From: jimruttshow8596
Introduction to Occam’s Razor
Occam’s razor is a principle originating from a 13th-century British Scholastic. It posits that “one should not Advocate or generate a plurality without necessity,” meaning one should always choose the simpler explanation for a phenomenon over a more complex one if it offers no additional insight [01:09:36]. This principle, also known as model selection or regularization, has been a foundational assumption in mathematical and physical sciences, leading to “beautiful simple things” like the Dirac theory of relativistic quantum mechanics [01:10:00].
The Challenge for Complex Systems
While Occam’s razor applies well to the physical sciences, it faces challenges in the complex world. Complex systems are characterized by “horrible High Dimensions” which often seem irreducible, making the direct application of Occam’s razor difficult [01:10:41].
Defining Meta Occam
The concept of Meta Occam addresses this challenge by shifting the focus of parsimony. Instead of the parsimony being in the final object or outcome, it is found in the process that generates the object [01:11:19].
Key characteristics of Meta Occam:
- Parsimony in Process, Not Object The physical sciences produce parsimonious theories of minimal objects (e.g., the atom). In contrast, domains governed by Meta Occam have parsimonious theories or processes for generating complicated objects [01:11:30].
- Arbitrary Complexity from Simple Principles This concept applies to sciences where simple processes can elaborate over time to produce arbitrarily complex objects [01:13:47]. For example, the theory of evolution by natural selection can be expressed in a few sentences, yet it explains objects as diverse and complex as a worm or an elephant without becoming a more complicated theory itself [01:11:00].
- Examples of Processes Reinforcement learning and evolution by natural selection are mathematically equivalent processes that exemplify Meta Occam, as they generate complex outcomes from simple, selective feedback mechanisms [01:11:39].
- Contrast with Physics Physical theory often has “infinite models for minimal objects” (e.g., multiverses to explain fine-tuned constants), whereas Meta Occam approaches utilize parsimonious processes to create non-parsimonious, complex objects [01:13:54], [01:14:50].
Relevance to Complex Systems and Machine Learning
Complexity science can be understood as “the search for Meta Occam processes” [01:15:08]. It seeks relatively simple rule systems that possess open-ended properties, much like alphabets are simple but open-ended in their composability and evolution [01:15:18].
This concept is particularly relevant in the context of machine learning and large language models:
- Generating Theories: Training a deep neural network, while generating a massive, highly dimensional model (e.g., GPT-4 with 1.3 trillion parameters), is seen as creating a “theory” of the phenomenon it models [00:13:03], [00:50:27]. These models are essentially “rule systems” or “complex systems” themselves [00:50:33].
- Extracting Parsimony: Scientists are exploring methods to use these massive, data-driven models as “pre-processors for parsimonious science.” This involves training a neural network as a “surrogate for reality,” then sparsifying it (removing connections, quantizing data) and applying symbolic regression (a genetic algorithm-based process) to infer algebraic formulas that encode the underlying regularities [02:50], [02:52], [02:53]. This approach allows for a “new way of doing science” by having a large engine for prediction and a smaller, more specified model for understanding [03:06].
- High Dimensionality and Optimization: The effectiveness of gradient descent in modern deep learning models, despite their non-differentiable elements, is attributed to the “miracle of ultra high dimensionality.” In such vast spaces, there is almost always a dimension pointing “down” for optimization, ameliorating the local minima problem that previously hindered adaptive computation [01:03:03].
- The Future of Science: If large language models are the “steam engines of the 21st century,” then Meta Occam suggests seeking the “statistical mechanics” that emerge from their study [01:46:16]. This could lead to new principles for explaining adaptive reality and effective laws for the complex systems we study, such as a truly working economic theory [01:47:07]. This new paradigm of science seeks to derive new principles from complex phenomena that were previously intractable due to data processing limitations [01:47:09], [01:53:55].