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Abstract: Modern industrial recommender systems must optimize across competing objectives, balancing semantic relevance with business metrics such as engagement and revenue. While bi-encoders dominate large-scale retrieval due to their efficiency, they collapse these heterogeneous signals into a single static embedding space. This design creates a fundamental limitation: once trained, the retriever cannot adapt to shifting objective priorities at serving time without retraining. Moreover, joint optimization with multi-objective losses often induces interference between objectives, leading to suboptimal trade-offs. We propose Embedding Subspace Partitioning (ESP), a retrieval framework that decomposes the embedding into task-aware subspaces and replaces the single dot product with a weighted sum of per-subspace similarities, whose weights are tunable at serving time. For Transformer bi-encoders, ESP uses the model's native end-of-sequence token as a segment delimiter, with segment-aware attention masking and position encoding resets to guarantee subspace isolation in a single forward pass. Serving is performed via GPU-accelerated exhaustive kNN over one concatenated index, eliminating the need for per-objective Approximate Nearest Neighbor (ANN) infrastructure required by multi-head approaches. We evaluate ESP on an open-source benchmark built from MS MARCO. A single ESP model traces a broad Pareto frontier, consistently outperforming strong multi-task baselines across diverse operating points. In LinkedIn's job matching platform (70M+ weekly users), ESP enabled dynamic retrieval reconfiguration and delivered significant key business metric lifts.

Abstract: Scaling model capacity has emerged as an effective approach to overcoming performance bottlenecks in industrial recommender systems. However, repeatedly training larger dense models from scratch demands substantial data and time, while their growing computation conflicts with the strict serving budgets of industrial systems. Parameter inheritance provides a promising route for both dense model growth and sparse conversion, yet existing methods are primarily designed for static corpora and can suffer sharp performance drops under dynamically evolving recommendation data. To address these challenges, we propose Inherit4Rec, a parameter-inheritance framework that supports both Dense-to-Dense (D2D) growth and Dense-to-Sparse (D2S) conversion. Inherit4Rec-D2D combines hybrid growth with asymmetric training to preserve the forward function at expansion and maintain update continuity. Inherit4Rec-D2S constructs SMoE networks through co-activation-aware partitioning and a load-balancing loss, preserving dense-model capabilities while promoting balanced expert activation. Experiments on KuaiRand-1K and an industrial short-video recommendation dataset show that both transformations consistently outperform the evaluated inheritance baselines across all prediction objectives. These results demonstrate the effectiveness of Inherit4Rec for continual capacity expansion and computation-efficient sparse conversion in industrial recommender systems.

Abstract: We study a fractional assignment setting where $n$ objects are to be assigned to $n$ agents with unit capacity, and each agent specifies an ideal distribution over the objects. Unlike in classic random assignment, these ideal distributions are not necessarily degenerate, as agents may prefer a mixture of objects rather than any single object. We assume that agents seek to minimize the $\ell_1$ distance between their ideal distribution and the distribution they receive, which is equivalent to maximizing the overlap between the two distributions. We propose two mechanisms, one based on water filling (WF) and the other on quadratic programming (QP), and show that both mechanisms are utilitarian-optimal (and hence Pareto efficient), envy-free, strategyproof, and satisfy equal treatment of equals. Moreover, we highlight a distinct advantage of each mechanism: while the WF mechanism satisfies the stronger property of group-strategyproofness, the QP mechanism is more robust in terms of egalitarian overlap welfare.