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--- compai [2024/10/13 22:44] – [Induction and AI] pedroortega
+++ compai [2024/10/14 14:15] (current) – [Conclusions] pedroortega
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-If we identify rules and premises with the information contained in a program, computation appears to correspond to a type of deduction restricted to processes that can be carried out through mechanical means. Induction, on the other hand, can be regarded as a process that finds rules and premises from conclusions. This suggests the following parallels:
+If we identify rules and premises with the information contained in a program, computation appears to correspond to a type of deduction restricted to processes that can be carried out through mechanical means. Induction, on the other hand, can be regarded as a process that finds rules and premises from conclusions. This suggests the following parallels between logic and computer science:
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 But **universal pattern recognition**—the inverse of universal computation—tells a different story. Unlike computation, recognizing patterns from observations cannot be fully captured by a program. This is because determining whether a given program will halt ([[https://en.wikipedia.org/wiki/Halting_problem|Turing's halting problem]]) is undecidable, hence determining whether a candidate program will halt and produce the desired output is undecidable too. (For those who know, this is basically the reason why [[http://www.scholarpedia.org/article/Algorithmic_probability|Solomonoff induction]] is incomputable).
+A naive attempt to encapsulate universal pattern recognition could involve a cheat list: an infinite binary sequence where the bit in position $n$ indicates whether the $n$th-program would terminate. But this sequence contains incompressible information, and thus the resulting description of universal pattern recognition would overall involve an infinite amount of bits, which by definition isn't a program.
-A naive attempt to encapsulate universal pattern recognition could involve a cheat list: an infinite binary sequence where the bit in position $n$ indicates whether the $n$th-program would terminate. But this sequence contains incompressible information, and thus the resulting description of universal pattern recognition would overall involve an infinite amount of bits, which isn't a program by definition.
 Thus, while universal computation is simple, the infinite complexity of universal pattern recognition defies any finite rule set.
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 ===== Induction and the computational complexity classes =====
-The relationship between deterministic and nondeterministic complexity classes mirrors the divide between deduction and induction.
+The above results apply to the limit case when we have unlimited resources to run and invert programs. But similar results hold when we take into account computational complexity. In fact, the relationship between deterministic and nondeterministic complexity classes mirrors the divide between deduction and induction.
-The **P vs NP** problem can be thought of as a question about pattern recognition. In P, you're given an input and tasked with computing the output efficiently, like running a program. In NP, it’s the reverse: you're given a desired output and need to find the input—or "program"—that produces it.
+The **P vs NP** problem can be thought of as a question about pattern recognition. In P, you're given an input and tasked with computing the output efficiently—in polynomial time. In NP, it’s the reverse: you're given a desired output and need to find the input—or "program"—that produces the output in polynomial time.
 For example, with NP problems like the Boolean satisfiability problem (SAT), verifying if a given solution works is easy (in P), but **finding** that solution is hard, much like trying to reverse-engineer a program to figure out what input created a specific result.
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 I've highlighted that pattern recognition is fundamental to intelligence, driving key AI capabilities like learning and reasoning. Many AI applications, from machine learning to natural language processing, depend on recognizing patterns in data. However, while humans excel at this across diverse contexts, AI struggles to generalize beyond specific tasks, underscoring the difficulty of pattern recognition.
-**Universal pattern recognition is non-computable, but feasible in restricted domains**:
+**Universal pattern recognition is incomputable, but feasible in restricted domains**:
 Though universal pattern recognition is incomputable, it's possible within finite limits. Perfect pattern recognition works when restricted to a finite set of candidate programs. This means that while AI can solve problems within specific, bounded domains (e.g., diagnosing diseases or navigating traffic), **building better AIs will forever remain open-ended**.
-**The challenge of inverting computation**:
+**The challenge of inverting computation and the general structure of AI algorithms**:
-The **P vs NP** problem is essentially about pattern recognition. In P, computing the output from a given input is easy. In NP, it's much harder: you must reverse the process and find the input (or "program") that generates a specific output. If **P = NP**, AI could solve many currently intractable problems efficiently. But since **P ≠ NP** is widely believed, it highlights that solving some AI problems—like planning or optimization—may always be more complex than verifying their solutions.
+The **P vs NP** problem fundamentally revolves around the difficulty of pattern recognition. In class **P**, given an input, computing the output is efficient. In class **NP**, however, the challenge is reversed: you need to find the input (or "program") that produces a specific output, a task that is much harder. This highlights a general framework for pattern recognition algorithms: first, analyze the data, then iteratively hypothesize potential programs, verifying at each step whether a given program generates the observed data.
 **AI as a core branch of computer science**:
 AI isn't just an engineering branch about practical problem-solving—it's deeply rooted in computer science theory. Concepts like computation, logic, and complexity are essential for understanding and advancing AI, though their importance is often underplayed. Strengthening these links could unlock new AI breakthroughs by helping researchers better understand the limits and possibilities of computation and pattern recognition. AI's future lies in its deep integration with computer science, focusing more on foundational concepts like algorithmic complexity.