Product search systems must not only return relevant items but also understand users' implicit preferences beyond their explicit queries. For instance, when searching for "steak", most users implicitly prefer beef steak over equally relevant alternatives like pork steak. Predicting such engagement preferences presents a more complex challenge than traditional relevance modeling, as it requires capturing nuanced query-item relationships that reflect both relevance and user intent. To capture these nuances, we extend semantic understanding to engagement prediction by learning directly from query-item text with engagement labels as supervision rather than relying on historical engagement statistics as input. Our approach effectively captures users' implicit preferences across diverse query types, from tail queries where historical signals are sparse to broad queries where understanding latent intent is critical. Extensive experiments on Walmart's production search data demonstrate significant improvements over production model with a strong relevance foundation: +1.71% add-to-cart lift in interleaving tests and +0.33% in overall search sessions with add-to-cart. Our model is deployed in the production environment of Walmart.com.

Embedding-based retrieval (EBR) is foundational to large-scale e-commerce search, yet its effectiveness is often constrained by the quality of training signals and the representational capacity of the encoder. Standard dual-encoders suffer from a training-inference gap: they are optimized on narrow candidate pools but must discriminate against hundreds of millions of items during inference. Furthermore, while transitioning to higher-capacity backbones can mitigate this gap, simply replacing a mature model can lead to inconsistent retrieval behavior and a loss of the domain-specific knowledge established in previous iterations. In this paper, we present a unified pipeline deployed at Walmart that addresses both signal quality and model evolution. Our contributions are two-fold: (1) Hybrid Hard Negative Mining: We integrate Online Cross-Batch Sampling to increase negative diversity by an order of magnitude and Hybrid Offline Mining, which combines cross-encoder predictions with metadata heuristics to identify nuanced mismatches. (2) Legacy-Aware Distillation: We transition from DistilBERT to a higher-capacity GTE-base encoder. To ensure a smooth and superior transition, we introduce a Warm-Start Distillation technique that transfers domain-specific expertise from the legacy model to the new backbone. Validated through extensive offline experiments and online A/B testing, the proposed pipeline is deployed in live production, delivering a +7.34% improvement in NDCG@5 and a +0.50% lift in gross revenue.

Re-ranking plays a crucial role in product search by reassessing products from the primary retrieval system based on specific engagement and relevance criteria. While transformer-based models like the cross encoder have advanced the relevance of ranking models in recent years, a significant challenge arises from the high latency cost associated with running a cross encoder model at runtime. This challenge becomes more pronounced in the long-tail segment, where conventional techniques like caching prove ineffective. To tackle these issues, our paper introduces a scalable framework featuring a BERT-based cross encoder model for re-ranking, deployed in the Walmart search engine. We employ strategies such as intermediate representations, operator fusion, and vectorization to improve the inference latency of the cross encoder model. Furthermore, we provide a detailed discussion on the runtime implementation, highlighting key learnings and practical tricks that ensured minimal impact on response latency during production. Finally, we present the results of online experiments, including manual evaluation and interleaving test conducted on real-world e-commerce search traffic.

E-commerce retailers increasingly offer diverse fulfillment options (e.g., in-store pickup, same-day delivery from store, standard shipping from fulfillment centers and marketplace sellers), creating a need for search systems that understand and cater to individual customer preferences. This paper addresses the challenge of incorporating fulfillment intent into product search ranking. We propose a model that predicts customer fulfillment intent based on the search query, past user interactions, and other contextual information. A fulfillment match signal is introduced to quantify the alignment between a product's available fulfillment methods and the predicted customer intent. Integrating this signal into the ranking process ensures that search results prioritize products matching the user's preferred fulfillment type. Offline and online experiments demonstrate the efficacy of our approach and highlight the importance of fulfillment-aware ranking in omnichannel e-commerce.

Metric learning has become a widespreadly used tool in machine learning. To reduce expensive costs brought in by increasing dimensionality, low-rank metric learning arises as it can be more economical in storage and computation. However, existing low-rank metric learning algorithms usually adopt nonconvex objectives, and are hence sensitive to the choice of a heuristic low-rank basis. In this paper, we propose a novel low-rank metric learning algorithm to yield bilinear similarity functions. This algorithm scales linearly with input dimensionality in both space and time, therefore applicable to high-dimensional data domains. A convex objective free of heuristics is formulated by leveraging trace norm regularization to promote low-rankness. Crucially, we prove that all globally optimal metric solutions must retain a certain low-rank structure, which enables our algorithm to decompose the high-dimensional learning task into two steps: an SVD-based projection and a metric learning problem with reduced dimensionality. The latter step can be tackled efficiently through employing a linearized Alternating Direction Method of Multipliers. The efficacy of the proposed algorithm is demonstrated through experiments performed on four benchmark datasets with tens of thousands of dimensions.

Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms (SNN) of the unfolding matrices of the tensor. We show that this approach can be substantially suboptimal: reliably recovering a K-way n\timesn\times⋯\times n tensor of Tucker rank (r, r, \ldots, r) from Gaussian measurements requires Ω( r n^K-1 ) observations. In contrast, a certain (intractable) nonconvex formulation needs only O(r^K + nrK) observations. We introduce a simple, new convex relaxation, which partially bridges this gap. Our new formulation succeeds with O(r^⌊K/2 ⌋n^⌈K/2 ⌉) observations. The lower bound for the SNN model follows from our new result on recovering signals with multiple structures (e.g. sparse, low rank), which indicates the significant suboptimality of the common approach of minimizing the sum of individual sparsity inducing norms (e.g. \ell_1, nuclear norm). Our new tractable formulation for low-rank tensor recovery shows how the sample complexity can be reduced by designing convex regularizers that exploit several structures jointly.

Illumination variation remains a central challenge in object detection and recognition. Existing analyses of illumination variation typically pertain to convex, Lambertian objects, and guarantee quality of approximation in an average case sense. We show that it is possible to build models for the set of images across illumination variation with worst-case performance guarantees, for nonconvex Lambertian objects. Namely, a natural verification test based on the distance to the model guarantees to accept any image which can be sufficiently well-approximated by an image of the object under some admissible lighting condition, and guarantees to reject any image that does not have a sufficiently good approximation. These models are generated by sampling illumination directions with sufficient density, which follows from a new perturbation bound for directional illuminated images in the Lambertian model. As the number of such images required for guaranteed verification may be large, we introduce a new formulation for cone preserving dimensionality reduction, which leverages tools from sparse and low-rank decomposition to reduce the complexity, while controlling the approximation error with respect to the original model.