Large Language Models (LLMs) face significant computational and memory constraints when processing long contexts, despite growing demand for applications requiring reasoning over extensive documents, multi-session dialogues, and book length texts. While recent advances have extended context windows to 100K-1M tokens, such approaches incur prohibitive costs for resource constrained deployments. We propose BudgetMem, a novel memory augmented architecture that learns what to remember rather than remembering everything. Our system combines selective memory policies with feature based salience scoring (entity density, TF-IDF, discourse markers, position bias) to decide which information merits storage under strict budget constraints. Unlike existing retrieval augmented generation (RAG) systems that store all chunks, BudgetMem employs learned gating mechanisms coupled with BM25 sparse retrieval for efficient information access. Through comprehensive experiments on 700 question answer pairs across short (237 tokens) and long (5K-10K tokens) documents with Llama-3.2-3B-Instruct, we demonstrate that BudgetMem achieves remarkable results on long documents: only 1.0% F1 score degradation while saving 72.4% memory compared to baseline RAG. We validate our approach through budget sensitivity analysis (testing 7 budget ratios), naive baseline comparisons, and document length analysis, showing that BudgetMem's benefits increase with document length. Our work provides a practical pathway for deploying capable long context systems on modest hardware, democratizing access to advanced language understanding capabilities.

The foundation for the research of summarization in the Czech language was laid by the work of Straka et al. (2018). They published the SumeCzech, a large Czech news-based summarization dataset, and proposed several baseline approaches. However, it is clear from the achieved results that there is a large space for improvement. In our work, we focus on the impact of named entities on the summarization of Czech news articles. First, we annotate SumeCzech with named entities. We propose a new metric ROUGE_NE that measures the overlap of named entities between the true and generated summaries, and we show that it is still challenging for summarization systems to reach a high score in it. We propose an extractive summarization approach Named Entity Density that selects a sentence with the highest ratio between a number of entities and the length of the sentence as the summary of the article. The experiments show that the proposed approach reached results close to the solid baseline in the domain of news articles selecting the first sentence. Moreover, we demonstrate that the selected sentence reflects the style of reports concisely identifying to whom, when, where, and what happened. We propose that such a summary is beneficial in combination with the first sentence of an article in voice applications presenting news articles. We propose two abstractive summarization approaches based on Seq2Seq architecture. The first approach uses the tokens of the article. The second approach has access to the named entity annotations. The experiments show that both approaches exceed state-of-the-art results previously reported by Straka et al. (2018), with the latter achieving slightly better results on SumeCzech's out-of-domain testing set.