BDH-CQ
When an AI shows you its reasoning, that reasoning is text. The model writes each step out and reads it back before carrying on. A system called BDH-CQ, from a company called Pathway, keeps every step as numbers inside itself.
The worked examples are the only place the rule exists
The puzzles BDH-CQ solves are small grids of coloured squares. Each puzzle hands you a few worked examples: here is a grid, here is what it should turn into. Then you get a new grid to do yourself. The rule is different in every puzzle, and the rule is never written down. You work it out from the examples, usually three of them. BDH-CQ is a hundred and fifty million parameters, the adjustable numbers a model is made of. Pathway has published the paper and nothing else: no weights, no code, no demo.
The model that finishes a puzzle is identical to the one that started it
Pathway kept all four hundred of these puzzles out of training, and their worked examples too. BDH-CQ meets every puzzle cold. It works the rule out while it answers, and the numbers inside the model stay exactly as they were. Some of the other systems on this test work a different way. They train on the evaluation puzzles, and each puzzle carries an identity the model has seen before.
The examples go into one memory that does not grow
from the memory before it, plus that example
Paste examples into a chatbot and the chatbot keeps the whole pile, and reads all of it again for every new word it produces. BDH-CQ folds each worked example into a single running memory, one example at a time. The memory after the third example is built from the memory after the second, plus the third example. The simplest version the paper spells out is one you can picture: take what each example contributes and add it onto what is already there. The memory does not grow as the examples arrive. Pathway's own reason for building the memory this way is the cost. There is no growing pile to re-read.
Only the last pass becomes an answer
With every example folded in, BDH-CQ builds a second space to work in, out of the new grid and that memory. Then it goes back over that working space, pass after pass. Each pass is built from the pass before it and from that same memory, and the memory stays frozen. The passes in between stay as numbers. There is no writing out and no reading back. How much refinement to do is a dial, set at answer time. BDH-CQ solves twenty one percent of the puzzles at the low setting, twenty seven percent at medium, and twenty nine and a half percent at high. The leaderboard allows two answers per puzzle, and those scores use both. Pathway published the architecture family BDH-CQ is built on last year, with code anyone can read, and keeps this system's dimensions, update rules and training recipe private.
BDH-CQ solves 29.5% of 400 public puzzles for a fraction of a cent
On the four hundred public puzzles of the first version of the ARC test, BDH-CQ gets a hundred and eighteen right. The systems at the top of this test solve close to ninety percent of those puzzles, and OpenAI's GPT-5.6 Luna scores higher than BDH-CQ at its cheapest setting. Pathway works its own cost out from hardware time, at an assumed three dollars an hour for the chip. The systems on the same chart are priced off what they charge to use. Pathway reports its own figure twice: seven hundredths of a cent in one section, a quarter of a cent in another, for the same score.
One more worked example takes sorting from 0 of 24 to 13 of 24
Across a hundred and sixty puzzles with three test grids each, fifty two of those puzzles had one or two grids right and still counted as missed. The authors read those partial successes as a rule the model inferred but did not apply to every grid. What decides whether a rule carries is what you show it. On a different family of puzzles, the researchers held the test grids byte for byte identical and changed only the examples. Add one worked example at the difficulty being tested, and sorting eight items goes from zero correct out of twenty four grids to thirteen. Nesting five levels deep goes from nineteen of twenty four grids to all twenty four.
The reasoning stays as numbers inside the model until the last pass turns it into an answer
So the thinking happens as numbers, and the answer is the first part of it anyone can read. Every published evaluation of this system is Pathway's own, and there are no weights, no code and no demo. The authors name the harder second version of this test as their next target.
