Kernelized Linear Attention: Breaking the Capacity Wall with Symmetric Cones
arXiv:2607. 17419v1 Announce Type: cross Abstract: Linear attention promises constant-time recurrent inference but degrades sharply on associative recall.
arXiv:2607. 11897v1 Announce Type: new Abstract: Linear attention replaces softmax attention's growing KV cache with a fixed recurrent state, but this compression limits exact state tracking and long-context memory.
arXiv:2607. 17419v1 Announce Type: cross Abstract: Linear attention promises constant-time recurrent inference but degrades sharply on associative recall.
arXiv:2608.30386v1 Announce Type: cross Abstract: Hybrid linear-attention architectures have recently scaled to large open-weight models, offering quality competitive with full attention while substa...
Fast Weight Attention for Continual Learning introduces recurrent fast‑weight memories and selective state‑space models that compress expanding context into a fixed‑size recurrent state, enabling an online learning rule for state transitions. The paper derives normalized first‑order updates for squared‑error regression and negative inner‑product objectives, presenting several variants (Falcon‑1, Falcon‑2, Falcon‑3 and their inner‑product counterparts) with recurrent, masked‑parallel, and chunk‑parallel implementations. These methods demonstrate competitive performance in language modeling and improved length extrapolation on variable‑digit addition tasks.
Long-sequence memory tracking places two opposing demands on a recurrent state: near-lossless retention of stored bindings over long horizons, and active overwriting of stale ones. In our diagnostic suite, the strongest efficient baselines tend to solve only one side well.
arXiv:2607. 21000v1 Announce Type: new Abstract: Long-sequence memory tracking places two opposing demands on a recurrent state: near-lossless retention of stored bindings over long horizons, and active overwriting of stale ones.
arXiv:2606. 09862v1 Announce Type: cross Abstract: The Softmax Attention operation in Transformer language models has a quadratic complexity in the sequence length and a growing state size in the form of KV cache, which becomes a bottleneck in long context scenarios.
arXiv:2606. 27229v1 Announce Type: cross Abstract: Recurrent models must forget in order to remember, yet the state of the art decides what to erase without consulting what is stored -- the gate sees only the arriving token, not the memory it is about to modify.
arXiv:2607. 09889v1 Announce Type: cross Abstract: Fixed-state sequence models compress an unbounded past into a bounded state, which caps their associative recall at roughly the state dimension; attention escapes the cap by keeping a key-value entry for every token, at quadratic compute and a cache that grows with the sequence.
arXiv:2609.36062v1 Announce Type: new Abstract: Long-context sequence models face a fundamental tradeoff: softmax attention uses flexible token-level interactions at quadratic cost, whereas linear at...
arXiv:2606. 25156v1 Announce Type: new Abstract: Modern large language models based on softmax scaled-dot-product attention are constrained by their training sequence length: as the key-value sequence grows, softmax probability mass can dilute across a wider distribution, inducing activation shift and long-context performance collapse.
FlashBoB introduces an I/O‑efficient algorithm for exact backward‑over‑backward (BoB) in softmax attention, enabling precise second‑order differentiation without large intermediate tensors. By exploiting a hierarchical affine structure, the method confines computation to on‑chip tiles and limits off‑chip memory traffic, achieving θ(N² d²/M) HBM usage. Experiments show FlashBoB scales to sequence lengths of 262K on a single A100 GPU, outperforming prior exact baselines and FlashBack by up to 6.3×.
The paper investigates how block‑diffusion language models can use a constant‑size cache to enable efficient parallel decoding. By employing sequence mixers that summarize completed blocks into a reusable state and a block‑causal training objective, the authors pretrain three 3B block‑diffusion denoisers (attention, Mamba, and hybrid) on 300 B tokens. The resulting state‑space cache remains O(1) in memory and latency regardless of context length, yielding significant speed‑up and memory savings compared to traditional attention‑based caches, especially at very long sequences.