Recursive Decomposition: Solving Problems Too Big for AI скачать в хорошем качестве

Recursive Decomposition: Solving Problems Too Big for AI

This video lecture introduces the Decomposition Framework for solving complex problems using AI, covering Component 3: Cross Validation. It also goes into advanced topics like Error Propagation with uncertainty and methods for Quantifying System Performance using metrics such as Task Success Rate. The lecture addresses Algorithmic Complexity Considerations and common pitfalls to avoid, like over-decomposition, in the context of AI model validation. Large language models can be brilliant yet unreliable on long, multi-step problems because small per-step error rates compound exponentially. This lecture presents a rigorous framework—decomposition, independent verification, retries, and integration testing—that dramatically boosts end-to-end accuracy across physics and real-world pipelines. This lecture is a practical playbook for making AI (especially large language models) more reliable on complex problems. The key diagnosis is that long, step-by-step solutions silently accumulate mistakes: a small chance of error per step compounds into a big chance of failure over an entire chain. The proposed fix is systematic decomposition—split one big task into smaller subtasks with clear interfaces, verify each subtask independently, and only then integrate the result. That turns fragile “one-shot” reasoning into a workflow where errors are caught early and do not propagate. You then get a structured framework: analyze the problem, choose a decomposition strategy (sequential, parallel, or hierarchical), solve each subtask, run verification checks, and finally do integration testing. A physics example (projectile motion) demonstrates the method: compute components, solve vertical motion, then compute range—each step is validated using an alternative check (geometry, conservation reasoning, and known special-case formulas). The lecture adds a confidence scoring idea (internal consistency, verification pass rate, and cross-checking) and shows how to measure and manage reliability at scale with testing, sample-size thinking, and performance metrics such as subtask pass rate, retries, end-to-end accuracy, and verification coverage. What you will learn: Why AI errors compound in long solution chains and why that causes “confident wrong” outputs How to decompose problems into verifiable subtasks with clean inputs/outputs When to use sequential vs parallel vs hierarchical decomposition How to build verification protocols: unit checks, limiting cases, symmetry, conservation laws, sanity checks How retries and “fix only the failed subtask” dramatically improve reliability How to score confidence per subtask and track performance with clear metrics How decomposition enables debugging, reuse, and parallel execution Common pitfalls: over-decomposition, weak verification, hidden dependencies, missing error budgets Future directions: automated decomposition, adaptive verification, and verifying the verifier Timestamps: 00:00 — Why AI makes subtle errors and why decomposition is the antidote 01:09 — How small per-step error rates collapse long multi-step solutions 01:47 — Breaking a big problem into verified chunks and retrying failures 02:23 — Five-phase framework: analyze, decompose, solve, verify, integrate 03:36 — Decomposition types: sequential, parallel, hierarchical 04:11 — Case study setup: turning a physics problem into three subtasks 04:49 — Subtask solutions + independent verification checks 07:16 — Confidence scoring: consistency, verification, cross-validation 08:27 — Estimating AI error rates with proper test design 09:11 — Verification toolkit: units, limits, symmetry, conservation, sanity checks 10:28 — Error propagation and uncertainty accumulation concepts 11:47 — Integration testing: interface checks and end-to-end validation 12:20 — Real pipeline example: decomposition in computational drug discovery 13:32 — Metrics that make reliability measurable 14:07 — Empirical results: why decomposition wins on harder problems 14:46 — Recursive decomposition: keep splitting until subtasks are “atomic” 15:26 — Cost vs benefit: extra overhead for large accuracy gains 16:01 — Complexity and speedups via subtask structure and parallelism 16:40 — Limitations: when problems do not decompose cleanly 17:16 — Research directions: automated strategies and adaptive verification 17:48 — Implementation guide: taxonomy, check libraries, logging, iteration 19:01 — Pitfalls to avoid in real deployments 19:37 — Key takeaways recap 20:11 — Why this is scientifically grounded, not just heuristics 20:44 — Evidence across many test cases and domains 21:18 — Closing: applying the method immediately #AIReliability #ProblemSolving #Decomposition #PromptEngineering #ErrorReduction #ChainOfThought #ScientificWorkflow