Furthermore, we propose an adapted embedding method to incorporate numerical awareness.

The $ρ$-posterior framework provides universal Bayesian estimation with explicit contamination rates and optimal convergence guarantees, but has remained computationally difficult due to an optimization over reference distributions that precludes intractable posterior computation. We develop a PAC-Bayesian framework that recovers these theoretical guarantees through temperature-dependent Gibbs posteriors, deriving finite-sample oracle inequalities with explicit rates and introducing tractable variational approximations that inherit the robustness properties of exact $ρ$-posteriors. Numerical experiments demonstrate that this approach achieves theoretical contamination rates while remaining computationally feasible, providing the first practical implementation of $ρ$-posterior inference with rigorous finite-sample guarantees.

Complementary product recommendation, which aims to suggest items that are used together to enhance customer value, is a crucial yet challenging task in e-commerce. While existing graph neural network (GNN) approaches have made significant progress in capturing complex product relationships, they often struggle with the accuracy-diversity tradeoff, particularly for long-tail items. This paper introduces a model-agnostic approach that leverages Large Language Models (LLMs) to enhance the reranking of complementary product recommendations. Unlike previous works that use LLMs primarily for data preprocessing and graph augmentation, our method applies LLM-based prompting strategies directly to rerank candidate items retrieved from existing recommendation models, eliminating the need for model retraining. Through extensive experiments on public datasets, we demonstrate that our approach effectively balances accuracy and diversity in complementary product recommendations, with at least 50% lift in accuracy metrics and 2% lift in diversity metrics on average for the top recommended items across datasets.

Recent advances in sequence modeling have introduced selective SSMs as promising alternatives to Transformer architectures, offering theoretical computational efficiency and sequence processing advantages. A comprehensive understanding of selective SSMs in runtime behavior, resource utilization patterns, and scaling characteristics still remains unexplored, thus obstructing their optimal deployment and further architectural improvements. This paper presents a thorough empirical study of Mamba-1 and Mamba-2, systematically profiled for performance to assess the design principles that contribute to their efficiency in state-space modeling. A detailed analysis of computation patterns, memory access, I/O characteristics, and scaling properties was performed for sequence lengths ranging from 64 to 16384 tokens. Our findings show that the SSM component, a central part of the selective SSM architecture, demands a significant portion of computational resources compared to other components in the Mamba block. Based on these insights, we propose a pruning technique that selectively removes low-activity states within the SSM component, achieving measurable throughput and memory gains while maintaining accuracy within a moderate pruning regime. This approach results in performance improvements across varying sequence lengths, achieving a 1.14x speedup and reducing memory usage by 11.50\%. These results offer valuable guidance for designing more efficient SSM architectures that can be applied to a wide range of real-world applications.

Given a matrix of observed data, Principal Components Analysis (PCA) computes a small number of orthogonal directions that contain most of its variability. Provably accurate solutions for PCA have been in use for a long time. However, to the best of our knowledge, all existing theoretical guarantees for it assume that the data and the corrupting noise are mutually independent, or at least uncorrelated. This is valid in practice often, but not always. In this paper, we study the PCA problem in the setting where the data and noise can be correlated. Such noise is often also referred to as "data-dependent noise". We obtain a correctness result for the standard eigenvalue decomposition (EVD) based solution to PCA under simple assumptions on the data-noise correlation. We also develop and analyze a generalization of EVD, cluster-EVD, that improves upon EVD in certain regimes.

The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into N subproblems, and utilizes an augmented Lagrangian based primal-dual scheme to solve it in a distributed and stochastic manner.

Neural Information Processing Systems http://nips.cc/

Recent work on generating adversarial attacks have shown that it is computationally feasible for a bad actor to fool a DRL policy into behaving sub optimally.