Attribution Rollout in Process-Based Systems

• Attribution Rollout is a framework that assigns influence along trajectories of generative, routing, or causal processes to enhance model performance.
• It is applied in diverse settings including PPO post-training, generative explanations, hierarchical AI routing, web-enabled search, and advertising incrementality.
• Key methods involve gradient dot product filtering, explicit attribution contracts, hierarchical routing weights, citation trace auditing, and causal incrementality models.

Attribution Rollout denotes a class of attribution procedures defined over a process rather than a static example. In contemporary usage, the term is applied to at least five distinct settings: PPO-based LLM post-training, where generated episodes in a rollout buffer are scored by their alignment with a held-out validation objective; feature attribution for generative LLMs, where attribution is rolled along an autoregressive or diffusion process under an explicit explanatory contract; hierarchical compound AI systems, where routing weights are propagated from root to leaf to yield multi-resolution component attribution; web-enabled LLM search, where retrieval traces and citations are audited to measure an attribution gap; and advertising systems, where experimental lift estimates are rolled through bidding and conversion attribution pipelines (Shu et al., 2 Apr 2026, Nguyen, 21 May 2026, Armstrong, 19 May 2026, Strauss et al., 27 Jun 2025, Lewis et al., 2022). Taken together, these usages suggest a common structural idea: attribution depends on the generative, routing, retrieval, or causal process through which outputs are produced.

1. Shared structure across attribution rollout settings

Across the cited literatures, the rolled object is not the same, but the operational pattern is closely related. Attribution is assigned to units that lie along a trajectory, chain, or hierarchy, and the attribution rule is defined relative to an explicit score, objective, or observable process state.

Setting	Rolled object	Attributed quantity
PPO post-training	rollout-buffer episodes	influence on validation-aligned policy update
Generative explanation	autoregressive or diffusion chain	feature contribution under a specified contract
Compound AI routing	root-to-leaf hierarchy	deployed trust over nodes or leaves
LLM search	retrieval and citation trace	grounded source credit and uncited gap
Advertising incrementality	exposure and conversion timeline	causal contribution to conversion and bid value

A central distinction among these usages is whether attribution is counterfactual, descriptive, or optimization-oriented. PPO-based attribution rollout is optimization-oriented, because episodes are filtered before parameter updates. The Attribution Contract framework is explanatory, because it specifies what output, feature set, and generative process an attribution claim refers to. BOHM is descriptive of deployed routing trust rather than of coalition marginal contributions. Search attribution is an observability and accountability problem centered on source consumption versus source citation. Incrementality attribution is causal, tying attribution to randomized variation and potential outcomes. This suggests that “attribution rollout” is not a single algorithmic primitive, but a recurrent design pattern adapted to different process models.

2. PPO-based LLM post-training and attribution-refined buffers

In PPO-based LLM post-training, attribution rollout refers to computing, for every generated episode in the rollout buffer, a scalar influence score that measures whether the PPO gradient induced by that episode is aligned or anti-aligned with a validation gradient derived from human-preferred chain-of-thought completions (Shu et al., 2 Apr 2026). The validation gradient is

$$\bar g_{\mathrm{val}}=\nabla_\theta \mathcal{L}_{\mathrm{SFT}}(\mathcal{D}_{\mathrm{val}},\theta_\tau),$$

and the per-episode PPO gradient is

$$g_{\mathrm{train}}^{(i)}=\nabla_\theta \mathcal{L}_{\mathrm{PPO}}(z_i,\theta_\tau).$$

The influence score is the gradient dot product

$$\mathrm{Score}(z_i)=g_{\mathrm{train}}^{(i)}\cdot \bar g_{\mathrm{val}}.$$

Episodes with $\mathrm{Score}(z_i)\le 0$ are filtered out, and retained episodes are reweighted by

$$w_i=\frac{\mathrm{Score}(z_i)}{\frac{1}{|\mathcal D'|}\sum_{z_j\in \mathcal D'} \mathrm{Score}(z_j)}.$$

The episode definition is

$$z_i=(x,y_i,r_i,\{V_\psi(s_t)\}_{t=1}^T,\{\hat A_t\}_{t=1}^T).$$

At each training iteration, the actor samples $n=8$ responses per prompt over 64 prompts, filling a rollout buffer of capacity 512 episodes. Influence scores are recomputed every iteration. If no positive-score episodes remain, training stops early. PPO optimization then proceeds for 2 epochs over the refined buffer, with KL early stopping if mean KL exceeds 1.5; policy and critic are updated with AdamW at learning rate $1\times 10^{-6}$.

