Exercises

Practice evidence levels, trace shapes, weighted values, vector norms, diagnostic projections, ablation effects, patch recovery, necessity and sufficiency, feature vocabulary, and report repair.

Use the Chapter 9 clean margin 6.4618 and corrupted margin -5.7350 unless an exercise provides other values.

Q1. Order the evidence

A researcher records a head's weights, compares them across two prompts, zeros the head, and then proposes a tested component account. Put the four evidence levels in order.

Choose the correct order

observation, association, intervention, mechanistic account

intervention, observation, association, mechanistic account

mechanistic account, observation, intervention, association

Select one choice, then check.

Hint

Begin with reading one value and end with the tested account.

Solution

The order is observation, association, intervention, then mechanistic account.

Q2. Recover a trace shape

For $B=2$ , $h=4$ , and $T=5$ , what is the attention-weight tensor shape under the convention $(B,h,T,T)$ ?

Your answer

Answer it first, then check.

Hint

Both final axes are sequence positions.

Solution

The shape is

(2,4,5,5)

Q3. Separate weights from written content

Weights [0.25,0.75] mix value rows [2,0] and [0,4]. Calculate the mixed value before its output projection.

Your answer

Compute it first, then check your number.

Hint

Scale each row, then add coordinate by coordinate.

Solution

0.25[2,0]+0.75[0,4]=[0.5,3]

Q4. Calculate a write norm

An attention write is [3,-4,0,0]. Calculate its $L_2$ norm. Does that number alone determine its effect on the target logit?

Your answer

Answer it first, then check.

Hint

Use the square root of the sum of squared coordinates.

Solution

The norm is

\sqrt{9+16}=5

. It does not determine alignment with the readout or later effects.

Q5. Interpret a diagnostic projection

An intermediate residual projects to top token Y, while the final model predicts X. Which statement is justified?

Choose one

The frozen diagnostic readout favors Y at that stage; later computation yields the actual X output.

The model consciously believed Y and then changed its mind.

The final X output must be an implementation error.

Select one choice, then check.

Hint

The model does not normally apply its final readout at that stage.

Solution

The diagnostic readout favors Y at that stage; the actual forward pass continues and finally predicts X.

Q6. Calculate a zero-ablation effect

The clean margin is 6.4618. A zero ablation gives -2.6127. Calculate $\Delta m$ to four decimal places.

Your answer

Compute it first, then check your number.

Hint

Use ablated minus clean.

Solution

-2.6127-6.4618=-9.0745

using the rounded inputs.

Q7. Interpret recovery above one

Clean margin is 5, corrupted margin is -3, and a patch gives margin 7. Calculate recovery and interpret it.

Choose the calculation and interpretation

1.25; the patched margin overshoots the clean margin.

1.25; the patch has an invalid probability above one.

0.50; the patch recovers half of the clean-corrupted gap.

Select one choice, then check.

Hint

Use

(7-(-3))/(5-(-3))

Solution

Recovery is

10/8=1.25

. The patched metric exceeds the clean baseline; this is allowed and needs investigation.

Q8. Distinguish necessity and sufficiency

Removing component A damages the output, but inserting A alone into a baseline does not restore it. Which result is supported?

Choose one

A is needed under the tested removal, but it was not sufficient under the tested insertion.

A alone is sufficient because its removal caused damage.

A is the complete and unique mechanism.

Select one choice, then check.

Hint

Use the result of each intervention separately.

Solution

A is necessary under that removal test but not sufficient under that insertion test.

Q9. Separate neuron and feature

Which statement uses the vocabulary correctly?

Choose one

A neuron is a coordinate; a feature is a hypothesized represented property that may span coordinates.

Every positive neuron activation is one named feature.

One active neuron is already a complete circuit.

Select one choice, then check.

Hint

A feature may be distributed or represented in superposition.

Solution

A neuron is a coordinate in a chosen activation basis; a feature is a representation hypothesis and may use several coordinates.

Q10. Repair an interpretation report

A report gives only its strongest patch, says it “proves the circuit,” and does not name the corruption or metric. Name three missing requirements.

Choose the three required repairs

Report all tested sites, define the corruption and metric, and limit the claim to the intervention evidence.

Keep only the strongest patch, add a circuit name, and omit weak results for clarity.

Repeat the strongest patch three times; no corruption definition or controls are needed.

Select one choice, then check.

Hint

Check what was omitted, what cannot be rerun, and what was overstated.

Solution

Report all tested sites rather than only the maximum, define the corruption and output metric, and replace “proves the circuit” with a claim bounded to the tested patch effect. Controls and alternative explanations should also be included.

Q1. Order the evidence

Q2. Recover a trace shape

Q3. Separate weights from written content

Q4. Calculate a write norm

Q5. Interpret a diagnostic projection

Q6. Calculate a zero-ablation effect

Q7. Interpret recovery above one

Q8. Distinguish necessity and sufficiency

Q9. Separate neuron and feature

Q10. Repair an interpretation report

Pause and reflect