finding

active

finding:learned-checkerboard-generation-circuit-reduces-to-just-5-active-logic-gates-after-pruning-6-with-one-redundant-and

Learned checkerboard generation circuit reduces to just 5 active logic gates after pruning (6 with one redundant AND)

Remarkably minimal circuit discovered for checkerboard pattern generation

Source paper

extracted_from

Differentiable Logic Cellular Automata: From Game of Life to pattern generation with learned recurrent circuits

Neighborhood — ranked by edge-count

Claims (1)

claim

Different tasks yield distinct distributions of logic gate types between perception kernels and update networks
supports
Interpretive claim based on circuit analysis across experiments

Concepts (1)

concept

Minimal Circuit Description
supports
Hypothesis that discretization finds minimum-size circuits equivalent to minimal algorithmic descriptions of patterns

Questions (1)

question

Could the discretization and minimal circuit size be finding some minimal procedural description for generating patterns of interest?
supports
Open question raised by the 5-gate checkerboard solution and its generalization properties

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

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

Total active gates in checkerboard circuit is 22 (excluding pass-through gates A and B)finding0.847
Circuit size finding for checkerboard experiment before pruning
Learned Google G circuit uses 927 active gates (excluding pass-through gates A and B)finding0.822
Circuit complexity metric for colored pattern experiment, largest of all experiments
Learned Game of Life circuit uses 336 active gates (excluding pass-through gates A and B), predominantly OR and ANDfinding0.821
Circuit analysis result for Game of Life experiment
Checkerboard circuit trained on 16x16 grid successfully generalizes to 64x64 grid with 4x more time stepsfinding0.811
Grid scaling generalization result demonstrating boundary-size invariance
Learned lizard pattern circuit uses 577 active gates (excluding pass-through gates A and B)finding0.783
Circuit complexity metric for lizard experiment
Mean-difference patching in a two-layer ReLU circuit flips the decision to class-A by activating a third hidden unit that is silent for all natural class-A inputsfinding0.750
Synthetic theoretical example showing pernicious divergence via hidden pathway activation
Circuits could act as an epistemic foundation for interpretability by breaking down model behavior into falsifiable statements about small subgraphs.claim0.727
Normative vision for how the circuits agenda could resolve the pre-paradigmatic state of interpretability
Asynchronous DiffLogic CA requires 50 steps vs 20 steps for synchronous training to reconstruct checkerboard patternfinding0.724
Cost of asynchronous training in terms of convergence time steps