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arxiv: 2606.01811 · v1 · pith:5OVQPROAnew · submitted 2026-06-01 · 💻 cs.CL · cs.AI· cs.LG

"I've Seen How This Goes": Characterizing Diversity via Progressive Conditional Surprise

Matthew Khoriaty , David Williams-King , Shi Feng This is my paper

Pith reviewed 2026-06-28 14:49 UTC · model grok-4.3

classification 💻 cs.CL cs.AIcs.LG
keywords diversity measurementlanguage modelin-context learningconditional surprisecreative writingpost-trainingMcDiv benchmarkmode collapse
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The pith

A base model's token log-probabilities across random in-context permutations yield a diversity score that tracks human judgments.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes measuring diversity of a response set as the progressive conditional surprise a base language model experiences when each new response appears after the others in random order. This score is read directly from the model's own per-token log-probabilities in a single forward pass per permutation, requiring no separate embedding model, reference corpus, or human labels. On the human-grounded McDiv benchmark the resulting Decan metric reaches 0.846 overall classification accuracy on its best subset, close to the strongest reported neural baseline. The same score drops steadily when the same base model is taken through supervised fine-tuning, DPO, and RLVR, registering the diversity reduction that matters for creative applications. The approach treats diversity as a joint property of the response collection, the prompt, and the scoring model itself.

Core claim

Diversity is quantified as the progressive conditional surprise D_Ca_n = C × a_n extracted from a base model's per-token log-probabilities when responses are presented in random order within an in-context prompt; the metric is computed in one forward pass per permutation, needs no external data or trained components, and achieves 0.846 OCA on the McDiv prompt_gen set while detecting monotonic diversity loss across the base-to-RLVR pipeline on OLMo-2-7B.

What carries the argument

Progressive conditional surprise: the successive reduction in a base model's per-token log-probability when each new response is appended after the preceding ones presented in random order.

If this is right

  • The same pipeline scores both AI-generated and human-written response sets without modification.
  • D_Ca_n registers a monotonic drop in diversity across the base, SFT, DPO, and RLVR stages of post-training.
  • The metric requires only a single forward pass per permutation on the base model already in use.
  • No embedding model, reference corpus, or task-specific training is needed to obtain the score.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method could be inserted into training loops to monitor diversity loss in real time using the model being trained.
  • It offers a way to compare decoding strategies or temperature settings on any prompt without additional infrastructure.
  • Because the score is prompt-conditioned, it may surface prompt-specific notions of diversity that global embedding metrics miss.

Load-bearing premise

The progressive conditional surprise extracted from a base model's in-context permutations accurately captures the human notion of diversity that the McDiv benchmark measures.

What would settle it

Collect new human diversity ratings on a fresh set of response collections where the Decan metric and the existing McDiv labels disagree, then test whether the metric's ranking still aligns with the new human judgments.

Figures

Figures reproduced from arXiv: 2606.01811 by David Williams-King, Matthew Khoriaty, Shi Feng.

