Multi-Attribution Benchmark (MAC)

Updated 13 July 2026

The paper introduces multiple attribution mechanisms to enrich CVR prediction, enabling models to learn from diverse conversion signals.
MAC is a public dataset with click-level labels from last-click, first-click, linear, and DDA mechanisms to support multi-attribution learning.
MoAE uses a mixture of experts with asymmetric transfer to effectively fuse auxiliary signals, outperforming single-attribution baselines.

The Multi-Attribution Benchmark (MAC) is a public benchmark for conversion rate (CVR) prediction under multiple attribution mechanisms, introduced to support multi-attribution learning (MAL) in advertising systems (Wu et al., 2 Mar 2026). In MAC, each click is annotated with attribution weights and derived binary conversion labels under four mechanisms—last-click, first-click, linear, and data-driven attribution (DDA)—so that one mechanism can be treated as the primary target while the others provide auxiliary supervision (Wu et al., 2 Mar 2026). The benchmark was released together with PyMAL, an open-source library of baseline methods, and the accompanying study proposes Mixture of Asymmetric Experts (MoAE) as an MAL architecture motivated by empirical findings on objective design, auxiliary-task selection, and knowledge transfer (Wu et al., 2 Mar 2026).

1. Conceptual role in CVR prediction

CVR prediction determines how ad platforms bid, allocate traffic, and optimize revenue (Wu et al., 2 Mar 2026). In deployed systems, conversion labels are not intrinsic observations but are generated by an attribution mechanism, namely the rule that allocates credit for a conversion to one or more user touchpoints, typically ad clicks (Wu et al., 2 Mar 2026). Nearly all public CVR datasets and most published models assume a single attribution mechanism, such as last-click, which limits learning to one view of touchpoint contribution (Wu et al., 2 Mar 2026).

MAC was introduced to close this data gap by providing the first public CVR dataset featuring labels from multiple attribution mechanisms, specifically last-click, first-click, linear, and DDA (Wu et al., 2 Mar 2026). This benchmark is designed for MAL, a paradigm in which models jointly learn from conversion signals produced under multiple attribution mechanisms (Wu et al., 2 Mar 2026). By integrating supervision from different attribution views, MAL is intended to learn a richer representation of user intent and path contributions and to improve performance on a chosen system target mechanism (Wu et al., 2 Mar 2026).

The benchmark’s scope is explicitly click-level. This matters because attribution rules operate over user paths, whereas the learning task in MAC is formulated over individual click instances with mechanism-specific labels and, optionally, mechanism-specific positive sample weights (Wu et al., 2 Mar 2026). This click-level design makes systematic comparison of single-target and multi-attribution objectives possible under a unified protocol.

2. Formalization of attribution and MAL

MAC formalizes a user’s ad exposure path as

$P_i = \{(e_{i,1}, t_{i,1}), \ldots, (e_{i,m_i}, t_{i,m_i})\},$

where $e_{i,j}$ is the $j$ -th clicked ad for a specific item at timestamp $t_{i,j}$ (Wu et al., 2 Mar 2026). A binary variable $c_i \in \{0,1\}$ indicates whether a conversion occurred, and $t_i^c$ denotes the conversion time when $c_i=1$ (Wu et al., 2 Mar 2026). An attribution mechanism $a \in A$ maps the path $P_i$ and, when applicable, the conversion event into attribution labels for clicks within a fixed attribution window; MAC uses direct conversion attribution, meaning that conversions are attributed only to clicks on ads for the same item (Wu et al., 2 Mar 2026).

For each click instance $x$ , mechanism $e_{i,j}$ 0 assigns an attribution weight $e_{i,j}$ 1 (Wu et al., 2 Mar 2026). The corresponding binary mechanism-specific label is

$e_{i,j}$ 2

with positivity defined by $e_{i,j}$ 3 and negativity by $e_{i,j}$ 4 (Wu et al., 2 Mar 2026). The weights can also be used as per-sample importance weights for positive examples (Wu et al., 2 Mar 2026).

The four attribution mechanisms in MAC are defined as follows (Wu et al., 2 Mar 2026):

Last-click: if a conversion occurs, 100% of the attribution weight is assigned to the final click preceding the conversion.
First-click: if a conversion occurs, 100% of the attribution weight is assigned to the first click.
Linear: if a conversion occurs, the unit credit is split uniformly across all clicks in the path that are deemed part of the conversion under the attribution window.
DDA: attribution weights are learned via a causal inference model; MAC uses CausalMTA.

