Checkerboard pattern formation exhibits directional propagation from bottom-left to top-right despite no built-in directional bias in the model

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

• Reflection-inducing directions emerge more clearly in higher layers (ℓ>5) for both models and datasetsfinding0.768
  Empirical observation about which network layers encode reflection-relevant information.
• Checkerboard circuit trained on 16x16 grid successfully generalizes to 64x64 grid with 4x more time stepsfinding0.764
  Grid scaling generalization result demonstrating boundary-size invariance
• DiffLogic CA fully converges to 16x16 checkerboard target pattern with both soft and hard losses reaching zerofinding0.740
  Core result of pattern generation experiment demonstrating recurrent circuit learning
• Superposition hypothesis: neural networks represent more features than dimensions using almost-orthogonal directions.hypothesis0.739
  Explanation for why dictionary learning can recover many more features than dimensions.
• Truth directions emerge in earlier layers for factual tasks and later layers for arithmetic tasks.claim0.736
  Core empirical claim about the layer-dependence of truth direction emergence as a function of task type.
• The model converges to a more stable truth direction in middle-to-late layers, as evidenced by increasing cosine similarity between layer-wise probes.claim0.736
  Supported by the geometric transition visible in cosine similarity heatmaps for F0-F3.
• Alternation of squares and rectangles was superior to simple checkerboard for Martinez floorfinding0.735
  In pattern trials, alternating square and rectangular elements felt more harmonious than a plain checkerboard.
• 80% of Radcliffe students grouped black-and-white patterns by left-right reading, not by overall wholeness.finding0.735
  Experimental result showing that highly educated adults tend to ignore the wholeness of simple patterns.