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.

The performance of Transformer models has been enhanced by increasing the number of parameters and the length of the processed text. Consequently, fine-tuning the entire model becomes a memory-intensive process. High-performance methods for parameter-efficient fine-tuning (PEFT) typically work with Attention blocks and often overlook MLP blocks, which contain about half of the model parameters. We propose a new selective PEFT method, namely SparseGrad, that performs well on MLP blocks. We transfer layer gradients to a space where only about 1\% of the layer's elements remain significant. By converting gradients into a sparse structure, we reduce the number of updated parameters. We apply SparseGrad to fine-tune BERT and RoBERTa for the NLU task and LLaMa-2 for the Question-Answering task. In these experiments, with identical memory requirements, our method outperforms LoRA and MeProp, robust popular state-of-the-art PEFT approaches.