In this paper, we propose new randomized algorithms for estimating the two-to-infinity and one-to-two norms in a matrix-free setting, using only matrix-vector multiplications. Our methods are based on appropriate modifications of Hutchinson's diagonal estimator and its Hutch++ version. We provide oracle complexity bounds for both modifications. We further illustrate the practical utility of our algorithms for Jacobian-based regularization in deep neural network training on image classification tasks. We also demonstrate that our methodology can be applied to mitigate the effect of adversarial attacks in the domain of recommender systems.

Quantization has shown strong results in preserving model quality under compression.However, under aggressive bit-width reductions, even quantization may require additional information to prevent performance degradation.A natural source of it is the second-order curvature information, captured by the Hessian.Since the Hessian of the model layers is prohibitively large, direct computation is infeasible, making structured parameterizations and approximations crucial in practice.In this work, we propose an efficient Kroneckerfactored approximation yielding state-of-theart performance when integrated into existing quantization schemes.Evaluations on the LLaMA and Qwen model families show near-baseline quality at 4-bit compression and only a 5-6% degradation at 2-bit for models with 7-8B parameters.Moreover, our method substantially accelerates the most expensive component in second-order quantization -Hessian parameterization -achieving up to a 10× speedup over prior approaches.Quantized model checkpoints are available at https://huggingface.co/collections/ timo13113/fastkron-collection.

Off-policy evaluation (OPE) is widely used to compare contextual bandit policies in recommender systems. While there a lot of recent methodological developments, suggesting novel OPE schemes, they are typically validated in the synthetic environments, which not necessarily possess the structure of the real-world datasets. In this paper, we consider the inverse propensity score (IPS) method and its modifications, and study how empirical conclusions inferred from the data depend on evaluation pipelines. We show, that even in the synthetic environments, rankings of different estimators are sensitive to random seeds, log generators, and sample size. Using the popular benchmark, the Open Bandit Dataset, we analyze logging behavior and data characteristics that may violate the i.i.d. assumptions of the log generation.

In this paper, we propose a new geometric approach for knowledge graph completion via low rank tensor approximation. We augment a pretrained and well-established Euclidean model based on a Tucker tensor decomposition with a novel hyperbolic interaction term. This correction enables more nuanced capturing of distributional properties in data better aligned with real-world knowledge graphs. By combining two geometries together, our approach improves expressivity of the resulting model achieving new state-of-the-art link prediction accuracy with a significantly lower number of parameters compared to the previous Euclidean and hyperbolic models.

In this work, we present a fast and effective Linear approach for updating recommendations in a scalable graph-based recommender system UltraGCN. Solving this task is extremely important to maintain the relevance of the recommendations under the conditions of a large amount of new data and changing user preferences. To address this issue, we adapt the simple yet effective low-rank approximation approach to the graph-based model. Our method delivers instantaneous recommendations that are up to 30 times faster than conventional methods, with gains in recommendation quality, and demonstrates high scalability even on the large catalogue datasets.

In modern recommender systems, experimental settings typically include filtering out cold users and items based on a minimum interaction threshold.However, these thresholds are often chosen arbitrarily and vary widely across studies, leading to inconsistencies that can significantly affect the comparability and reliability of evaluation results.In this paper, we systematically explore the cold-start boundary by examining the criteria used to determine whether a user or an item should be considered cold.Our experiments incrementally vary the number of interactions for different items during training, and gradually update the length of user interaction histories during inference.We investigate the thresholds across several widely used datasets, commonly represented in recent papers from top-tier conferences, and on multiple established recommender baselines.Our findings show that inconsistent selection of cold-start thresholds can either result in the unnecessary removal of valuable data or lead to the misclassification of cold instances as warm, introducing more noise into the system.

Train & Test sequences Test target Valid target

Scalability is a major challenge in modern recommender systems. In sequential recommendations, full Cross-Entropy (CE) loss achieves state-of-the-art recommendation quality but consumes excessive GPU memory with large item catalogs, limiting its practicality. Using a GPU-efficient locality-sensitive hashing-like algorithm for approximating large tensor of logits, this paper introduces a novel RECE (REduced Cross-Entropy) loss. RECE significantly reduces memory consumption while allowing one to enjoy the state-of-the-art performance of full CE loss. Experimental results on various datasets show that RECE cuts training peak memory usage by up to 12 times compared to existing methods while retaining or exceeding performance metrics of CE loss. The approach also opens up new possibilities for large-scale applications in other domains.