The stated motivation is that PPO buffers often contain noisy or unfaithful reasoning, including correct answers reached through flawed logic, nonsensical steps, or shortcuts. Filtering by gradient alignment changes the buffer from a raw collection of self-generated episodes into an attribution-refined buffer. The method uses only gradient dot products; no Hessian-vector products or Fisher approximations are required. Early iterations incur higher overhead, but later iterations become cheaper as more episodes receive negative scores and are pruned, yielding dynamic buffer shrinkage and intrinsic early stopping.

Reported results show consistent improvements over SFT and PPO baselines on Math, Science, and social commonsense tasks. On GSM8K with Rho-1B, PPO reached MV 50.05, EM 41.11, PK 73.09, whereas I-PPO reached MV 51.93$(\pm0.56)$, EM 46.10$(\pm0.73)$, PK 74.83$$g_{\mathrm{train}}^{(i)}=\nabla_\theta \mathcal{L}_{\mathrm{PPO}}(z_i,\theta_\tau).$$0. On GSM8K with Gemma-2-2B, PPO reached MV 72.94, EM 63.98, PK 84.39, whereas I-PPO reached MV 75.04$$g_{\mathrm{train}}^{(i)}=\nabla_\theta \mathcal{L}_{\mathrm{PPO}}(z_i,\theta_\tau).$$1, EM 68.41$$g_{\mathrm{train}}^{(i)}=\nabla_\theta \mathcal{L}_{\mathrm{PPO}}(z_i,\theta_\tau).$$2, PK 85.23$$g_{\mathrm{train}}^{(i)}=\nabla_\theta \mathcal{L}_{\mathrm{PPO}}(z_i,\theta_\tau).$$3. On MATH with Phi-3-4B, PPO reached MV 49.86, EM 41.40, PK 65.40, whereas I-PPO reached MV 52.91$$g_{\mathrm{train}}^{(i)}=\nabla_\theta \mathcal{L}_{\mathrm{PPO}}(z_i,\theta_\tau).$$4, EM 46.46$$g_{\mathrm{train}}^{(i)}=\nabla_\theta \mathcal{L}_{\mathrm{PPO}}(z_i,\theta_\tau).$$5, PK 67.50$$g_{\mathrm{train}}^{(i)}=\nabla_\theta \mathcal{L}_{\mathrm{PPO}}(z_i,\theta_\tau).$$6. The paper notes that PK sometimes saturates and that PPO can marginally exceed I-PPO on PK in a few cases, while MV and EM still favor I-PPO.

The paper further reports a reduction of unfaithful chain-of-thought. Automated labels for false positives, nonsensical reasoning, reasoning shortcuts, and logic-following errors achieved a 93% exact match with human annotators. Negative-influence episodes exhibited markedly higher rates of unfaithful patterns than positive-influence episodes; for Rho-1B on Math, negative false positives were 9.10% versus positive false positives at 3.61%, and negative reasoning shortcuts were 30.43% versus positive reasoning shortcuts at 18.79%. This supports the claim that attribution filtering removes many unfaithful reasoning trajectories that are not eliminated by outcome-based rewards alone. The main stated limitations are dependence on validation-set quality, risk of overfitting to the validation distribution, possible robustness loss under domain shift, and added compute for influence scoring.