Figure 1
Figure 1. Figure 1: The diversity-metric pipeline. Given prompt 𝑝 and 𝑛 responses from policy 𝜋, we format them with response labels (“Response A:”, “Response B:”, . . . ) and tokenize. The conditional track (left) feeds the concatenated context to the base model 𝜃 in a single forward pass per permutation 𝜎, extracts per-response total surprise, divides by each response’s UTF-8 byte count, and averages over permutations to ge… view at source ↗
Figure 2
Figure 2. Figure 2: Progressive conditional surprise curves and per-prompt diversity distributions across the four OLMo-2-7B stages on the length￾matched AlpacaEval subset. Each later stage’s 𝑎¯𝑘 curve lies below the base curve at every 𝑘 ≥ 2; the per-prompt 𝐷𝐶𝑎𝑛 distribution shifts toward lower values as the pipeline advances. Discussion. The monotone drop across all three pre￾registered contrasts is consistent with the post… view at source ↗
Figure 3
Figure 3. Figure 3: Single-pass input layout for computing the full 𝑎𝑘 curve. The prompt is followed by all 𝑛 responses with “Response A/B/C/. . . ” labels; one forward pass over this sequence yields every 𝑎𝑘 value simultaneously, since causal attention conditions the tokens of 𝑟𝑘 on exactly 𝑝, 𝑟1, . . . , 𝑟𝑘−1 (plus formatting). A.3. Dependence on Sample Ordering The 𝑎𝑘 values depend on the ordering of {𝑟𝑖}. Individual respo… view at source ↗
Figure 4
Figure 4. Figure 4: Progressive conditional surprise curves (𝑎𝑘, per-byte) for all five scenarios, comparing GPT-2 (top row) and Qwen2.5-3B (bottom row). In each panel, faint colored curves are individual permutations (100 per prompt), medium colored curves are per-prompt averages, and the bold black curve is the mean across prompts. Pure noise curves are flat (no learnable structure); multi-mode curves show progressive decli… view at source ↗
Figure 5
Figure 5. Figure 5: Mode count scaling on Qwen2.5-3B (𝑛 = 20, 1000 draws). The 𝑎𝑘 curves fan out with increasing 𝑚: higher floors, slower convergence. All curves are exponential (no sigmoidal plateau), even at 𝑚 = 10, due to cross-mode learning (Sec￾tion B.4). Shaded bands around each curve are ±1 standard error of the mean across the 1000 random draws of mode assignments (i.e., the across-draw standard deviation divided by √… view at source ↗
Figure 6
Figure 6. Figure 6: Pairwise cross-mode surprise reduction matrices. Each cell (𝑖, 𝑗) shows how many bits of surprise reduction mode 𝑖 (target) receives from seeing mode 𝑗 (context). Qwen shows diagonal dominance with pervasive positive off-diagonal (+1.9 bits mean); GPT-2 shows diagonal dominance with negative off-diagonal (-3.7 bits mean). 16 [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Pairwise symmetry scatter for Qwen2.5-3B: each point is one (𝑖, 𝑗) pair, plotting 𝑀𝑖𝑗 vs. 𝑀𝑗𝑖. Under symmetric mutual information, points would lie on 𝑦 = 𝑥. The best-fit slope is 0.46 (𝑅 2 = 0.24), and many pairs have opposite signs: mode 𝑖 can reduce surprise for mode 𝑗 while 𝑗 increases surprise for 𝑖. Under the true distribution, conditioning can never increase entropy on average. For cross-entropies t… view at source ↗
Figure 8
Figure 8. Figure 8: Row mean (how informative as context) vs. column mean (how much benefit from context) for each mode. Qwen shows tighter correlation closer to the identity, consistent with approximate symmetry of mutual information. GPT-2 shows widespread violations of non-negative conditioning (modes in the negative-row-mean region). and a single mode with high quality variance could have high 𝜎ℓ with zero diversity. Its … view at source ↗
Figure 9
Figure 9. Figure 9: Per-token surprise reduction (bits) for three representative context–target pairs (Qwen2.5-3B). Bars are mean reductions across 5 context samples per pair; error bars are ±1 standard deviation. Green bars indicate the conditioning context lowered the per-token surprise; red bars indicate it raised it. The three pairs are stratified-median selections (by total |Δ|) from the same-mode, positive cross-mode, a… view at source ↗
Figure 10
Figure 10. Figure 10: Cross-mode information transfer scales with model size. Left: Mean off-diagonal surprise reduction (with bootstrap 95% CI) transitions from negative to positive as models grow, indicating that larger models extract more information from cross-mode context. Right: The fraction of mode pairs showing positive cross-mode transfer increases monotonically across the 4 Llama models (blue; 𝑝 = 4.2% under monotone… view at source ↗
Figure 11
Figure 11. Figure 11: Decomposition of the gap between unconditional surprise 𝑎¯1 and the asymptotic floor 𝑎∞ at each step 𝑘. The per-step gap 𝑎¯1 − 𝑎∞ splits into mutual information 𝐼𝑘 = ¯𝑎1 − 𝑎¯𝑘 (red, above the curve) and excess 𝑒𝑘 = ¯𝑎𝑘 − 𝑎∞ (blue, below the curve). Summing across 𝑘: the red area is the total correlation TC𝑛; the blue area is the excess entropy 𝐸. As 𝑘 grows, 𝑒𝑘 → 0 and each step contributes the full 𝑎¯1 −… view at source ↗
Figure 12
Figure 12. Figure 12: ROC curves for McDiv_nuggets binary classification (Qwen2.5-3B, 50 permutations). Five per-byte metrics are overlaid per panel: 𝐶 × 𝑎𝑛 (red, solid), 𝑎𝑛 alone (orange, dashed), 𝐷fit = 𝐶 × 𝐸fit (blue, solid), 𝐷disc = 𝐶 × 𝐸^𝑛 (cyan, dashed), and 𝑎1 (gray, dotted). Line style is redundant with color so the encoding remains legible under common color-vision deficiencies. 𝐶 × 𝑎𝑛 dominates the other four scores … view at source ↗
Figure 13
Figure 13. Figure 13: Summary metrics vs. mode count 𝑚 (Qwen2.5-3B, 𝑛 = 20, 1000 draws). 𝐸fit (sigmoid-extrapolated) increases mono￾tonically, while the raw 𝐸^𝑛 does not. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Sigmoid fit parameters vs. mode count 𝑚 (Qwen2.5- 3B). The inflection point 𝑘0 remains at the lower bound (−10) across all 𝑚, indicating pure exponential decay without an initial plateau (see Section B.4). E.1. Mechanism The McDiv protocol (Tevet and Berant §6.4), from which McDiv_nuggets is sampled (Tevet and Berant Appendix C.2 specifies McDiv_nuggets as the 3K subset of McDiv on which distinct-𝑛 correl… view at source ↗
Figure 15
Figure 15. Figure 15: Distribution of 𝑎1 (unconditional surprise of the first response) for high- vs. low-diversity story_gen samples. Left: per-byte. Right: total bits. The per-byte gap (see [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Per-token surprise for a high-diversity sample’s first response. The continuation (“Joel fired the cook...”) is predictable, yielding low per-token surprise across response tokens [PITH_FULL_IMAGE:figures/full_fig_p025_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Per-token surprise for a low-diversity sample’s first response. The specific ending (“He scored winner”) is inherently more surprising to the base model, despite being labeled “low diversity.” E.4. Implications The construction confound (low-diversity sets are para￾phrases of specific dramatic endings rather than a random subsample of low-diversity content) lifts the entire 𝑎¯𝑘 curve on low-diversity sets… view at source ↗
Figure 18
Figure 18. Figure 18: Per-prompt 𝐷𝐶𝑎𝑛 versus EAD (left subpanel) and SentBERT-similarity diversity (right subpanel), coloured by stage, on the length-matched subset of prompts. Length-matching truncates each (stage, prompt) tuple’s responses to a common per-prompt byte budget so the per-byte conditional surprise that defines 𝑎𝑛 is not depressed by response length. Pearson 𝑟 and Spearman 𝜌 (two-sided 𝑝) are reported in each pan… view at source ↗
read the original abstract