Given click-level features $e_{i,j}$ 5, an MAL model predicts a probability $e_{i,j}$ 6 for each mechanism $e_{i,j}$ 7 (Wu et al., 2 Mar 2026). The per-mechanism binary cross-entropy is

$e_{i,j}$ 8

and the overall MAL objective is

$e_{i,j}$ 9

where $j$ 0 is the primary target mechanism and the remaining mechanisms act as auxiliary tasks (Wu et al., 2 Mar 2026). In the reported experiments, a single coefficient $j$ 1 is tuned and shared across auxiliary tasks; the paper also tests dynamic weighting through GCS but reports no significant gains over fixed $j$ 2 in this setting (Wu et al., 2 Mar 2026).

MAC also studies a Cartesian-style auxiliary target (CAT), which converts the $j$ 3 binary attribution labels for a click into a single $j$ 4-class label using little-endian binary encoding:

$j$ 5

CAT is trained with softmax cross-entropy and is used to enrich the representation for the primary task; its logits are not used directly at inference time (Wu et al., 2 Mar 2026).

3. Dataset composition and schema

MAC is sourced from the Taobao advertising system operated by Alibaba and spans 21 consecutive days of traffic (Wu et al., 2 Mar 2026). The data are obtained through stratified user sampling, with higher rates for highly active users, in order to keep the release at a manageable academic scale (Wu et al., 2 Mar 2026). The dataset is rigorously anonymized, all identifiers are irreversibly hashed, and the logs are historical rather than real-time operational metrics (Wu et al., 2 Mar 2026).

The reported dataset statistics are as follows (Wu et al., 2 Mar 2026):

Component	Value
Users	0.8 million
Clicks	79 million
Items	15.1 million in the main table; 9.6 million distinct items in the text

The paper explicitly contains the two item figures above and does not resolve the discrepancy (Wu et al., 2 Mar 2026).

Positive ratios, defined as the fraction of clicks with $j$ 6, vary substantially by mechanism (Wu et al., 2 Mar 2026):

Attribution mechanism	Positive ratio
Last-click	1.6%
First-click	1.8%
DDA	4.3%
Linear	5.3%

MAC combines several feature modalities (Wu et al., 2 Mar 2026). The categorical schema includes 7 user features, 10 item features, and 3 context features. The user features include user ID and profile features; the item features include item, shop, category, and adgroup IDs; and the context features include ad scenario ID (Wu et al., 2 Mar 2026). In addition, MAC includes a user purchase-item behavior sequence truncated to a maximum length of 20 (Wu et al., 2 Mar 2026). For each item in that sequence, the data include item, shop, and category IDs, together with a visual similarity score to the target advertised item (Wu et al., 2 Mar 2026). The visual features used to compute that similarity come from an image encoder pre-trained via contrastive learning (Wu et al., 2 Mar 2026).

The label schema is unusually rich for public CVR data. For every click, MAC provides continuous attribution weights under all four mechanisms, and the binary labels $j$ 7 are derived by thresholding those weights at zero (Wu et al., 2 Mar 2026). This permits both binary target construction and weighted positive training/evaluation.

The temporal split is also fixed. The last day serves as the test set, while preceding days are used for training (Wu et al., 2 Mar 2026). Validation is defined by training the model up to day $j$ 8 and evaluating it on day $j$ 9 (Wu et al., 2 Mar 2026). All models are trained for one epoch with Adam, batch size 4096, and a grid search over learning rates $t_{i,j}$ 0 scaled by $t_{i,j}$ 1 (Wu et al., 2 Mar 2026).

4. Tasks, evaluation protocol, and objective complexity

The primary tasks in MAC are CVR prediction under a chosen target attribution mechanism

$t_{i,j}$ 2

with the remaining mechanisms available as auxiliary tasks (Wu et al., 2 Mar 2026). Positive samples are clicks satisfying $t_{i,j}$ 3 for the relevant mechanism, and the continuous positive weights may be used as importance weights; negative samples are clicks with zero attribution weight (Wu et al., 2 Mar 2026).

Evaluation centers on AUC and GAUC (Wu et al., 2 Mar 2026). The global AUC is defined as

$t_{i,j}$ 4

while group AUC, the primary metric, is

$t_{i,j}$ 5

The use of GAUC reflects within-user ranking quality and is presented as more aligned with the operational setting (Wu et al., 2 Mar 2026). Although log loss is sometimes mentioned in surrounding discussions, the paper uses binary cross-entropy, and PR-AUC is not reported (Wu et al., 2 Mar 2026).

