Large language models (LLMs) have demonstrated remarkable capabilities across a variety of tasks. One of the main challenges towards the successful deployment of LLMs is memory management, since they typically involve billions of parameters. To this end, architectures based on Mixture-of-Experts have been proposed, which aim to reduce the size of the parameters that are activated when producing a token. This raises the equally critical issue of efficiently managing the limited cache of the system, in that frequently used experts should be stored in the fast cache rather than in the slower secondary memory. In this work, we introduce and study a new paging problem that models expert management optimization. Our formulation captures both the layered architecture of LLMs and the requirement that experts are cached efficiently. We first present lower bounds on the competitive ratio of both deterministic and randomized algorithms, which show that under mild assumptions, LRU-like policies have good theoretical competitive performance. We then propose a layer-based extension of LRU that is tailored to the problem at hand. Extensive simulations on both synthetic datasets and actual traces of MoE usage show that our algorithm outperforms policies for the classic paging problem, such as the standard LRU.

Large Language Models (LLMs) encounter severe memory inefficiencies during long-context inference due to conventional handling of key-value (KV) caches. In this work, we introduce a novel integration of PagedAttention with PyTorch's FlexAttention, addressing internal fragmentation and inefficiencies associated with monolithic KV cache allocations. Implemented within IBM's Foundation Model Stack (FMS), our fused attention kernel efficiently gathers scattered KV data. Our benchmarks on an NVIDIA L4 GPU (24GB) demonstrate significantly reduced inference latency, growing only linearly (~2x) with sequence length from 128 to 2048 tokens when utilizing a global KV cache, compared to exponential latency increases without caching. While peak memory usage remains largely unchanged for single-step evaluations (dominated by model weights and activations), paged attention causes minimal incremental memory usage, observable only at sequence lengths exceeding 2048 tokens due to its power-of-two cache allocations. We open-source the full implementation and discuss its implications for future long-context model deployment.

Online paging is a fundamental problem in the field of online algorithms, in which one maintains a cache of $k$ slots as requests for fetching pages arrive online. In the weighted variant of this problem, each page has its own fetching cost; a substantial line of work on this problem culminated in an (optimal) $O(\log k)$-competitive randomized algorithm, due to Bansal, Buchbinder and Naor (FOCS'07). Existing work for weighted paging assumes that page weights are known in advance, which is not always the case in practice. For example, in multi-level caching architectures, the expected cost of fetching a memory block is a function of its probability of being in a mid-level cache rather than the main memory. This complex property cannot be predicted in advance; over time, however, one may glean information about page weights through sampling their fetching cost multiple times. We present the first algorithm for online weighted paging that does not know page weights in advance, but rather learns from weight samples. In terms of techniques, this requires providing (integral) samples to a fractional solver, requiring a delicate interface between this solver and the randomized rounding scheme; we believe that our work can inspire online algorithms to other problems that involve cost sampling.

Paging is a prototypical problem in the area of online algorithms. It has also played a central role in the development of learning-augmented algorithms -- a recent line of research that aims to ameliorate the shortcomings of classical worst-case analysis by giving algorithms access to predictions. Such predictions can typically be generated using a machine learning approach, but they are inherently imperfect. Previous work on learning-augmented paging has investigated predictions on (i) when the current page will be requested again (reoccurrence predictions), (ii) the current state of the cache in an optimal algorithm (state predictions), (iii) all requests until the current page gets requested again, and (iv) the relative order in which pages are requested. We study learning-augmented paging from the new perspective of requiring the least possible amount of predicted information. More specifically, the predictions obtained alongside each page request are limited to one bit only. We consider two natural such setups: (i) discard predictions, in which the predicted bit denotes whether or not it is ``safe'' to evict this page, and (ii) phase predictions, where the bit denotes whether the current page will be requested in the next phase (for an appropriate partitioning of the input into phases). We develop algorithms for each of the two setups that satisfy all three desirable properties of learning-augmented algorithms -- that is, they are consistent, robust and smooth -- despite being limited to a one-bit prediction per request. We also present lower bounds establishing that our algorithms are essentially best possible.

Fine-tuning models on edge devices like mobile phones would enable privacy-preserving personalization over sensitive data. However, edge training has historically been limited to relatively small models with simple architectures because training is both memory and energy intensive. We present POET, an algorithm to enable training large neural networks on memory-scarce battery-operated edge devices. POET jointly optimizes the integrated search search spaces of rematerialization and paging, two algorithms to reduce the memory consumption of backpropagation. Given a memory budget and a run-time constraint, we formulate a mixed-integer linear program (MILP) for energy-optimal training. Our approach enables training significantly larger models on embedded devices while reducing energy consumption while not modifying mathematical correctness of backpropagation. We demonstrate that it is possible to fine-tune both ResNet-18 and BERT within the memory constraints of a Cortex-M class embedded device while outperforming current edge training methods in energy efficiency. POET is an open-source project available at https://github.com/ShishirPatil/poet