Building a User Foundation Model for the Open Web

Offsite conversion rate (OCVR) prediction is an important ranking problem in computational recommendation systems. This task presents a modeling challenge: click signals are abundant and exhibit short temporal horizons, whereas conversion signals are inherently sparse, long-delayed, and frequently unattributed. Despite these statistical disparities, both signal types must inform models that operate within strict serving-latency constraints. Prior pre-training approaches address this heterogeneity with a single, undifferentiated encoder applied uniformly across both data streams. We propose DUET (Dual User Embedding Transformers), a framework that explicitly partitions user behavioral data into two domain-coherent streams -- clicks and conversions -- and pre-trains dedicated transformer encoders with architectures tailored to each stream's statistical characteristics: multi-layer self-attention for the dense click stream and interleaved cross- and self-attention for the sparse conversion stream. The resulting complementary embeddings are jointly consumed by a downstream ranker without exceeding serving-latency budgets. Evaluation demonstrates up to 0.38% normalized entropy (NE) reduction relative to the strongest baseline, and A/B test shows consistent improvements in OCVR prediction accuracy.

Foundation models are increasingly trained on sequences of user actions in recommendation, payments, fraud, and commerce, but these models still lack the kind of compute calibration that scaling laws provide for language models. We study a common two-part behavioral-model architecture: a feature-based event embedder maps each multi-modal item to a vector, and a decoder-only transformer predicts the next event from the resulting sequence. Across roughly 600 runs on real interaction data, spanning $10^{15}$-$10^{19}$ training FLOPs, we jointly vary four deployment-relevant axes: the two-part parameter split, critical batch size, model/data allocation, and the number of sampled negatives used after freezing the embedder. A small embedder ($s^{\star}\!\approx\!2\%$ of parameters) is compute-optimal at every budget we test because embedder parameters are both more expensive per step and exposed to far more repeated items than contextualizer parameters. Compute-optimal training is data-heavy relative to text at low compute, but its $D/N$ ratio moves toward the Chinchilla heuristic as compute increases. The sampled training objective and deployed ranking metrics disagree in ways that themselves scale: critical batch size, optimal negative count after freezing, and the agreement between loss and ranking quality all shift with compute and with the chosen evaluation metric. For negative sampling, larger budgets increasingly prefer more negatives; by $10^{19}$ FLOPs the active constraint is candidate-axis memory rather than FLOPs. In behavioral foundation models, the evaluation metric is therefore part of the scaling law: changing it can change the compute-optimal recipe.

User behavior in the real world is diverse, cross-domain, and spans long time horizons. Existing user modeling benchmarks however remain narrow, focusing mainly on short sessions and next-item prediction within a single domain. Such limitations hinder progress toward robust and generalizable user models. We present HORIZON, a new benchmark that reformulates user modeling along three axes i.e. dataset, task, and evaluation. Built from a large-scale, cross-domain reformulation of Amazon Reviews, HORIZON covers 54M users and 35M items, enabling both pretraining and realistic evaluation of models in heterogeneous environments. Unlike prior benchmarks, it challenges models to generalize across domains, users, and time, moving beyond standard missing-positive prediction in the same domain. We propose new tasks and evaluation setups that better reflect real-world deployment scenarios. These include temporal generalization, sequence-length variation, and modeling unseen users, with metrics designed to assess general user behavior understanding rather than isolated next-item prediction. We benchmark popular sequential recommendation architectures alongside LLM-based baselines that leverage long-term interaction histories. Our results highlight the gap between current methods and the demands of real-world user modeling, while establishing HORIZON as a foundation for research on temporally robust, cross-domain, and general-purpose user models.