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Proof Planning as Understanding as Cortical Functions

Proof Planning as Understanding as Cortical Functions. Brendan Juba With Manuel Blum Matt Humphrey Ryan Williams. WHAT and WHY. WANTED: proof-clustering algorithm Characterizes high-level idea Aid theorem-provers WANTED: define CONSCSness Aid in answering fundamental questions

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Proof Planning as Understanding as Cortical Functions

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  1. Proof Planning as Understanding asCortical Functions Brendan Juba With Manuel Blum Matt Humphrey Ryan Williams

  2. WHAT and WHY • WANTED: proof-clustering algorithm • Characterizes high-level idea • Aid theorem-provers • WANTED: define CONSCSness • Aid in answering fundamental questions • Basis for developing protocols • Directing development of robots, etc.

  3. CONTENTS • NO algorithms •  • INSTEAD: • Where to discover an algorithm • Viewing neocortex as a proof planner • Why expect suitability • Link to understanding

  4. Proof Planning in the Memory-Prediction Framework • Suppose Alice is studying proofs… • Under the Framework: • Regions of cortex representing proof steps switch on in sequence • Hierarchically higher regions form “names” • “names” and “names of patterns of names” • Alice can recall the patterns later • Patterns serve as proof plans (more…)

  5. Patterns serve as proof plans? • Proof plan: • Generates sequence of proof steps • Features: • Expectancy • Generality • Satisfied by named patterns in cortex • Proof steps encoded in lower regions

  6. Where’s the algorithm? • Critical link between cortical regions • Cortical region forms name for an input pattern • Translated: forms proof plan from pattern of already-formed proof plans • Our algorithm! • Presently: not understood.

  7. Proof Planning and the Cortical Algorithms • Conservative learning algorithm  lower bounds • Proof Planning: restricted domain • Decoded cortical algorithms system for learning and utilizing proof plans • “But, is it any good?”

  8. YOU ARE HERE • CONTENTS • Where to discover an algorithm • Viewing neocortex as a proof planner • Why expect suitability • Link to understanding

  9. Understanding in the Memory-Prediction Framework

  10. Understanding as Proof Plans • Share several characteristics • Identifying a proof plan permits • Prediction • Correction of “minor” mistakes • Re-use of ideas and/or techniques • Generation of summaries

  11. Ideal Proof Plans • Goals of proof-planning • Mimic human theorem-proving • Produce human-oriented output • Goal for CONSCS • Characterize high-level ideas

  12. Directions for Future Work • Decipher cortical algorithms!! • Automate learning of proof plans • Analyze cortical functions • Refine definitions for CONSCS

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