2. ua Q. 4. lia. Word2Qualia3. d2. ua Q. 4. lia. Word2Qualia3. d2. Word2Qualia3. ua Q. 4. lia. W or. Word1Qualia1. or W. 2. Word1Qualia1 Word2Qualia1. or W. or W. lia. 4. 4 Word1Qualia1 Word2Qualia1. lia. lia. 4. d2. ua. ua. ua. lia. or W. ua Q. 4. lia. Word2Qualia3. d2. ua Q. Word2Qualia3. d2. 4. lia. 4. lia. ua Q. ua Q. Word2Qualia3. d2. or W. or W. or W. Word2Qualia3. d2. 4. lia. 4. lia. ua Q. ua Q. Word2Qualia3. d2. Word2Qualia3. d2. or W. or W. or W. Word2Qualia3. Q. Q. Q. ua. 4. 4. 4. 4. 4. 4. 4 d2. 4. Agent 10 d1 or W. d1 or W. Q. lia. lia. lia. lia. lia. lia. lia. Word1Qualia1 Word2Qualia1. lia. 4. lia. Agent 9. ua. Word2Qualia3. ua. 4. lia. d1 or W. ua. ua. ua. Q. Q. d1 or W. d1 or W. Q. ua. ua. ua. Q. d1 or W. d1 or W. Q. Q. d1 or W. d1 or W. ua W or. Word1Qualia1. Q d2 or W. Q d2 or W. ua. Word2Qualia3. Q d2 or W. Word2Qualia3. 4. lia. 4. lia. ua. ua. 4. lia. Word2Qualia3. Q d2 or W. Q d2 or W. ua. Word2Qualia3. Q d2 or W. Word2Qualia3. 4. lia. 4. lia. ua. ua. 4. lia. Word2Qualia3. Q d2 or W. Q d2 or W. ua. 4. lia. Word2Qualia3. Q d2 or W. Word2Qualia3. ua. Q. Simulation Run N° 2. 4 lia ua Q d1 or W. 4 lia ua Q d1 or W. 4 lia ua Q d1 or W. 4 lia ua Q d1 or W. Word1Qualia1 Word2Qualia1. Agent 8. Word1Qualia1 Word2Qualia1. Agent 10. Word1Qualia1 Word2Qualia1. Agent 7. Word1Qualia1 Word2Qualia1. Agent 9. Word1Qualia1 Word2Qualia1. Agent 6. Word1Qualia1 Word2Qualia1. Agent 8. Word1Qualia1 Word2Qualia1. Agent 5. Word1Qualia1 Word2Qualia1. Agent 7. Word1Qualia1 Word2Qualia1. Agent 4. Word1Qualia1 Word2Qualia1. 4 lia ua Q d1 or W. Word1Qualia1 Word2Qualia1. Agent 3. Word1Qualia1 Word2Qualia1. 4 lia ua Q d1 or W. 4 lia ua Q d1 or W. 4 lia ua Q d1 or W. 4 lia ua Q d1 or W. Word1Qualia1 Word2Qualia1. Agent 2. Word2Qualia1. Simulation With 10 Agents Agent 5 Agent 6. Agent 4. Word1Qualia1 Word2Qualia1. Agent 1 d1 or W. e h t d l ou w r e w ? u ans o y t e a v h i g W o n i s a c fa o r e n w o. Absolute Differences in Qualia between Word1 and Word2 self−reinforced not self−reinforced. 4000. 3000. 2000. 1000. 10. 10. 9. 9. 8. 8. 7. 7. 6. 6. 5. 0 5. Reinforcement Learning with Polya Urns. • In the simulation, we keep stable the number of reinforcements per agent. • The bigger the (complete) network, the less differentiated the submeanings. • If the speaker reinforces himself, differentiation is more important than if he does not reinforce himself. • Differentiation strongly depends on the initial tendency. Self-reinforcement and small network size increase the chance of moving away from the initial configuration.. 4. • Is (language) learning influenced by network size and structure? (Yes!, see, e.g., Mühlenbernd and Franke, 2012) • I will investigate reinforcement learning of (internally differenciated) lexical items in social networks, by performing multi-agent simulations.. is the absolute difference of submeaningi of Word1 and submeaningi of Word2, or: ∣submeaningi (Word1) − submeaningi (Word2)∣. 4. Jede Veränderung des Sprachusus ist ein Produkt aus den spontanen Trieben der einzelnen Individuen einerseits und den [. . . ] Verkehrsverhältnissen andererseits. (Paul, 1995, §25). Definition: Lexical Differentiation between Word1 and Word2 at Submeaningi. 3. • Humans are an unusually social and cooperative species (for primates). As a consequence, all langage learning (and most of language use) takes place in social networks. • Network analysis is flourishing in the Social Sciences (see, e.g., Jackson, 2008), and is emerging in linguistics (see, e.g., Mühlenbernd and Franke, 2012). A convergence is developing between game theory, social network analysis, and fairly old explanations developed by Hermann Paul in his Prinzipien der Sprachgeschichte.. Complete Networks: Lexical Differentiation and Network Size. 3. Language and Social Networks. Lexical Differentiation. • If random plays an important role, is it worth investigating?. Agent 3. Word1Qualia1 Word2Qualia1. Q d2 or W. – 19th century and before: horse-drawn carriage – today: automobile, car The old meaning is still available today, even if it has become marginal.. Agent 2. Word2Qualia1. Word2Qualia3. Example: French voiture. Agent 1 4 lia ua Q d1 or W. • Lexical Change is typically