Trained on massive cross-species DNA corpora, DNA large language models (LLMs) learn the fundamental "grammar" and evolutionary patterns of genomic sequences. This makes them powerful priors for DNA sequence modeling, particularly over long ranges. However, two major constraints hinder their use in practice: the quadratic computational cost of self-attention and the growing memory required for key-value (KV) caches during autoregressive decoding. These constraints force the use of heuristics such as fixed-window truncation or sliding windows, which compromise fidelity on ultra-long sequences by discarding distant information. We introduce FOCUS (Feature-Oriented Compression for Ultra-long Self-attention), a progressive context-compression module that can be plugged into pretrained DNA LLMs. FOCUS combines the established k-mer representation in genomics with learnable hierarchical compression: it inserts summary tokens at k-mer granularity and progressively compresses attention key and value activations across multiple Transformer layers, retaining only the summary KV states across windows while discarding ordinary-token KV. A shared-boundary windowing scheme yields a stationary cross-window interface that propagates long-range information with minimal loss. We validate FOCUS on an Evo-2-based DNA LLM fine-tuned on GRCh38 chromosome 1 with self-supervised training and randomized compression schedules to promote robustness across compression ratios. On held-out human chromosomes, FOCUS achieves near-lossless fidelity: compressing a 1 kb context into only 10 summary tokens (about 100x) shifts the average per-nucleotide probability by only about 0.0004. Compared to a baseline without compression, FOCUS reduces KV-cache memory and converts effective inference scaling from O(N^2) to near-linear O(N), enabling about 100x longer inference windows on commodity GPUs with near-lossless fidelity.

We agree that our notation of the focus token was confusing.

Especially in the community of Digital Humanities, the automated processing of Latin texts has always been a popular research topic. In a variety of computational applications, such as text reuse detection [Franzini et al, 2015], it is desirable to annotate and augment Latin texts with useful morpho-syntactical or lexical information, such as lemmas. In this paper, we will focus on two sequence tagging tasks for medieval Latin: part-of-speech tagging and lemmatization. Given a piece of Latin text, the task of lemmatization involves assigning each word to a single dictionary headword or'lemma': a baseform label (preferably in a normalized orthography) grouping all word tokens which only differ in spelling and/or inflection [Knowles et al, 2004]. The task of lemmatization is closely related to that of part-of-speech (PoS) tagging [Jurafsky et al, 2000], in which each word in a running text should be assigned a tag indicating its part of speech or word class (e.g.