arXiv:2608. 24971v1 Announce Type: cross Abstract: We study the Lipschitz stability of attention retrieval in hyperbolic spaces.
arXiv:2608. 10416v1 Announce Type: cross Abstract: We present a theoretical foundation for inverse-distance attention, from its Euclidean prototype (Resolver) to its non-Euclidean realization (Riemann GeoResolver).
arXiv:2608. 06849v1 Announce Type: cross Abstract: Long-context LLM inference is bottlenecked by quadratic attention computation and growing KV-cache costs.
arXiv:2608.28150v2 Announce Type: replace Abstract: How much matrix rank is required to preserve every bounded value output of normalized softmax attention? We study the unrestricted maximum-row-\(\e...
arXiv:2602. 07739v2 Announce Type: replace-cross Abstract: Embedding geometry plays a fundamental role in retrieval quality, yet dense retrievers for retrieval-augmented generation (RAG) remain largely confined to Euclidean space.
arXiv:2609.37261v1 Announce Type: new Abstract: Softmax attention is ubiquitous in modern machine learning, but its quadratic scaling with sequence length makes it costly. To reduce this cost, attent...
arXiv:2607. 24555v1 Announce Type: cross Abstract: Serving large language models at long context is bottlenecked by the key-value (KV) cache, which is read in full at every decode step.
The paper introduces Hyper^2, a dual‑space consistency framework that applies hyperbolic geometry consistently to both the loss and the encoder in point‑cloud completion tasks. By reusing the same arcosh(1+αd²) function as a positional bias in refinement attention and as the Chamfer loss, Hyper^2 achieves significant Chamfer error reductions—up to 22.9% on ShapeNet‑55 and 37.5% on unseen ShapeNet‑34—while adding only ~1.6% FLOPs. The authors demonstrate that geometric consistency across encoder and loss, rather than either component alone, is key to effective hyperbolic supervision, supported by two model‑agnostic indicators that peak only when both are hyperbolic.
arXiv:2606. 01294v1 Announce Type: cross Abstract: Linear attention reduces the quadratic cost of softmax attention by maintaining a recurrent fast-weight state, but it consistently lags on in-context retrieval and long-context tasks.
arXiv:2606. 11780v1 Announce Type: cross Abstract: We establish conditions for embedding a corpus of $N$ documents as $d$-dimensional vectors such that every $k$-subset $S \subseteq [N]$ is realizable as a result of top-$k$ retrieval by some query vector.
arXiv:2605. 05189v2 Announce Type: replace-cross Abstract: How many key-value associations can a $d\times d$ linear memory store?
arXiv:2607. 27692v1 Announce Type: cross Abstract: Top-$K$ sparse attention reduces the cost of Softmax and value aggregation by attending to only a small subset of key--value (KV) entries.
arXiv:2609.14485v1 Announce Type: new Abstract: Retrieval-Guided Fine-Tuning (RAG-FT) incorporates retrieved data directly into the training objective, but the statistical consequences of noisy retri...