Overview of Abstraction Space

Category: Abstraction

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Ideas foundational to abstraction

1. Generalization
2. Memory Limitations
3. Discrete vs. Continuous Abstractions
4. Coarse / fine vs. high / low vs. specific / general framing of abstraction
5. Concept of ‘type’ of abstraction, the way in which the abstraction is done
6. Structure
   1. There is a true structure to information that we’re looking to model
7. Compression
   1. Fundamental tradeoff between the amount of compute necessary and the accuracy of the abstractions reasoned over (in contexts where lower is strictly better, say in object-oriented programming)
8. Hierarchy

Ideas that are a result of abstraction

1. Pitfalls of Abstraction
   1. Abstracting over unlike objects
   2. Excessive height obscures information inside abstraction
      1. Leaky Abstractions
   3. Level of abstraction as a hidden assumption
   4. Inferential distance, where ideas build on top of one another and there’s a struggle to communicate across the gap
      1. If idea can be expressed without the abstractions over it, it may be less general but more accessible
      2. The way that fields develop their own language to build ideas on top of one another
2. Ability to represent huge amounts of information
   1. Value to breaking tasks / domains / problems down into hierarchical representations
   2. The way that fields develop their own language to build ideas on top of one another
3. All modeling processes as an act of abstraction
   1. Mental Models as all examples of abstraction
   2. Causal models (including rules for establishing causal structure) as abstractions
   3. Need for abstraction in order to model formal systems, ex. Utility in Econ or an Environment in RL
4. Transfer
   1. Transfer in causal models vs. intuitive transfer
5. Value to operating at multiple levels of abstraction
6. Value to attacking problems at the right level of abstraction
   1. Definitions and the outcome you choose to care about can be a function of the level of abstraction you’re working at (often we take the level of abstraction for granted and it informs our understanding of the problem itself, it’s an unspoken assumption)
7. Examples of Abstraction
   1. Abstraction in planning, where nearby events are planned in fine grain and far events are coarse
   2. Language as a discrete proxy for thought, an abstraction over a distributed representation of an idea
   3. Scientific disciplines as distinguished by the grade at which we interact with reality
8. Evaluating the Quality of an Abstraction
   1. Generalization, on top of an abstraction - which framing leads to the best model for the system? How can we abstract so as to generalize with extraordinary accuracy?

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