Does a weight edit teach Qwen3.5-0.8B math, or stop it looping?

A team at MIT CSAIL gave an AI agent a hard job. Make Qwen3.5-0.8B better at math, with no training and no gradient descent. The agent had a Python session over the weights and 50 forward passes on practice problems.

It changed 131,072 weights in two layers, 0.016% of the model. With thinking on, the model’s MATH-500 score rose from 7.9% to 48.1%. The write-up calls this weight-space programming.

Watching an agent do this is thrilling. The authors say plainly that it traced the model’s thinking loops. Much of the excitement online read it as an agent teaching a model math. Those are different claims, so we tested the difference.

The short answer is that the edit stops a loop. It adds very little math.

Each layer of the model ends with an MLP. Its last matrix, down_proj, takes 3,584 neuron values and writes them into the residual stream, the 1,024-number vector that every token carries from layer to layer.

We subtracted the original weights from the published edited weights. Only two matrices differ, the down_proj of layers 15 and 19. In each one, 64 neurons were changed.

Each change has rank one. Every changed neuron now writes a little less along one shared direction. The directions of the two layers are nearly the same, with a cosine of 0.85.

So the edit works like this. When those 64 neurons fire together, a fixed direction is taken out of the residual stream. The harder they fire, the more is taken out.

The authors published 20 answers from the unedited model with thinking on. 19 of the 20 run to the token limit. We read the first 12,000 tokens of each answer back through the unedited model. At every token we measured how much the edit would take away there.

We marked a token as repeated when the 16 tokens ending at it had already appeared in the same answer. That gave 105,107 repeated tokens and 133,483 new ones.

In 92 of 100 pairs of one repeated token and one new token, the edit takes away more at the repeated one. In layer 19, it takes away 4.5 times as much at a repeated token as at a new one.

One problem shows this clearly. The model has to convert the point (0, 3) to polar coordinates.

The unedited model finds θ = π/2 by token 1,423 and writes the full answer by token 2,553. Then it keeps checking. At token 7,200 it starts to write one line over and over: “Wait, tan(3π/2) = tan(π + π/2) = tan(π/2) = ∞.” It writes that line until the limit of 32,768 tokens and never gives an answer.

The value stays below 1.5 while the model reasons, and climbs past 4 as soon as the loop starts. The edited model answers the same problem correctly in 10,097 tokens, and on its answer the value stays low throughout.

The agent found a real mechanism. These neurons track the loop, and what they write keeps the loop going. Take it away and the model stops going round in circles.

The model card says Qwen3.5-0.8B runs without thinking by default. It also warns that in thinking mode the model is more prone to thinking loops. So we ran MATH-500 the way the card suggests.

With thinking off, the unedited model scores 43.6%, and the edited model scores 45.2%. The edit is worth 1.6 points here.

The answers that finish are just as good with and without the edit. 65.1% of the unedited model’s finished answers are right, and 65.5% of the edited model’s. The edit lets 1,371 of 2,000 answers finish, against 1,331 without it. That small gain is the whole difference.

We also kept thinking on and gave it a budget. Thinking that had not ended by 8,192 tokens was closed, and the model was asked for its answer. 946 of 1,000 answers were still thinking at that point. Asked to stop, the model got 30.7% of them right. All 53 answers that finished on their own were right. Overall it scored 34.3%.

Any large change to a small model can shake it out of a loop. So we made a control edit. It changes the same 64 neurons in the same two layers by exactly as much. The only difference is the direction, which is random.

We ran all three models on the first 100 problems of MATH-500, with thinking on and one answer a problem.

The random edit moves the score a little, within what chance gives on 100 problems. It leaves 80 of 100 answers stuck at the limit. The agent’s edit leaves 34. The direction is what matters, and the agent found the right one.

We love this result. An agent read a model’s weights, found the direction that traps it, and removed it with 0.016% of the parameters. That is interpretability done by a machine, and it worked.

The jump from 7.9% to 48.1% measures something narrower than math. The unedited model already solves 43.6% of the problems when it is not allowed to loop. The edit gets it to roughly that point with thinking on.

A fair baseline for an edit like this is the model at its best settings, not at its worst. Against that baseline, the gain is 1.6 points.