arXiv:2502.07861v3 Announce Type: replace-cross Abstract: Large language models (LLMs) have achieved impressive success, but their high memory requirements present challenges for long-context token generation. In this paper we study the streaming complexity of attention approximation, a key computational primitive underlying token generation. Our main contribution is BalanceKV, a streaming algorithm for $\epsilon$-approximating attention computations based on geometric process for selecting a balanced collection of Key and Value tokens as per Banaszczyk's vector balancing theory. We complement our algorithm with space lower bounds for streaming attention computation. Besides strong theoretical guarantees, BalanceKV exhibits empirically validated performance improvements over existing methods, both for attention approximation and end-to-end performance on various long context benchmarks.

arXiv:2603.12592v1 Announce Type: cross Abstract: Routing algorithms for public transport, particularly the widely used RAPTOR and its variants, often face performance bottlenecks during the transfer relaxation phase, especially on dense transfer graphs, when supporting unlimited transfers. This inefficiency arises from iterating over many potential inter-stop connections (walks, bikes, e-scooters, etc.). To maintain acceptable performance, practitioners often limit transfer distances or exclude certain transfer options, which can reduce path optimality and restrict the multimodal options presented to travellers. This paper introduces Early Pruning, a low-overhead technique that accelerates routing algorithms without compromising optimality. By pre-sorting transfer connections by duration and applying a pruning rule within the transfer loop, the method discards longer transfers at a stop once they cannot yield an earlier arrival than the current best solution. Early Pruning can be integrated with minimal changes to existing codebases and requires only a one-time preprocessing step. Across multiple state-of-the-art RAPTOR-based solutions, including RAPTOR, ULTRA-RAPTOR, McRAPTOR, BM-RAPTOR, ULTRA-McRAPTOR, and UBM-RAPTOR and tested on the Switzerland and London transit networks, we achieved query time reductions of up to 57%. This approach provides a generalizable improvement to the efficiency of transit pathfinding algorithms. Beyond algorithmic performance, Early Pruning has practical implications for transport planning. By reducing computational costs, it enables transit agencies to expand transfer radii and incorporate additional mobility modes into journey planners without requiring extra server infrastructure. This is particularly relevant for passengers in areas with sparse direct transit coverage, such as outer suburbs and smaller towns, where richer multimodal routing can reveal viable alternatives to private car use.

arXiv:2603.06624v1 Announce Type: cross Abstract: Location-based recommender systems have achieved considerable sophistication, yet none provides a formal, lattice-theoretic representation of prerequisite dependencies among points of interest -- the semantic reality that meaningfully experiencing certain locations presupposes contextual knowledge gained from others -- nor the structural guarantees that such a representation entails. We introduce Exploration Space Theory (EST), a formal framework that transposes Knowledge Space Theory into location-based recommendation. We prove that the valid user exploration states -- the order ideals of a surmise partial order on points of interest -- form a finite distributive lattice and a well-graded learning space; Birkhoff's representation theorem, combined with the structural isomorphism between lattices of order ideals and concept lattices, connects the exploration space canonically to Formal Concept Analysis. These structural results yield four direct consequences: linear-time fringe computation, a validity certificate guaranteeing that every fringe-guided recommendation is a structurally sound next step, sub-path optimality for dynamic-programming path generation, and provably existing structural explanations for every recommendation. Building on these foundations, we specify the Exploration Space Recommender System (ESRS) -- a memoized dynamic program over the exploration lattice, a Bayesian state estimator with beam approximation and EM parameter learning, an online feedback loop enforcing the downward-closure invariant, an incremental surmise-relation inference pipeline, and three cold-start strategies, the structural one being the only approach in the literature to provide a formal validity guarantee conditional on the correctness of the inferred surmise relation. All results are established through proof and illustrated on a fully traced five-POI numerical example.

arXiv:2603.03476v1 Announce Type: new Abstract: We propose a novel computational framework for analyzing electroencephalography (EEG) time series using methods from stringology, the study of efficient algorithms for string processing, to systematically identify and characterize recurrent temporal patterns in neural signals. The primary aim is to introduce quantitative measures to understand neural signal dynamics, with the present findings serving as a proof-of-concept. The framework adapts order-preserving matching (OPM) and Cartesian tree matching (CTM) to detect temporal motifs that preserve relative ordering and hierarchical structure while remaining invariant to amplitude scaling. This approach provides a temporally precise representation of EEG dynamics that complements traditional spectral and global complexity analyses. To evaluate its utility, we applied the framework to multichannel EEG recordings from individuals with attention-deficit/hyperactivity disorder (ADHD) and matched controls using a publicly available dataset. Highly recurrent, group-specific motifs were extracted and quantified using both OPM and CTM. The ADHD group exhibited significantly higher motif frequencies, suggesting increased repetitiveness in neural activity. OPM analysis revealed shorter motif lengths and greater gradient instability in ADHD, reflected in larger mean and maximal inter-sample amplitude changes. CTM analysis further demonstrated reduced hierarchical complexity in ADHD, characterized by shallower tree structures and fewer hierarchical levels despite comparable motif lengths. These findings suggest that ADHD-related EEG alterations involve systematic differences in the structure, stability, and hierarchical organization of recurrent temporal patterns. The proposed stringology-based motif framework provides a complementary computational tool with potential applications for objective biomarker development in neurodevelopmental disorders.