In recent years, self-attentive sequential learning models have surpassed conventional collaborative filtering techniques in next-item recommendation tasks. However, Euclidean geometry utilized in these models may not be optimal for capturing a complex structure of behavioral data. Building on recent advances in the application of hyperbolic geometry to collaborative filtering tasks, we propose a novel approach that leverages hyperbolic geometry in the sequential learning setting. Our approach replaces final output of the Euclidean models with a linear predictor in the non-linear hyperbolic space, which increases the representational capacity and improves recommendation quality.

Scalability issue plays a crucial role in productionizing modern recommender systems. Even lightweight architectures may suffer from high computational overload due to intermediate calculations, limiting their practicality in real-world applications. Specifically, applying full Cross-Entropy (CE) loss often yields state-of-the-art performance in terms of recommendations quality. Still, it suffers from excessive GPU memory utilization when dealing with large item catalogs. This paper introduces a novel Scalable Cross-Entropy (SCE) loss function in the sequential learning setup. It approximates the CE loss for datasets with large-size catalogs, enhancing both time efficiency and memory usage without compromising recommendations quality. Unlike traditional negative sampling methods, our approach utilizes a selective GPU-efficient computation strategy, focusing on the most informative elements of the catalog, particularly those most likely to be false positives. This is achieved by approximating the softmax distribution over a subset of the model outputs through the maximum inner product search. Experimental results on multiple datasets demonstrate the effectiveness of SCE in reducing peak memory usage by a factor of up to 100 compared to the alternatives, retaining or even exceeding their metrics values. The proposed approach also opens new perspectives for large-scale developments in different domains, such as large language models.

Data sparsity has been one of the long-standing problems for recommender systems. One of the solutions to mitigate this issue is to exploit knowledge available in other source domains. However, many cross-domain recommender systems introduce a complex architecture that makes them less scalable in practice. On the other hand, matrix factorization methods are still considered to be strong baselines for single-domain recommendations. In this paper, we introduce the CDIMF, a model that extends the standard implicit matrix factorization with ALS to cross-domain scenarios. We apply the Alternating Direction Method of Multipliers to learn shared latent factors for overlapped users while factorizing the interaction matrix. In a dual-domain setting, experiments on industrial datasets demonstrate a competing performance of CDIMF for both cold-start and warm-start. The proposed model can outperform most other recent cross-domain and single-domain models. We also provide the code to reproduce experiments on GitHub.

In domains where users tend to develop long-term preferences that do not change too frequently, the stability of recommendations is an important factor of the perceived quality of a recommender system. In such cases, unstable recommendations may lead to poor personalization experience and distrust, driving users away from a recommendation service. We propose an incremental learning scheme that mitigates such problems via the dynamic modeling approach. It incorporates a generalized matrix form of a partial differential equation integrator that yields a dynamic low-rank approximation of time-dependent matrices representing user preferences. The scheme allows extending the famous PureSVD approach to time-aware settings and significantly improves its stability without sacrificing the accuracy in standard top-n recommendations tasks.

We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably, even with such a minimalistic approach, we not only outperform the Euclidean counterpart but also achieve a competitive performance with respect to the current state-of-the-art. We additionally explore the effects of space curvature on the quality of hyperbolic models and propose an efficient data-driven method for estimating its optimal value.

We propose a new hybrid algorithm that allows incorporating both user and item side information within the standard collaborative filtering technique. One of its key features is that it naturally extends a simple PureSVD approach and inherits its unique advantages, such as highly efficient Lanczos-based optimization procedure, simplified hyper-parameter tuning and a quick folding-in computation for generating recommendations instantly even in highly dynamic online environments. The algorithm utilizes a generalized formulation of the singular value decomposition, which adds flexibility to the solution and allows imposing the desired structure on its latent space. Conveniently, the resulting model also admits an efficient and straightforward solution for the cold start scenario. We evaluate our approach on a diverse set of datasets and show its superiority over similar classes of hybrid models.

Conventional collaborative filtering techniques treat a top-n recommendations problem as a task of generating a list of the most relevant items. This formulation, however, disregards an opposite -- avoiding recommendations with completely irrelevant items. Due to that bias, standard algorithms, as well as commonly used evaluation metrics, become insensitive to negative feedback. In order to resolve this problem we propose to treat user feedback as a categorical variable and model it with users and items in a ternary way. We employ a third-order tensor factorization technique and implement a higher order folding-in method to support online recommendations. The method is equally sensitive to entire spectrum of user ratings and is able to accurately predict relevant items even from a negative only feedback. Our method may partially eliminate the need for complicated rating elicitation process as it provides means for personalized recommendations from the very beginning of an interaction with a recommender system. We also propose a modification of standard metrics which helps to reveal unwanted biases and account for sensitivity to a negative feedback. Our model achieves state-of-the-art quality in standard recommendation tasks while significantly outperforming other methods in the cold-start "no-positive-feedback" scenarios.