Develop AI systems to efficiently learn new skills and solve open-ended problems, rather than depend exclusively on AI systems trained with extensive datasets
Before even getting into tackling the reasoning aspect of ARC, I'm thinking about how we encode the data.
I think we'd be handicapped by traditional methods because of the sequential nature of those encoding methods. So much of reasoning relies on being able to see the whole of the input and output at once.
We have a 3D input space, and classical computing methods are going to encode that as 1D or 2D. A 3D matrix in classical terms is just an array of arrays - and arrays are inherently a 1-dimensional data structure. Nesting them only gives the illusion of proper dimensionality. You use indexing tricks to manage the object as if it was 3D.
So we come to the idea of holograms.
A hologram is a three-dimensional image created using light interference patterns. Unlike traditional 2D images, holograms can show different perspectives of an object as you move around them, providing depth and parallax effects.
Holograms record the following properties:
X and Y position, encoded in the spatial distribution of the interference pattern
Phase, crucial for depth information
Amplitude, contributes to the intensity of the reconstructed image.
Parallel processing: Holographic encoding could allow for simultaneous access to all parts of the input, potentially mimicking how human vision processes scenes holistically.
Pattern recognition: The interference patterns in holograms might naturally highlight relationships and patterns within the data.
Dimensionality preservation: Holographic encoding preserves 3D relationships in a way that could be more intuitive for reasoning tasks.
Discretization: ARC inputs are discrete grids, while holograms typically encode continuous fields. We'd need to develop a method to "discretize" the holographic representation.
Computational complexity: Generating and interpreting holographic patterns is computationally intensive.
Abstraction: While holograms are good for spatial relationships, we'd need to develop methods to encode abstract concepts and rules that are crucial for ARC tasks.
Develop a mapping between discrete grid states and holographic interference patterns.
Explore how transformations in the ARC tasks (rotations, color changes, etc.) could be represented as operations on the holographic encoding.
Investigate how machine learning models could be adapted to work with holographic data representations.
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We're going to need to get an algorithm to figure this out...