Attention is central to modern AI models for language, vision, and scientific modeling. However, direct evaluation compares every query with every key, requiring quadratic time in the context length,...
arXiv:2605.23751v2 Announce Type: replace Abstract: We revisit the I/O complexity of attention in large language models. Given query-key-value matrices $Q,K,V\in\mathbb{R}^{n\times d}$, and a machine...
arXiv:2609.06327v2 Announce Type: replace-cross Abstract: A query-oblivious coreset for a softmax-attention head is a subset of the key-value pairs whose attention output is within $\varepsilon$ of t...
The paper introduces a conic programming framework for certifying transformer attention, providing guarantees on how far an attention head’s output can shift under input perturbations. It shows that the main challenge lies in the bilinear interaction between varying queries and keys, making certification NP-hard over boxes and inapproximable when logits can shift by a constant. The authors present an exponential cone moment relaxation that yields a quadratic error bound in the perturbation radius, and demonstrate that this approach outperforms linear bound propagation on GPT‑2, achieving tighter bounds and matching predicted second‑order accuracy.
arXiv:2608. 28150v1 Announce Type: new Abstract: Which geometry controls the rank complexity of normalized softmax attention?
arXiv:2610. 20637v1 Announce Type: new Abstract: We expand the exponential kernel of attention into a truncated Taylor series of $n$ terms and factorize each term into a tensor-power inner product, which collapses the causal history into exactly $n$ recurrent states, each updated by one rank-one outer product per token and independent of context length $N$.
arXiv:2610.10135v1 Announce Type: cross Abstract: Sparse attention mechanisms estimate attention over $n$ tokens using a small subset of keys. Many existing approaches use maximum inner product searc...
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: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:2512. 10656v3 Announce Type: replace Abstract: As context windows in large language models continue to expand, it is essential to characterize how attention behaves at extreme sequence lengths.
The paper proposes a new update geometry for the language‑model head by treating the head and softmax as a single module and using Hilbert’s projective distance to measure functional change. It replaces the spectral norm with the Euclidean row diameter, derives a tractable RowNorm update rule, and demonstrates that RowNorm substantially reduces step diameters and Hilbert perturbations while only slightly increasing validation loss.
arXiv:2610. 22191v1 Announce Type: cross Abstract: In Hebbian learning from examples a Hopfield network of $N$ neurons is not supplied with the $K$ archetypes it has to retrieve but with $M$ blurred examples of each, of quality $r$, and whether it can infer them depends on the load $\alpha=K/N$ (interference among them) and on the dataset entropy $\rho=(1-r^2)/(Mr^2)$ (how little the examples say about them).