A central analytical construct in the MAC study is “objective complexity,” defined as the number and diversity of auxiliary objectives included, such as the addition of first-click, last-click, linear, DDA, and CAT (Wu et al., 2 Mar 2026). Empirically, performance usually scales with higher objective complexity, but the first-click target setting is an exception: some auxiliary objectives become counterproductive (Wu et al., 2 Mar 2026). This suggests that objective design in MAL is not reducible to simply increasing the number of losses.

The paper also examines long-path users. Users are grouped by the ratio

$t_{i,j}$ 6

where higher ratios imply more clicks per conversion (Wu et al., 2 Mar 2026). MAL yields larger AUC lifts for these users under last-click, linear, and DDA targets, whereas the trend is less clear for first-click, which the paper attributes to noisier labels (Wu et al., 2 Mar 2026). A plausible implication is that MAC is not only a benchmark for multi-task supervision but also a benchmark for path-complexity sensitivity in click-level CVR modeling.

5. Baseline ecosystem, PyMAL, and MoAE

PyMAL provides a unified PyTorch framework implementing representative MAL baselines for fair comparison and reproducibility (Wu et al., 2 Mar 2026). The single-attribution baseline, denoted BASE, is trained only on primary target labels and uses DIN-style target attention for sequence modeling, SimTier for multimodal fusion, and an MLP predictor (Wu et al., 2 Mar 2026).

The benchmark includes several multi-task learning architectures adapted to MAL (Wu et al., 2 Mar 2026):

Shared-Bottom: shared lower layers with task-specific heads.
MMoE: mixture-of-experts with task-specific gating for combining shared experts.
PLE: progressive layered extraction with separate shared and task-specific experts to reduce negative transfer.
HoME: an MoE variant with Self-Gate and Feature-Gate to modulate expert selection and Swish activations.

MAC also benchmarks NATAL, a MAL-specific architecture centered on knowledge aggregation with Cartesian auxiliary training (Wu et al., 2 Mar 2026). NATAL includes Attribution Knowledge Aggregation (AKA), a Primary Target Predictor (PTP), and CAT for encoding the full joint pattern of binary attribution outcomes into a multi-class auxiliary target (Wu et al., 2 Mar 2026).

MoAE is the paper’s proposed model and is explicitly motivated by two design principles: fully learning multi-attribution knowledge and fully leveraging that knowledge for the main task (Wu et al., 2 Mar 2026). Its bottom backbone is an MoE structure with one shared expert $t_{i,j}$ 7 and attribution-specific experts $t_{i,j}$ 8 to capture both general conversion patterns and mechanism-specific signals (Wu et al., 2 Mar 2026). For mechanism $t_{i,j}$ 9, a gating network produces mixture coefficients through softmax,

$c_i \in \{0,1\}$ 0

and the representation is formed as

$c_i \in \{0,1\}$ 1

A task-specific MLP then maps $c_i \in \{0,1\}$ 2 to $c_i \in \{0,1\}$ 3 (Wu et al., 2 Mar 2026).

Above the MoE backbone, MoAE introduces asymmetric transfer that aggregates auxiliary representations into the main task tower in a main-task–centric manner (Wu et al., 2 Mar 2026). The exact transfer equations are not fully specified in the paper; the description remains conceptual (Wu et al., 2 Mar 2026). CAT can also be added, contributing a softmax cross-entropy term and a representation fused into the primary path (Wu et al., 2 Mar 2026). Regularization and some transfer details are not elaborated further (Wu et al., 2 Mar 2026).

Training across these baselines is standardized: Adam, batch size 4096, one epoch, learning-rate grid search, and auxiliary-task weights $c_i \in \{0,1\}$ 4 (Wu et al., 2 Mar 2026). The paper also tests GCS and PCGrad as optional auxiliary-task learning features, but reports limited or inconsistent benefits (Wu et al., 2 Mar 2026).

