Daily Papers

LLM agents that cache recovery suggestions from API errors can skip re-derivation in later episodes, spending fewer tokens and fewer model calls on constraints they have already learned. Server-side data drift turns those cached fixes into silent failures, and the usual remedy, re-deriving on every episode, gives the savings back. We introduce invalidation contracts, a protocol layer that attaches version stamps and cacheability hints to every recovery suggestion so the client can evict stale entries without trial and error, and keep the rest. The contract decomposes realized savings into two independent factors: validity, the fraction of cached suggestions that remain correct after a drift event, and compliance, the fraction the planner applies on the first attempt. Validity depends only on the protocol and is vendor-independent. Compliance depends on the planner model: identical wire bytes yield 100% first-try compliance on Claude Haiku 4.5 and 11% or below on Claude Sonnet 5, which exhibits input-schema conservatism, refusing fixes that add fields the original request did not contain. We evaluate across seven models, three serving paths, two domains, and approximately 9,400 episodes. Row-level invalidation raises compliance by 0 to 66.7 percentage points across the seven models, 55.6 to 66.7 on three, and recovers 29-33% of baseline token cost on four of seven models, while table-level invalidation destroys co-located entries and drops post-drift first-try rates to 0% on five of seven. Eviction precision is 1.00 at row granularity on every model under the row-level oracle of Section 4.1. The contract adds 15% to response payload. Version-stamp validity is deterministic by construction and produced identical results across every model and serving path, with zero contract failures in the entire evaluation.

Edge deployment of large language models (LLMs) increasingly relies on libraries of lightweight LoRA adapters, yet GPU/DRAM can keep only a small resident subset at a time. Serving a request through a non-resident adapter requires paging its weights from storage, incurring measurable latency. This creates a two-timescale online control problem: on a slow timescale, the system selects which adapters remain resident in fast memory, while on a fast timescale it routes each request to an adapter whose context-dependent utility is unknown a priori. The two decisions are tightly coupled: the cache determines the cost of exploration, and the router determines which adapters receive informative feedback. We formulate this joint caching-and-routing problem as a two-timescale contextual bandit and propose POLAR (Paging and Online Learning for Adapter Routing). POLAR pairs a cache-aware LinUCB router with an epoch-based cache controller. We study two variants. A fixed-epoch version provides a robust baseline with worst-case regret guarantees under arbitrary contexts. An epoch-doubling version, POLAR+, adds forced exploration and improved cache optimization to achieve mathcal{O}(dNT+KT) sublinear regret under stochastic regularity and cacheability conditions, where N is the adapter count, K the cache size, d the context dimension, and T the horizon. The routing term matches the standard contextual-bandit rate up to logarithmic factors, showing that the memory hierarchy does not fundamentally slow routing learning. Experiments using 15 real LoRA adapters for Qwen2.5-7B together with measured GPU paging latencies show that adaptive cache control substantially outperforms non-adaptive baselines and exhibits scaling trends consistent with the theory.

We present GRAPE (Group RepresentAtional Position Encoding), a unified framework for positional encoding based on group actions. GRAPE brings together two families of mechanisms: (i) multiplicative rotations (Multiplicative GRAPE) in SO(d) and (ii) additive logit biases (Additive GRAPE) arising from unipotent actions in the general linear group GL. In Multiplicative GRAPE, a position n in Z (or t in R) acts as G(n)=exp(n,ω,L) with a rank-2 skew generator L in R^{d times d}, yielding a relative, compositional, norm-preserving map with a closed-form matrix exponential. RoPE is recovered exactly when the d/2 planes are the canonical coordinate pairs with log-uniform spectrum. Learned commuting subspaces and compact non-commuting mixtures strictly extend this geometry to capture cross-subspace feature coupling at O(d) and O(r d) cost per head, respectively. In Additive GRAPE, additive logits arise as rank-1 (or low-rank) unipotent actions, recovering ALiBi and the Forgetting Transformer (FoX) as exact special cases while preserving an exact relative law and streaming cacheability. Altogether, GRAPE supplies a principled design space for positional geometry in long-context models, subsuming RoPE and ALiBi as special cases. Project Page: https://github.com/model-architectures/GRAPE.