Day 4 · Thursday · In-class concept studio

From geometry to accountable evidence

Setting. Six depots have behavioural indices

K-means begins with centres \((0,0)\) and \((8,4)\).

1. The first assignment

   Which initial partition follows Euclidean distance?

   1. \(\{A,B,C\}\) and \(\{D,E,F\}\).

   2. \(\{A,D\}\) and \(\{B,C,E,F\}\).

   3. \(\{A,B,D,E\}\) and \(\{C,F\}\).

   4. Every partition has the same distance.

2. Change the ruler

   Every \(y\)-coordinate is multiplied by 10 while \(x\) is unchanged. Which statement is correct?

   1. The algorithm changed from K-means to PCA.

   2. The meaning of near changed because squared \(y\)-differences now receive 100 times their former weight.

   3. The original partition must remain optimal.

   4. Scaling can change scores but not neighbours.

3. A large silhouette

   Depot B has silhouette approximately 0.755 in the original representation. What does that support?

   1. B is internally well separated under this distance, but stability, usefulness, and substantive meaning remain untested.

   2. B belongs to the true efficient-depot type.

   3. The two-cluster solution will persist in every year.

   4. The clustering is causally correct.

4. Read PC1 without inventing importance

   For the original cloud, \(SS_x=96\), \(SS_y=16\), and cross-covariance is zero. Which statement is correct?

   1. PC1 lies along \(x\) and explains \(96/(96+16)=6/7\) of variation; this does not make \(x\) a cause of performance.

   2. PC1 lies along \(y\) because \(y\) has more distinct values.

   3. PC1 proves the right-hand depots are more efficient.

   4. PC1 is the K-means cluster label.

1. Same chunks, different rankings

   BM25 and an LSA-style method rank the same 474 chunks differently. Which is a legitimate explanation?

   1. BM25 emphasises exact terms while the latent representation can connect co-occurring terms; both may be working as designed.

   2. The lower-scoring method must have lost some chunks.

   3. Different rankings prove the qrels are wrong.

   4. Identical candidates must produce identical rankings.

2. Hit@5 and MRR answer different questions

   BM25 has higher Hit@5; the latent method has slightly higher MRR. Which statement is best?

   1. BM25 more often places a known item within five results; the latent method places the first known item slightly earlier on average.

   2. MRR is the proportion of all relevant passages retrieved.

   3. Hit@5 proves answer faithfulness.

   4. The two results establish truth outside the corpus.

3. Locate the failed link

   The correct passage is ranked first, but the generated answer adds a factual claim absent from that passage. What failed?

   1. Corpus coverage.

   2. Ranking only.

   3. Answer faithfulness after successful retrieval.

   4. The citation identifier format.

Setting. A flag sends a payment to investigation and temporarily suspends it.

1. Equal recall, unequal burden

   Both groups have recall 0.80. Which additional comparison matters directly for needless suspension?

   1. False-positive rate: \(10/50=0.20\) for A and \(2/90=0.022\) for B.

   2. Training loss only.

   3. The number of variables.

   4. Whether both groups have 100 rows.

2. Selective labels

   Only flagged cases are investigated; every unflagged case is recorded as “no fraud.” What is the main failure?

   1. The training set is too large.

   2. Missing outcomes are converted into negative labels, so the decision changes the evidence used for retraining.

   3. Precision and recall become identical.

   4. Appeals are no longer needed.

3. What a citation cannot decide

   A retrieved policy passage faithfully supports the factual summary. What does that still not establish?

   1. That the passage exists in the corpus.

   2. That the summary cites a source.

   3. Who has authority to suspend payment, which threshold is proportionate, and how affected people can appeal.

   4. That retrieval preceded generation.

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