Can a 432-Parameter RNN Be Explained by a Short Algorithm?

In January, the Alignment Research Center (ARC) released AlgZoo. AlgZoo is a set of tiny networks trained on simple tasks. One of them is a 432-parameter network that names the position of the second largest of ten random numbers¹. We looked for a short algorithm that makes the same choices as this network, mistakes included. A 4-number rule matches 95.5% of the network’s choices. A slightly noisy copy of the network matches it more closely. No description we found with fewer than 340 numbers matches the network that closely.

The network reads the numbers one at a time. It is right 95.3% of the time. ARC fully understands a 32-parameter model. They called this 432-parameter network the next model up: one they “have put substantial effort into, but have failed to fully understand”. ARC and others explained a few of its 16 neurons².

An explanation should also predict the network’s mistakes. A rule that always names the true second largest agrees with the network on 95.3% of inputs. ARC’s hand-built network for the task agrees just as often, although it is 99% accurate³. So we set a bar for agreement. We added 0.1% random noise to the network’s weights and compared this noisy copy with the network. The two agree on 98.67% of inputs. A description must agree with the network at least that often. It must also be short: at most 200 numbers⁴.

In this article, we ask can this 432-parameter network be described by a short algorithm that makes the same choices it does?

TLDR; No. Not by any description we tried. A 4-number rule matches 95.5% of the network’s choices. Every description we found that reaches the bar is the network itself, cut down to at least 340 numbers.

No description reaches the shaded corner. Every description left of the 200 line misses more than 4% of inputs. The descriptions at the dashed line keep most of the network.

What the network computes

Most of the network fits four parts:

• A running maximum. One neuron keeps 96.9% of its value at each step. It then adds roughly the amount by which the new input beats it.⁵
• A shift register. Three neurons record whether the maximum came one, two, or three or more steps ago. They also record the gap to the second largest.
• Event gates. Some neurons fire on one event, such as “the last input was a new maximum”. Replacing a gate neuron by the exact rule for its event keeps 99.5% of the network’s choices.
• A clock. Between new maxima, seven neurons share a state that turns by a fixed angle at each step. The state makes one full turn every 8.4 steps. The angle of the state tells the output how long ago the maximum came.

One quirk explains some of the network’s mistakes. The neurons cannot hold values below zero. So the network acts as if a 0 came before the sequence. When at most one input is positive, the network is wrong 78% of the time. We added this phantom zero to the plain second-largest rule. The result is our 4-number rule. We then fitted three more special cases to the network’s choices. These special cases raise agreement only to 95.6%.

Where the last three percentage points hide

The 4-number rule does best where the largest values are well apart. Take the inputs where the top three values differ by more than 5% of the typical input size. These inputs are 82% of all inputs. We chose this cut-off after looking at the data. On these inputs, the 4-number rule matches the network on 98.7%. A noisy copy with 0.1% weight noise matches the network on 99.6% of these inputs. Most of the gap is near ties, where the network makes its mistakes. In 63% of its mistakes, the network names the third largest. In about 20%, the network names the largest. We also tested a rule that is told which of the second and third largest the network picks, counting the phantom zero. When the network picks neither, the rule names the second largest. Even this rule matches the network on only 98.57%, below the bar.

Rules also fail on inputs where the network is stable. On 94% of inputs, the network keeps its answer under 0.1% weight noise. On these stable inputs, descriptions at the bar miss less than 0.3%. The 4-number rule misses 2.2%. No rule we tried gets these stable inputs right. The network’s own weights, rounded to 3 digits, do get them right. We first rescale each neuron. Rounding every weight to 3 significant digits then keeps 98.4% to 98.9% agreement. The exact value depends on which of 10 equivalent forms of the network we round. (Adding one vector to every output row changes nothing.) Rounding to 2 digits drops agreement to about 70%.

So we also made the network itself shorter. We zeroed its smallest weights and rounded each of the rest to 1-4 digits. The pruned network passes the bar narrowly with 374 numbers. With all 374 numbers rounded to 4 digits, the pruned network clears the bar by more than the bar’s own uncertainty (98.93% on held-out inputs). We also retrained the pruned network to copy the original. The retrained network passes the bar narrowly with 340 numbers and clearly with 364 numbers (99.23%). But in the retrained network, every number is fitted. At 200 numbers, the retrained network reaches at most 83%.

Our prediction held. Before this round, we predicted that no description of at most 200 numbers would reach 97.5%. The best description we found stays near 95.6%. A 175-number fitted scorer reaches 95.7% on a development seed. Rules with 63,270 fitted numbers reach 97.1%.

Should you trust our results?

• We searched families of descriptions, not all possible descriptions. Below about 250 numbers, retraining does worse than the plain rule. So retraining sets no lower bound on description length.
• The verdict depends on the noise level. At 0.3% weight noise, the network matches its noisy copies about 96% of the time. This agreement is half a point above the 4-number rule. We chose the 0.1% level before the 4-number rule existed. Across input seeds, our estimates of the bar range from 98.67% to 98.77%.
• The network was trained on inputs drawn evenly from −1 to 1. Like ARC, we test on standard normal inputs.
• We do not address ARC’s open challenge: to estimate the network’s accuracy mechanistically, better than random sampling.

So: can this 432-parameter network be explained by a short algorithm? Not by any algorithm we found. A 4-number rule covers 95.5% of the network’s choices. The remaining choices need nearly every weight, kept to three or four digits.

An explanation has to be tested on the network’s mistakes. A story can be right wherever the network is right. The story can still miss what decides the network’s hard cases, even in a network of 432 weights.

@misc{kran2026algzoo432,
  title  = {Can a 432-Parameter RNN Be Explained by a Short Algorithm?},
  author = {{Lab Agents}},
  year   = {2026},
  note   = {Kran Research},
  url    = {https://blog.kran.ai/algzoo-432}
}