We present an ultra-fast and flexible search algorithm that enables search over trillion-scale natural language corpora in under 0.3 seconds while handling semantic variations (substitution, insertion, and deletion). Our approach employs string matching based on suffix arrays that scales well with corpus size. To mitigate the combinatorial explosion induced by the semantic relaxation of queries, our method is built on two key algorithmic ideas: fast exact lookup enabled by a disk-aware design, and dynamic corpus-aware pruning. We theoretically show that the proposed method suppresses exponential growth in the search space with respect to query length by leveraging statistical properties of natural language. In experiments on FineWeb-Edu (Lozhkov et al., 2024) (1.4T tokens), we show that our method achieves significantly lower search latency than existing methods: infini-gram (Liu et al., 2024), infini-gram mini (Xu et al., 2025), and SoftMatcha (Deguchi et al., 2025). As a practical application, we demonstrate that our method identifies benchmark contamination in training corpora, unidentified by existing approaches. We also provide an online demo of fast, soft search across corpora in seven languages.

Reinforcement learning(RL) post-training has become essential for aligning large language models (LLMs), yet its efficiency is increasingly constrained by the rollout phase, where long trajectories are generated token by token. We identify a major bottleneck:the long-tail distribution of rollout lengths, where a small fraction of long generations dominates wall clock time and a complementary opportunity; the availability of historical rollouts that reveal stable prompt level patterns across training epochs. Motivated by these observations, we propose DAS, a Distribution Aware Speculative decoding framework that accelerates RL rollouts without altering model outputs. DAS integrates two key ideas: an adaptive, nonparametric drafter built from recent rollouts using an incrementally maintained suffix tree, and a length aware speculation policy that allocates more aggressive draft budgets to long trajectories that dominate makespan. This design exploits rollout history to sustain acceptance while balancing base and token level costs during decoding. Experiments on math and code reasoning tasks show that DAS reduces rollout time up to 50% while preserving identical training curves, demonstrating that distribution-aware speculative decoding can significantly accelerate RL post training without compromising learning quality.

We present CREST (Compact Retrieval-Based Speculative Decoding), a redesign of REST that allows it to be effectively "compacted". REST is a drafting technique for speculative decoding based on retrieving exact n-gram matches of the most recent n tokens generated by the target LLM from a datastore. The key idea of CREST is to only store a subset of the smallest and most common n-grams in the datastore with the hope of achieving comparable performance with less storage space. We found that storing a subset of n-grams both reduces storage space and improves performance. CREST matches REST's accepted token length with 10.6-13.5x Although REST can achieve a high draft token acceptance rate, the static nature of the datastore introduces a new challenge Recently, Speculative Decoding has gained traction for accelerating regarding storage space.

Are n-gram language models still relevant in this era of neural large language models (LLMs)? Our answer is yes, and we show their values in both text analysis and improving neural LLMs. Yet this necessitates modernizing n-gram models in two aspects. First, we train them at the same data scale as neural LLMs -- 1.4 trillion tokens. This is the largest n-gram model ever built. Second, existing n-gram models use small n which hinders their performance; we instead allow n to be arbitrarily large, by introducing a new $\infty$-gram LM with backoff. Instead of pre-computing n-gram count tables (which would be very expensive), we develop an engine named infini-gram -- powered by suffix arrays -- that can compute $\infty$-gram (as well as n-gram with arbitrary n) probabilities with millisecond-level latency. The $\infty$-gram framework and infini-gram engine enable us to conduct many novel and interesting analyses of human-written and machine-generated text: we find that the $\infty$-gram LM has fairly high accuracy for next-token prediction (47%), and can complement neural LLMs to greatly reduce their language modeling perplexities. When analyzing machine-generated text, we also observe irregularities in the machine--$\infty$-gram agreement level with respect to the suffix length, which indicates deficiencies in neural LLM pretraining and the positional embeddings of Transformers. We open-source our infini-gram engine in the hopes of enabling more study on how to best use verbatim information retrieved from large text corpora.

Data Structures and Algorithms - A data structure is a named location that can be used to store and organize data. And, an algorithm is a collection of steps to

Precision Medicine aims to design individualized strategies for diagnostic or therapeutic decision-making, based on both genotypic and phenotypic information. It allows scientists and clinicians to understand which therapeutic and preventive approaches to a specific illness can work effectively in subgroups of patients based on their genetic makeup, lifestyle, and environmental factors [15]. The diffusion of high-throughput assays, such as next-generation sequencing (NGS) and mass spectrometry (MS), has led to fast accumulation of sequences and other omics data which can be used to enable Precision Medicine in practice. As an example, specific disease biomarkers may be identified by cleaning up raw data generated by NGS or MS, and then experimentally validated in laboratory. An important problem in this context is the indexing of NGS data [8].

When William Legrand finally decrypted the string, it did not seem to make much more sense than it did before. But at least it did sound more like natural language, and eventually guided the main character of Edgar Allan Poe's "The Gold-Bug"36 to discover the treasure he had been after. Legrand solved a substitution cipher using symbol frequencies. He first looked for the most frequent symbol and changed it into the most frequent letter of English, then similarly inferred the most frequent word, then punctuation marks, and so on. Both before and after 1843, the natural impulse when faced with some mysterious message has been to count frequencies of individual tokens or subassemblies in search of a clue. Perhaps one of the most intense and fascinating subjects for this kind of scrutiny have been biosequences. As soon as some such sequences became available, statistical analysts tried to link characters or blocks of characters to relevant biological functions.

Unsupervised discovery of synonymous phrases is useful in a variety of tasks ranging from text mining and search engines to semantic analysis and machine translation. This paper presents an unsupervised corpus-based conditional model: Near-Synonym System (NeSS) for finding phrasal synonyms and near synonyms that requires only a large monolingual corpus. The method is based on maximizing information-theoretic combinations of shared contexts and is parallelizable for large-scale processing. An evaluation framework with crowd-sourced judgments is proposed and results are compared with alternate methods, demonstrating considerably superior results to the literature and to thesaurus look up for multi-word phrases. Moreover, the results show that the statistical scoring functions and overall scalability of the system are more important than language specific NLP tools. The method is language-independent and practically useable due to accuracy and real-time performance via parallel decomposition.

The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered trees on the basis of their subpaths, which are vertical substructures of trees responsible for hierarchical information in them. Their kernel exhibits practically good performance in terms of accuracy and speed; however, linear-time computation is not guaranteed theoretically, unlike the case of the other unordered tree kernel proposed by Vishwanathan and Smola (2003). In this paper, we propose a theoretically guaranteed linear-time kernel computation algorithm that is practically fast, and we present an efficient prediction algorithm whose running time depends only on the size of the input tree. Experimental results show that the proposed algorithms are quite efficient in practice.