3. Attribution Contract and rollout over generative processes

For generative LLMs, attribution rollout is formalized through the Attribution Contract, a tuple

$$g_{\mathrm{train}}^{(i)}=\nabla_\theta \mathcal{L}_{\mathrm{PPO}}(z_i,\theta_\tau).$$7

where $$g_{\mathrm{train}}^{(i)}=\nabla_\theta \mathcal{L}_{\mathrm{PPO}}(z_i,\theta_\tau).$$8 is the model score, $$g_{\mathrm{train}}^{(i)}=\nabla_\theta \mathcal{L}_{\mathrm{PPO}}(z_i,\theta_\tau).$$9 is what is held fixed, $$\mathrm{Score}(z_i)=g_{\mathrm{train}}^{(i)}\cdot \bar g_{\mathrm{val}}.$$0 is the output being explained, $$\mathrm{Score}(z_i)=g_{\mathrm{train}}^{(i)}\cdot \bar g_{\mathrm{val}}.$$1 is the generative process, and $$\mathrm{Score}(z_i)=g_{\mathrm{train}}^{(i)}\cdot \bar g_{\mathrm{val}}.$$2 is the set of eligible features (Nguyen, 21 May 2026). The tuple is read in order as SCOPE. The paper’s central claim is that feature-attribution methods in generative LLMs should be evaluated as method–contract pairs, because the same method can answer different questions under different contracts.

In autoregressive models, the generative process is

$$\mathrm{Score}(z_i)=g_{\mathrm{train}}^{(i)}\cdot \bar g_{\mathrm{val}}.$$3

with scores such as

$$\mathrm{Score}(z_i)=g_{\mathrm{train}}^{(i)}\cdot \bar g_{\mathrm{val}}.$$4

for a local next-token explanation, or

$$\mathrm{Score}(z_i)=g_{\mathrm{train}}^{(i)}\cdot \bar g_{\mathrm{val}}.$$5

for a sequence-level explanation. Under a local next-token contract, eligible features can include both prompt tokens and generated-prefix tokens. Under a prompt-conditioned token contract, the generated prefix is held fixed in the forward pass but removed from the attribution path, so only prompt tokens are eligible. Under a span-level prompt contract, the full output span is held fixed and the attribution target is the sequence score, aggregated across timesteps.

The paper identifies the self-attribution fallacy as a recurrent interpretive error. Attribution mass on generated-prefix tokens is informative when the question is “which available context features helped predict $$\mathrm{Score}(z_i)=g_{\mathrm{train}}^{(i)}\cdot \bar g_{\mathrm{val}}.$$6?”, because the prefix is an actual input to the next-token distribution. It becomes misleading when that same map is read as a prompt-level explanation of the semantic origin of the final response. The issue is therefore not merely algorithmic; it is contractual.

In diffusion LLMs, the process is represented as

$$\mathrm{Score}(z_i)=g_{\mathrm{train}}^{(i)}\cdot \bar g_{\mathrm{val}}.$$7

The paper distinguishes at least three contracts. State-level attribution explains an intermediate state $$\mathrm{Score}(z_i)=g_{\mathrm{train}}^{(i)}\cdot \bar g_{\mathrm{val}}.$$8 in terms of prompt features and prior states. Denoising-stage attribution assigns importance to stages rather than tokens, using the counterfactual score

$$\mathrm{Score}(z_i)=g_{\mathrm{train}}^{(i)}\cdot \bar g_{\mathrm{val}}.$$9

Prompt-to-output attribution explains the final output $\mathrm{Score}(z_i)\le 0$0 in terms of prompt features propagated through the entire denoising chain. A key point is that the marginal $\mathrm{Score}(z_i)\le 0$1 does not decompose over denoising stages in the way autoregressive likelihood decomposes over next-token factors, so stage-level perturbation is required.

Evaluation is likewise contract-specific. Local next-token attribution is tested by perturbing prompt and prefix tokens and measuring the change in $\mathrm{Score}(z_i)\le 0$2. Prompt-conditioned token attribution perturbs prompt tokens while keeping $\mathrm{Score}(z_i)\le 0$3 fixed. Span-level attribution perturbs prompt tokens while rescoring the fixed output $\mathrm{Score}(z_i)\le 0$4. Diffusion state-level attribution perturbs prompt features or earlier states and measures the change in $\mathrm{Score}(z_i)\le 0$5, whereas denoising-stage attribution perturbs stages directly and measures $\mathrm{Score}(z_i)\le 0$6. The paper’s broader significance lies in relocating disagreement from attribution algorithms to unstated explanatory contracts.