messy (as opposed to grammaticalization): – influenced by changes in the world (technology, etc.) – influenced by ±random events (‘‘big’’ history, behavioral micropatterns, etc.) • It is not always clear whether changes are about meaning, or about prototypical usage patterns.. Simulation Run N° 1. Background: The Problem of Lexical Change. Number of Agents per Network. Learning in Behaviorism Learning = shifting the probability of some behavior in an agent • Polya-Urns provide a mathematical model of reinforcement learning. • Randomly draw a ball from the urn. • If the ball corresponds to the correct answer, a further ball will be added to the urn.. URNt white:1 red:1. Lexical Distance Reflects Network Structure. URNt+1 white:2 red:1. Definition: Lexical Distance between Agent1 and Agent2 The lexical distance between two agents is the sum of the absolute differences of their respective pondered submeanings, or: ∑ki=1 ∣submeaningi (Ag1) − submeaningi (Ag2)∣. The probability of drawing ‘‘white’’ rises from 0.5 to 0.6̇. Lexical Distances: 6 Agents in 2 Cliques 12000. is represented as array of pondered submeanings with respect to these 2 words: W1Q1 W1Q2 W1Q3 W1Q4 W2Q1 W2Q2 W2Q3 W2Q4 Ag 1 1000 1000 1000 1000 1000 1000 1000 1000 Ag 2 2000 2000 2000 1 1 1 1 2000. 8000. 6000. 4000. 2000. r e k a e sp a t a h u t fl e n i sum refore s a e w e h d t l u d o n a Sh ( s e e c h r t o f r ? n fo elf s rei s e c m i n h e ) u s q e e c s en on c s a h s i Th ! e m o outc. DiffAg2Ag5. DiffAg2Ag4. DiffAg1Ag5. DiffAg1Ag4. DiffAg3Ag5. DiffAg3Ag4. DiffAg2Ag6. DiffAg1Ag6. DiffAg3Ag6. DiffAg5Ag6. DiffAg4Ag6. DiffAg2Ag3. DiffAg1Ag3. 0 DiffAg1Ag2. • I assume internally differentiated lexical representations like Pustejovsky’s qualia-structure. The basic theoretical commitment boils down to independently ponderable submeanings. • Motivation: meaning shifts generally follow patterns of polysemy • Scenario: – We have two words that are absolute synonyms (see Skyrms, 2010): any draw = success – Each submeaning is an independent Polya urn (balls correspond to Word1 & Word2) – Speaker draws a word, and signals to hearer – Hearer updates the weight for the chosen word (and maybe the speaker, too) Lexical Usage Profile of an Agent w.r.t. Denotation-Equivalents. Lexical Distance. 10000. DiffAg4Ag5. Learning Internally Differentiated Lexical Items. PIC IWC DCA CCWC PCC. Underlying Network:. Underlying Network:. Ag7. Ag1 2. 2. 2. Ag3 2 2. Ag2. Ag4. 2. 1 1. 2. 2. 2 2. 2 2 2 2. Ag6. Ag5 2. 2. 2. 2 2. Ag9. 2. 2 Ag3. 2. 2. Ag8 Ag1. 2. 1 1 1 1. Ag6. Ag2. 2 2 Ag4. 2. 2. 2 2. Ag5. Acknowledgements & Sample References I had the opportunity to present a previous version at the University Lille 3, and I would like the audience for their input. I would also like to thank Sylvain Billiard and Cédric Patin for their comments and encouragements. All errors and omissions are mine alone. All simulations have been performed with sbcl Common Lisp, using the graph-library by Eric Schulte (https://github.com/eschulte/graph). Networks have been drawn with graphviz (Gansner and North, 2000). Data analysis has been performed with GNU R. [1] Gansner, E. R. and S. C. North (2000). “An Open Graph Visualization System and its Applications to Software Engineering”. In: Software — Practice and Experience 30.11: pp. 1203–1233. [2] Jackson, M. O. (2008). Social and Economic Networks. Princeton: Princeton University Press. [3] Mühlenbernd, R. and M. Franke (2012). “Signaling Conventions: Who Learns What Where and When in a Social Network”. In: The Evolution of Language: Proceedings of EvoLang9. Ed. by T. C. Scott-Philips et al. Singapore: World Scientific: pp. 242–249. [4] Paul, H. (1995). Prinzipien der Sprachgeschichte. 9th ed. Tübingen: Niemeyer. [5] Pustejovsky, J. (1995). The Generative Lexicon. Cambridge: MIT Press. [6] Schaden, G. (2014). “Markedness, Frequency and Lexical Change in Unstable Environments”. In: Proceedings of the Formal & Experimental Pragmatics Workshop. Ed. by J. Degen, M. Franke, and N. Goodman. ESSLLI. Tübingen: pp. 43–50. [7] Skyrms, B. (2010). Signals. Evolution, Learning, & Information. Oxford: Oxford University Press..
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