# Reviewer Gqmg
## Strengths
Grounds diversity, theory is solid, evaluation is broad, ablations are the strongest part. Selection is cheap relative to generation.
## Weaknesses
1. Gains are task-dependent and modest on GSM8K. 
2. Diversity is capped by the pool: how many gold interpretations does it contain?
## Questions
Q1: W2
Q2: On GSM8K, does the determinant reward different reasoning or surface artifacts?

# Response to Reviewer Gqmg

Thank you for the thoughtful review. We appreciate the recognition of the method and theory, and in particular the reading of the ablations. We address the weaknesses and questions below.

## W1. Gains are task-dependent

Our focus is on the novelty and generality of the approach. We did not do an exhaustive search or optimization of the experimental setup, and this is a great point to add: by putting a bit of effort into instructing the embedder to focus on the math derivation, the GSM8K performance can be improved.

| GSM8K | pass@K | avg unique answers | log-det |
|---|---|---|---|
| Ancestral (best temperature) | 0.929 | 2.80 | -20.0 |
| PoolDPP-Samp, submitted kernel | 0.929 | 3.52 | -15.9 |
| PoolDPP-MAP, submitted kernel | 0.929 | 2.79 | -16.1 |
| PoolDPP-Samp, instructed embedder | 0.930 | 3.64 | -16.2 |
| PoolDPP-MAP, instructed embedder | 0.937 | 3.49 | -14.5 |

We will update the paper to plot the instructed kernel.

We also ran an extra experiment for this question, by asking ourselves how could we measure potential gains without running the full method. The requirement is that the supplied geometry separates task-relevant differences from surface-level ones. We test it with paired edits whose labels are verified (SQL by execution, GSM8K by final answer and stated arithmetic). The table measures P(the correctness-critical edit moves the embedding further than a surface-only one), so that we can see how well the geometry separates semantics from surface-level changes:

| embedder | GSM8K, flip the answer token | GSM8K, flip semantic operator | SQL, semantic edit |
|---|---|---|---|
| MiniLM-L6-v2 *(the Ambrosia kernel)* | 0.004 [0.001, 0.009] | 0.106 [0.088, 0.125] | 0.965 [0.922, 1.000] |
| Qwen3-Embedding-0.6B *(submitted GSM8K kernel)* | 0.042 [0.033, 0.053] | 0.318 [0.288, 0.347] | 0.760 [0.729, 0.789] |
| Qwen3-Embedding-0.6B (instructed) | 0.166 [0.144, 0.188] | 0.817 [0.793, 0.840] | 0.894 [0.869, 0.918] |

(n = 572 / 538 / 470 pairs, bootstrap 95% CIs.)

We conclude that, for any task, appropriate encoders are easy to construct so that the geometry carries relevant domain-specific semantics. Modern embedders can be finetuned or simply instructed to focus on the relevant semantic features, which improves substantially the marginal gains previously observed in GSM8K, as seen on the table. We will add this discussion to the revision.

## W2 / Q1. Diversity is capped by the pool: how many gold interpretations does it contain?

The best Ambrosia pools contain 42.6% of the gold interpretations, and the average pool contains 38.8%. Thanks! It is indeed a good rescaling to report the selected recall as a fraction of the pool ceiling:

| method | selected recall | fraction of ceiling |
|---|---|---|
| Ancestral (sT=1.0) | 0.234 | 0.639 |
| k-Means (sT=1.0) | 0.239 | 0.658 |
| PoolDPP-Samp (tT=0.4) | 0.240 | 0.654 |
| **PoolDPP-MAP (tT=5)** | **0.253** | 0.688 |

Selection operates close to what the pool maximally attainable scores, so the cap definetely matters. However, the method is not expected to uncover new capabilities of the model, but rather to faithfully extract the range of diverse and high-quality outputs that the model can produce.

Our next work involves autoregressive steering with the same DPP objective at generation time, usable for GRPO-style training or test-time exploration. Characterizing the diversity model and its selection ceiling is the necessary first step.

## Q2. On GSM8K, does the determinant reward different reasoning or surface artifacts?

Mostly different final answers, and fewer surface pairs than any baseline. We decomposed every selected set into its 45 pairs and used Gemini 3.6 Flash to score whether each same-answer pair is a different derivation, or a superficial variation of the same one.

| method | different answer | same answer, different derivation | surface only |
|---|---|---|---|
| Ancestral sT=1.0 | 0.120 | 0.094 | 0.786 |
| k-Means sT=1.0 | 0.157 | 0.115 | 0.728 |
| PoolDPP-Samp tT=500 | 0.245 | 0.116 | 0.639 |
| PoolDPP-MAP tT=500 | **0.307** | 0.144 | **0.539** |

The determinant rewards answer-level diversity most of all: the different-answer share rises monotonically from ancestral to PoolDPP-MAP and the surface-only share falls by 25 points. We can conclude that PoolDPP helps to distinguish semantically different outputs, and as seen on W1, the quality of the embedding is examinable and crucial to this effect.