A rough set of ideas grounding the reasoning behind my initial approach to the ARC.
In reasoning, it seems to me that there are multiple resolutions or granularities we can take as we work to solve the problem.
This would be the first step, where we learn what kind of task we need to reason about.
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.
Sharing the angle I'm going after to start! It's a physics inspired angle, where the grids we are given are "universes" that have matter in them which can be interacted with via other matter and forces.
Why physics-based?
One thing I want to use this space for is getting some examples of the thought process that goes on as a problem is being solved.
Goal: Watch your mind think from a 3rd person perspective so that you can report on the processes it goes through. If we can get enough examples from watching our minds reason, we may get insight into how we can formalize the process.
This team is for collaboration around the ARC 2024 on Kaggle. Here's some background from the Kaggle page.
Any additional information, as well as an interactive app to explore the objective of this competition is found at the
We've got a color palette in the top left we use to recolor the main structure. How do we know that's it's purpose? When it's left untransformed in the output, we sort of get the idea that it's used as information rather than the target of some transformation.
See through the noise. Lots of unnecessary background noise that would hide the pattern from an algorithm. Human vision does an incredible job at seeing the structure within the chaos.
It seems like we'll be challenged to develop rules and formalities for each universe depending on the patterns we learn. Again, to the point of not learning accurate physical simulations, but a simulation none-the-less.
The rule is the blue is our form/structure, which may be hollow allowing fluid to travel through and fill the space. We get an initial color seed placed somewhere in the structure that we need to let propagate to the entire connected structure.
This one's daunting looking, but pretty simple when you see it. The light blue section defines the output section. We're able to easily see the that the larger matrix is symmetric over the X and Y axis, so for the unknown output we'd be able to look at the reflection of the light blue input space.
Walking through this one with language.
Look at the top left two squares. These determine the side colors, first square to horizontal, second square to vertical.
We need to draw a spiral, as long as we can. Start at the blue square defining the starting point, go to the left two square, using the horizontal coloring.
Denoising, chaos to order, sharpening?
In this one, our reasoning points to the idea that we shouldn't really worry about trying to transform all the isolated particles (squares) into the expected form, but rather learn to see the expected form underneath the noise.
Holy smokes...
I'm actually looking for counter-examples to the physics approach, but I think this one only continues to solidify the need for it.
The problem with this one is we see that we aren't actually looking for a realistic physics simulation. Not every "material" will behave the same way, and even within the same universe the same material doesn't necessarily have the same characteristics.
We're going to need to get an algorithm to figure this out...
I feel like the physics based approach works well here again. We talked about how the grids are actually 3D spaces, and that color and depth are interchangeable. So you could have a form inhabit the same (X,Y) coordinate and that'd be no problem because they are differentiated by the Z-axis.
This one actually is a little trickier. The form (given by red) is consistent from input to output, but the shading rules are what we discover we need to reason about.
From the examples, we see we have cyan, yellow, or green as options. The first thing I thought to look for was to shade based on location of the form. Maybe left-most gets one color, etc. or if it was based on the relative relation between multiple forms.
This one's interesting. Again, seeing a new pattern I've never seen before, but still quite easy to reason about. We can pick up on two forms in each example, one of which is replicated to the output with a change in color, and the other omitted.
In this example, we identify horizontal columns as groupings that will persist. We notice the column colors change from input to output. We're unsure if it's the columns moving or if the colors are being translated, and how that translation takes place.
Another new concept to learn! This time, working with set theory. It's certainly part of physics, but hard to make the direct connection like you could with a force transformation or other macro physical phenomenon. This could be seen in spin systems of quantum physics.
A good example of an attractive force (gravity). In this case, the force is always oriented from red to blue instead of always top to bottom.