Amirmehdi Jafari Fesharaki

arXiv2026

Effective Context in Transformers: An Analysis of Fragmentation and Tokenization

Transformers predict over a representation of a sequence. The same data can be written as bytes, characters, or subword tokens, and these representations may be lossless. Yet, under a fixed context window, they need not expose the same information to the model. This raises a basic question: how does the choice of representation change what a finite-context predictor can achieve? We study this question on Markov sources and uncover two complementary phenomena. First, we observe that moving to smaller representation units can hurt prediction even when the context window is enlarged to cover the relevant source history. To explain this, we introduce fragmentation: a lossless recoding that replaces each source symbol by several smaller units. We prove that fragmentation can strictly increase the optimal finite-context log-loss, showing that the gap is not merely an optimization or capacity issue, but can be intrinsic to the representation. This gives a theoretical account of the finite-context gap observed in byte- and character-level models such as ByT5 and CANINE relative to subword-tokenized models. Second, we study the opposite direction: greedy tokenization -- BPE, WordPiece, and related methods -- which groups source symbols into larger units. We show that tokenization can make a short token window behave like a longer source-context window, and we give a loss guarantee describing when this is achievable. The guarantee depends on how reliably token windows span the needed source history, together with the compression rate of the tokenizer. This also yields a simple diagnostic for real tokenizers: measuring how much source context a fixed token window reliably contains. Together, the two directions establish a finite-context information-theoretic framework for reasoning about representation choices in Transformers.

cs.LG↗

arXiv2024

Dependency-Aware Online Caching

We consider a variant of the online caching problem where the items exhibit dependencies among each other: an item can reside in the cache only if all its dependent items are also in the cache. The dependency relations can form any directed acyclic graph. These requirements arise e.g., in systems such as CacheFlow (SOSR 2016) that cache forwarding rules for packet classification in IP-based communication networks. First, we present an optimal randomized online caching algorithm which accounts for dependencies among the items. Our randomized algorithm is $O( \log k)$-competitive, where $k$ is the size of the cache, meaning that our algorithm never incurs the cost of $O(\log k)$ times higher than even an optimal algorithm that knows the future input sequence. Second, we consider the bypassing model, where requests can be served at a fixed price without fetching the item and its dependencies into the cache -- a variant of caching with dependencies introduced by Bienkowski et al. at SPAA 2017. For this setting, we give an $O( \sqrt{k \cdot \log k})$-competitive algorithm, which significantly improves the best known competitiveness. We conduct a small case study, to find out that our algorithm incurs on average 2x lower cost.

cs.DS↗