6. Empirical findings, interpretation, and practical constraints

The main reported results are given in GAUC, with AUC showing similar trends (Wu et al., 2 Mar 2026):

Primary target	BASE	NATAL	MoAE
Last-click	0.7424	0.7613	0.7636
First-click	0.6969	0.6990	0.7003
DDA	0.7470	0.7617	0.7644
Linear	0.7602	0.7643	0.7682

These numbers support three empirical insights emphasized by the paper (Wu et al., 2 Mar 2026). First, MAL consistently improves CVR prediction across all target attribution mechanisms, with the largest gains under last-click and DDA; for MoAE, these correspond to $c_i \in \{0,1\}$ 5 points and $c_i \in \{0,1\}$ 6 points GAUC over BASE, respectively (Wu et al., 2 Mar 2026). Second, performance generally scales with objective complexity for last-click, DDA, and linear targets, but not for first-click (Wu et al., 2 Mar 2026). For first-click, adding last-click helps, whereas adding DDA or linear hurts; adding all auxiliary tasks plus CAT also does not help (Wu et al., 2 Mar 2026). The paper interprets this as evidence that first-click labels are noisier because they are farther from the conversion and more exposed to confounding (Wu et al., 2 Mar 2026).

Third, architecture design matters more than generic gradient-conflict heuristics in this setting (Wu et al., 2 Mar 2026). MoE-based multi-task learning architectures such as PLE and HoME outperform Shared-Bottom on both primary and auxiliary metrics, indicating better shared-structure capture and reduced gradient conflicts (Wu et al., 2 Mar 2026). NATAL, by contrast, achieves the best primary metric among the baselines because of asymmetric transfer, even though it underperforms PLE and HoME on auxiliary metrics (Wu et al., 2 Mar 2026). MoAE combines these two principles—MoE-based knowledge learning and asymmetric main-task–centric transfer—and outperforms NATAL on all four targets while also improving auxiliary metrics (Wu et al., 2 Mar 2026).

The study further controls for parameter count. When auxiliary loss weights are set to zero while preserving the same parameter count, GAUC changes are negligible relative to BASE, which the paper uses to argue that gains come from multi-attribution supervision rather than from parameter scaling alone (Wu et al., 2 Mar 2026). This is an important clarification because it addresses a common misconception that MAL improvements may merely reflect larger models.

Practical guidance in the paper remains concise. The dataset is publicly available on Hugging Face, and PyMAL provides baselines and training code (Wu et al., 2 Mar 2026). Researchers are instructed to prepare categorical features, behavior sequences, and visual similarity features as described; derive binary labels as $c_i \in \{0,1\}$ 7 when $c_i \in \{0,1\}$ 8; optionally use weights as positive importance weights; start from BASE and then explore Shared-Bottom, MMoE, PLE, HoME, NATAL, and MoAE; tune learning rate and $c_i \in \{0,1\}$ 9 through validation; and report AUC and GAUC on the primary target (Wu et al., 2 Mar 2026). The paper notes that auxiliary targets should be selected per target mechanism and says that a greedy forward-selection procedure is used, but code details are not provided in the text (Wu et al., 2 Mar 2026).

The benchmark also has explicit limitations (Wu et al., 2 Mar 2026). Only four attribution mechanisms are included; the attribution window length is confidential; DDA depends on CausalMTA and thus on causal-model assumptions; direct attribution is limited to same-item clicks; first-click labels are inherently noisier; domain coverage is limited to e-commerce on Taobao; and the paper does not specify the dataset license (Wu et al., 2 Mar 2026). These constraints do not invalidate the benchmark, but they delimit the regimes in which results should be generalized.

7. Terminological scope and naming ambiguity

The acronym “MAC” is not unique across the recent literature. In the benchmark introduced for CVR prediction, MAC denotes “A Conversion Rate Prediction Benchmark Featuring Labels Under Multiple Attribution Mechanisms” (Wu et al., 2 Mar 2026). Other works use “MAC” for different concepts, including a benchmark for multiple attributes compositional zero-shot learning (Xu et al., 2024) and a Massive Attribute Classifier used for large-scale face-attribute annotation (Neto et al., 2024). A separate work on multimodal-attributed graphs, OpenMAG, is also presented as fulfilling a “Multi-Attribution Benchmark” role in a graph-learning sense, but it concerns multimodal-attributed graphs rather than conversion attribution in advertising (Wan et al., 5 Feb 2026).

Within recommender systems and advertising, however, MAC has a specific and narrower meaning: a click-level CVR benchmark with labels derived under last-click, first-click, linear, and DDA attribution rules, intended to support systematic MAL research (Wu et al., 2 Mar 2026). This benchmark’s significance lies in making previously inaccessible supervision structure public. A plausible implication is that its main long-term contribution is methodological rather than merely empirical: it provides a stable substrate for studying when auxiliary attribution views help, when they interfere, and how model architecture mediates that trade-off (Wu et al., 2 Mar 2026).