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Causal Neural Paradox (Thought Curvature)

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Thought curvature theory postulates naively, of non-trivial artificial intelligence as a curvature of subsuming manifolds on the temporal difference paradigm.

Proposed by: Jordan Micah Bennett on May 23, 2016

A particular manifold paradox emerges qua markov neural sequences’ [1] confluence abound non-trivial causal instruction.[2]

Some C∞(Rn), 'causal neural perturbation curvature' (of the Supermanifold genera), generates uniform symbols on the boundary of its Rn, 'causal neural manifold' (of the manifold genera), betwixt some Uα, 'causal neural atoms' of φi.

Ergo, the paradox axiomatizes.

Introduction[edit]

Deepmind's atari q architecture [1] encompasses non pooling convolutions, therein generating object shift sensitivity, whence the model maximizes some reward over said shifts together with separate changing states for each sampled t state; translation non invariance.

Separately, uetorch,[2] encodes an object trajectory behaviour physics learner, particularly on pooling layers; translation invariance.
It is quite observable, that the childhood neocortical framework pre-encodes certain causal physical laws in the neurons,[3] postulating in perceptual learning abstractions into non-childhood.
As such, it is perhaps exigent that non invariant fabric composes in the invariant, therein engendering time-space complex optimal causal, conscious artificial construction.

If this confluence is reasonable, is such paradoxical?

Partial paradox reduction[edit]

Paradoxical strings have been perturbed to reduce in factor variant/invariant manifold interaction paradigms (Bengio et al.,[4] Kihyuk et al.[5]), that effectively learn to disentangle varying factors.

However, such models relent factors betwixt causal embedding. See Non-partial paradox reduction

Ergo, the paradox, abound causal instruction/abstraction generation, on the temporal difference learning plane, persists.

Non-partial paradox reduction[edit]

∃ some translation invariant karp reducible quantities causal neural atoms -Uα, encoding φi. As such, some causal neural manifold - Rn, stipulates in causal neural atom terms, an interaction sequence.

Some translation variant construct causal neural perturbation curvature - C∞(Rn), generates nominally infinite descriptions in cnm, on some temporal difference horizon. This fabric generates pseudo-novel representations in cna.

Separately, Kihyuk et al.[6] laments a quite prompt, time-space complex optimal manifold construction paradigm, on the order of generic quantity priors/factors.

In contrast, abound the causal perturbation curvature C∞(Rn), some temporal difference horizon Vπ, enumerates distinct descriptions R, in causal neural manifold - Rn lemma, particularly on the order of non-generic causal neural atom - quantity priors/factors, φπ ∈ Uα.

Conclusion[edit]

The absorption of R in Vπ, on non-generic quantity priors/factors φiπ, via some C∞(Rn) curvature, descries a causal neural basis, betwixt R bound perceptual abstractions.

References[edit]

  1. 1.0 1.1 Human Level Control Through Deep Reinforcement Learning; Mnih et al
  2. 2.0 2.1 Learning Physical Intuition of Block Towers by Example; Lerer et al
  3. Observing the unexpected enhances infants’ learning and exploration; Stahl et al
  4. Disentangling Factors of Variation for Facial Expression Recognition; Bengio et al
  5. Learning to Disentangle Factors of Variation with Manifold Interaction; Yuting et al
  6. Efficient learning of sparse, distributed, convolutional feature representations for object recognition; Kihyuk et al

7. Joseph Bernstein, `Lectures on Supersymmetry` (notes by Dennis Gaitsgory) [1], "Quantum Field Theory program at IAS: Fall Term"
9. A. Schwarz, `Geometry of Batalin-Vilkovisky quantization`, hep-th/9205088
10. C. Bartocci, U. Bruzzo, D. Hernandez Ruiperez, The Geometry of Supermanifolds (Kluwer, 1991) ISBN 0-7923-1440-9
11. A. Rogers, Supermanifolds: Theory and Applications (World Scientific, 2007) ISBN 981-02-1228-3
12. L. Mangiarotti, G. Sardanashvily, Connections in Classical and Quantum Field Theory (World Scientific, 2000) ISBN 981-02-2013-8 (arXiv: 0910.0092)
13. Freedman, Michael H., and Quinn, Frank (1990) Topology of 4-Manifolds. Princeton University Press. ISBN 0-691-08577-3.
14. Guillemin, Victor and Pollack, Alan (1974) Differential Topology. Prentice-Hall. ISBN 0-13-212605-2. Inspired by Milnor and commonly used in undergraduate courses.
15. Hempel, John (1976) 3-Manifolds. Princeton University Press. ISBN 0-8218-3695-1.
16. Hirsch, Morris, (1997) Differential Topology. Springer Verlag. ISBN 0-387-90148-5. The most complete account, with historical insights and excellent, but difficult, problems. The standard reference for those wishing to have a deep understanding of the subject.
17. Kirby, Robion C. and Siebenmann, Laurence C. (1977) Foundational Essays on Topological Manifolds. Smoothings, and Triangulations. Princeton University Press. ISBN 0-691-08190-5. A detailed study of thecategory of topological manifolds.
18. Lee, John M. (2000) Introduction to Topological Manifolds. Springer-Verlag. ISBN 0-387-98759-2.
19. Lee, John M. (2002), Introduction to Smooth Manifolds, Springer, ISBN 978-0-387-95448-6
20. Lee, John M. (2003) Introduction to Smooth Manifolds. Springer-Verlag. ISBN 0-387-95495-3.
21. Massey, William S. (1977) Algebraic Topology: An Introduction. Springer-Verlag. ISBN 0-387-90271-6.
22. Milnor, John (1997) Topology from the Differentiable Viewpoint. Princeton University Press. ISBN 0-691-04833-9.
23. Munkres, James R. (2000) Topology. Prentice Hall. ISBN 0-13-181629-2.
24. Neuwirth, L. P., ed. (1975) Knots, Groups, and 3-Manifolds. Papers Dedicated to the Memory of R. H. Fox. Princeton University Press. ISBN 978-0-691-08170-0.
25. Riemann, Bernhard, Gesammelte mathematische Werke und wissenschaftlicher Nachlass, Sändig Reprint. ISBN 3-253-03059-8.
Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse. The 1851 doctoral thesis in which "manifold" (Mannigfaltigkeit) first appears.
26. Ueber die Hypothesen, welche der Geometrie zu Grunde liegen. The 1854 Göttingen inaugural lecture (Habilitationsschrift).
27. Spivak, Michael (1965) Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus. HarperCollins Publishers. ISBN 0-8053-9021-9. The standard graduate text.
28. Sutton, R.S., Barto A.G. (1990). "Time Derivative Models of Pavlovian Reinforcement" (PDF). Learning and Computational Neuroscience: Foundations of Adaptive Networks: 497–537.
29. Gerald Tesauro (March 1995). "Temporal Difference Learning and TD-Gammon". Communications of the ACM 38 (3). doi:10.1145/203330.203343. 20. Imran Ghory. Reinforcement Learning in Board Games.
31. S. P. Meyn, 2007. Control Techniques for Complex Networks, Cambridge University Press, 2007. See final chapter, and appendix with abridged Meyn & Tweedie.


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