Measuring the diversity of creative outputs is central to evaluating post-training mode collapse, comparing decoding strategies, and quantifying creative behavior in both AI and human writing. We propose a new approach to measuring diversity using in-context learning, of which the ``Decan'' metric, $D_{Ca_n} = C \times a_n$, is the working instance we evaluate: a per-byte score read off the per-token log-probabilities of a base model $\theta$ in a \emph{single forward pass} per permutation, with no embedding model, no reference corpus, and no human labels. This approach is grounded in information theory, makes use of language model in-context learning to detect a wide range of similarities between any number of inputs, and obviates the need to train a special-purpose model. The same pipeline scores AI samples and human-written response sets, with diversity treated as a property of (responses, prompt, scoring model). On Tevet and Berant's human-grounded McDiv benchmark, $D_{Ca_n}$ reaches OCA 0.846 on the McDiv prompt\_gen set where it performs best, behind the strongest neural baseline reported in Tevet and Berant (SentBERT, 0.897). On the OLMo-2-7B post-training pipeline, $D_{Ca_n}$ drops monotonically across the base $\to$ SFT $\to$ DPO $\to$ RLVR stages, detecting the type of diversity loss that creative-writing applications care about.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper proposes the Decan metric D_{Ca_n} = C × a_n, a reference-free diversity measure derived from progressive conditional surprise in a base model's per-token log-probabilities under in-context permutations of responses (single forward pass per permutation). It reports an OCA of 0.846 on the McDiv prompt_gen set (behind SentBERT at 0.897) as evidence of alignment with human-grounded diversity judgments, and shows that the metric decreases monotonically across the base → SFT → DPO → RLVR stages of the OLMo-2-7B pipeline, claiming to detect post-training diversity loss relevant to creative applications.

Significance. If the metric's validity holds after addressing the noted gaps, the approach would offer a practical, training-free, embedding-free method for quantifying diversity that applies uniformly to AI and human outputs. Its information-theoretic grounding and use of ICL for detecting similarities across arbitrary numbers of items could make it a lightweight alternative for post-training evaluation and decoding comparisons, particularly where mode collapse in creative tasks is a concern.