4. Hierarchical attribution rollout in compound AI systems

For compound AI systems, attribution rollout is instantiated as BOHM, a zero-cost hierarchical attribution method for systems that route tasks through a rooted tree of specialized components (Armstrong, 19 May 2026). Each router $\mathrm{Score}(z_i)\le 0$7 maintains row-stochastic routing weights over its children, $\mathrm{Score}(z_i)\le 0$8 with $\mathrm{Score}(z_i)\le 0$9. BOHM interprets these weights as deployed trust assignments and extracts attribution directly from them, without coalition ablations.

Leaf attribution is defined by the path product

$$w_i=\frac{\mathrm{Score}(z_i)}{\frac{1}{|\mathcal D'|}\sum_{z_j\in \mathcal D'} \mathrm{Score}(z_j)}.$$0

where $$w_i=\frac{\mathrm{Score}(z_i)}{\frac{1}{|\mathcal D'|}\sum_{z_j\in \mathcal D'} \mathrm{Score}(z_j)}.$$1 is the root-to-leaf path. Level-$$w_i=\frac{\mathrm{Score}(z_i)}{\frac{1}{|\mathcal D'|}\sum_{z_j\in \mathcal D'} \mathrm{Score}(z_j)}.$$2 attribution for a node $$w_i=\frac{\mathrm{Score}(z_i)}{\frac{1}{|\mathcal D'|}\sum_{z_j\in \mathcal D'} \mathrm{Score}(z_j)}.$$3 at depth $$w_i=\frac{\mathrm{Score}(z_i)}{\frac{1}{|\mathcal D'|}\sum_{z_j\in \mathcal D'} \mathrm{Score}(z_j)}.$$4 is

$$w_i=\frac{\mathrm{Score}(z_i)}{\frac{1}{|\mathcal D'|}\sum_{z_j\in \mathcal D'} \mathrm{Score}(z_j)}.$$5

The matrix formulation is

$$w_i=\frac{\mathrm{Score}(z_i)}{\frac{1}{|\mathcal D'|}\sum_{z_j\in \mathcal D'} \mathrm{Score}(z_j)}.$$6

and for leaves at depth $$w_i=\frac{\mathrm{Score}(z_i)}{\frac{1}{|\mathcal D'|}\sum_{z_j\in \mathcal D'} \mathrm{Score}(z_j)}.$$7,

$$w_i=\frac{\mathrm{Score}(z_i)}{\frac{1}{|\mathcal D'|}\sum_{z_j\in \mathcal D'} \mathrm{Score}(z_j)}.$$8

Under row-stochastic routing, the depth-$$w_i=\frac{\mathrm{Score}(z_i)}{\frac{1}{|\mathcal D'|}\sum_{z_j\in \mathcal D'} \mathrm{Score}(z_j)}.$$9 distribution sums to 1, and BOHM satisfies efficiency. The paper further states monotonicity and symmetry at equilibrium, weak suppression for below-average children, and non-satisfaction of Shapley additivity.

BOHM is explicitly positioned against SHAP. SHAP asks for counterfactual marginal contributions under a coalition value function $$z_i=(x,y_i,r_i,\{V_\psi(s_t)\}_{t=1}^T,\{\hat A_t\}_{t=1}^T).$$0 and requires evaluation on arbitrary subsets of components. BOHM asks what trust assignment the deployed hierarchical router currently expresses. The two are therefore said to answer different questions. Convergence is expected when the router is near-optimal, with weights monotone in true component quality. Disagreements are treated as diagnostic of routing suboptimality or of mismatch introduced by re-prompting a different orchestrator during coalition evaluation.

