18-01-25 Valuable Properties of Representations

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Valuable properties of representations, born out of the frustration with the obsession over disentangling representations to the exclusion of other critical concepts. Many of these properties exist, to a greater or lesser extent, in human cognition.

1. Decomposition of representation
   1. This gives you a controllable, interpretable, recombinable representation
2. Alignment of representation where shared structure exists
   1. Want concepts with the same mechanisms / structure to update simultaneously when there’s new information that informs their working
   2. Can be through compositionality
   3. Trades off against decomposition?
3. Modifiability of complexity of the representation depending on task
   1. Representation that becomes more granular upon zooming in
   2. Necessary for computational efficiency
      1. Memory Constraints
      2. Compute Time
      3. Attention Constraints
   3. Ideally would be on a continuum
      1. Give me the n principal components (non-linear) of the representation, while preserving clean conceptual (semantic) decomposition
4. Transferability
   1. Ability for the representation to be repurposed for different tasks, generally through learning sufficiently high level structure that there is an appropriate level at which to do transfer between representations of problems and solutions
5. Appropriate tradeoff of Simplicity / Compressedness vs. Representational capacity
6. Sparsity
   1. Necessary for the discovery of compute intensive structure (say, graphical / relational / network, or concept recombination) in the representation
7. Interpretability
   1. Optimizability of representation for interpretability.
   2. Quality translation from representation to natural language.
   3. Clean isolation of parts of the representation (or a sparse approximation of the used representation) for any prediction made or action taken.
8. Control
   1. Control through modification, freezing, or freeing of sub-parts of the representation
9. Discrete and Continuous Modes
   1. Discreteness
      1. For Interpretability, self-examination, sparsity.
   2. Continuity
      1. For representational capacity, predictive accuracy.
10. Fully general translation into and out of the representation
11. Want to be able to flexibly represent any category of object, situation, etc. in a merged representation
12. Reserve category errors for a particular mode of action, ‘rigor mode’

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