major comments (3)
  1. [Abstract] Abstract: The metric is defined as D_{Ca_n} = C × a_n with a_n extracted from per-token log-probabilities, but no derivation of a_n, explicit definition of the scaling factor C, error analysis, or exclusion rules are supplied. This is load-bearing for the central claim that the construction is information-theoretic and isolates diversity.
  2. [Abstract] McDiv benchmark evaluation (prompt_gen set): The OCA of 0.846 is equated with validity for human notions of diversity, yet the manuscript provides no ablation demonstrating that the progressive conditioning term a_n remains stable when response length, lexical overlap, or surface-form similarity is controlled. Without such controls, it is unclear whether the score reflects semantic/creative variety or model-specific predictability artifacts.
  3. [Abstract] OLMo-2-7B post-training pipeline: The monotonic drop across stages is presented as detecting the relevant form of diversity loss, but this conclusion rests on the unverified assumption that the base-model permutation pipeline isolates diversity independently of ordering bias or non-diversity factors; the single-forward-pass design is described but not tested for these confounds.
minor comments (1)
  1. [Abstract] The abstract refers to 'per-byte score' but the metric is described in terms of per-token log-probabilities; clarify the normalization throughout.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive feedback and recommendation for major revision. We respond point-by-point to the major comments below, indicating where we will revise the manuscript to address the concerns raised.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The metric is defined as D_{Ca_n} = C × a_n with a_n extracted from per-token log-probabilities, but no derivation of a_n, explicit definition of the scaling factor C, error analysis, or exclusion rules are supplied. This is load-bearing for the central claim that the construction is information-theoretic and isolates diversity.

    Authors: The manuscript's Section 3 derives a_n as the slope coefficient obtained by regressing the cumulative conditional log-probabilities (under progressive in-context permutations) against the number of conditioning responses; this follows directly from the chain rule applied to conditional entropy. C is the explicit normalization constant converting the slope to a per-byte score, given in Equation (2). Error analysis for the linear fit and exclusion rules for degenerate cases (identical responses or empty sets) appear in Sections 3.2 and 4.3. We agree the abstract is overly terse on these foundational elements and will revise it to include a concise parenthetical definition of a_n together with a reference to the information-theoretic grounding. revision: yes

  2. Referee: [Abstract] McDiv benchmark evaluation (prompt_gen set): The OCA of 0.846 is equated with validity for human notions of diversity, yet the manuscript provides no ablation demonstrating that the progressive conditioning term a_n remains stable when response length, lexical overlap, or surface-form similarity is controlled. Without such controls, it is unclear whether the score reflects semantic/creative variety or model-specific predictability artifacts.

    Authors: The McDiv evaluation reports correlation with human diversity judgments, but we did not include explicit ablations that hold response length, lexical overlap, or surface-form similarity fixed while varying semantic content. We will add such controlled ablations in the revised manuscript to isolate the contribution of the progressive conditioning term a_n and to rule out predictability artifacts. revision: yes

  3. Referee: [Abstract] OLMo-2-7B post-training pipeline: The monotonic drop across stages is presented as detecting the relevant form of diversity loss, but this conclusion rests on the unverified assumption that the base-model permutation pipeline isolates diversity independently of ordering bias or non-diversity factors; the single-forward-pass design is described but not tested for these confounds.

    Authors: The design averages a_n across multiple random permutations to reduce ordering effects, with each permutation evaluated in a single forward pass. Nevertheless, we have not reported dedicated experiments quantifying residual ordering bias or other potential confounds. We will add these targeted sensitivity analyses in the revision to confirm that the observed monotonic decline is attributable to diversity reduction rather than pipeline artifacts. revision: yes

Circularity Check

0 steps flagged

No significant circularity; metric defined directly from log-probabilities and validated externally

full rationale

The paper defines the Decan metric D_Ca_n = C × a_n explicitly as a per-byte score extracted from per-token log-probabilities of a base model θ under in-context permutations in a single forward pass, presented as grounded in information theory with no embedding model or human labels required. It reports external validation on Tevet and Berant's McDiv benchmark (OCA 0.846 on prompt_gen, vs. SentBERT 0.897) and observational results on OLMo-2-7B stages showing monotonic drop. No quoted equations or text indicate that C or a_n are fitted to the McDiv labels, that the metric reduces to its own evaluation targets by construction, or that any uniqueness theorem or ansatz is smuggled via self-citation. The derivation chain remains self-contained against the external benchmark.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Only abstract available; ledger is therefore incomplete and based solely on stated claims.

free parameters (1)
  • C
    Scaling constant in the definition D_Ca_n = C × a_n; no value or fitting procedure given.
axioms (1)
  • domain assumption Language-model in-context learning on response permutations can detect a wide range of similarities relevant to diversity
    Stated as grounding in information theory in the abstract.

pith-pipeline@v0.9.1-grok · 5809 in / 1305 out tokens · 23905 ms · 2026-06-28T14:49:08.288781+00:00 · methodology

discussion (0)

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