The reported empirical cost difference is substantial. On 18 LLMs in a 3-level hierarchy over 880 LiveCodeBench problems, BOHM yields seed-averaged Kendall $$z_i=(x,y_i,r_i,\{V_\psi(s_t)\}_{t=1}^T,\{\hat A_t\}_{t=1}^T).$$1, while SHAP reaches $$z_i=(x,y_i,r_i,\{V_\psi(s_t)\}_{t=1}^T,\{\hat A_t\}_{t=1}^T).$$2 at approximately 9,000x more coalition evaluations per seed. In a 5-driver, 7-benchmark agentic study covering 35 cells, deployed routing concentrated on a single tool with top-share median 0.65 and range 0.39–1.00. Cell-level $$z_i=(x,y_i,r_i,\{V_\psi(s_t)\}_{t=1}^T,\{\hat A_t\}_{t=1}^T).$$3 ranged from $$z_i=(x,y_i,r_i,\{V_\psi(s_t)\}_{t=1}^T,\{\hat A_t\}_{t=1}^T).$$4 to $$z_i=(x,y_i,r_i,\{V_\psi(s_t)\}_{t=1}^T,\{\hat A_t\}_{t=1}^T).$$5, and the mean agreement was +0.22 when the driver’s top pick was the empirically best tool, versus approximately +0.01 otherwise. On a 4-level US Census hierarchy with 475 leaves, BOHM recovered ground-truth rankings at every level simultaneously, with Kendall $$z_i=(x,y_i,r_i,\{V_\psi(s_t)\}_{t=1}^T,\{\hat A_t\}_{t=1}^T).$$6 up to 0.722 at Division level, 0.533 at State level, and 0.686 at PUMA level.

The method’s scope is limited to hierarchical systems with stateful routing weights. It does not replace feature attribution methods and does not apply to architectures that expose only token-conditional gating without state across rounds unless wrapped by a stateful substrate. The paper also stresses sensitivity to hierarchy design: misaligned tiering can degrade attribution, while disagreements with SHAP can be operationally useful because they expose router or tool mismatch.

5. Retrieval-to-citation rollout in web-enabled LLM search

In web-enabled LLM search, attribution rollout is operationalized as an end-to-end accounting of what sources were consumed, which of those sources were cited, and how much relevant material remained uncited (Strauss et al., 27 Jun 2025). The central metric is the attribution gap. For query $$z_i=(x,y_i,r_i,\{V_\psi(s_t)\}_{t=1}^T,\{\hat A_t\}_{t=1}^T).$$7, let $$z_i=(x,y_i,r_i,\{V_\psi(s_t)\}_{t=1}^T,\{\hat A_t\}_{t=1}^T).$$8 denote the count of unique relevant pages visited from the search log and $$z_i=(x,y_i,r_i,\{V_\psi(s_t)\}_{t=1}^T,\{\hat A_t\}_{t=1}^T).$$9 the count of unique grounded citations appearing in the answer and also in the search log. Then

$n=8$0

and the aggregate mean gap is

$n=8$1

Citation efficiency is defined as

$n=8$2

the marginal citations produced per additional relevant web page visited.

The empirical study used approximately 14,000 LMArena conversation logs covering approximately 7,000 queries and 11 search-enabled LLM variants, with a final analytic sample of $n=8$3 observations from March–April 2025. Relevant pages visited were all URLs in the model’s search trace; grounded citations were in-text URLs that also appeared in the search trace, after excluding hallucinated and ungrounded citations and deduplicating to base URLs. Reported no-search rates in search mode were approximately 34% for Gemini, 24% for GPT-4o, and 15.6% overall. Reported no-citation rates were approximately 92% of answers for Gemini and approximately 30% overall. Sonar displayed a high-volume, low-credit pattern, with a median of approximately 10 relevant pages visited per query but only approximately 3–5 citations, giving a median gap of approximately 5.

To model uncited relevant pages, the paper uses a hurdle model with a zero component for perfect-match probability and a negative binomial count component for positive gaps. At median conditions, the expected total gap was approximately 3.04 for Gemini, 3.12 for Sonar, and 0.18 for GPT-4o, with the paper arguing that GPT-4o’s tiny gap is best explained by selective log disclosures rather than better attribution. The probability of a gap was approximately 10.5% for GPT-4o, 70.3% for Gemini, and 99.3% for Sonar. The citation-efficiency slope $n=8$4 ranged approximately from 0.19 to 0.45 across models. In the count stage, each additional web page read inflated expected uncited count by approximately 13% and doubling logged response length reduced expected missing citations by approximately 11%.

The architecture proposed for robust source attribution is based on standardized telemetry and full trace disclosure. The paper recommends OpenTelemetry GenAI semantic conventions, stable source identifiers such as canonical URLs and URL hashes, retrieval spans recording scores, ranks, actions, timestamps, robots and license flags, generation spans listing context documents used, and citation spans recording clickable citations, grounding status, and deduplication notes. A citation should count as grounded only if its canonical URL or hash appears in the retrieval log for the same query. The production rule for relevance is to treat as relevant any retrieved document whose retrieval score exceeds a threshold $n=8$5 or falls within top-$n=8$6 at a retrieval step, while logging both the raw score and the threshold decision.

A major controversy in this area concerns observability rather than attribution mathematics. The paper argues that selective log disclosure can produce apparently small attribution gaps without genuinely better source credit. It therefore treats trace completeness as foundational. This differs from the generative-feature setting, where the main controversy is contractual interpretation, and from BOHM, where the principal distinction is between deployed trust and coalition marginal contribution.

6. Incrementality, bidding, and causal attribution rollout

In advertising, attribution rollout is grounded in incrementality: the causal effect of showing an ad versus not showing it (Lewis et al., 2022). The potential-outcomes framework is explicit. With treatment $n=8$7 and conversion outcome $n=8$8, the average treatment effect is

$n=8$9

and the conditional average treatment effect is

$1\times 10^{-6}$0

The paper links causal lift directly to bidding and attribution. In the simplest model with exposure counts $1\times 10^{-6}$1,

$1\times 10^{-6}$2

An impression should be bought when

$1\times 10^{-6}$3

where $1\times 10^{-6}$4 is value per conversion and $1\times 10^{-6}$5 is margin.

The paper’s core dynamic model is continuous-time ad stock. For impression $1\times 10^{-6}$6 at time $1\times 10^{-6}$7,

$1\times 10^{-6}$8

and heterogeneous effects are modeled as

$1\times 10^{-6}$9

Time-integrated incremental value is

$(\pm0.56)$0

This is the basis for real-time bidding, scoring, and subsequent attribution of conversions to impressions.

The identification strategy centers on experimentation and instrumental variables. Recommended randomization schemes include auction-level or bid-level randomization, user-level holdouts, geo or time splits, budget-based randomization, and creative or campaign randomization. Ghost bids and predicted win probabilities are used to form instruments. Standard causal estimators such as IPW and doubly robust estimators are described for settings in which IV is not feasible, and Hausman Causal Correction is proposed as a production-oriented compromise between correlational and IV estimates.

Conversion attribution is formulated as an incrementality share. At conversion time $(\pm0.56)$1, the impression-level share is

$(\pm0.56)$2

These shares add to user-level incremental contribution across impressions. The paper further connects this causal attribution layer to economic metrics such as CPiC, CPIA, and iROAS, and to off-policy evaluation via IPS, self-normalized IPS, and doubly robust OPE. The proposed rollout plan spans data foundation, offline validation and simulation, shadow mode, controlled experiments, gradual ramp, and post-launch monitoring, with explicit guardrails for interference, first-stage strength, price calibration, and variance control.

Taken together, these literatures show that attribution rollout is best understood as process-indexed attribution. In PPO post-training, the process is a policy-improvement loop over self-generated episodes; in generative explanation, it is an autoregressive or diffusion chain; in compound AI, it is a routing hierarchy; in search systems, it is a retrieval-to-citation trace; and in advertising, it is a randomized exposure-to-conversion timeline. The recurrent methodological lesson is that attribution is only as well-defined as the process model, held-fixed assumptions, and observability regime that support it.